text:
Abu Zubaydah

Abu Zubaydah (ابو زبيدة, Abū Zubaydah; born March 12, 1971, as Zayn al-Abidin Muhammad Husayn) is a Palestinian citizen and alleged terrorist born in Saudi Arabia currently held by the U.S. in the Guantanamo Bay detention camp in Cuba. He is held under the authority of Authorization for Use of Military Force Against Terrorists (AUMF).

Zubaydah was captured in Pakistan in March 2002 and has been in United States custody ever since, including $4 1/2$ years in the secret prison network of the Central Intelligence Agency (CIA). He was transferred among prisons in various countries including a year in Poland, as part of a United States extraordinary rendition program. During his time in CIA custody, Zubaydah was extensively interrogated; he was waterboarded 83 times and subjected to numerous other torture techniques including forced nudity, sleep deprivation, confinement in small dark boxes, deprivation of solid food, stress positions, and physical assaults. Videotapes of some of Zubaydah's interrogations are allegedly amongst those destroyed by the CIA in 2005.

Zubaydah and ten other "high-value detainees" were transferred to Guantanamo in September 2006. He and other former CIA detainees are held in Camp 7, where conditions are the most isolating.

On July 24, 2014, the European Court of Human Rights ordered the Polish government to pay Zubaydah damages. Zubaydah stated through his US lawyer that he would be donating the awarded funds to victims of torture.

Biography and early activities
According to his younger brother Hesham, they had eight siblings. Hesham remembers his older brother "as a happy-go-lucky guy, and something of a womanizer". Born in Saudi Arabia, Zubaydah is reported to have studied computer science in Mysore, India, prior to his travel to Afghanistan/Pakistan at the age of 20 in 1991. In 1991 he joined the mujahideen and fought against Afghan Communist Government forces during the Afghan Civil War, perhaps serving under Mohamad Kamal Elzahabi. In 1992, Zubaydah was injured in an Afghan mortar attack, which left shrapnel in his head and caused severe memory loss, as well as the loss of the ability to speak for over one year.

Zubaydah eventually became involved in the training camp known as the Khalden training camp, where he oversaw the flow of recruits and obtained passports and paperwork for men transferring out of Khalden. He may also have worked as an instructor there. Although originally described as an al-Qaeda training camp, this alleged connection, which has been used as justification for holding Zubaydah and others as enemy combatants, has come under scrutiny from multiple sources,  and the camp may have shut its doors in 2001 in response to an ideological division with al-Qaeda.

By 1999, the United States government was attempting to surveil Zubaydah. By March 2000, United States officials were reporting that Zubaydah was a "senior bin Laden official", the "former head of Egypt-based Islamic Jihad", a "trusted aide" to bin Laden with "growing power", who had "played a key role in the East Africa embassy attacks". Zubaydah was convicted in absentia in Jordan and sentenced to death by a Jordanian court for his role in plots to bomb U.S. and Israeli targets there. A senior Middle East security official said Zubaydah had directed the Jordanian cell and was part of "bin Laden's inner circle".

In August 2001, the classified FBI report, "Bin Ladin Determined To Strike in US", said that the foiled millennium bomber, Ahmed Ressam, had confessed that Zubaydah had encouraged him to blow up the Los Angeles airport and facilitated his mission. The report said that Zubaydah was also planning his own attack on the U.S. However, when Ressam was tried in December 2001, federal prosecutors did not try to connect him to Zubaydah or refer to any of this supposed evidence in its case. After the trial, Ressam recanted his confession, saying he had been coerced into giving it.

According to a psychological evaluation conducted upon his capture, Zubaydah allegedly served as Osama bin Laden's senior lieutenant and counter-intelligence officer (i.e. third or fourth highest-ranking member of al Qaeda), managed a network of training camps, was involved in every major terrorist operation carried out by al Qaeda (including the planning of 9/11), and was engaged in planning future terrorist attacks against U.S. interests. These statements were widely echoed by members of the George W. Bush administration and other US officials. Zubaydah's perceived "value" as a detainee would later be used by George W. Bush to justify the use of "enhanced interrogation techniques" and Zubaydah's detention in secret CIA prisons around the world. However, Zubaydah's connection to al Qaeda is now often said to have been – according to Rebecca Gordon writing about "The al Qaeda Leader Who Wasn't" – a fictitious charge. Others have said instead that it is merely overstated,   and in response to his habeas corpus petition, the U.S. Government stated in 2009 that it did not contend Zubaydah had any involvement with the 9/11 attacks, or that he had even been a member of al Qaeda, simply because they did not have to: "In simple terms, the issue in this habeas corpus action is Petitioner's conduct", rather than membership or inclination: "Petitioner's personal philosophy is not relevant except to the extent that it is reflected in his actions".

Capture
On March 28, 2002, CIA and FBI agents, in conjunction with Pakistani intelligence agency, raided several safe houses in Pakistan searching for Zubaydah. Zubaydah was apprehended from one of the targeted safe houses in Faisalabad, Pakistan. The Pakistani intelligence service had paid a small amount for a tip on his whereabouts. The United States paid far more to Pakistan for its assistance; a CIA source later said: "We paid $10 million for Zubaydah."

During the raid, Zubaydah was shot in the thigh, the testicle, and the stomach with rounds from a Kalashnikov assault rifle. Not recognized at first, he was piled into a pickup truck along with other prisoners by the Pakistani forces until a senior CIA officer identified him. He was taken by the Pakistanis to a Pakistani hospital nearby and treated for his wounds. The attending doctor told the CIA lead officer of the group which apprehended Zubaydah that he had never before seen a patient survive such severe wounds. The CIA flew in a doctor from Johns Hopkins University to ensure Zubaydah would survive during transit out of Pakistan.

His pocket litter supposedly contained two bank cards, which showed that he had access to Saudi and Kuwaiti bank accounts; most al-Qaeda members used the preferred, untraceable hawala banking. According to James Risen: "It is not clear whether an investigation of the cards simply fell through the cracks, or whether they were ignored because no one wanted to know the answers about connections between al Qaeda and important figures in the Middle East—particularly in Saudi Arabia." One of Risen's sources chalks up the failure to investigate the cards to incompetence rather than foul play: "The cards were sent back to Washington and were never fully exploited. I think nobody ever looked at them because of incompetence."

When Americans investigated the cards, Risen wrote that they worked with "a Muslim financier with a questionable past, and with connections to the Afghan Taliban, al Qaeda, and Saudi intelligence. ... Saudi intelligence officials had seized all of the records related to the card from the Saudi financial institution in question; the records then disappeared. There was no longer any way to trace the money that had gone into the account."

A search of the safehouse turned up Zubaydah's 10,000-page diaries, in which he recorded his thoughts as a young boy, older man, and at his current age. What appears to be multiple separate identities is how Zubaydah was piecing his memories together after his 1992 shrapnel head wound. As part of his therapy to regain his memories, he began recording a diary that detailed his life, emotions, and what people were telling him. He split information into categories, such as what he knew about himself and what people told him, and listed them under different names to distinguish one set from the other. This was later interpreted by some analysts reviewing the diary as symptoms of Dissociative Identity Disorder, which some others disputed and said to be incorrect.

Zubaydah was handed to the CIA. Reports later alleged that he was transferred to secret CIA-operated prisons, known as black sites, in Pakistan, Thailand, Afghanistan, Poland, Northern Africa, and Diego Garcia. Historically, renditions of prisoners to countries which commit torture have been illegal. A memo written by John Yoo and signed by Jay Bybee of the Office of the Legal Counsel, DOJ, days before Zubaydah's capture, provided a legal opinion providing for CIA renditions of detainees to places such as Thailand. In March 2009, the U.S. Senate Intelligence Committee launched a year-long study on how the CIA operated the secret prisons, or black sites, around the world.

Top U.S. officials approved torture techniques
In the spring of 2002, immediately following the capture of Zubaydah, top Bush administration officials, Vice President Dick Cheney, Secretary of State Colin Powell, CIA Director George Tenet, National Security Adviser Condoleezza Rice, Secretary of Defense Rumsfeld, and US Attorney General John Ashcroft discussed at length whether or not the CIA could legally use harsh techniques against him. Condoleezza Rice specifically mentioned the SERE program during the meeting, saying, "I recall being told that U.S. military personnel were subjected to training to certain physical and psychological interrogation techniques".

In addition, in 2002 and 2003, the administration briefed several Democratic Congressional leaders on the proposed "enhanced interrogation techniques". These congressional leaders included Nancy Pelosi, the future Speaker of the House, and Representative Jane Harman. Congressional officials have stated that the attitude in the briefings ranged from "quiet acquiescence, if not downright support". The documents show that top U.S. officials were intimately involved in the discussion and approval of the harsher interrogation techniques used on Zubaydah. Condoleezza Rice ultimately told the CIA the harsher interrogation tactics were acceptable, and Dick Cheney stated, "I signed off on it; so did others." During the discussions, US Attorney General John Ashcroft is reported as saying, "Why are we talking about this in the White House? History will not judge this kindly."

Torture drawings
In December 2019, The New York Times published an article in partnership with the Pulitzer Center on Crisis Reporting which was based upon drawings made by Zubaydah, showing how he was tortured in "vivid and disturbing ways". The article includes some of the drawings as well as a link to a 61-page report titled "How America Tortures", and asserts that Zubaydah was never a member of Al Qaeda. In the article Zubaydah gives gruesome details of numerous types of torture including being locked up inside a small box called "the dog box" for "countless hours", which caused muscle contractions. "The very strong pain", he said, "made me scream unconsciously". According to the Senate Intelligence Committee report on CIA torture, over a single 20 day period, Zubaydah spent over 11 days locked in a "coffin size" box, and 29 hours in a box measuring 21 inches wide, 21⁄2 feet deep, and 21⁄2 feet high (21 x). On May 9, 2023, Zubaydah's former attorney, Mark Denbeaux of Seton Hall Law School, published a detailed report annotating the drawings.

Interrogation of Zubaydah
Zubaydah was interrogated by two separate interrogation teams: the first from the FBI and one from the CIA. Ali Soufan, one of the FBI interrogators, later testified in 2009 on these issues to the Senate Committee that was investigating detainee treatment. Soufan, who witnessed part of the CIA interrogation of Zubaydah, described his treatment under the CIA as torture. The International Committee of the Red Cross and others later reached the same conclusion. While in CIA custody, Zubaydah previously damaged left eye was surgically removed.

Because of the urgency felt about the interrogation of Zubaydah, the CIA had consulted with the president about how to proceed. The General Counsel of the CIA asked for a legal opinion from the Office of Legal Counsel, Department of Justice about what was permissible during interrogation.

August 2002 memo
In early July 2002, the Associate General Counsel CTC/Legal Group started drafting a memo to the Attorney General requesting the approval of "aggressive" interrogation methods, which otherwise would be prohibited under the provisions of Section 2340-2340B, Title 18, United States Code, on Abu Zubaydah. This memo, drafted by Office of Legal Counsel, Jay Bybee and his assistant John Yoo, is also referred to as the first Torture Memo. Addressed to CIA acting General Counsel John A. Rizzo at his request, the purpose of the memo was to describe and authorize specific "enhanced interrogation techniques" to be used on Zubaydah. On July 26, 2002, Deputy Assistant Attorney General John Yoo informed the CIA that Attorney General John Ashcroft had approved waterboarding of Abu Zubaydah.

Journalists including Jane Mayer, Joby Warrick and Peter Finn, and Alex Koppelman have reported the CIA was already using these harsh tactics before the memo authorizing their use was written,  and that it was used to provide after-the-fact legal support for harsh interrogation techniques. A Department of Justice 2009 report regarding prisoner abuses reportedly stated the memos were prepared one month after Zubaydah had already been subjected to the specific techniques authorized in an August 1, 2002, memo. John Kiriakou stated in July 2009 that Zubaydah was waterboarded in the early summer of 2002, months before the August 1, 2002, memo was written.

The memo described ten techniques which the interrogators wanted to use: "(1) attention grasp, (2) walling, (3) facial hold, (4) facial slap (insult slap), (5) cramped confinement, (6) wall standing, (7) stress positions, (8) sleep deprivation, (9) insects placed in a confinement box, and (10) the waterboard." Many of the techniques were, until then, generally considered illegal. Many other techniques developed by the CIA were held to constitute inhumane and degrading treatment and torture under the United Nations Convention against Torture and Article 3 of the European Convention on Human Rights.

As reported later, many of these interrogation techniques were previously considered illegal under U.S. and international law and treaties at the time of Zubaydah's capture. For instance, the United States had prosecuted Japanese military officials after World War II and American soldiers after the Vietnam War for waterboarding. Since 1930, the United States had defined sleep deprivation as an illegal form of torture. Many other techniques developed by the CIA constitute inhuman and degrading treatment and torture under the United Nations Convention against Torture, and Article 3 of the European Convention on Human Rights.

Ensuing interrogation
At a CIA black site in Thailand, Zubaydah was subjected to various forms of increasingly harsh interrogation techniques, including temperature extremes, music played at debilitating volumes, and sexual humiliation. Zubaydah was also subjected to beatings, isolation, waterboarding, long-time standing, continuous cramped confinement, and sleep deprivation.

Former CIA analyst and case officer John Kiriakou asserted that while Zubaydah was in CIA custody, a box of cockroaches were poured on him inside of a coffin he was confined to for two weeks, because of an irrational fear Zubaydah has of cockroaches.

During Zubaydah's interrogation, Bush learned he was on painkillers for his wounds and was proving resistant. He said to the CIA director George Tenet, "Who authorized putting him on pain medication?" It was later reported that Zubaydah was denied painkillers during his interrogation.

Waterboarding
Zubaydah was one of three or more high-value detainees to be waterboarded. The Bush administration in 2007 said that Zubaydah had been waterboarded once. John Kiriakou, a CIA officer who had seen the cables regarding Zubaydah's interrogation, publicly said in 2009 that Zubaydah was waterboarded once for 35 seconds before he started talking.

Intelligence sources claimed as early as 2008 that Zubaydah had been waterboarded no less than ten times in the span of one week. Zubaydah was waterboarded 83 times within the month of August 2002, the month the CIA was authorized to use this enhanced interrogation techniques for him. In January 2010, Kiriakou, in a memoir, said, "Now we know that Zubaydah was waterboarded eighty-three times in a single month, raising questions about how much useful information he actually supplied."

2003 transfer to Guantanamo
In August 2010, the Associated Press reported that the CIA, having concluded its agents had gotten most of the information from Zubaydah, in September 2003 transferred him and three other high-value detainees to Guantanamo. They were held at what was informally known as "Strawberry Fields", a secret camp within the complex built especially for former CIA detainees. Concerned that a pending Supreme Court decision, Rasul v. Bush (2004), might go against the Bush administration and require providing the prisoners with counsel and having to reveal data about them, on March 27, 2004, the CIA took the four men back into custody and transported them out of Guantanamo to one of their secret sites. At the time, the moves were all kept secret.

International Committee of the Red Cross report
In February 2007, the International Committee of the Red Cross concluded a report on the treatment of "14 high-value detainees", who had been held by the CIA and, after September 2006, by the military at Guantanamo. The ICRC described the twelve enhanced interrogation techniques covered in the OLC memos to the CIA: suffocation by water (which is described as "torture" by numerous US officials ), prolonged stress standing position, beatings by use of a collar, beating and kicking, confinement in a box, prolonged nudity, sleep deprivation, exposure to cold temperature, prolonged shackling, threats of ill-treatment, forced shaving, and deprivation/restricted provision of solid food. Zubaydah was the only detainee of the 14 interviewed who had been subjected to all 12 of these interrogation techniques. He was also the only one of the 14 detainees to be put into close confinement.

May 30, 2005, memo
The final memo mentioned Zubaydah several times. It claimed that due to the enhanced interrogation techniques, Zubaydah "provided significant information on two operatives, [including] José Padilla[,] who planned to build and detonate a 'dirty bomb' in the Washington DC area." This claim is strongly disputed by Ali Soufan, the FBI interrogator who first interrogated Zubaydah following his capture, by traditional means. He said the most valuable information was gained before torture was used. Other intelligence officers have also disputed that claim. Soufan, when asked in 2009 by Senator Sheldon Whitehouse during a Congressional hearing if the memo was incorrect, testified that it was. The memo noted that not all of the waterboarding sessions were necessary for Zubaydah, since the on-scene interrogation team determined he had stopped producing actionable intelligence. The memo reads: This is not to say that the interrogation program has worked perfectly. According to the IG Report, the CIA, at least initially, could not always distinguish detainees who had information but were successfully resisting interrogation from those who did not actually have the information. See IG Report at 83–85. On at least one occasion, this may have resulted in what might be deemed in retrospect to have been the unnecessary use of enhanced techniques. On that occasion, although the on-scene interrogation team judged Zubaydah to be compliant, elements within CIA Headquarters still believed he was withholding information. See id at 84. At the direction of CIA Headquarters, interrogators therefore used the waterboard one more time on Zubaydah.

John McLaughlin, former acting CIA director, stated in 2006, "I totally disagree with the view that the capture of Zubaydah was unimportant. Zubaydah was woven through all of the intelligence prior to 9/11 that signaled a major attack was coming, and his capture yielded a great deal of important information."

In his 2007 memoir, former CIA Director George Tenet writes: "A published report in 2006 contended that Zubaydah was mentally unstable and that the administration had overstated his importance. Baloney. Zubaydah had been at the crossroads of many al-Qa'ida operations and was in position to—and did—share critical information with his interrogators. Apparently, the source of the rumor that Zubaydah was unbalanced was his personal diary, in which he adopted various personas. From that shaky perch, some junior Freudians leapt to the conclusion that Zubaydah had multiple personalities. In fact, Agency psychiatrists eventually determined that in his diary he was using a sophisticated literary device to express himself."

Intelligence obtained from Zubaydah and its after effects
Zubaydah's capture was touted as the biggest of the War on Terror until that of Khalid Sheikh Mohammed. The director of the FBI stated Zubaydah's capture would help deter future attacks.

In a speech in 2006, Bush claimed that Zubaydah revealed useful intelligence when enhanced interrogation was used, including identification of two important suspects and information that allegedly helped foil a terrorist attack on American soil. These claims directly conflict with the reports of the FBI agents who first interrogated Zubaydah. He gave them the names before torture was used, and the third piece of information came from other sources who had been receiving crucial pieces of information from him without the use of harsher techniques, as well as other government officials.

Iraq War (2003)
The Bush administration relied on some of Zubaydah's claims in justifying the invasion of Iraq. U.S. officials stated that the allegations that Iraq and al-Qaeda were linked in the training of people on chemical weapons came from Zubaydah. The officials noted there was no independent verification of his claims.

The U.S. government included statements made by Zubaydah in regards to al Qaeda's ability to obtain a dirty bomb to show a link between Iraq and al Qaeda. According to a Senate Intelligence Committee report of 2004, Zubaydah said that "he had heard that an important al Qaeda associate, Abu Musab al Zarqawi, and others had good relationships with Iraqi intelligence." However, the year before, in June 2003, Zubaydah and Khalid Sheikh Mohammed were reported as saying there was no link between Saddam Hussein and al Qaeda.

In the Senate Armed Services Committee 2008 report on the abuses of detainees, the Bush administration was described as having applied pressure to interrogators to find a link between Iraq and al Qaeda prior to the Iraq War. Major Paul Burney, a psychiatrist with the United States Army, said to the committee, "while we were [at Guantanamo] a large part of the time we were focused on trying to establish a link between al Qaeda and Iraq and we were not being successful." He said that higher-ups were "frustrated" and applied "more and more pressure to resort to measures that might produce more immediate results."

Colonel Lawrence B. Wilkerson, the former chief of staff for former Secretary of State Colin Powell said: Likewise, what I have learned is that as the administration authorized harsh interrogation in April and May 2002—well before the Justice Department had rendered any legal opinion—its principal priority for intelligence was not aimed at pre-empting another terrorist attack on the U.S. but discovering a smoking gun linking Iraq and al-Qa'ida.

So furious was this effort that on one particular detainee, even when the interrogation team had reported to Cheney's office that their detainee "was compliant" (meaning the team recommended no more torture), the VP's office ordered them to continue the enhanced methods. The detainee had not revealed any al-Qa'ida-Baghdad contacts yet. This ceased only after Ibn al-Shaykh al-Libi, under waterboarding in Egypt, "revealed" such contacts. Of course, later we learned that al-Libi revealed these contacts only to get the torture to stop.

Concerns
In 2004, media coverage of Abu Zubaydah began listing him as a "disappeared" prisoner, stating he had no access to the International Red Cross. In February 2005, the CIA was reported as uncomfortable keeping Zubaydah in indefinite custody. Less than 18 months later, Zubaydah and the thirteen other high-value detainees who had been in secret CIA custody were transferred to the Guantanamo Bay detention camp.

After his transfer, the CIA denied access to Zubaydah. In 2008, the Office of the Inspector General, Department of Justice, complained that it had been prevented from seeing him, although it was conducting a study of the US treatment of its detainees.

Zubaydah's mental health
Some people are concerned about Zubaydah's mental stability and how that has affected information he has given to interrogators. Ron Suskind noted in his book, The One Percent Doctrine: Deep Inside America's Pursuit of Its Enemies Since 9/11 (2006), that Zubaydah was mentally ill or disabled due to a severe head injury. He described Zubaydah as keeping a diary "in the voice of three people: Hani 1, Hani 2, and Hani 3"—a boy, a young man and a middle-aged alter ego. Zubaydah's diaries spanned ten years and recorded in numbing detail "what he ate, or wore, or trifling things [people] said". Dan Coleman, then the FBI's top al-Qaeda analyst, told a senior bureau official, "This guy is insane, certifiable, split personality." According to Suskind, this judgment was "echoed at the top of CIA and was briefed to the President and Vice President." Coleman stated Zubaydah was a "safehouse keeper" with mental problems, who "claimed to know more about al-Qaeda and its inner workings than he really did."

Joseph Margulies, Zubaydah's co-counsel, wrote in an op-ed in the Los Angeles Times in 2009: "Partly as a result of injuries he suffered while he was fighting the communists in Afghanistan, partly as a result of how those injuries were exacerbated by the CIA and partly as a result of his extended isolation, Zubaydah's mental grasp is slipping away. Today, he suffers blinding headaches and has permanent brain damage. He has an excruciating sensitivity to sounds, hearing what others do not. The slightest noise drives him nearly insane. In the last two years alone, he has experienced about 200 seizures. Already, he cannot picture his mother's face or recall his father's name. Gradually, his past, like his future, eludes him."

Legal status
President Bush referred to Zubaydah in a speech to Congress September 2006 requesting a bill to authorize military commissions, following the U.S. Supreme Court ruling in Hamdan v. Rumsfeld (2006) that held the tribunals as formulated by the executive branch were unconstitutional. Congress rapidly passed legislation that was signed by the president.

Less than one month after Zubaydah's capture, Justice Department officials said Zubaydah was "a near-ideal candidate for a tribunal trial". Several months later in 2002, US officials said there was "no rush" to try Zubaydah via military commission.

At his Combatant Status Review Tribunal in 2007, Zubaydah said he was told that the CIA realized he was not significant. "'They told me, 'Sorry, we discover that you are not Number 3, not a partner, not even a fighter, said Zubaydah, speaking in broken English, according to the new transcript of a Combatant Status Review Tribunal held at the U.S. military prison in Guantanamo Bay, Cuba."

Abu Zubaydah's lawyers, including Joseph Margulies and George Brent Mickum IV, filed a lawsuit in July 2008 challenging his detention at Guantanamo Bay detention camps after the Boumediene v. Bush ruling. The judge overseeing the case, Richard W. Roberts, failed to rule on any motions related to the case, even the preliminary ones. This led Zubaydah's lawyers to file a motion asking Judge Roberts to recuse himself for nonfeasance in January 2015. On March 16, 2016, Roberts retired early from the federal bench, citing unspecified health issues.

The U.S. government has not officially charged Zubaydah with any crimes. The Senate Intelligence Committee report on CIA torture reported that Zubaydah's CIA interrogators wanted him to "remain in isolation and incommunicado for the remainder of his life."

Joint Review Task Force
When he assumed Presidential office in January 2009, Barack Obama made a number of promises about the future of Guantanamo. He promised the use of torture would cease at the camp. He promised to institute a new review system. That new review system was composed of officials from six departments, where the OARDEC reviews were conducted entirely by the Department of Defense. When it reported back, a year later, the Joint Review Task Force classified some individuals as too dangerous to be transferred from Guantanamo, even though there was no evidence to justify laying charges against them. On April 9, 2013, that document was made public after a Freedom of Information Act request. Zayn al-lbidin Muhammed Husayn was one of the 71 individuals deemed too innocent to charge but too dangerous to release. Although Obama promised that those deemed too innocent to charge but too dangerous to release would start to receive reviews from a Periodic Review Board, less than a quarter of men have received a review. Husayn was denied approval for transfer on September 22, 2016.

European Court of Human Rights decision
On 24 July 2014, the European Court of Human Rights (ECHR) ruled that Poland had violated the European Convention on Human Rights when it cooperated with US allowing the CIA to hold and torture Zubaydah and Abd al-Rahim al-Nashiri on its territory in 2002–2003. The court ordered the Polish government to pay each of the men €100,000 in damages. It also awarded Zubaydah €30,000 to cover his costs.

On 31 May 2018, the ECHR ruled that Romania and Lithuania also violated the rights of Abu Zubaydah and Abd al-Rahim al-Nashiri in 2003–2005 and in 2005–2006 respectively, and Lithuania and Romania were ordered to pay €100,000 in damages each to Abu Zubaydah and Abd al-Nashiri.

U.S. Supreme Court decision
In connection with the European Court of Human Rights proceedings, Zubaydah filed suit in the U.S. seeking disclosure of information related to the matter. The U.S. government intervened, seeking to assert a state secrets privilege. The U.S. district court decided in favor of the government and dismissed the case. On appeal, the dismissal was reversed on a ruling that the state secrets privilege did not apply to information that was already publicly known. The Supreme Court reversed the appeal ruling in United States v. Zubaydah, explaining that the state secrets privilege applies to the existence (or nonexistence) of a secret CIA facility and that revelation by government would confirm or deny that state secret.

title: Abu Zubaydah


text:
Arithmetic

Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms.

Arithmetic systems can be distinguished based on the type of numbers they operate on. Integer arithmetic is about calculations with positive and negative integers. Rational number arithmetic involves operations on fractions of integers. Real number arithmetic is about calculations with real numbers, which include both rational and irrational numbers.

Another distinction is based on the numeral system employed to perform calculations. Decimal arithmetic is the most common. It uses the basic numerals from 0 to 9 and their combinations to express numbers. Binary arithmetic, by contrast, is used by most computers and represents numbers as combinations of the basic numerals 0 and 1. Computer arithmetic deals with the specificities of the implementation of binary arithmetic on computers. Some arithmetic systems operate on mathematical objects other than numbers, such as interval arithmetic and matrix arithmetic.

Arithmetic operations form the basis of many branches of mathematics, such as algebra, calculus, and statistics. They play a similar role in the sciences, like physics and economics. Arithmetic is present in many aspects of daily life, for example, to calculate change while shopping or to manage personal finances. It is one of the earliest forms of mathematics education that students encounter. Its cognitive and conceptual foundations are studied by psychology and philosophy.

The practice of arithmetic is at least thousands and possibly tens of thousands of years old. Ancient civilizations like the Egyptians and the Sumerians invented numeral systems to solve practical arithmetic problems in about 3000 BCE. Starting in the 7th and 6th centuries BCE, the ancient Greeks initiated a more abstract study of numbers and introduced the method of rigorous mathematical proofs. The ancient Indians developed the concept of zero and the decimal system, which Arab mathematicians further refined and spread to the Western world during the medieval period. The first mechanical calculators were invented in the 17th century. The 18th and 19th centuries saw the development of modern number theory and the formulation of axiomatic foundations of arithmetic. In the 20th century, the emergence of electronic calculators and computers revolutionized the accuracy and speed with which arithmetic calculations could be performed.

Definition, etymology, and related fields
Arithmetic is the fundamental branch of mathematics that studies numbers and their operations. In particular, it deals with numerical calculations using the arithmetic operations of addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and logarithm. The term "arithmetic" has its root in the Latin term "" which derives from the Ancient Greek words (arithmos), meaning "number", and   (arithmetike tekhne), meaning "the art of counting".

There are disagreements about its precise definition. According to a narrow characterization, arithmetic deals only with natural numbers. However, the more common view is to include operations on integers, rational numbers, real numbers, and sometimes also complex numbers in its scope. Some definitions restrict arithmetic to the field of numerical calculations. When understood in a wider sense, it also includes the study of how the concept of numbers developed, the analysis of properties of and relations between numbers, and the examination of the axiomatic structure of arithmetic operations.

Arithmetic is closely related to number theory and some authors use the terms as synonyms. However, in a more specific sense, number theory is restricted to the study of integers and focuses on their properties and relationships such as divisibility, factorization, and primality. Traditionally, it is known as higher arithmetic.

Numbers
Numbers are mathematical objects used to count quantities and measure magnitudes. They are fundamental elements in arithmetic since all arithmetic operations are performed on numbers. There are different kinds of numbers and different numeral systems to represent them.

Kinds

The main kinds of numbers employed in arithmetic are natural numbers, whole numbers, integers, rational numbers, and real numbers. The natural numbers are whole numbers that start from 1 and go to infinity. They exclude 0 and negative numbers. They are also known as counting numbers and can be expressed as $$\{1, 2, 3, 4, ...\}$$. The symbol of the natural numbers is $$\N$$. The whole numbers are identical to the natural numbers with the only difference being that they include 0. They can be represented as $$\{0, 1, 2, 3, 4, ...\}$$ and have the symbol $$\N_0$$. Some mathematicians do not draw the distinction between the natural and the whole numbers by including 0 in the set of natural numbers. The set of integers encompasses both positive and negative whole numbers. It has the symbol $$\Z$$ and can be expressed as $$\{..., -2, -1, 0, 1, 2, ...\}$$.

Based on how natural and whole numbers are used, they can be distinguished into cardinal and ordinal numbers. Cardinal numbers, like one, two, and three, are numbers that express the quantity of objects. They answer the question "how many?". Ordinal numbers, such as first, second, and third, indicate order or placement in a series. They answer the question "what position?".

A number is rational if it can be represented as the ratio of two integers. For instance, the rational number $$\tfrac{1}{2}$$ is formed by dividing the integer 1, called the numerator, by the integer 2, called the denominator. Other examples are $$\tfrac{3}{4}$$ and $$\tfrac{281}{3}$$. The set of rational numbers includes all integers, which are fractions with a denominator of 1. The symbol of the rational numbers is $$\Q$$. Decimal fractions like 0.3 and 25.12 are a special type of rational numbers since their denominator is a power of 10. For instance, 0.3 is equal to $$\tfrac{3}{10}$$, and 25.12 is equal to $$\tfrac{2512}{100}$$. Every rational number corresponds to a finite or a repeating decimal.

Irrational numbers are numbers that cannot be expressed through the ratio of two integers. They are often required to describe geometric magnitudes. For example, if a right triangle has legs of the length 1 then the length of its hypotenuse is given by the irrational number $$\sqrt 2$$. $\pi$ is another irrational number and describes the ratio of a circle's circumference to its diameter. The decimal representation of an irrational number is infinite without repeating decimals. The set of rational numbers together with the set of irrational numbers makes up the set of real numbers. The symbol of the real numbers is $$\R$$. Even wider classes of numbers include complex numbers and quaternions.

Numeral systems
A numeral is a symbol to represent a number and numeral systems are representational frameworks. They usually have a limited amount of basic numerals, which directly refer to certain numbers. The system governs how these basic numerals may be combined to express any number. Numeral systems are either positional or non-positional. All early numeral systems were non-positional. For non-positional numeral systems, the value of a digit does not depend on its position in the numeral.

The simplest non-positional system is the unary numeral system. It relies on one symbol for the number 1. All higher numbers are written by repeating this symbol. For example, the number 7 can be represented by repeating the symbol for 1 seven times. This system makes it cumbersome to write large numbers, which is why many non-positional systems include additional symbols to directly represent larger numbers. Variations of the unary numeral systems are employed in tally sticks using dents and in tally marks.

Egyptian hieroglyphics had a more complex non-positional numeral system. They have additional symbols for numbers like 10, 100, 1000, and 10,000. These symbols can be combined into a sum to more conveniently express larger numbers. For instance, the numeral for 10,405 uses one time the symbol for 10,000, four times the symbol for 100, and five times the symbol for 1. A similar well-known framework is the Roman numeral system. It has the symbols I, V, X, L, C, D, M as its basic numerals to represent the numbers 1, 5, 10, 50, 100, 500, and 1000.

A numeral system is positional if the position of a basic numeral in a compound expression determines its value. Positional numeral systems have a radix that acts as a multiplicand of the different positions. For each subsequent position, the radix is raised to a higher power. In the common decimal system, also called the Hindu–Arabic numeral system, the radix is 10. This means that the first digit is multiplied by $$10^0$$, the next digit is multiplied by $$10^1$$, and so on. For example, the decimal numeral 532 stands for $$5 \cdot 10^2 + 3 \cdot 10^1 + 2 \cdot 10^0$$. Because of the effect of the digits' positions, the numeral 532 differs from the numerals 325 and 253 even though they have the same digits.

Another positional numeral system used extensively in computer arithmetic is the binary system, which has a radix of 2. This means that the first digit is multiplied by $$2^0$$, the next digit by $$2^1$$, and so on. For example, the number 13 is written as 1101 in the binary notation, which stands for $$1 \cdot 2^3 + 1 \cdot 2^2 + 0 \cdot 2^1 + 1 \cdot 2^0$$. In computing, each digit in the binary notation corresponds to one bit. The earliest positional system was developed by ancient Babylonians and had a radix of 60.

Operations
Arithmetic operations are ways of combining, transforming, or manipulating numbers. They are functions that have numbers both as input and output. The most important operations in arithmetic are addition, subtraction, multiplication, and division. Further operations include exponentiation, extraction of roots, and logarithm. If these operations are performed on variables rather than numbers, they are sometimes referred to as algebraic operations.

Two important concepts in relation to arithmetic operations are identity elements and inverse elements. The identity element or neutral element of an operation does not cause any change if it is applied to another element. For example, the identity element of addition is 0 since any sum of a number and 0 results in the same number. The inverse element is the element that results in the identity element when combined with another element. For instance, the additive inverse of the number 6 is -6 since their sum is 0.

There are not only inverse elements but also inverse operations. In an informal sense, one operation is the inverse of another operation if it undoes the first operation. For example, subtraction is the inverse of addition since a number returns to its original value if a second number is first added and subsequently subtracted, as in $$13 + 4 - 4 = 13$$. Defined more formally, the operation "$$\star$$" is an inverse of the operation "$$\circ$$" if it fulfills the following condition: $$t \star s = r$$ if and only if $$r \circ s = t$$.

Commutativity and associativity are laws governing the order in which some arithmetic operations can be carried out. An operation is commutative if the order of the arguments can be changed without affecting the results. This is the case for addition, for instance, $$7 + 9$$ is the same as $$9 + 7$$. Associativity is a rule that affects the order in which a series of operations can be carried out. An operation is associative if, in a series of two operations, it does not matter which operation is carried out first. This is the case for multiplication, for example, since $$(5 \times 4) \times 2$$ is the same as $$5 \times (4 \times 2)$$.

Addition and subtraction
Addition is an arithmetic operation in which two numbers, called the addends, are combined into a single number, called the sum. The symbol of addition is $$+$$. Examples are $$2 + 2 = 4$$ and $$6.3 + 1.26 = 7.56$$. The term summation is used if several additions are performed in a row. Counting is a type of repeated addition in which the number 1 is continuously added.

Subtraction is the inverse of addition. In it, one number, known as the subtrahend, is taken away from another, known as the minuend. The result of this operation is called the difference. The symbol of subtraction is $$-$$. Examples are $$14 - 8 = 6$$ and $$45 - 1.7 = 43.3$$. Subtraction is often treated as a special case of addition: instead of subtracting a positive number, it is also possible to add a negative number. For instance $$14 - 8 = 14 + (-8)$$. This helps to simplify mathematical computations by reducing the number of basic arithmetic operations needed to perform calculations.

The additive identity element is 0 and the additive inverse of a number is the negative of that number. For instance, $$13 + 0 = 13$$ and $$13 + (-13) = 0$$. Addition is both commutative and associative.

Multiplication and division
Multiplication is an arithmetic operation in which two numbers, called the multiplier and the multiplicand, are combined into a single number called the product. The symbols of multiplication are $$\times$$, $$\cdot$$, and *. Examples are $$2 \times 3 = 6$$ and $$0.3 \cdot 5 = 1.5$$. If the multiplicand is a natural number then multiplication is the same as repeated addition, as in $$2 \times 3 = 2 + 2 + 2$$.

Division is the inverse of multiplication. In it, one number, known as the dividend, is split into several equal parts by another number, known as the divisor. The result of this operation is called the quotient. The symbols of division are $$\div$$ and $$/$$. Examples are $$48 \div 8 = 6$$ and $$29.4 / 1.4 = 21$$. Division is often treated as a special case of multiplication: instead of dividing by a number, it is also possible to multiply by its reciprocal. The reciprocal of a number is 1 divided by that number. For instance, $$48 \div 8 = 48 \times \tfrac{1}{8}$$.

The multiplicative identity element is 1 and the multiplicative inverse of a number is the reciprocal of that number. For example, $$13 \times 1 = 13$$ and $$13 \times \tfrac{1}{13} = 1$$. Multiplication is both commutative and associative.

Exponentiation and logarithm
Exponentiation is an arithmetic operation in which a number, known as the base, is raised to the power of another number, known as the exponent. The result of this operation is called the power. Exponentiation is sometimes expressed using the symbol ^ but the more common way is to write the exponent in superscript right after the base. Examples are $$2^4 = 16$$ and $$3$$^$$3 = 27$$. If the exponent is a natural number then exponentiation is the same as repeated multiplication, as in $$2^4 = 2 \times 2 \times 2 \times 2$$.

Roots are a special type of exponentiation using a fractional exponent. For example, the square root of a number is the same as raising the number to the power of $$\tfrac{1}{2}$$ and the cube root of a number is the same as raising the number to the power of $$\tfrac{1}{3}$$. Examples are $$\sqrt{4} = 4^{\frac{1}{2}} = 2$$ and $$\sqrt[3]{27} = 27^{\frac{1}{3}} = 3$$.

Logarithm is the inverse of exponentiation. The logarithm of a number $$x$$ to the base $$b$$ is the exponent to which $$b$$ must be raised to produce $$x$$. For instance, since $$1000 = 10^3$$, the logarithm base 10 of 1000 is 3. The logarithm of $$x$$ to base $$b$$ is denoted as $$\log_b (x)$$, or without parentheses, $$\log_b x$$, or even without the explicit base, $$\log x$$, when the base can be understood from context. So, the previous example can be written $$\log_{10} 1000 = 3$$.

Exponentiation and logarithm do not have general identity elements and inverse elements like addition and multiplication. The neutral element of exponentiation in relation to the exponent is 1, as in $$14^1 = 14$$. However, exponentiation does not have a general identity element since 1 is not the neutral element for the base. Exponentiation and logarithm are neither commutative nor associative.

Types
Different types of arithmetic systems are discussed in the academic literature. They differ from each other based on what type of number they operate on, what numeral system they use to represent them, and whether they operate on mathematical objects other than numbers.

Integer arithmetic

Integer arithmetic is the branch of arithmetic that deals with the manipulation of positive and negative whole numbers. Simple one-digit operations can be performed by following or memorizing a table that presents the results of all possible combinations, like an addition table or a multiplication table. Other common methods are verbal counting and finger-counting.

For operations on numbers with more than one digit, different techniques can be employed to calculate the result by using several one-digit operations in a row. For example, in the method addition with carries, the two numbers are written one above the other. Starting from the rightmost digit, each pair of digits is added together. The rightmost digit of the sum is written below them. If the sum is a two-digit number then the leftmost digit, called the "carry", is added to the next pair of digits to the left. This process is repeated until all digits have been added. Other methods used for integer additions are the number line method, the partial sum method, and the compensation method. A similar technique is utilized for subtraction: it also starts with the rightmost digit and uses a "borrow" or a negative carry for the column on the left if the result of the one-digit subtraction is negative.

A basic technique of integer multiplication employs repeated addition. For example, the product of $$3 \times 4$$ can be calculated as $$3 + 3 + 3 + 3$$. A common technique for multiplication with larger numbers is called long multiplication. This method starts by writing the multiplier above the multiplicand. The calculation begins by multiplying the multiplier only with the rightmost digit of the multiplicand and writing the result below, starting in the rightmost column. The same is done for each digit of the multiplicand and the result in each case is shifted one position to the left. As a final step, all the individual products are added to arrive at the total product of the two multi-digit numbers. Other techniques used for multiplication are the grid method and the lattice method. Computer science is interested in multiplication algorithms with a low computational complexity to be able to efficiently multiply very large integers, such as the Karatsuba algorithm, the Schönhage-Strassen algorithm, and the Toom-Cook algorithm. A common technique used for division is called long division. Other methods include short division and chunking.

Integer arithmetic is not closed under division. This means that when dividing one integer by another integer, the result is not always an integer. For instance, 7 divided by 2 is not a whole number but 3.5. One way to ensure that the result is an integer is to round the result to a whole number. However, this method leads to inaccuracies as the original value is altered. Another method is to perform the division only partially and retain the remainder. For example, 7 divided by 2 is 3 with a remainder of 1. These difficulties are avoided by rational number arithmetic, which allows for the exact representation of fractions.

A simple method to calculate exponentiation is by repeated multiplication. For instance, the exponentiation of $$3^4$$ can be calculated as $$3 \times 3 \times 3 \times 3$$. A more efficient technique used for large exponents is exponentiation by squaring. It breaks down the calculation into a number of squaring operations. For example, the exponentiation $$3^{65}$$ can be written as $$(((((3^2)^2)^2)^2)^2)^2 \times 3$$. By taking advantage of repeated squaring operations, only 7 individual operations are needed rather than the 64 operations required for regular repeated multiplication. Methods to calculate logarithms include the Taylor series and continued fractions. Integer arithmetic is not closed under logarithm and under exponentiation with negative exponents, meaning that the result of these operations is not always an integer.

Number theory
Number theory studies the structure and properties of integers as well as the relations and laws between them. Some of the main branches of modern number theory include elementary number theory, analytic number theory, algebraic number theory, and geometric number theory. Elementary number theory studies aspects of integers that can be investigated using elementary methods. Its topics include divisibility, factorization, and primality. Analytic number theory, by contrast, relies on techniques from analysis and calculus. It examines problems like how prime numbers are distributed and the claim that every even number is a sum of two prime numbers. Algebraic number theory employs algebraic structures to analyze the properties of and relations between numbers. Examples are the use of fields and rings, as in algebraic number fields like the ring of integers. Geometric number theory uses concepts from geometry to study numbers. For instance, it investigates how lattice points with integer coordinates behave in a plane. Further branches of number theory are probabilistic number theory, which employs methods from probability theory, combinatorial number theory, which relies on the field of combinatorics, computational number theory, which approaches number-theoretic problems with computational methods, and applied number theory, which examines the application of number theory to fields like physics, biology, and cryptography.

Influential theorems in number theory include the fundamental theorem of arithmetic, Euclid's theorem, and Fermat's last theorem. According to the fundamental theorem of arithmetic, every integer greater than 1 is either a prime number or can be represented as a unique product of prime numbers. For example, the number 18 is not a prime number and can be represented as $$2 \times 3 \times 3$$, all of which are prime numbers. The number 19, by contrast, is a prime number that has no other prime factorization. Euclid's theorem states that there are infinitely many prime numbers. Fermat's last theorem is the statement that no positive integer values can be found for $$a$$, $$b$$, and $$c$$, to solve the equation $$a^n + b^n = c^n$$ if $$n$$ is greater than $$2$$.

Rational number arithmetic
Rational number arithmetic is the branch of arithmetic that deals with the manipulation of numbers that can be expressed as a ratio of two integers. Most arithmetic operations on rational numbers can be calculated by performing a series of integer arithmetic operations on the numerators and the denominators of the involved numbers. If two rational numbers have the same denominator then they can be added by adding their numerators and keeping the common denominator. For example, $$\tfrac{2}{7} + \tfrac{3}{7} = \tfrac{5}{7}$$. A similar procedure is used for subtraction. If the two numbers do not have the same denominator then they must be transformed to find a common denominator. This can be achieved by scaling the first number with the denominator of the second number while scaling the second number with the denominator of the first number. For instance, $$\tfrac{1}{3} + \tfrac{1}{2} = \tfrac{1 \cdot 2}{3 \cdot 2} + \tfrac{1 \cdot 3}{2 \cdot 3} = \tfrac{2}{6} + \tfrac{3}{6} = \tfrac{5}{6}$$.

Two rational numbers are multiplied by multiplying their numerators and their denominators respectively, as in $$\tfrac{2}{3} \cdot \tfrac{2}{5} = \tfrac{2 \cdot 2}{3 \cdot 5} = \tfrac{4}{15}$$. Dividing one rational number by another can be achieved by multiplying the first number with the reciprocal of the second number. This means that the numerator and the denominator of the second number change position. For example, $$\tfrac{3}{5} : \tfrac{2}{7} = \tfrac{3}{5} \cdot \tfrac{7}{2} = \tfrac{21}{10}$$. Unlike integer arithmetic, rational number arithmetic is closed under division as long as the divisor is not 0.

Both integer arithmetic and rational number arithmetic are not closed under exponentiation and logarithm. One way to calculate exponentiation with a fractional exponent is to perform two separate calculations: one exponentiation using the numerator of the exponent followed by drawing the nth root of the result based on the denominator of the exponent. For example, $$5^\frac{2}{3} = \sqrt[3]{5^2}$$. The first operation can be completed using methods like repeated multiplication or exponentiation by squaring. One way to get an approximate result for the second operation is to employ Newton's method, which uses a series of steps to gradually refine an initial guess until it reaches the desired level of accuracy. The Taylor series or the continued fraction method can be utilized to calculate logarithms.

The decimal fraction notation is a special way of representing rational numbers whose denominator is a power of 10. For instance, the rational numbers $$\tfrac{1}{10}$$, $$\tfrac{371}{100}$$, and $$\tfrac{44}{10000}$$ are written as 0.1, 3.71, and 0.0044 in the decimal fraction notation. Modified versions of integer calculation methods like addition with carry and long multiplication can be applied to calculations with decimal fractions. Not all rational numbers have a finite representation in the decimal notation. For example, the rational number $$\tfrac{1}{3}$$ corresponds to 0.333... with an infinite number of 3s. The shortened notation for this type of repeating decimal is 0.$\overline{3}$. Every repeating decimal expresses a rational number.

Real number arithmetic
Real number arithmetic is the branch of arithmetic that deals with the manipulation of both rational and irrational numbers. Irrational numbers are numbers that cannot be expressed through fractions or repeated decimals, like the root of 2 and π. Unlike rational number arithmetic, real number arithmetic is closed under exponentiation as long as it uses a positive number as its base. The same is true for the logarithm of positive real numbers as long as the logarithm base is positive and not 1.

Irrational numbers involve an infinite non-repeating series of decimal digits. Because of this, there is often no simple and accurate way to express the results of arithmetic operations like $$\sqrt{2} + \pi$$ or $e \cdot \sqrt{3}$. In cases where absolute precision is not required, the problem of calculating arithmetic operations on real numbers is usually addressed by truncation or rounding. For truncation, a certain number of leftmost digits are kept and remaining digits are discarded or replaced by zeros. For example, the number π has an infinite number of digits starting with 3.14159.... If this number is truncated to 4 decimal places, the result is 3.141. Rounding is a similar process in which the last preserved digit is increased by one if the next digit is 5 or greater but remains the same if the next digit is less than 5, so that the rounded number is the best approximation of a given precision for the original number. For instance, if the number π is rounded to 4 decimal places, the result is 3.142 because the following digit is a 5, so 3.142 is closer to π than 3.141. These methods allow computers to efficiently perform approximate calculations on real numbers.

Approximations and errors
In science and engineering, numbers represent estimates of physical quantities derived from measurement or modeling. Unlike mathematically exact numbers such as π or $\sqrt2$, scientifically relevant numerical data are inherently inexact, involving some measurement uncertainty. One basic way to express the degree of certainty about each number's value and avoid false precision is to round each measurement to a certain number of digits, called significant digits, which are implied to be accurate. For example, a person's height measured with a tape measure might only be precisely known to the nearest centimeter, so should be presented as 1.62 meters rather than 1.6217 meters. If converted to imperial units, this quantity should be rounded to 64 inches or 63.8 inches rather than 63.7795 inches, to clearly convey the precision of the measurement. When a number is written using ordinary decimal notation, leading zeros are not significant, and trailing zeros of numbers not written with a decimal point are implicitly considered to be non-significant. For example, the numbers 0.056 and 1200 each have only 2 significant digits, but the number 40.00 has 4 significant digits. Representing uncertainty using only significant digits is a relatively crude method, with some unintuitive subtleties; explicitly keeping track of an estimate or upper bound of the approximation error is a more sophisticated approach. In the example, the person's height might be represented as 1.62 ± 0.005 meters or 63.8 ± 0.2 inches.

In performing calculations with uncertain quantities, the uncertainty should be propagated to calculated quantities. When adding or subtracting two or more quantities, add the absolute uncertainties of each summand together to obtain the absolute uncertainty of the sum. When multiplying or dividing two or more quantities, add the relative uncertainties of each factor together to obtain the relative uncertainty of the product. When representing uncertainty by significant digits, uncertainty can be coarsely propagated by rounding the result of adding or subtracting two or more quantities to the leftmost last significant decimal place among the summands, and by rounding the result of multiplying or dividing two or more quantities to the least number of significant digits among the factors. (See .)

More sophisticated methods of dealing with uncertain values include interval arithmetic and affine arithmetic. Interval arithmetic describes operations on intervals. Intervals can be used to represent a range of values if one does not know the precise magnitude, for example, because of measurement errors. Interval arithmetic includes operations like addition and multiplication on intervals, as in $$[1, 2] + [3, 4] = [4, 6]$$ and $$[1, 2] \times [3, 4] = [3, 8]$$. It is closely related to affine arithmetic, which aims to give more precise results by performing calculations on affine forms rather than intervals. An affine form is a number together with error terms that describe how the number may deviate from the actual magnitude.

The precision of numerical quantities can be expressed uniformly using normalized scientific notation, which is also convenient for concisely representing numbers which are much larger or smaller than 1. Using scientific notation, a number is decomposed into the product of a number between 1 and 10, called the significand, and 10 raised to some integer power, called the exponent. The significand consists of the significant digits of the number, and is written as a leading digit 1–9 followed by a decimal point and a sequence of digits 0–9. For example, the normalized scientific notation of the number 8276000 is $$8.276 \times 10^6$$ with significand 8.276 and exponent 6, and the normalized scientific notation of the number 0.00735 is $$7.35 \times 10^{-3}$$ with significand 7.35 and exponent −3. Unlike ordinary decimal notation, where trailing zeros of large numbers are implicitly considered to be non-significant, in scientific notation every digit in the significand is considered significant, and adding trailing zeros indicates higher precision. For example, while the number 1200 implicitly has only 2 significant digits, the number $1.20 \times 10^3$ explicitly has 3.

A common method employed by computers to approximate real number arithmetic is called floating-point arithmetic. It represents real numbers similar to the scientific notation through three numbers: a significand, a base, and an exponent. The precision of the significand is limited by the number of bits allocated to represent it. If an arithmetic operation results in a number that requires more bits than are available, the computer rounds the result to the closest representable number. This leads to rounding errors. A consequence of this behavior is that certain laws of arithmetic are violated by floating-point arithmetic. For example, floating-point addition is not associative since the rounding errors introduced can depend on the order of the additions. This means that the result of $$(a + b) + c$$ is sometimes different from the result of $a + (b + c)$. The most common technical standard used for floating-point arithmetic is called IEEE 754. Among other things, it determines how numbers are represented, how arithmetic operations and rounding are performed, and how errors and exceptions are handled. In cases where computation speed is not a limiting factor, it is possible to use arbitrary-precision arithmetic, for which the precision of calculations is only restricted by the computer's memory.

Tool use

Forms of arithmetic can also be distinguished by the tools employed to perform calculations and include many approaches besides the regular use of pen and paper. Mental arithmetic relies exclusively on the mind without external tools. Instead, it utilizes visualization, memorization, and certain calculation techniques to solve arithmetic problems. One such technique is the compensation method, which consists in altering the numbers to make the calculation easier and then adjusting the result afterward. For example, instead of calculating $$85-47$$, one calculates $$85-50$$ which is easier because it uses a round number. In the next step, one adds $$3$$ to the result to compensate for the earlier adjustment. Mental arithmetic is often taught in primary education to train the numerical abilities of the students.

The human body can also be employed as an arithmetic tool. The use of hands in finger counting is often introduced to young children to teach them numbers and simple calculations. In its most basic form, the number of extended fingers corresponds to the represented quantity and arithmetic operations like addition and subtraction are performed by extending or retracting fingers. This system is limited to small numbers while more advanced systems employ different approaches to represent larger quantities as well. The human voice is used as an arithmetic aid in verbal counting.

Tally marks are a simple system based on external tools other than the body. It relies on strokes drawn on a surface or notches in a wooden stick to keep track of quantities. Some forms of tally marks arrange the strokes in groups of five to make them easier to read. The abacus is a more advanced tool to represent numbers and perform calculations. An abacus usually consists of a series of rods, each holding several beads. Each bead represents a quantity, which is counted if the bead is moved from one end of a rod to the other. Calculations happen by manipulating the positions of beads until the final bead pattern reveals the result. Related aids include counting boards, which use tokens whose value depends on the area on the board in which they are placed, and counting rods, which are arranged in horizontal and vertical patterns to represent different numbers. Sectors and slide rules are more refined calculating instruments that rely on geometric relationships between different scales to perform both basic and advanced arithmetic operations. Printed tables were particularly relevant as an aid to look up the results of operations like logarithm and trigonometric functions.

Mechanical calculators automate manual calculation processes. They present the user with some form of input device to enter numbers by turning dials or pressing keys. They include an internal mechanism usually consisting of gears, levers, and wheels to perform calculations and display the results. For electronic calculators and computers, this procedure is further refined by replacing the mechanical components with electronic circuits like processors that combine and transform electric signals to perform calculations.

Others

There are many other types of arithmetic. Modular arithmetic operates on a finite set of numbers. If an operation would result in a number outside this finite set then the number is adjusted back into the set, similar to how the hands of clocks start at the beginning again after having completed one cycle. The number at which this adjustment happens is called the modulus. For example, a regular clock has a modulus of 12. In the case of adding 4 to 9, this means that the result is not 13 but 1. The same principle applies also to other operations, such as subtraction, multiplication, and division.

Some forms of arithmetic deal with operations performed on mathematical objects other than numbers. Interval arithmetic describes operations on intervals. Vector arithmetic and matrix arithmetic describe arithmetic operations on vectors and matrices, like vector addition and matrix multiplication.

Arithmetic systems can be classified based on the numeral system they rely on. For instance, decimal arithmetic describes arithmetic operations in the decimal system. Other examples are binary arithmetic, octal arithmetic, and hexadecimal arithmetic.

Compound unit arithmetic describes arithmetic operations performed on magnitudes with compound units. It involves additional operations to govern the transformation between single unit and compound unit quantities. For example, the operation of reduction is used to transform the compound quantity 1 h 90 min into the single unit quantity 150 min.

Non-Diophantine arithmetics are arithmetic systems that violate traditional arithmetic intuitions and include equations like $$1 + 1 = 1$$ and $$2 + 2 = 5$$. They can be employed to represent some real-world situations in modern physics and everyday life. For instance, the equation $$1 + 1 = 1$$ can be used to describe the observation that if one raindrop is added to another raindrop then they do not remain two separate entities but become one.

Axiomatic foundations
Axiomatic foundations of arithmetic try to provide a small set of laws, called axioms, from which all fundamental properties of and operations on numbers can be derived. They constitute logically consistent and systematic frameworks that can be used to formulate mathematical proofs in a rigorous manner. Two well-known approaches are the Dedekind–Peano axioms and set-theoretic constructions.

The Dedekind–Peano axioms provide an axiomatization of the arithmetic of natural numbers. Their basic principles were first formulated by Richard Dedekind and later refined by Giuseppe Peano. They rely only on a small number of primitive mathematical concepts, such as 0, natural number, and successor. The Peano axioms determine how these concepts are related to each other. All other arithmetic concepts can then be defined in terms of these primitive concepts.

 * 1) 0 is a natural number.
 * 2) For every natural number, there is a successor, which is also a natural number.
 * 3) The successors of two different natural numbers are never identical.
 * 4) 0 is not the successor of a natural number.
 * 5) If a set contains 0 and every successor then it contains every natural number.

Numbers greater than 0 are expressed by repeated application of the successor function $$s$$. For example, $$1$$ is $$s(0)$$ and $$3$$ is $$s(s(s(0)))$$. Arithmetic operations can be defined as mechanisms that affect how the successor function is applied. For instance, to add $$2$$ to any number is the same as applying the successor function two times to this number.

Various axiomatizations of arithmetic rely on set theory. They cover natural numbers but can also be extended to integers, rational numbers, and real numbers. Each natural number is represented by a unique set. 0 is usually defined as the empty set $$\varnothing$$. Each subsequent number can be defined as the union of the previous number with the set containing the previous number. For example, $$1 = 0 \cup \{0\} = \{0\}$$, $$2 = 1 \cup \{1\} = \{0, 1\}$$, and $$3 = 2 \cup \{2\} = \{0, 1, 2\}$$. Integers can be defined as ordered pairs of natural numbers where the second number is subtracted from the first one. For instance, the pair (9, 0) represents the number 9 while the pair (0, 9) represents the number -9. Rational numbers are defined as pairs of integers where the first number represents the numerator and the second number represents the denominator. For example, the pair (3, 7) represents the rational number $$\tfrac{3}{7}$$. One way to construct the real numbers relies on the concept of Dedekind cuts. According to this approach, each real number is represented by a partition of all rational numbers into two sets, one for all numbers below the represented real number and the other for the rest. Arithmetic operations are defined as functions that perform various set-theoretic transformations on the sets representing the input numbers to arrive at the set representing the result.

History

The earliest forms of arithmetic are sometimes traced back to counting and tally marks used to keep track of quantities. Some historians suggest that the Lebombo bone (dated about 43,000 years ago) and the Ishango bone (dated about 22,000 to 30,000 years ago) are the oldest arithmetic artifacts but this interpretation is disputed. However, a basic sense of numbers may predate these findings and might even have existed before the development of language.

It was not until the emergence of ancient civilizations that a more complex and structured approach to arithmetic began to evolve, starting around 3000 BCE. This became necessary because of the increased need to keep track of stored items, manage land ownership, and arrange exchanges. All the major ancient civilizations developed non-positional numeral systems to facilitate the representation of numbers. They also had symbols for operations like addition and subtraction and were aware of fractions. Examples are Egyptian hieroglyphics as well as the numeral systems invented in Sumeria, China, and India. The first positional numeral system was developed by the Babylonians starting around 1800 BCE. This was a significant improvement over earlier numeral systems since it made the representation of large numbers and calculations on them more efficient. Abacuses have been utilized as hand-operated calculating tools since ancient times as efficient means for performing complex calculations.

Early civilizations primarily used numbers for concrete practical purposes, like commercial activities and tax records, but lacked an abstract concept of number itself. This changed with the ancient Greek mathematicians, who began to explore the abstract nature of numbers rather than studying how they are applied to specific problems. Another novel feature was their use of proofs to establish mathematical truths and validate theories. A further contribution was their distinction of various classes of numbers, such as even numbers, odd numbers, and prime numbers. This included the discovery that numbers for certain geometrical lengths are irrational and therefore cannot be expressed as a fraction. The works of Thales of Miletus and Pythagoras in the 7th and 6th centuries BCE are often regarded as the inception of Greek mathematics. Diophantus was an influential figure in Greek arithmetic in the 3rd century BCE because of his numerous contributions to number theory and his exploration of the application of arithmetic operations to algebraic equations.

The ancient Indians were the first to develop the concept of zero as a number to be used in calculations. The exact rules of its operation were written down by Brahmagupta in around 628 CE. The concept of zero or none existed long before, but it was not considered an object of arithmetic operations. Brahmagupta further provided a detailed discussion of calculations with negative numbers and their application to problems like credit and debt. The concept of negative numbers itself is significantly older and was first explored in Chinese mathematics in the first millennium BCE.

Indian mathematicians also developed the positional decimal system used today, in particular the concept of a zero digit instead of empty or missing positions. For example, a detailed treatment of its operations was provided by Aryabhata around the turn of the 6th century CE. The Indian decimal system was further refined and expanded to non-integers during the Islamic Golden Age by Arab mathematicians such as Al-Khwarizmi. His work was influential in introducing the decimal numeral system to the Western world, which at that time relied on the Roman numeral system. There, it was popularized by mathematicians like Leonardo Fibonacci, who lived in the 12th and 13th centuries and also developed the Fibonacci sequence. During the Middle Ages and Renaissance, many popular textbooks were published to cover the practical calculations for commerce. The use of abacuses also became widespread in this period. In the 16th century, the mathematician Gerolamo Cardano conceived the concept of complex numbers as a way to solve cubic equations.

The first mechanical calculators were developed in the 17th century and greatly facilitated complex mathematical calculations, such as Blaise Pascal's calculator and Gottfried Wilhelm Leibniz's stepped reckoner. The 17th century also saw the discovery of the logarithm by John Napier.

In the 18th and 19th centuries, mathematicians such as Leonhard Euler and Carl Friedrich Gauss laid the foundations of modern number theory. Another development in this period concerned work on the formalization and foundations of arithmetic, such as Georg Cantor's set theory and the Dedekind–Peano axioms used as an axiomatization of natural-number arithmetic. Computers and electronic calculators were first developed in the 20th century. Their widespread use revolutionized both the accuracy and speed with which even complex arithmetic computations can be calculated.

Education
Arithmetic education forms part of primary education. It is one of the first forms of mathematics education that children encounter. Elementary arithmetic aims to give students a basic sense of numbers and to familiarize them with fundamental numerical operations like addition, subtraction, multiplication, and division. It is usually introduced in relation to concrete scenarios, like counting beads, dividing the class into groups of children of the same size, and calculating change when buying items. Common tools in early arithmetic education are number lines, addition and multiplication tables, counting blocks, and abacuses.

Later stages focus on a more abstract understanding and introduce the students to different types of numbers, such as negative numbers, fractions, real numbers, and complex numbers. They further cover more advanced numerical operations, like exponentiation, extraction of roots, and logarithm. They also show how arithmetic operations are employed in other branches of mathematics, such as their application to describe geometrical shapes and the use of variables in algebra. Another aspect is to teach the students the use of algorithms and calculators to solve complex arithmetic problems.

Psychology
The psychology of arithmetic is interested in how humans and animals learn about numbers, represent them, and use them for calculations. It examines how mathematical problems are understood and solved and how arithmetic abilities are related to perception, memory, judgment, and decision making. For example, it investigates how collections of concrete items are first encountered in perception and subsequently associated with numbers. A further field of inquiry concerns the relation between numerical calculations and the use of language to form representations. Psychology also explores the biological origin of arithmetic as an inborn ability. This concerns pre-verbal and pre-symbolic cognitive processes implementing arithmetic-like operations required to successfully represent the world and perform tasks like spatial navigation.

One of the concepts studied by psychology is numeracy, which is the capability to comprehend numerical concepts, apply them to concrete situations, and reason with them. It includes a fundamental number sense as well as being able to estimate and compare quantities. It further encompasses the abilities to symbolically represent numbers in numbering systems, interpret numerical data, and evaluate arithmetic calculations. Numeracy is a key skill in many academic fields. A lack of numeracy can inhibit academic success and lead to bad economic decisions in everyday life, for example, by misunderstanding mortgage plans and insurance policies.

Philosophy
The philosophy of arithmetic studies the fundamental concepts and principles underlying numbers and arithmetic operations. It explores the nature and ontological status of numbers, the relation of arithmetic to language and logic, and how it is possible to acquire arithmetic knowledge.

According to Platonism, numbers have mind-independent existence: they exist as abstract objects outside spacetime and without causal powers. This view is rejected by intuitionists, who claim that mathematical objects are mental constructions. Further theories are logicism, which holds that mathematical truths are reducible to logical truths, and formalism, which states that mathematical principles are rules of how symbols are manipulated without claiming that they correspond to entities outside the rule-governed activity.

The traditionally dominant view in the epistemology of arithmetic is that arithmetic truths are knowable a priori. This means that they can be known by thinking alone without the need to rely on sensory experience. Some proponents of this view state that arithmetic knowledge is innate while others claim that there is some form of rational intuition through which mathematical truths can be apprehended. A more recent alternative view was suggested by naturalist philosophers like Willard Van Orman Quine, who argue that mathematical principles are high-level generalizations that are ultimately grounded in the sensory world as described by the empirical sciences.

Others
Arithmetic is relevant to many fields. In daily life, it is required to calculate change when shopping, manage personal finances, and adjust a cooking recipe for a different number of servings. Businesses use arithmetic to calculate profits and losses and analyze market trends. In the field of engineering, it is used to measure quantities, calculate loads and forces, and design structures. Cryptography relies on arithmetic operations to protect sensitive information by encrypting data and messages.

Arithmetic is intimately connected to many branches of mathematics that depend on numerical operations. Algebra relies on arithmetic principles to solve equations using variables. These principles also play a key role in calculus in its attempt to determine rates of change and areas under curves. Geometry uses arithmetic operations to measure the properties of shapes while statistics utilizes them to analyze numerical data. Due to the relevance of arithmetic operations throughout mathematics, the influence of arithmetic extends to most sciences such as physics, computer science, and economics. These operations are used in calculations, problem-solving, data analysis, and algorithms, making them integral to scientific research, technological development, and economic modeling.

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

title: Arithmetic


text:
Andersonville, Georgia

Andersonville is a city in Sumter County, Georgia, United States. As of the 2020 census, the city had a population of 237. It is located in the southwest part of the state, approximately 60 mi southwest of Macon on the Central of Georgia railroad. During the American Civil War, it was the site of a prisoner-of-war camp, which is now Andersonville National Historic Site.

Andersonville is part of the Americus micropolitan statistical area.

History
The hamlet of Anderson was named for John Anderson, a director of the South Western Railroad in 1853 when it was extended from Oglethorpe to Americus. It was known as Anderson Station until the US post office was established in November 1855. The government changed the name of the station from "Anderson" to "Andersonville" in order to avoid confusion with the post office in Anderson, South Carolina.

During the Civil War, the Confederate army established Camp Sumter at Andersonville to house incoming Union prisoners of war. The overcrowded Andersonville Prison was notorious for its bad conditions, and nearly 13,000 prisoners died there. After the war, Henry Wirz was convicted for war crimes related to the command of the camp. His trial was later regarded as unfair by several pro-confederacy groups, and a monument in his honor has been erected in Andersonville by the United Daughters of the Confederacy.

The town also served as a supply depot during the war period. It included a post office, a depot, a blacksmith shop and stable, a couple of general stores, two saloons, a school, a Methodist church, and about a dozen houses. Ben Dykes, who owned the land on which the prison was built, was both depot agent and postmaster.

Until the establishment of the prison, the area was entirely dependent on agriculture, supported by dark reddish brown sandy loams later mapped as Greenville and Red Bay soil series. After the close of the prison and end of the war, the town continued economically dependent on agriculture, primarily the cultivation of cotton as a commodity crop.

It was not until 1968, when the large-scale mining of kaolin, bauxitic kaolin, and bauxite was begun by Mulcoa, Mullite Company of America, that the town was dramatically altered. This operation exploited 2000 acre of scrub oak wilderness into a massive mining and refining operation. The company now ships more than 2000 tons of refined ore from Andersonville each week.

In 1974, long-time mayor Lewis Easterlin and a group of concerned citizens decided to promote tourism in the town, redeveloping Main Street to look much as it did during the American Civil War. The city of Andersonville and the Andersonville National Historic Site, location of the prison camp, are now tourist attractions.

Demographics
As of the census of 2000, there were 331 people, 124 households, and 86 families residing in the city. The population density was 254.1 PD/sqmi. There were 142 housing units at an average density of 109.0 /sqmi. The racial makeup of the city was 65.26% White and 34.74% African American. Hispanic or Latino of any race were 1.21% of the population.

There were 124 households, out of which 34.7% had children under the age of 18 living with them, 46.0% were married couples living together, 17.7% had a female householder with no husband present, and 30.6% were non-families. 26.6% of all households were made up of individuals, and 10.5% had someone living alone who was 65 years of age or older. The average household size was 2.67 and the average family size was 3.21.

In the city, the population was spread out, with 27.8% under the age of 18, 9.4% from 18 to 24, 31.4% from 25 to 44, 19.3% from 45 to 64, and 12.1% who were 65 years of age or older. The median age was 36 years. For every 100 females, there were 105.6 males. For every 100 females age 18 and over, there were 97.5 males.

The median income for a household in the city was $29,107, and the median income for a family was $30,972. Males had a median income of $26,591 versus $20,000 for females. The per capita income for the city was $15,168. About 19.8% of families and 23.0% of the population were below the poverty line, including 29.3% of those under age 18 and 13.5% of those age 65 or over.

title: Andersonville, Georgia


text:
Andersonville

Andersonville may refer to:

United States

 * Andersonville, Georgia, site of an American Civil War prisoner of war camp
 * Andersonville Prison, Confederate prisoner of war camp in Georgia holding Union soldiers
 * Andersonville, Chicago, a neighborhood in Chicago, Illinois
 * Andersonville Commercial Historic District, an historic district in Chicago
 * Andersonville, Iowa
 * Andersonville, Indiana
 * Andersonville, Michigan
 * Andersonville, Ohio, an unincorporated community
 * Andersonville, South Carolina
 * Andersonville, Tennessee
 * Andersonville, Virginia
 * Andersonville, West Virginia

Elsewhere

 * Andersonville, New Brunswick, Canada

Other uses

 * Andersonville (novel), Pulitzer Prize–winning 1956 novel by MacKinlay Kantor
 * Andersonville (film), 1996 film based on a prisoner of war camp prisoner's diary
 * Andersonville Theological Seminary, Camilla, Georgia, U.S.
 * "Andersonville", a song by Dave Alvin from his 1991 album Blue Blvd

title: Andersonville


text:
Agra Canal

The Agra Canal is an important Indian irrigation work which starts from Okhla in Delhi. The Agra canal originates at the Okhla barrage, downstream of Nizamuddin bridge.

The canal receives its water from the Yamuna River at Okhla, about 10 km to the south of New Delhi. The weir across the Yamuna was constructed of locally quarried stone. It was about 800 yd long, and rises seven feet above the summer level of the river.

From Okhla the canal follows a route south then southeast for 140 miles in the high land between the Khari-Nadi and the Yamuna and finally joins the Utanga River about 27 miles below Agra. Navigable branches connect the canal with Mathura and Agra. The canal irrigates about undefined ha in Agra, and Mathura in Uttar Pradesh, Faridabad in Haryana, Bharatpur in Rajasthan and also some parts of Delhi.

History
The canal opened in the year 1874. In the beginning, it was available for navigation, in Delhi, erstwhile Gurgaon, Mathura and Agra Districts, and Bharatpur State. Later, navigation was stopped in 1904 and the canal has, since then, been exclusively used for irrigation purposes only. At present, the canal does not flow in Gurgaon district, but only in Faridabad, which was earlier a part of Gurgaon.

In recent times, Agra canal is an important landmark which separates Greater Faridabad from Faridabad.

title: Agra Canal


text:
Amakusa

Amakusa (天草), which means "Heaven's Grass," is a series of islands off the west coast of Kyushu, the southernmost of the four main islands of Japan.

Geography
The largest island of the Amakusa group is Shimoshima, which is 26.5 miles long and 13.5 miles at its widest (26.5 x). It is situated at 32°20'N, 130°E, separated from the rest of Kumamoto Prefecture by the Yatsushiro Sea.

While lacking high mountains with only four peaks surpassing 1500 ft, the island terrain is ruggedly hilly. To cope with the lack of flat arable land, farming is carried out on a terrace system of cultivation.

History
Amakusa, along with the neighboring Shimabara Peninsula, became the site of the Shimabara rebellion in the 17th century, led by Christians. Following the rebellion, Kakure Kirishitan, the Christians who had survived, continued to practice their faith in secret, despite severe persecution.

Economy
Amakusa produces a little coal and pottery stone, both being used by the potters of Hirado ware and Satsuma ware. Many kilns remain on the islands today, and pottery and pottery stone are still exported.

Amakusa pottery has been recognised by the government. The retail company Muji brought out its own line of Hakuji home ware, which is produced out of ground translucent Amakusa stones kneaded into clay, using traditional techniques.

People
Hidenoshin Koyama, who built Thomas Blake Glover's House in Glover Garden, came from this island.

Kenta and Ko-shin, two of the three members of Wanima come from the island of Amakusa.

Government
At present, the islands are organized as Amakusa District, Amakusa City, and Kami-amakusa City, all of which are under the administration of Kumamoto Prefecture.

Transport

The islands are served by Amakusa Airfield, located on the north end of Shimoshima. The islands are connected to the mainland by the Five Bridges of Amakusa and by ferry from Hondo and Matsushima.

There are also ferries between the islands and the neighboring prefectures of Kagoshima Prefecture and Nagasaki Prefecture. The ferry from Oniike on the north Shimoshima to Kuchinotsu, at the southern tip of the Shimabara Peninsula, is run by the Shimabara Railway and operates hourly each day. The ferry boat from Tomioka Port in Reihoku, sailing north to Mogi in Nagasaki Prefecture, is operated by Yasuda Sangyo Kisen Co. Ltd. Two ferries from Shinwa and Ushibuka, in the south of Shimoshima, connect Amakusa to Nagashima in Kagoshima Prefecture.

title: Amakusa


text:
Afterglow

An afterglow in meteorology consists of several atmospheric optical phenomena, with a general definition as a broad arch of whitish or pinkish sunlight in the twilight sky, consisting of the bright segment and the purple light. Purple light mainly occurs when the Sun is 2–6° below the horizon, from civil to nautical twilight, while the bright segment lasts until the end of the nautical twilight. Afterglow is often in cases of volcanic eruptions discussed, while its purple light is discussed as a different particular volcanic purple light. Specifically in volcanic occurrences it is light scattered by fine particulates, like dust, suspended in the atmosphere. In the case of alpenglow, which is similar to the Belt of Venus, afterglow is used in general for the golden-red glowing light from the sunset and sunrise reflected in the sky, and in particularly for its last stage, when the purple light is reflected. The opposite of an afterglow is a foreglow, which occurs before sunrise.

Sunlight reaches Earth around civil twilight during golden hour intensely in its low-energy and low-frequency red component. During this part of civil twilight after sunset and before sundawn the red sunlight remains visible by scattering through particles in the air. Backscattering, possibly after being reflected off clouds or high snowfields in mountain regions, furthermore creates a reddish to pinkish light. The high-energy and high-frequency components of light towards blue are scattered out broadly, producing the broader blue light of nautical twilight before or after the reddish light of civil twilight, while in combination with the reddish light producing the purple light. This period of blue dominating is referred to as the blue hour and is, like the golden hour, widely treasured by photographers and painters.

After the 1883 eruption of the volcano Krakatoa, a remarkable series of red sunsets appeared worldwide. An enormous amount of exceedingly fine dust were blown to a great height by the volcano's explosion, and then globally diffused by the high atmospheric winds. Edvard Munch's painting The Scream possibly depicts an afterglow during this period.

title: Afterglow


text:
Ammonius Grammaticus

Ammonius Grammaticus (Ἀμμώνιος Γραμματικός) was a 4th-century Egyptian priest.

In 391, he was involved in a violent revolt centred at Alexandria's Serapeum, where the pagan rebels tortured and killed captured Christians. After the suppression of the revolt and the destruction of the temple, Ammonius fled to Constantinople, where he became the tutor of the ecclesiastical historian Socrates.

Ammonius was formerly identified as the author of a treatise titled Peri homoíōn kai diaphórōn léxeōn (περὶ ὁμοίων καὶ διαφόρων λέξεων, On the Differences of Synonymous Expressions). But it seems more probable that the real author was Herennius Philo of Byblus, who was born during the reign of Nero and lived till the reign of Hadrian, and that the treatise in its present form is a revision prepared by a later Byzantine editor, whose name may have been Ammonius.

title: Ammonius Grammaticus


text:
Talk:Arsenic

What does glassy mean?
In the physical characteristics section black arsenic is described as “glassy”, what does that mean?

”It is glassy and brittle. Black arsenic is also a poor electrical conductor.” Ombabsail (talk) 17:24, 11 August 2023 (UTC)

 * Like a glass. Polyamorph (talk) 06:46, 13 August 2023 (UTC)
 * I have found out what it should mean, it means that it is non crystalline, also known as amorphous supposedly.
 * left is to edit that section in physical characteristics to make it more clear or replace the word glassy with amorphous as a better solution. Ombabsail (talk) 22:23, 18 August 2023 (UTC)

SOLUBILITY! Where is it?
Wow, an entire page on an element with no mention of what solvents this element and it's main compounds are soluble in.

Does nobody care? 2600:6C46:6800:3322:4846:CCD0:7AAA:EADC (talk) 15:25, 14 May 2024 (UTC)

 * The solubility of arsenic compounds is discussed under "Inorganic compounds" and "Agricultural" uses. Elemental arsenic itself is insoluble but it does not appear in the elemental form often enough for the solubility to be relevant to any major discussion in the article. Recon  rabbit  16:05, 14 May 2024 (UTC)

Chemistry
আর্সেনিক কে বিশের রাজা বলা হয় কেন? 103.115.242.249 (talk) 08:04, 3 June 2024 (UTC)
 * এটি আপনার ভাষায় প্রশ্নের জন্য ভুল ওয়েবসাইট। হয়ত পরিবর্তে এই নিবন্ধটি চেষ্টা করুন?
 * (translation: This is the wrong website for questions in Bangla. Maybe try this article instead?)
 * Ragamuffiln19 🜺 (talk) 22:11, 4 June 2024 (UTC)

title: Talk:Arsenic