title: Repeating decimal

text: If 0 never occurs as a remainder, then the division process continues forever, and eventually, a remainder must occur that has occurred before. The next step in the division will yield the same new digit in the quotient, and the same new remainder, as the previous time the remainder was the same. Therefore, the following division will repeat the same results. The repeating sequence of digits is called "repetend" which has a certain length greater than 0, also called "period".


title: Repeating decimal

text: Each repeating decimal number satisfies a linear equation with integer coefficients, and its unique solution is a rational number. To illustrate the latter point, the number above satisfies the equation , whose solution is . The process of how to find these integer coefficients is described below.


title: Repeating decimal

text: For comparison, the lengths "ℓ"("n") of the binary repetends of the fractions , "n" = 1, 2, 3, ..., are:


title: Repeating decimal

text: A fraction in lowest terms with a prime denominator other than 2 or 5 (i.e. coprime to 10) always produces a repeating decimal. The length of the repetend (period of the repeating decimal segment) of is equal to the order of 10 modulo "p". If 10 is a primitive root modulo "p", then the repetend length is equal to "p" − 1; if not, then the repetend length is a factor of "p" − 1. This result can be deduced from Fermat's little theorem, which states that .


title: Repeating decimal

text: The base-10 digital root of the repetend of the reciprocal of any prime number greater than 5 is divisible by 9.


title: Repeating decimal

text: If the repetend length of for prime "p" is equal to "p" − 1 then the repetend, expressed as an integer, is called a cyclic number.


title: Repeating decimal

text: Every "proper" multiple of a cyclic number (that is, a multiple having the same number of digits) is a rotation:


title: Repeating decimal

text: The reason for the cyclic behavior is apparent from an arithmetic exercise of long division of : the sequential remainders are the cyclic sequence . See also the article 142,857 for more properties of this cyclic number.


title: Repeating decimal

text: A fraction which is cyclic thus has a recurring decimal of even length that divides into two sequences in nines' complement form. For example starts '142' and is followed by '857' while (by rotation) starts '857' followed by "its" nines' complement '142'.


title: Repeating decimal

text: The rotation of the repetend of a cyclic number always happens in such a way that each successive repetend is a bigger number than the previous one. In the succession above, for instance, we see that 0.142857... < 0.285714... < 0.428571... < 0.571428... < 0.714285... < 0.857142... This, for cyclic fractions with long repetends, allows us to easily predict what the result of multiplying the fraction by any natural number n will be, as long as the repetend is known.


title: Repeating decimal

text: A "proper prime" is a prime "p" which ends in the digit 1 in base 10 and whose reciprocal in base 10 has a repetend with length "p" − 1. In such primes, each digit 0, 1..., 9 appears in the repeating sequence the same number of times as does each other digit (namely, times). They are:


title: Repeating decimal

text: If a prime "p" is both full reptend prime and safe prime, then will produce a stream of "p" − 1 pseudo-random digits. Those primes are


title: Repeating decimal

text: To find the period of , we can check whether the prime "p" divides some number 999...999 in which the number of digits divides "p" − 1. Since the period is never greater than "p" − 1, we can obtain this by calculating . For example, for 11 we get


title: Repeating decimal

text: Those reciprocals of primes can be associated with several sequences of repeating decimals. For example, the multiples of can be divided into two sets, with different repetends. The first set is:


title: Repeating decimal

text: In general, the set of proper multiples of reciprocals of a prime "p" consists of "n" subsets, each with repetend length "k", where "nk" = "p" − 1.


title: Repeating decimal

text: For an arbitrary integer "n", the length "L"("n") of the decimal repetend of divides "φ"("n"), where "φ" is the totient function. The length is equal to if and only if 10 is a primitive root modulo "n".


title: Repeating decimal

text: In particular, it follows that if and only if "p" is a prime and 10 is a primitive root modulo "p". Then, the decimal expansions of for "n" = 1, 2, ..., "p" − 1, all have period "p" − 1 and differ only by a cyclic permutation. Such numbers "p" are called full repetend primes.


title: Repeating decimal

text: The period (repetend length) "L"(49) must be a factor of "λ"(49) = 42, where "λ"("n") is known as the Carmichael function. This follows from Carmichael's theorem which states that if "n" is a positive integer then "λ"("n") is the smallest integer "m" such that


title: Repeating decimal

text: The period of is usually "pT", where "T" is the period of . There are three known primes for which this is not true, and for those the period of is the same as the period of because "p" divides 10−1. These three primes are 3, 487, and 56598313 .


title: Repeating decimal

text: If "p" and "q" are primes other than 2 or 5, the decimal representation of the fraction repeats. An example is :


title: Repeating decimal

text: If "p", "q", "r", etc. are primes other than 2 or 5, and "k", "ℓ", "m", etc. are positive integers, then


title: Repeating decimal

text: where "T", "T", "T"... are respectively the period of the repeating decimals , , ... as defined above.


title: Repeating decimal

text: An integer that is not coprime to 10 but has a prime factor other than 2 or 5 has a reciprocal that is eventually periodic, but with a non-repeating sequence of digits that precede the repeating part. The reciprocal can be expressed as:


title: Repeating decimal

text: The procedure below can be applied in particular if the repetend has "n" digits, all of which are 0 except the final one which is 1. For instance for "n" = 7:


title: Repeating decimal

text: So this particular repeating decimal corresponds to the fraction , where the denominator is the number written as "n" 9s. Knowing just that, a general repeating decimal can be expressed as a fraction without having to solve an equation. For example, one could reason:


title: Repeating decimal

text: It is possible to get a general formula expressing a repeating decimal with an "n"-digit period (repetend length), beginning right after the decimal point, as a fraction:


title: Repeating decimal

text: If the repeating decimal is between 0 and 1, and the repeating block is "n" digits long, first occurring right after the decimal point, then the fraction (not necessarily reduced) will be the integer number represented by the "n"-digit block divided by the one represented by "n" 9s. For example,


title: Repeating decimal

text: If the repeating decimal is as above, except that there are "k" (extra) digits 0 between the decimal point and the repeating "n"-digit block, then one can simply add "k" digits 0 after the "n" digits 9 of the denominator (and, as before, the fraction may subsequently be simplified). For example,


title: Repeating decimal

text: Any repeating decimal not of the form described above can be written as a sum of a terminating decimal and a repeating decimal of one of the two above types (actually the first type suffices, but that could require the terminating decimal to be negative). For example,


title: Repeating decimal

text: It follows that any repeating decimal with period "n", and "k" digits after the decimal point that do not belong to the repeating part, can be written as a (not necessarily reduced) fraction whose denominator is (10 − 1)10.


title: Repeating decimal

text: Conversely the period of the repeating decimal of a fraction will be (at most) the smallest number "n" such that 10 − 1 is divisible by "d".


title: Repeating decimal

text: For example, the fraction has "d" = 7, and the smallest "k" that makes 10 − 1 divisible by 7 is "k" = 6, because 999999 = 7 × 142857. The period of the fraction is therefore 6.


title: Repeating decimal

text: Thereby formula_12 represents the digits of the integer part of the decimal number (to the left of the decimal point), formula_13 makes up the string of digits of the preperiod and formula_14 its length, and formula_15 being the string of repeated digits (the period) with length formula_16 which is nonzero.


title: Repeating decimal

text: In the generated fraction, the digit formula_17 will be repeated formula_16 times, and the digit formula_19 will be repeated formula_14 times.


title: Repeating decimal

text: Note that in the absence of an integer part in the decimal, formula_12 will be represented by zero, which being to the left of the other digits, will not affect the final result, and may be omitted in the calculation of the generating function.


title: Repeating decimal

text: The symbol formula_23 in the examples above denotes the absence of digits of part formula_13 in the decimal, and therefore formula_25 and a corresponding absence in the generated fraction.


title: Repeating decimal

text: A repeating decimal can also be expressed as an infinite series. That is, a repeating decimal can be regarded as the sum of an infinite number of rational numbers. To take the simplest example,


title: Repeating decimal

text: The above series is a geometric series with the first term as and the common factor . Because the absolute value of the common factor is less than 1, we can say that the geometric series converges and find the exact value in the form of a fraction by using the following formula where "a" is the first term of the series and "r" is the common factor.


title: Repeating decimal

text: The cyclic behavior of repeating decimals in multiplication also leads to the construction of integers which are cyclically permuted when multiplied by certain numbers. For example, . 102564 is the repetend of and 410256 the repetend of .


title: Repeating decimal

text: Various features of repeating decimals extend to the representation of numbers in all other integer bases, not just base 10:


title: Repeating decimal

text: For example, in duodecimal, = 0.6, = 0.4, = 0.3 and = 0.2 all terminate; = 0. repeats with period length 4, in contrast with the equivalent decimal expansion of 0.2; = 0. has period 6 in duodecimal, just as it does in decimal.


title: Repeating decimal

text: For a rational (and base ) there is the following algorithm producing the repetend together with its length:


title: Repeating decimal

text: The subsequent line calculates the new remainder of the division modulo the denominator . As a consequence of the floor function codice_1 we have


title: Repeating decimal

text: Because all these remainders are non-negative integers less than , there can be only a finite number of them with the consequence that they must recur in the codice_2 loop. Such a recurrence is detected by the associative array codice_3. The new digit is formed in the yellow line, where is the only non-constant. The length of the repetend equals the number of the remainders (see also section Every rational number is either a terminating or repeating decimal).


title: Repeating decimal

text: Repeating decimals (also called decimal sequences) have found cryptographic and error-correction coding applications. In these applications repeating decimals to base 2 are generally used which gives rise to binary sequences. The maximum length binary sequence for (when 2 is a primitive root of "p") is given by:


title: Repeating decimal

text: These sequences of period "p" − 1 have an autocorrelation function that has a negative peak of −1 for shift of . The randomness of these sequences has been examined by diehard tests.


title: Steel-cut oats

text: Steel-cut oats (US), also called pinhead oats, coarse oatmeal (UK), or Irish oatmeal, are groats (the inner kernel with the inedible hull removed) of whole oats which have been chopped into two or three pinhead-sized pieces (hence the names; "steel-cut" comes from the steel blades). The pieces can then be sold, or processed further to make rolled oat flakes, of smaller size than flakes of whole groats. Steel-cutting produces oatmeal with a chewier and coarser texture than other processes.


title: Steel-cut oats

text: Steel-cut oats, and other types, are traditionally used to make porridge. They take longer to cook than instant, ground, or rolled oats, typically 15–30 minutes for porridge (or about half this time if pre-soaked). Steel-cut oats are described as being nuttier and chewier than other types of oats. They can be used to make oatcakes, blended uncooked in smoothies and for other culinary purposes.


title: Trial by combat

text: Trial by combat (also wager of battle, trial by battle or judicial duel) was a method of Germanic law to settle accusations in the absence of witnesses or a confession in which two parties in dispute fought in single combat; the winner of the fight was proclaimed to be right. In essence, it was a judicially sanctioned duel. It remained in use throughout the European Middle Ages, gradually disappearing in the course of the 16th century.


title: Trial by combat

text: Unlike trial by ordeal in general, which is known to many cultures worldwide, trial by combat is known primarily from the customs of the Germanic peoples. The practice was "almost universal in Europe" according to medievalist Eric Jager. It was in use among the ancient Burgundians, Ripuarian Franks, Alamans, Lombards, and Swedes.


title: Trial by combat

text: It was unknown in Anglo-Saxon law and Roman law and it does not figure in the traditions of Middle Eastern antiquity such as the code of Hammurabi or the Torah. However, it is recorded in the medieval Irish Brehon Laws, such as "Din Techtugad".


title: Trial by combat

text: The practice is regulated in various Germanic legal codes. Being rooted in Germanic tribal law, the various regional laws of the Frankish Empire (and the later Holy Roman Empire) prescribed different particulars, such as equipment and rules of combat. The "Lex Alamannorum" ("recension Lantfridana" 81, dated to 712–730 AD) prescribes a trial by combat in the event of two families disputing the boundary between their lands. A handful of earth taken from the disputed piece of land is put between the contestants and they are required to touch it with their swords, each swearing that their claim is lawful. The losing party besides forfeiting their claim to the land is required to pay a fine.


title: Trial by combat

text: Capitularies governing its use appear from the year 803 onwards. Louis the Pious prescribed combat between witnesses of each side, rather than between the accuser and the accused, and briefly allowed for the Ordeal of the Cross in cases involving clerics.


title: Trial by combat

text: In medieval Scandinavia, the practice survived throughout the Viking Age in the form of the "holmgang".


title: Trial by combat

text: An unusual variant, the marital duel, involved combat between a husband and wife, with the former physically handicapped in some way. The loser was killed.


title: Trial by combat

text: Otto the Great in 967 expressly sanctioned the practice of Germanic tribal law even if it did not figure in the more "imperial" Roman law. The celebrated case of Gero, Count of Alsleben, is a good example. The Fourth Lateran Council of 1215 deprecated judicial duels, and Pope Honorius III in 1216 asked the Teutonic order to cease its imposition of judicial duels on their newly converted subjects in Livonia. For the following three centuries, there was latent tension between the traditional regional laws and Roman law.


title: Trial by combat

text: The "Sachsenspiegel" of 1230 recognises the judicial duel as an important function to establish guilt or innocence in cases of insult, injury, or theft. The combatants are armed with swords and shields and may wear linen and leather clothing, but their heads and feet must be bare and their hands only protected by light gloves. The accuser is to await the accused at the designated place of combat. If the accused does not appear after being summoned three times, the accuser may execute two cuts and two stabs against the wind, and his matter will be treated as if he had won the fight.


title: Trial by combat

text: The "Kleines Kaiserrecht", an anonymous legal code of c. 1300, prohibits judicial duels altogether, stating that the emperor had come to this decision on seeing that too many innocent men were convicted by the practice just for being physically weak. Nevertheless, judicial duels continued to be popular throughout the 14th and 15th centuries.


title: Trial by combat

text: Trial by combat plays a significant role in the German schools of fencing in the 15th century. Notably, Hans Talhoffer depicts techniques to be applied in such duels, separately for the Swabian (sword and shield) and Franconian (mace and shield) variants, although other "Fechtbücher" such as that of Paulus Kal and the "Codex Wallerstein" show similar material. While commoners were required to present their case to a judge before duelling, members of the nobility did have the right to challenge each other for duels without the involvement of the judiciary, so that duels of this kind were separate from the judicial duel already in the Middle Ages and were not affected by the latter's abolition in the early 16th century by Emperor Maximilian I, evolving into the gentlemanly duel of modern times which was outlawed only as late as in the 19th century.


title: Trial by combat

text: Hans Talhoffer in his 1459 "Thott" codex names seven offences that in the absence of witnesses were considered grave enough to warrant a judicial duel, viz. murder, treason, heresy, desertion of one's lord, "imprisonment" (possibly in the sense of abduction), perjury/fraud and rape.


title: Trial by combat

text: Wager of battle, as the trial by combat was called in English, appears to have been introduced into the common law of the Kingdom of England following the Norman Conquest and remained in use for the duration of the High and Late Middle Ages.


title: Trial by combat

text: The last certain trial by battle in England occurred in 1446: a servant accused his master of treason, and the master drank too much wine before the battle and was slain by the servant. In Scotland and Ireland, the practice was continued into the sixteenth century. In 1446, a trial by combat was arranged between two quarrelling Irish magnates, James Butler, 5th Earl of Ormonde, and the Prior of Kilmainham, but King Henry VI intervened personally to persuade them to settle their differences peacefully.


title: Trial by combat

text: The wager of battle was not always available to the defendant in an appeal of murder. If the defendant were taken in the "mainour" (that is, in the act of committing his crime), if he attempted to escape from prison, or if there was such strong evidence of guilt that there could be no effective denial, the defendant could not challenge. Similarly, if the plaintiff was a woman, above 60 years of age, a minor, lame or blind, they could decline the challenge, and the case would be determined by a jury. Peers of the realm, priests, and citizens of the City of London (the last pursuant to their guarantee of ancient liberties under Magna Carta) could also decline the battle if challenged. If the actual battle took place, it would occur in judicial lists, square, following the taking of oaths against witchcraft and sorcery. If the defendant was defeated and still alive, he was to be hanged on the spot. However, if he defeated his opponent, or if he were able to fend off his opponent from sunrise to sunset, he would go free. If the plaintiff said the word "craven" ("I am vanquished") and gave up the fight, he was to be declared infamous, deprived of the privileges of a freeman, and was liable for damages to his successful opponent.


title: Trial by combat

text: The earliest case in which wager of battle is recorded was "Wulfstan v. Walter" (1077), eleven years after the Conquest. Significantly, the names of the parties suggest that it was a dispute between a Saxon and a Norman. The "Tractatus of Glanvill", from around 1187, appears to have considered it the chief mode of trial, at least among aristocrats entitled to bear arms.


title: Trial by combat

text: Around 1219, trial by jury replaced trial by ordeal, which had been the mode of proof for crown pleas since the Assize of Clarendon in 1166. With the emergence of the legal profession in the thirteenth century, lawyers, guarding the safety of the lives and limbs of their clients, steered people away from the wager of battle. A number of legal fictions were devised to enable litigants to avail themselves of the jury even in the sort of actions that were traditionally tried by wager of battle. The practice of averting trial by combat led to the modern concept of attorneys representing litigants.


title: Trial by combat

text: Civil disputes were handled differently from criminal cases. In civil cases, women, the elderly, the infirm of body, minors, and—after 1176—the clergy could choose a jury trial or could have champions named to fight in their stead. Hired champions were technically illegal but are obvious in the record. A 1276 document among Bishop Swinefield's household records makes the promise to pay Thomas of Brydges an annual retainer fee for acting as champion, with additional stipend and expenses paid for each fight. In criminal cases, an approver was often chosen from the accomplices of the accused or from prison to do the fighting for the crown. Approvers sometimes were given their freedom after winning five trials but sometimes were hanged anyway.


title: Trial by combat

text: In practice, a person facing trial by combat was assisted by a second, often referred to as a squire. The role of the squire was to attend the battle and to arrange the particulars of the ceremony with the opposing squire. Over time, squires would meet and resolve disputes during negotiations over combat. Ample time was made for this by creating a process for checking the saddle and bridle of horses for prayer scrolls and enchantments and requiring litigants to exchange gloves (the origin of "throwing down the gauntlet") and sometimes to go to separate churches and give five pence (for the five wounds of Christ) to the church.


title: Trial by combat

text: Early trials by combat allowed a variety of weapons, particularly for knights. Later, commoners were given war hammers, cudgels, or quarterstaves with sharp iron tips. The duelling ground was typically sixty feet square. Commoners were allowed a rectangular leather shield and could be armed with a suit of leather armour, bare to the knees and elbows and covered by a red surcoat of a light type of silk called "sendal". The litigants appeared in person. The combat was to begin before noon and be concluded before sunset.


title: Trial by combat

text: Either combatant could end the fight and lose his case by crying out the word "Craven!", from the Old French "cravanté", "defeated", which acknowledged "(I am) vanquished." The party who did so, however, whether litigant or champion, was punished with outlawry. Fighting continued until one party was dead or disabled. The last man standing won his case.


title: Trial by combat

text: By 1300, the wager of combat had all but died out in favour of trial by jury. One of the last mass trials by combat in Scotland, the "Battle of the Clans", took place in Perth in 1396. This event took the form of a pitched battle between teams of around thirty men each, representing Clan Macpherson and Clan Davidson, on the North Inch in front of King Robert III. The battle was intended to resolve a dispute over which clan was to hold the right flank in an upcoming battle of both clans (and several others) against Clan Cameron. The Clan Macpherson is thought to have won, but only twelve men survived from the original sixty.


title: Trial by combat

text: The last trial by combat under the authority of an English monarch is thought to have taken place during the reign of Elizabeth I in the inner courtyard of Dublin Castle in Ireland on 7 September 1583. The dispute was between members of the sept of O'Connor Faly from King's County (modern County Offaly), who were persuaded by two judges (referred to in the account below) to bring the matter before the Irish privy council for resolution.


title: Trial by combat

text: The dispute probably concerned dynastic power within the territory of the O'Connors, and the parties, Teig and Conor, had accused each other of treason; the privy council granted their wish for trial by combat to take place on the following day, and for another such trial between two other members of the same sept to take place on the Wednesday following. The first combat took place as appointed, with the combatants "in their shirts with swords, targetts and skulles". An account of the proceedings as observed by one of the privy councillors is given in the State papers Ireland 63/104/69 (spelling adapted):


title: Trial by combat

text: The Annals of the Four Masters also refers to the trial and censures the parties for having allowed the English to entice them into the proceedings. It is also referred to in Holinshed's chronicles. This was a trial not at common law but under consiliar jurisdiction.


title: Trial by combat

text: It is uncertain when the last actual trial by battle in Britain took place. While some references speak of such a trial being held in 1631, records indicate that King Charles I intervened to prevent the battle. A 1638 case is less clear: it involved a legal dispute between Ralf Claxton and Richard Lilburne (the latter the father of John Lilburne). The king again stepped in, and judges acted to delay proceedings. No record survives of the outcome of the case, but no contemporary account speaks of the trial by battle actually taking place. The last certain judicial battle in Britain was in Scotland in 1597, when Adam Bruntfield accused James Carmichael of murder and killed him in battle.


title: Trial by combat

text: Proposals to abolish trial by battle were made in the 17th century, and twice in the 18th, but were unsuccessful. In 1774, as part of the legislative response to the Boston Tea Party, Parliament considered a bill that would have abolished appeals of murder and trials by battle in the American colonies. It was successfully opposed by Member of Parliament John Dunning, who called the appeal of murder "that great pillar of the Constitution". Writer and MP Edmund Burke, on the other hand, supported the abolition, calling the appeal and wager "superstitious and barbarous to the last degree".


title: Trial by combat

text: The "writ of right" was the most direct way, in the common law, of challenging someone's right to a piece of real property. The "criminal appeal" was a private criminal prosecution instituted by the accuser directly against the accused. It was not, unlike the contemporary appeal, a proceeding in a court of superior jurisdiction reviewing the proceedings of a lower court.


title: Trial by combat

text: Such a private prosecution was last conducted in the case of "Ashford v Thornton" in 1818. Pronouncing judgement in favour of the accused's plea claiming the wager of battle, Justice Bayley of the King's Bench said that:


title: Trial by combat

text: One inconvenience attending this mode of proceeding is, that the party who institutes it must be willing, if required, to stake his life in support of his accusation.


title: Trial by combat

text: Parliament abolished wager of battle the following year, in February 1819, in an Act introduced by the Attorney General Samuel Shepherd. At the same time, they also abolished the writ of right and criminal appeals. Despite this abolition, in 2002, a Welshman in Bury St. Edmunds refusing to pay a small penalty charge for a vehicle-registration violation demanded trial by combat with the Driver and Vehicle Licensing Agency; his demand was rejected, and he was fined by a court.


title: Trial by combat

text: In December 1386, one of the last trials by combat authorised by the French King Charles VI was fought in Paris. The trial was fought to decide a case brought by Sir Jean de Carrouges against squire Jacques Le Gris, whom he accused of raping his wife Marguerite when Carrouges was in Paris conducting business. After lengthy hearings at the Parlement de Paris, with Jacques LeGris claiming that he had not committed the crime and Marguerite being with child, it was decided that guilt could not be decided through a standard jury trial, and a judicial duel was ordered. The duel put three lives in the hands of fate: Jacques LeGris, the accused, Jean de Carrouges, and the accuser, Marguerite. In the duel, the survivor of the said duel would be considered the winner of the claim. If Jacques LeGris won the duel, not only would Jean de Carrouges die but his pregnant wife would also be put to death for the crime of being a false accuser.


title: Trial by combat

text: In late December, shortly after Christmas, the combatants met just outside the walls of the abbey of Saint-Martin-des-Champs in the northern Paris suburbs. After a lengthy ceremony, the battle was joined, and after a furious and bloody encounter, Carrouges stabbed his opponent with a sword and claimed victory, being rewarded with substantial financial gifts and a position in the royal household. The duel was watched by the royal court, several royal dukes, and thousands of ordinary Parisians and was recorded in several notable chronicles including Froissart's Chronicles and Grandes Chroniques de France. It has since been covered by several notable texts, including Diderot's Encyclopédie, Voltaire and the Encyclopædia Britannica Eleventh Edition, and also by the 2004 book "" by Eric Jager.


title: Trial by combat

text: About AD 630, Gundeberga, wife of the Lombard King Arioald (626–636), is supposed to have been accused by a disappointed lover of a plot to poison the king and take another man. King Arioald consented that her innocence should be tested by single combat between her accuser and a nobleman who undertook to defend her. The accuser having been slain, Gundeberga was declared innocent. This was the first instance of a trial by combat in the history of Italy. In the 730s, the Lombard king Liutprand (712–744) had lost confidence in the likelihood that the trial by battle would provide justice. He knew that the practice was subject to abuse.


title: Trial by combat

text: The jurisprudence of judicial duelling in Italy is particularly well documented in the 15th and 16th centuries. In particular, the treatises of Achille Marozzo (1536), Giovanni Battista Pigna (1554) and Girolamo Mutio (1560) have contributed to shed considerable light on the subject.


title: Trial by combat

text: The fundamental aspects of Italy's duelling customs were the following. The offended party ( or agent) had to accuse the defendant () of an injury of words or deeds he received, in matters that could not be reliably proven in a courtroom. In turn, the defendant had to issue a "mentita", meaning that he had to tell the agent "you lie", which consisted of an injury of words. After this, the agent had to issue a notarised , or a notice of challenge, to the defendant, which, if accepted, would set the formal proceedings in motion.


title: Trial by combat

text: The defendant had the important advantage of the election of weapons. This was done to ensure that the institution would not be abused by the strong to overpower the weak, although the system was gamed in many ways bordering on the illegal.


title: Trial by combat

text: The duel would take place on the land of a lord impartial to both parties, or if this was not practicable, , meaning on public lands. The herald read the accusation out loud and gave the defendant one last chance to confess. If the latter did not do so, the duel would begin, and it was the responsibility of the issuer of the challenge to deliver (or attempt) the first blow. Incapacitating injuries or death would dictate victory, although other scenarios were possible as well. For instance, if the defendant could successfully parry all blows delivered by the agent until sundown, the defendant would be considered the victor.


title: Trial by combat

text: With the counter-reformation of the 16th century, duelling became illegal; however, its customs were maintained and utilised by most middle to upper social classes until the beginning of the 19th century.


title: Trial by combat

text: At the time of independence in 1776, trial by combat had not been abolished and it has never formally been abolished since. The question of whether trial by combat remains a valid alternative to civil action has been argued to remain open, at least in theory. In "McNatt v. Richards" (1983), the Delaware Court of Chancery rejected the defendant's request for "trial by combat to the death" on the grounds that dueling was illegal. In "Forgotten Trial Techniques: The Wager of Battle", Donald J. Evans set out the possibility of a trial by battle in the setting of a lawyer's office. A tongue-in-cheek motion during 2015 for trial by combat in response to a civil suit was rejected in 2016.


title: Trial by combat

text: In 2020, a man named David Zachary Ostrom requested a trial by combat in response to a custody and property dispute with his ex-wife over their children. Following Ostrom requesting trial by combat, he was court-ordered to be administered a sanity test and was temporarily restricted from parenting rights. Upon successfully clearing his sanity test, Ostrom's parenting time was restored. Ostrom has since admitted that he initially made the request for trial by combat in order to attract media attention to his case.


title: Trial by combat

text: Walter Scott's 1828 novel "The Fair Maid of Perth" dramatizes the lead-up to the Battle of the North Inch, where a judicial duel is among the violent events culminating in a judicial battle between the clans before King Robert III of Scotland. "" is a 2004 book by Eric Jager about the last sanctioned judicial duel in France in 1386. It was adapted into a 2008 BBC Four documentary and dramatized in a 2021 Ridley Scott film.


title: Aoife McArdle

text: She studied English Literature at Trinity College, Dublin where, alongside creative writing, she developed an interest in photography and cinematography, shooting and editing films on Super 8 and Mini DV. She went on to complete a Masters in Film & TV production at Bournemouth film school. She began her film and music video career upon moving to London in 2005.


title: Aoife McArdle

text: In 2022, she was a director and producer on the television series Severance which aired on Apple TV to universal acclaim. The show starred Adam Scott, Patricia Arquette, Christopher Walken and John Turturro.


title: Aoife McArdle

text: In 2021, she directed the short film and immersive installation "All of This Unreal Time" featuring Cillian Murphy performing a monologue written by Max Porter with music composed by Jon Hopkins, Aaron Dessner and Bryce Dessner. The piece launched at Manchester International Festival.


title: Aoife McArdle

text: Her debut feature-length film, "Kissing Candice", premiered at the Toronto International Film Festival in September 2017 and at Berlin International Film Festival in February 2018 to critical acclaim.


title: Aoife McArdle

text: In 2015, she was approached by Jefferson Hack from Dazed magazine to write and direct a short film to accompany U2's track Every Breaking Wave. The film received praise from Spike Jonze and Alejandro Gonzalez Inarritu and was nominated for four UK Music Video awards.


title: Aoife McArdle

text: She has created music videos for Jon Hopkins and Bryan Ferry, television commercials for Honda, and Nike and Super Bowl commercials for Audi and Toyota. Her work in advertising has promoted social equality.


title: Aoife McArdle

text: Her short-form work has won awards including a UK Music Video Award, D&AD Pencils, Lions at Cannes Lions International Festival of Creativity and Gold British Arrows.


title: Aoife McArdle

text: Her narratives often centre around outsider characters and existential themes, moving between the authentic and the surreal.


title: Aoife McArdle

text: McArdle's visual style is characterised by distinctive locations, long, choreographed tracking and crane shots and low-key lighting. She favours anamorphic lenses and shooting on 35mm film.


title: Atari 7800

text: The Atari 7800 ProSystem, or simply the Atari 7800, is a home video game console officially released by Atari Corporation in 1986 as the successor to both the Atari 2600 and Atari 5200. It can run almost all Atari 2600 cartridges, making it one of the first consoles with backward compatibility. It shipped with a different model of joystick from the 2600-standard CX40 and "Pole Position II" as the pack-in game. Most of the announced titles at launch were ports of 1981–83 arcade video games.


title: Atari 7800

text: Designed by General Computer Corporation, the 7800 has significantly improved graphics hardware over Atari's previous consoles, but the same Television Interface Adaptor chip that launched with the 2600 in 1977 is used to generate audio. In an effort to prevent the flood of poor quality games that contributed to the video game crash of 1983, cartridges had to be digitally signed by Atari.


title: Atari 7800

text: The Atari 7800 was first announced by Atari, Inc. on May 21, 1984, but a general release was shelved until May 1986 due to the sale of the company. Atari Corporation dropped support for the 7800, along with the 2600 and the Atari 8-bit family, on January 1, 1992.


title: Atari 7800

text: Atari had been facing pressure from Coleco and its ColecoVision console, which supported graphics that more closely mirrored arcade games of the time than either the Atari 2600 or 5200. The Atari 5200 (released as a successor to the Atari 2600) was criticized for not being able to play 2600 games without an adapter.


title: Atari 7800

text: The Atari 7800 ProSystem was the first console from Atari, Inc. designed by an outside company, General Computer Corporation. It was designed in 1983–84 with an intended mass market rollout in June 1984, but was canceled after the sale of the company to Tramel Technology Ltd on July 2, 1984. The project was originally called the Atari 3600.


title: Atari 7800

text: With a background in creating arcade games such as "Food Fight", GCC designed the new system with a graphics architecture similar to arcade machines of the time. The CPU is a slightly customized 6502 processor, the Atari SALLY, running at 1.79 MHz. By some measures the 7800 is more powerful, and by others less, than the 1983 Nintendo Entertainment System. It uses the 2600's Television Interface Adaptor chip, with the same restrictions, for generating two-channels of audio.


title: Atari 7800

text: The 7800 was announced on May 21, 1984. Thirteen games were announced for the system's launch: "Ms. Pac-Man", "Pole Position II", "Centipede", "Joust", "Dig Dug", "Nile Flyer" (eventually released as "Desert Falcon"), "", "Galaga", "Food Fight", "Ballblazer", "Rescue on Fractalus!", "Track & Field", and "Xevious".


title: Atari 7800

text: On July 2, 1984, Warner Communications sold Atari's Consumer Division to Jack Tramiel. All projects were halted during an initial evaluation period. GCC had not been paid for their development of the 7800, and Warner and Tramiel fought over who was accountable. In May 1985, Tramiel relented and paid GCC. This led to additional negotiations regarding the launch titles GCC had developed, then an effort to find someone to lead their new video game division, which was completed in November 1985. The original production run of the Atari 7800 languished in warehouses until it was introduced in January 1986.


title: Atari 7800

text: The console was released nationwide in May 1986 for $79.95. It launched with titles intended for the 7800's debut in 1984 and was aided by a marketing campaign with a budget in the "low millions" according to Atari Corporation officials. This was substantially less than the $9 million spent by Sega and the $16 million spent by Nintendo. The keyboard and high score cartridge planned by Warner were cancelled.


title: Atari 7800

text: In February 1987, "Computer Entertainer" reported that 100,000 Atari 7800 consoles had been sold in the United States, including those which had been warehoused since 1984. This was less than the Master System's 125,000 and the NES's 1.1 million. A complaint from owners in 1986 was the slow release of games. "Galaga" in August was followed by "Xevious" in November. By the end of 1986, the 7800 had 10 games, compared to Sega's 20 and Nintendo's 36. Atari would sell over 1 million 7800 consoles by June 1988.


title: Atari 7800

text: On January 1, 1992, Atari Corporation announced the end of production and support for the 7800, 2600, and the 8-bit computer family including the Atari XEGS. At least one game, an unreleased port of "Toki", was worked on past this date. By the time of the discontinuation, the Nintendo Entertainment System controlled 80% of the North American market while Atari had 12%.


title: Atari 7800

text: "Retro Gamer" magazine issue 132 reported that according to Atari UK Marketing Manager Darryl Still, "it was very well stocked by European retail; although it never got the consumer traction that the 2600 did, I remember we used to sell a lot of units through mail order catalogues and in the less affluent areas".


title: Atari 7800

text: Graphics are generated by the custom MARIA chip, which uses an approach common in contemporary arcade system boards and is different from other second and third generation consoles. Instead of a limited number of hardware sprites, MARIA treats everything as a sprite described in a series of display lists. Each display list contains pointers to graphics data and color and positioning information.


title: Atari 7800

text: MARIA supports a palette of 256 colors and graphics modes which are either 160 pixels wide or 320 pixels wide. While the 320 pixel modes theoretically enable the 7800 to create games at higher resolution than the 256 pixel wide graphics found in the Nintendo Entertainment System and Master System, the processing demands of MARIA result in most games using the 160 pixel mode.


title: Atari 7800

text: Each sprite can have from 1 to 12 colors, with 3 colors plus transparency being the most common. In this format, the sprite references one of 8 palettes, where each palette holds 3 colors. The background–visible when not covered by other objects–can also be assigned a color. In total, 25 colors can appear on a scan line.


title: Atari 7800

text: The graphics resolution, color palettes, and background color can be adjusted between scan lines. This can be used to render high resolution text in one area of the screen, while displaying more colorful graphics at lower resolution in the gameplay area.


title: Atari 7800

text: The 7800 uses the TIA chip for two channel audio, the same chip used in the 1977 Atari VCS, and the sound is of the same quality as that system. To compensate, GCC's engineers allowed games to include a POKEY audio chip in the cartridge. Only "Ballblazer" and "Commando" do this.


title: Atari 7800

text: GCC planned to make a low-cost, high performance sound chip, GUMBY, which could also be placed in 7800 cartridges to enhance its sound capabilities further. This project was cancelled when Atari was sold to Jack Tramiel.


title: Atari 7800

text: Following the large number of low quality, third party games for the Atari 2600, Atari required that cartridges for the 7800 be digitally signed. When a cartridge is inserted into the system, the BIOS generates a signature of the cartridge ROM and compares it to the one stored on the cartridge. If they match, the console operates in 7800 mode, granting the game access to MARIA and other features, otherwise the console operates as a 2600. This digital signature code is not present in PAL 7800s, which use various heuristics to detect 2600 cartridges, due to export restrictions.


title: Atari 7800

text: The 7800's compatibility with the Atari 2600 is made possible by including many of the same chips used in the 2600. When playing an Atari 2600 game, the 7800 uses a Television Interface Adapter chip to generate graphics and sound. The processor is slowed to 1.19 MHz, to mirror the performance of the 2600's 6507 chip. RAM is limited to 128 bytes and cartridge data is accessed in 4K blocks.


title: Atari 7800

text: When in 7800 mode (signified by the appearance of the full-screen Atari logo), the graphics are generated entirely by the MARIA graphics processing unit. All system RAM is available and cartridge data is accessed in larger 48K blocks. The system's SALLY 6502 runs at its normal 1.79 MHz. The 2600 chips are used to generate sound and to provide the interfaces to the controllers and console switches.


title: Atari 7800

text: The Atari 7800 came bundled with the Atari Pro-Line Joystick, a two-button controller with a joystick for movement. The Pro-Line was developed for the 2600 and advertised in 1983, but delayed until Atari proceeded with the 7800. The right fire button only works as a separate fire button for certain 7800 games; otherwise, it duplicates the left fire button, allowing either button to be used for 2600 games. While physically compatible, the 7800's controllers do not work with the Sega Master System, and Sega's controllers are unable to use the 7800's two-button mode.


title: Atari 7800

text: In response to criticism over ergonomic issues with the Pro-Line controllers, Atari later released a joypad controller with the European 7800. Similar in style to controllers found on Nintendo and Sega systems, it was not available in the United States.


title: Atari 7800

text: The Atari XG-1 light gun, bundled with the Atari XEGS and also sold separately, is compatible with the 7800. Atari released five 7800 light gun games: "Alien Brigade", "Barnyard Blaster", "Crossbow", "Meltdown", and "Sentinel".


title: Atari 7800

text: After the acquisition of the Atari Consumer Division by Jack Tramiel in 1984, several expansion options for the system were cancelled:


title: Atari 7800

text: While the system can play the over 400 games for the Atari 2600, there were only 59 official releases for the 7800. The lineup emphasized high-quality versions of games from the golden age of arcade video games. "Pole Position II", "Dig Dug", and "Galaga", by the time of the 1986 launch, were three, four, and five years old, respectively. A raster graphics version of 1979's "Asteroids" was released in 1987. In 1988, Atari published a conversion of Nintendo's "Donkey Kong", seven years after the original arcade game and five years after the Atari 8-bit family cartridge.


title: Atari 7800

text: Eleven games were developed and sold by three third-party companies under their own labels (Absolute Entertainment, Activision, and Froggo) with the rest published by Atari Corporation. Most of the games from Atari were developed by outside companies under contract.


title: Atari 7800

text: Some NES games were developed by companies who had licensed their title from a different arcade manufacturer. While the creator of the NES version would be restricted from making a competitive version of an NES game, the original arcade copyright holder was not precluded from licensing out rights for a home version of an arcade game to multiple systems. Through this loophole, Atari 7800 conversions of "Mario Bros.", "Double Dragon", "Commando", "Rampage", "Xenophobe", "Ikari Warriors", and "Kung-Fu Master" were licensed and developed.


title: Atari 7800

text: A final batch of games was released by Atari in 1990: "Alien Brigade", "Basketbrawl", "Fatal Run", "Meltdown", "Midnight Mutants", "MotorPsycho", "Ninja Golf", "Planet Smashers", and "Scrapyard Dog". "Scrapyard Dog" was later released for the Atari Lynx.


title: Atari 7800

text: In 2004, the Infogrames-owned version of Atari released the Atari Flashback console. It resembles a miniature Atari 7800 and has five 7800 and fifteen 2600 games built-in. Built using the NES-On-A-Chip hardware instead of recreating the Atari 7800 hardware, it was criticized for failing to properly replicate the actual gaming experience. A subsequent 7800 project was cancelled after prototypes were made.


title: Atari 7800

text: The digital signature long prevented aftermarket games from being developed. The signing software was eventually found and released at Classic Gaming Expo in 2001.


title: Atari 7800

text: Several new Atari 7800 games such as "Beef Drop", "B*nQ", "Combat 1990", "CrazyBrix", "Failsafe", and "Santa Simon" have been released..


title: Atari 7800

text: The source code for 13 games, the operating system, and the development tools which run on the Atari ST were discovered in a dumpster behind the Atari building in Sunnyvale, California. Commented assembly language source code was made available for "Centipede", "Commando", "Crossbow", "Desert Falcon", "Dig Dug", "Food Fight", "Galaga", "Hat Trick", "Joust", "Ms. Pac-Man", "Super Stunt Cycle", "", and "Xevious".


title: Ambiguity

text: Ambiguity is the type of meaning in which a phrase, statement or resolution is not explicitly defined, making several interpretations plausible. A common aspect of ambiguity is uncertainty. It is thus an attribute of any idea or statement whose intended meaning cannot be definitively resolved according to a rule or process with a finite number of steps. (The "ambi-" part of the term reflects an idea of "two", as in "two meanings".)


title: Ambiguity

text: The concept of ambiguity is generally contrasted with vagueness. In ambiguity, specific and distinct interpretations are permitted (although some may not be immediately obvious), whereas with information that is vague, it is difficult to form any interpretation at the desired level of specificity.


title: Ambiguity

text: Lexical ambiguity is contrasted with semantic ambiguity. The former represents a choice between a finite number of known and meaningful context-dependent interpretations. The latter represents a choice between any number of possible interpretations, none of which may have a standard agreed-upon meaning. This form of ambiguity is closely related to vagueness.


title: Ambiguity

text: Linguistic ambiguity can be a problem in law, because the interpretation of written documents and oral agreements is often of paramount importance.


title: Ambiguity

text: The lexical ambiguity of a word or phrase pertains to its having more than one meaning in the language to which the word belongs. "Meaning" here refers to whatever should be captured by a good dictionary. For instance, the word "bank" has several distinct lexical definitions, including "financial institution" and "edge of a river". Or consider "apothecary". One could say "I bought herbs from the apothecary". This could mean one actually spoke to the apothecary (pharmacist) or went to the apothecary (pharmacy).


title: Ambiguity

text: The context in which an ambiguous word is used often makes it evident which of the meanings is intended. If, for instance, someone says "I buried $100 in the bank", most people would not think someone used a shovel to dig in the mud. However, some linguistic contexts do not provide sufficient information to disambiguate a used word.


title: Ambiguity

text: Lexical ambiguity can be addressed by algorithmic methods that automatically associate the appropriate meaning with a word in context, a task referred to as word-sense disambiguation.


title: Ambiguity

text: The use of multi-defined words requires the author or speaker to clarify their context, and sometimes elaborate on their specific intended meaning (in which case, a less ambiguous term should have been used). The goal of clear concise communication is that the receiver(s) have no misunderstanding about what was meant to be conveyed. An exception to this could include a politician whose "weasel words" and obfuscation are necessary to gain support from multiple constituents with mutually exclusive conflicting desires from their candidate of choice. Ambiguity is a powerful tool of political science.


title: Ambiguity

text: More problematic are words whose senses express closely related concepts. "Good", for example, can mean "useful" or "functional" ("That's a good hammer"), "exemplary" ("She's a good student"), "pleasing" ("This is good soup"), "moral" ("a good person" versus "the lesson to be learned from a story"), "righteous", etc. "I have a good daughter" is not clear about which sense is intended. The various ways to apply prefixes and suffixes can also create ambiguity ("unlockable" can mean "capable of being unlocked" or "impossible to lock").


title: Ambiguity

text: Semantic ambiguity occurs when a word, phrase or sentence, taken out of context, has more than one interpretation. In "We saw her duck" (example due to Richard Nordquist), the words "her duck" can refer either


title: Ambiguity

text: Syntactic ambiguity arises when a sentence can have two (or more) different meanings because of the structure of the sentence—its syntax. This is often due to a modifying expression, such as a prepositional phrase, the application of which is unclear. "He ate the cookies on the couch", for example, could mean that he ate those cookies that were on the couch (as opposed to those that were on the table), or it could mean that he was sitting on the couch when he ate the cookies. "To get in, you will need an entrance fee of $10 or your voucher and your drivers' license." This could mean that you need EITHER ten dollars OR BOTH your voucher and your license. Or it could mean that you need your license AND you need EITHER ten dollars OR a voucher. Only rewriting the sentence, or placing appropriate punctuation can resolve a syntactic ambiguity.


title: Ambiguity

text: For the notion of, and theoretic results about, syntactic ambiguity in artificial, formal languages (such as computer programming languages), see Ambiguous grammar.


title: Ambiguity

text: Usually, semantic and syntactic ambiguity go hand in hand. The sentence "We saw her duck" is also syntactically ambiguous. Conversely, a sentence like "He ate the cookies on the couch" is also semantically ambiguous. Rarely, but occasionally, the different parsings of a syntactically ambiguous phrase result in the same meaning. For example, the command "Cook, cook!" can be parsed as "Cook (noun used as vocative), cook (imperative verb form)!", but also as "Cook (imperative verb form), cook (noun used as vocative)!". It is more common that a syntactically unambiguous phrase has a semantic ambiguity; for example, the lexical ambiguity in "Your boss is a funny man" is purely semantic, leading to the response "Funny ha-ha or funny peculiar?"


title: Ambiguity

text: Spoken language can contain many more types of ambiguities which are called phonological ambiguities, where there is more than one way to compose a set of sounds into words. For example, "ice cream" and "I scream". Such ambiguity is generally resolved according to the context. A mishearing of such, based on incorrectly resolved ambiguity, is called a mondegreen.


title: Ambiguity

text: Philosophers (and other users of logic) spend a lot of time and effort searching for and removing (or intentionally adding) ambiguity in arguments because it can lead to incorrect conclusions and can be used to deliberately conceal bad arguments. For example, a politician might say, "I oppose taxes which hinder economic growth", an example of a glittering generality. Some will think they oppose taxes in general because they hinder economic growth. Others may think they oppose only those taxes that they believe will hinder economic growth. In writing, the sentence can be rewritten to reduce possible misinterpretation, either by adding a comma after "taxes" (to convey the first sense) or by changing "which" to "that" (to convey the second sense) or by rewriting it in other ways. The devious politician hopes that each constituent will interpret the statement in the most desirable way, and think the politician supports everyone's opinion. However, the opposite can also be true—an opponent can turn a positive statement into a bad one if the speaker uses ambiguity (intentionally or not). The logical fallacies of amphiboly and equivocation rely heavily on the use of ambiguous words and phrases.


title: Ambiguity

text: In continental philosophy (particularly phenomenology and existentialism), there is much greater tolerance of ambiguity, as it is generally seen as an integral part of the human condition. Martin Heidegger argued that the relation between the subject and object is ambiguous, as is the relation of mind and body, and part and whole. In Heidegger's phenomenology, Dasein is always in a meaningful world, but there is always an underlying background for every instance of signification. Thus, although some things may be certain, they have little to do with Dasein's sense of care and existential anxiety, e.g., in the face of death. In calling his work Being and Nothingness an "essay in phenomenological ontology" Jean-Paul Sartre follows Heidegger in defining the human essence as ambiguous, or relating fundamentally to such ambiguity. Simone de Beauvoir tries to base an ethics on Heidegger's and Sartre's writings (The Ethics of Ambiguity), where she highlights the need to grapple with ambiguity: "as long as there have been philosophers and they have thought, most of them have tried to mask it... And the ethics which they have proposed to their disciples has always pursued the same goal. It has been a matter of eliminating the ambiguity by making oneself pure inwardness or pure externality, by escaping from the sensible world or being engulfed by it, by yielding to eternity or enclosing oneself in the pure moment." Ethics cannot be based on the authoritative certainty given by mathematics and logic, or prescribed directly from the empirical findings of science. She states: "Since we do not succeed in fleeing it, let us, therefore, try to look the truth in the face. Let us try to assume our fundamental ambiguity. It is in the knowledge of the genuine conditions of our life that we must draw our strength to live and our reason for acting". Other continental philosophers suggest that concepts such as life, nature, and sex are ambiguous. Corey Anton has argued that we cannot be certain what is separate from or unified with something else: language, he asserts, divides what is not, in fact, separate. Following Ernest Becker, he argues that the desire to 'authoritatively disambiguate' the world and existence has led to numerous ideologies and historical events such as genocide. On this basis, he argues that ethics must focus on 'dialectically integrating opposites' and balancing tension, rather than seeking a priori validation or certainty. Like the existentialists and phenomenologists, he sees the ambiguity of life as the basis of creativity.


title: Ambiguity

text: In literature and rhetoric, ambiguity can be a useful tool. Groucho Marx's classic joke depends on a grammatical ambiguity for its humor, for example: "Last night I shot an elephant in my pajamas. How he got in my pajamas, I'll never know". Songs and poetry often rely on ambiguous words for artistic effect, as in the song title "Don't It Make My Brown Eyes Blue" (where "blue" can refer to the color, or to sadness).


title: Ambiguity

text: In the narrative, ambiguity can be introduced in several ways: motive, plot, character. F. Scott Fitzgerald uses the latter type of ambiguity with notable effect in his novel "The Great Gatsby".


title: Ambiguity

text: Mathematical notation, widely used in physics and other sciences, avoids many ambiguities compared to expression in natural language. However, for various reasons, several lexical, syntactic and semantic ambiguities remain.


title: Ambiguity

text: The ambiguity in the style of writing a function should not be confused with a multivalued function, which can (and should) be defined in a deterministic and unambiguous way. Several special functions still do not have established notations. Usually, the conversion to another notation requires to scale the argument or the resulting value; sometimes, the same name of the function is used, causing confusions. Examples of such underestablished functions:


title: Ambiguity

text: It is common practice to omit multiplication signs in mathematical expressions. Also, it is common to give the same name to a variable and a function, for example, formula_1. Then, if one sees formula_2, there is no way to distinguish whether it means formula_1 multiplied by formula_4, or function formula_5 evaluated at argument equal to formula_4. In each case of use of such notations, the reader is supposed to be able to perform the deduction and reveal the true meaning.


title: Ambiguity

text: Creators of algorithmic languages try to avoid ambiguities. Many algorithmic languages (C++ and Fortran) require the character * as symbol of multiplication. The Wolfram Language used in Mathematica allows the user to omit the multiplication symbol, but requires square brackets to indicate the argument of a function; square brackets are not allowed for grouping of expressions. Fortran, in addition, does not allow use of the same name (identifier) for different objects, for example, function and variable; in particular, the expression f=f(x) is qualified as an error.


title: Ambiguity

text: The order of operations may depend on the context. In most programming languages, the operations of division and multiplication have equal priority and are executed from left to right. Until the last century, many editorials assumed that multiplication is performed first, for example, formula_7 is interpreted as formula_8; in this case, the insertion of parentheses is required when translating the formulas to an algorithmic language. In addition, it is common to write an argument of a function without parenthesis, which also may lead to ambiguity.


title: Ambiguity

text: In the scientific journal style, one uses roman letters to denote elementary functions, whereas variables are written using italics.


title: Ambiguity

text: Commas in multi-component subscripts and superscripts are sometimes omitted; this is also potentially ambiguous notation.


title: Ambiguity

text: For example, in the notation formula_14, the reader can only infer from the context whether it means a single-index object, taken with the subscript equal to product of variables formula_15, formula_12 and formula_17, or it is an indication to a trivalent tensor.


title: Ambiguity

text: An expression such as formula_18 can be understood to mean either formula_19 or formula_20. Often the author's intention can be understood from the context, in cases where only one of the two makes sense, but an ambiguity like this should be avoided, for example by writing formula_21 or formula_22.


title: Ambiguity

text: The expression formula_23 means formula_24 in several texts, though it might be thought to mean formula_25, since formula_26 commonly means formula_27. Conversely, formula_28 might seem to mean formula_29, as this exponentiation notation usually denotes function iteration: in general, formula_30 means formula_31. However, for trigonometric and hyperbolic functions, this notation conventionally means exponentiation of the result of function application.


title: Ambiguity

text: The expression formula_32 can be interpreted as meaning formula_33; however, it is more commonly understood to mean formula_34.


title: Ambiguity

text: It is common to define the coherent states in quantum optics with formula_35 and states with fixed number of photons with formula_36. Then, there is an "unwritten rule": the state is coherent if there are more Greek characters than Latin characters in the argument, and formula_37photon state if the Latin characters dominate. The ambiguity becomes even worse, if formula_38 is used for the states with certain value of the coordinate, and formula_39 means the state with certain value of the momentum, which may be used in books on quantum mechanics. Such ambiguities easily lead to confusions, especially if some normalized adimensional, dimensionless variables are used. Expression formula_40 may mean a state with single photon, or the coherent state with mean amplitude equal to 1, or state with momentum equal to unity, and so on. The reader is supposed to guess from the context.


title: Ambiguity

text: Some physical quantities do not yet have established notations; their value (and sometimes even dimension, as in the case of the Einstein coefficients), depends on the system of notations. Many terms are ambiguous. Each use of an ambiguous term should be preceded by the definition, suitable for a specific case. Just like Ludwig Wittgenstein states in Tractatus Logico-Philosophicus: "...Only in the context of a proposition has a name meaning."


title: Ambiguity

text: A highly confusing term is "gain". For example, the sentence "the gain of a system should be doubled", without context, means close to nothing.


title: Ambiguity

text: The term "intensity" is ambiguous when applied to light. The term can refer to any of irradiance, luminous intensity, radiant intensity, or radiance, depending on the background of the person using the term.


title: Ambiguity

text: Also, confusions may be related with the use of atomic percent as measure of concentration of a dopant, or resolution of an imaging system, as measure of the size of the smallest detail which still can be resolved at the background of statistical noise. See also Accuracy and precision and its talk.


title: Ambiguity

text: The Berry paradox arises as a result of systematic ambiguity in the meaning of terms such as "definable" or "nameable". Terms of this kind give rise to vicious circle fallacies. Other terms with this type of ambiguity are: satisfiable, true, false, function, property, class, relation, cardinal, and ordinal.


title: Ambiguity

text: In mathematics and logic, ambiguity can be considered to be an instance of the logical concept of underdetermination—for example, formula_41 leaves open what the value of "X" is—while its opposite is a self-contradiction, also called inconsistency, paradoxicalness, or oxymoron, or in mathematics an inconsistent system—such as formula_42, which has no solution.


title: Ambiguity

text: Logical ambiguity and self-contradiction is analogous to visual ambiguity and impossible objects, such as the Necker cube and impossible cube, or many of the drawings of M. C. Escher.


title: Ambiguity

text: Some languages have been created with the intention of avoiding ambiguity, especially lexical ambiguity. Lojban and Loglan are two related languages which have been created for this, focusing chiefly on syntactic ambiguity as well. The languages can be both spoken and written. These languages are intended to provide a greater technical precision over big natural languages, although historically, such attempts at language improvement have been criticized. Languages composed from many diverse sources contain much ambiguity and inconsistency. The many exceptions to syntax and semantic rules are time-consuming and difficult to learn.


title: Ambiguity

text: In structural biology, ambiguity has been recognized as a problem for studying protein conformations. The analysis of a protein three-dimensional structure consists in dividing the macromolecule into subunits called domains. The difficulty of this task arises from the fact that different definitions of what a domain is can be used (e.g. folding autonomy, function, thermodynamic stability, or domain motions), which sometimes results in a single protein having different—yet equally valid—domain assignments.


title: Ambiguity

text: Christianity and Judaism employ the concept of paradox synonymously with "ambiguity". Many Christians and Jews endorse Rudolf Otto's description of the sacred as 'mysterium tremendum et fascinans', the awe-inspiring mystery which fascinates humans. The apocryphal Book of Judith is noted for the "ingenious ambiguity" expressed by its heroine e.g. she says to the villain of the story, Holofernes, "my lord will not fail to achieve his purposes".


title: Ambiguity

text: The orthodox Catholic writer G. K. Chesterton regularly employed paradox to tease out the meanings in common concepts which he found ambiguous or to reveal meaning often overlooked or forgotten in common phrases: the title of one of his most famous books, "Orthodoxy" (1908), itself employed such a paradox.


title: Ambiguity

text: In music, pieces or sections which confound expectations and may be or are interpreted simultaneously in different ways are ambiguous, such as some polytonality, polymeter, other ambiguous meters or rhythms, and ambiguous phrasing, or (Stein 2005, p.79) any aspect of music. The music of Africa is often purposely ambiguous. To quote Sir Donald Francis Tovey (1935, p.195), "Theorists are apt to vex themselves with vain efforts to remove uncertainty just where it has a high aesthetic value."


title: Ambiguity

text: In visual art, certain images are visually ambiguous, such as the Necker cube, which can be interpreted in two ways. Perceptions of such objects remain stable for a time, then may flip, a phenomenon called multistable perception.


title: Ambiguity

text: Pictures or photographs may also be ambiguous at the semantic level: the visual image is unambiguous, but the meaning and narrative may be ambiguous: is a certain facial expression one of excitement or fear, for instance?


title: Ambiguity

text: In social psychology, ambiguity is a factor used in determining peoples' responses to various situations. High levels of ambiguity in an emergency (e.g. an unconscious man lying on a park bench) make witnesses less likely to offer any sort of assistance, due to the fear that they may have misinterpreted the situation and acted unnecessarily. Alternately, non-ambiguous emergencies (e.g. an injured person verbally asking for help) elicit more consistent intervention and assistance. With regard to the bystander effect, studies have shown that emergencies deemed ambiguous trigger the appearance of the classic bystander effect (wherein more witnesses decrease the likelihood of any of them helping) far more than non-ambiguous emergencies.


title: Ambiguity

text: In computer science, the SI prefixes kilo-, mega- and giga- were historically used in certain contexts to mean either the first three powers of 1024 (1024, 1024 and 1024) contrary to the metric system in which these units unambiguously mean one thousand, one million, and one billion. This usage is particularly prevalent with electronic memory devices (e.g. DRAM) addressed directly by a binary machine register where a decimal interpretation makes no practical sense.


title: Ambiguity

text: Subsequently, the Ki, Mi, and Gi prefixes were introduced so that binary prefixes could be written explicitly, also rendering k, M, and G "unambiguous" in texts conforming to the new standard—this led to a "new" ambiguity in engineering documents lacking outward trace of the binary prefixes (necessarily indicating the new style) as to whether the usage of k, M, and G remains ambiguous (old style) or not (new style). 1 M (where M is ambiguously 1,000,000 or 1,048,576) is "less" uncertain than the engineering value 1.0e6 (defined to designate the interval 950,000 to 1,050,000). As non-volatile storage devices begin to exceed 1 GB in capacity (where the ambiguity begins to routinely impact the second significant digit), GB and TB almost always mean 10 and 10 bytes.


title: AIFV

text: The AIFV ("Armored Infantry Fighting Vehicle") is a US tracked light armored vehicle that serves as an infantry fighting vehicle (IFV) in the armies of several countries. It is a development of the M113A1 armored personnel carrier.


title: AIFV

text: In 1967, funded by the US Army, the FMC corporation produced two prototype vehicles designated as XM765 - these were based on their experiences with the earlier XM701 vehicle, developed for the MICV-65 program. The XM765 was based on the M113A1, upgraded with an enclosed turret and firing ports, so that the infantry could fight from within the vehicle. The army evaluated the vehicle, but decided that they wanted a better protected and more mobile vehicle, selecting instead the M2 Bradley.


title: AIFV

text: FMC continued development as a private venture, resulting in the product improved (PI) M113A1 in 1970. The PI M113A1 had the driver and engine at the front, with an enclosed weapon station in the center of the hull and the commander seated at the rear. This arrangement meant that the commander had a very poor forward view. FMC went back to the drawing board and came up with a new design, which had the driver on the front left of the hull and the commander seated behind him. To the right of the commander was a one-man turret. The vehicle would later be designated the AIFV (armored infantry fighting vehicle).


title: AIFV

text: While the US was uninterested in the design, a number of other governments were interested in the vehicle, which was simpler, lighter, and cheaper than the Bradley. After a series of demonstrations and the delivery of four evaluation vehicles in 1974, the Netherlands government placed an order for 880 of the vehicles in 1975, which were designated YPR-765 when they entered service. Some changes were made at the request of the Dutch government, including shifting the weapon station to the right side and moving the commander behind the driver. The Netherlands ordered 2,079, of which 815 were produced locally under license. Under the YPR-2000 program, virtually all Dutch vehicles were upgraded to YPR-765A1 standard and are easily identified by the 3-tone NATO camouflage pattern. During the war in Afghanistan, several vehicles were fitted with additional armor.


title: AIFV

text: The Philippines also received 45 vehicles in 1979, these were intended to take 25mm cannons, although some were later modified to fit 12.7mm machine guns.


title: AIFV

text: In 1979, Belgium placed an order for 514 AIFV-B (to be produced locally) along with 525 M113A-B (similar to the M113A2). The first vehicles were delivered in 1982.


title: AIFV

text: Turkey selected the AIFV in 1989, after a competition involving the Alvis Vickers Warrior IFV, Krauss-Maffei PUMA and United Defense LP Armoured Infantry Fighting Vehicle. The total value of the contract for 1,698 vehicles was US$1.076 billion. The first 285 hulls were produced in Belgium, the remaining vehicles were produced entirely in Turkey. A little way into the production run, with 200 vehicles completed, the Turkish AIFV specification was updated to include a more powerful power pack developing 300 horsepower, an Allison X-200-4 transmission and hydrostatic steering from the M113A3. During the production run, a number of changes were made to the armament of the vehicle, including different turret packages, and power packs.


title: AIFV

text: The hull of the vehicle is made of welded aluminum, with spaced steel laminate armor bolted onto the side and front. The voids of the armor are filled with polyurethane foam, which gives the vehicle extra buoyancy when travelling in the water. Original production AIFVs can swim without deploying flotation curtains, using only a large front-mounted trim vane; they are propelled in the water by their tracks.


title: AIFV

text: The engine sits on the front right of the hull, behind a hatch that can be used to remove the complete powerpack. The powerpack is similar to the M113A1, except for a larger radiator capacity and turbocharger. The transmission is also fitted with heavy duty components from the M548 tracked cargo carrier. Immediately to the left of the engine is the driver, above whom is a hatch that opens to the right. The driver has four M27 day periscopes. The driver's center periscope can be replaced by a passive infra-red periscope for night driving. The commander sits immediately behind the driver, and has a cupola that can be completely traversed. The cupola has five periscopes, four of which are M17 day periscopes, the fifth has 1x to 6x variable magnification.


title: AIFV

text: The turret is fitted on the right side of the hull behind the engine. The turret, which has electro-hydraulic traverse, can elevate from -10 to +50° and can traverse and elevate at a speed of 60°/sec. The turret mounts an Oerlikon KBA 25 mm B02 cannon with a dual ammunition feed and 180 rounds of ready use ammo, with another 144 rounds stored in the hull. Mounted to the left of this gun is a 7.62 mm FN MAG machine gun, which has 230 rounds of ready ammo, with a further 1,610 in the hull.


title: AIFV

text: The troop compartment is at the rear of the hull; a large power operated ramp allows access through the rear of the vehicle, a door is also provided in the ramp. Additionally a single piece hatch covers the top of the troop compartment. The compartment contains seven troops in the Dutch variant, with six sitting back to back facing outwards and a single passenger sitting between the command and the turret facing backwards. There are two firing ports in each side of the hull and a single firing port in the rear. The side firing ports are provided with M17 periscopes, the rear one is fitted with an M27 periscope.


title: AIFV

text: The Philippine Army uses a mixed variant of earlier AIFVs similar to the Dutch YPR-765, and later variants from Turkey based on the ACV-300.


title: Cheick Kongo

text: Cheick Kongo is a French heavyweight Mixed Martial artist and former Kickboxer who fights in Bellator MMA. A professional MMA competitor since 2001, he has also competed for the Ultimate Fighting Championship. As of May 10, 2022, he is #4 in the Bellator Heavyweight Rankings.


title: Cheick Kongo

text: Born to a Burkinabé father and a Congolese mother, Kongo began training in martial arts when he was 5 years old, learning Kendo and Karate. As he grew older, he had already received black belt from both styles and began to expand his repertoire and trained in Boxing, Muay Thai, Savate, Wrestling and Shooto. at age of 19. At age 23, Silat, an Indonesian martial art, and was coached by Charles Joussot and Franck Ropers, men who brought Silat to France. He is also a cousin of rugby star Fulgence Ouedraogo, the French back-rower. Cheick is also a columnist for the French MMA magazine, Top Fight.


title: Cheick Kongo

text: On June 10, 2001, Kongo began his professional career by knocking out Doog Ward. Kongo then followed up that win with a TKO over Dave van der Veen. He then lost his third professional MMA fight to Rodney Faverus by decision. He faced Gilbert Yvel on May 20, losing for the second time in his career when he tapped to strikes in the second round. He trained with Anderson Silva and Wanderlei Silva in the early days of Pride Fighting Championships.


title: Cheick Kongo

text: Kongo entered the UFC to fight Gilbert Aldana at "UFC 61", whom he beat by TKO due to a doctor stoppage. Kongo followed up with a win over UFC newcomer Christian Wellisch by KO due to a knee strike, before losing to UFC newcomer Carmelo Marrero at "UFC 64". Then, Kongo defeated Assuerio Silva by majority decision at "UFC 70".


title: Cheick Kongo

text: At "UFC 75" on September 8, 2007, he defeated Mirko Cro Cop by unanimous decision. Though there was controversy as Kongo kneed Cro Cop in the groin several times without having any points deducted, inspiring American MMA fans to give Kongo the nickname "Cup Cheick".


title: Cheick Kongo

text: He fought against Heath Herring at "UFC 82", losing by split decision. At "UFC 87" he fought against UFC newcomer Dan "The Viking" Evensen, whom he defeated by first-round TKO.


title: Cheick Kongo

text: Kongo fought at UFC 92 on December 27, 2008, where he beat former Cage Rage British Heavyweight champion Mustapha al-Turk by TKO. Kongo dropped Al Turk with two right hands. Then fired on a vicious ground and pound attack, Kongo pounced on al-Turk with elbows and punches, opening up a big cut above the eye. Referee Steve Mazzagatti stopped the fight after 4:37 of the first round.


title: Cheick Kongo

text: Kongo replaced Heath Herring on three weeks notice at UFC 99 to face the up-and-coming Cain Velasquez in the co-main event. Kongo lost to Velasquez by unanimous decision in a one-sided affair. He did however, manage to drop Velasquez on two occasions with straight punches. It had been rumoured that if he was to defeat Velasquez, Kongo would earn a title shot against the winner of the UFC 100 Heavyweight Championship between Brock Lesnar and Frank Mir. Mir lost his bout against Lesnar and actually ended up fighting Kongo at UFC 107. During the pre-fight talk, Mir stated that Kongo had no ground game, so at the weigh ins Cheick Kongo turned his back to Mir, to be disrespectful. Mir won the fight by a submission. After connecting with a left overhand punch that dropped Kongo, Mir finished him with a guillotine choke, rendering Kongo unconscious just 72 seconds into the first round.


title: Cheick Kongo

text: Kongo was expected to face The Ultimate Fighter 10 winner Roy Nelson on July 3, 2010, at UFC 116 but a back injury to Kongo has caused the cancellation of the fight. Kongo would end up fighting Nelson almost 3 years later at UFC 159.


title: Cheick Kongo

text: Kongo's next fight was against undefeated Travis Browne at UFC 120. They fought to a unanimous draw. Kongo repeatedly grabbed Browne's shorts and had 1 point deducted in the final round.


title: Cheick Kongo

text: Kongo fought Pat Barry on June 26, 2011, at UFC on Versus 4. His fight against Barry became the main event since Nate Marquardt was not medically cleared for his welterweight debut against Rick Story. During the bout Kongo was dropped by a looping right hand. Visibly rocked, Kongo got back to his feet but was dropped again seconds later by another hard punch. Despite being dropped twice, Kongo was able to knock Barry out with a hard overhand right to the ear, followed by an uppercut to the chin to secure a win midway through the first round.


title: Cheick Kongo

text: Kongo faced Matt Mitrione on October 29, 2011, at UFC 137. He won the fight via unanimous decision by utilizing his reach with his jab and securing multiple takedowns.


title: Cheick Kongo

text: Kongo faced Mark Hunt on February 26, 2012, at UFC 144. He lost the fight via TKO in the first round.


title: Cheick Kongo

text: Kongo was expected to face Antônio Rodrigo Nogueira on July 21, 2012, at . However, Nogueira pulled out of the bout, citing that an arm injury sustained in his last bout against Frank Mir had not healed enough to resume the proper training and was replaced by Shawn Jordan. Kongo defeated Jordan via unanimous decision.


title: Cheick Kongo

text: Kongo finally faced Roy Nelson on April 27, 2013, at UFC 159, a bout that was supposed to happen almost 3 years before at UFC 116. He lost the fight via knockout in the first round. After his loss to Nelson, Kongo's UFC contract expired and he was released from the UFC.


title: Cheick Kongo

text: Before UFC 159 the UFC offered Kongo a four-fight deal, which he turned down. Kongo left the UFC with a 11-6-1 record.


title: Cheick Kongo

text: On May 4, 2013 Kongo stated that he is on good terms with the UFC and was quoted saying: "Don't believe he said-she said stories. I have not been cut by the UFC. I am Cheick Kongo so I know best what's next for me. It doesn't mean that I am leaving the UFC, it doesn't mean that I am staying – it means this is my life." Kongo has stated that he is open to the possibility of resigning a contract with the UFC.


title: Cheick Kongo

text: Shortly after it was announced that Cheick's teammate Rampage Jackson was going to Bellator, it was stated that Kongo will be following his teammate. Kongo's move to Bellator was official on August 28, 2013.


title: Cheick Kongo

text: Kongo made his debut in the . He faced Mark Godbeer on October 4, 2013, at . Kongo won the fight via TKO in the second round.


title: Cheick Kongo

text: He was then expected to face Vinicius Queiroz in the tournament finals, on November 2, 2013, at . However, due to a change in the line up, the bout was canceled.


title: Cheick Kongo

text: Kongo vs. Queiroz was then expected to take place on November 8, 2013, at Bellator 107. However, Queiroz was later forced to withdraw from the bout due to a knee injury and was replaced by Peter Graham. Kongo won the fight via unanimous decision.


title: Cheick Kongo

text: Kongo faced undefeated Bellator Heavyweight Champion Vitaly Minakov at Bellator 115 on April 4, 2014. He lost the back-and-forth fight via unanimous decision. Kongo faced Eric Smith at Bellator 120 on May 17, 2014. He won the fight via TKO by way of knees and punches at 4:35 of Round 2.


title: Cheick Kongo

text: Kongo faced fellow striker Lavar Johnson at Bellator 123 on September 5, 2014. He won the fight via rear-naked choke submission in the first round. This marked his first submission win that was not caused by strikes since 2003.


title: Cheick Kongo

text: Kongo faced King Mo Lawal at Bellator 134: The British Invasion on February 27, 2015. He lost the fight via split decision.


title: Cheick Kongo

text: Kongo faced former Bellator Heavyweight Champion Alexander Volkov on June 26, 2015, at Bellator 139. He won the fight via unanimous decision.


title: Cheick Kongo

text: Kongo faced Vinicius Queiroz at Bellator 150 on February 26, 2016. In the third round, Kongo was dropped by a right hand, however, he was able to recover and win a split decision.


title: Cheick Kongo

text: Kongo faced Tony Johnson at Bellator 161 on September 16, 2016. He won the fight via majority decision.


title: Cheick Kongo

text: Kongo faced former training partner Oli Thompson at Bellator 172 on February 18, 2017. He won the fight by unanimous decision.


title: Cheick Kongo

text: Kongo faced Javy Ayala at Bellator 199 on May 12 in San Jose, CA. He won the fight via knockout in the first round.


title: Cheick Kongo

text: Kongo faced Timothy Johnson on October 13, 2018, at Bellator 208. He won the fight by knockout in the first round.


title: Cheick Kongo

text: Kongo faced Vitaly Minakov for a second time on February 16, 2019, at Bellator 216 He won the fight by unanimous decision.


title: Cheick Kongo

text: On July 11, 2019, it was announced that Kongo will be facing Ryan Bader for the Bellator Heavyweight World Championship on September 7 at Bellator 226. The bout ended in a no contest at 3:52 of the first round after an accidental eye poke from Bader rendered Kongo unable to continue.


title: Cheick Kongo

text: On October 10, 2020, Kongo fought in a rematch Timothy Johnson at Bellator 248 in Paris, France. He lost via split decision.


title: Cheick Kongo

text: Kongo faced Sergei Kharitonov on August 20, 2021 at Bellator 265. He won the fight via a rear-naked choke in round two.


title: Cheick Kongo

text: Kongo faced Ryan Bader for the Bellator Heavyweight World Championship on May 6, 2022 at Bellator 280. He lost the bout via unanimous decision.


title: Seminole Tribe of Florida

text: The Seminole Tribe of Florida is a federally recognized Seminole tribe based in the U.S. state of Florida. Together with the Seminole Nation of Oklahoma and the Miccosukee Tribe of Indians of Florida, it is one of three federally recognized Seminole entities. It received that status in 1957; today it has six Indian reservations in Florida.


title: Seminole Tribe of Florida

text: In 1975, the Tribe established tax-free smoke shops and a high-stakes bingo operation that became one of the first tribal gaming endeavors in the United States. These ventures, particularly the gaming operation, have generated significant revenues for education, welfare and economic development. A 2005 tribal audit said it took in $1.1 billion in revenues that year. The tribe requires members to have at least one-quarter Seminole blood quantum.


title: Seminole Tribe of Florida

text: The Seminole emerged in a process of ethnogenesis from various Native American groups who settled in Florida in the 18th century, most significantly Creeks from what is now northern Florida, Georgia and Alabama. They distanced themselves increasingly from other Creek groups, and expanded and prospered owing to their thriving trade network during Florida's British and second Spanish periods (c. 1767–1821). These settlers joined with the survivors of Florida's ancient Native American communities (Tequesta, Calusa, etc.) in the interior of south Florida.


title: Seminole Tribe of Florida

text: During this period, the largely autonomous Native American villages developed alliances with African-American maroons, mostly self-emancipated former slaves from the South's Low Country and some free blacks from the Spanish period of rule. These people became known as Black Seminoles, establishing towns near Native American settlements.


title: Seminole Tribe of Florida

text: During the Seminole Wars against the United States in the 19th century, however, particularly after the second war, most Seminole and Black Seminole were forced by the US to relocate west of the Mississippi River to Indian Territory. A smaller group – possibly fewer than 500 – refused to leave Florida and moved deep into the Everglades, where they avoided settlers and thrived in pseudo isolation. They fostered a culture of staunch independence. The modern Florida Seminole, about 17,233 at the 2010 census, Miccosukee and Traditionals descend from these survivors.


title: Seminole Tribe of Florida

text: The Florida Seminole re-established limited relations with the United States and Florida governments in the late 19th century, and by the early 20th century were concentrated in five camps in the Everglades. The portion who spoke more Muskogee consolidated in the northern part of the Everglades near the Cow Creek Camp, becoming known as the Cow Creek Seminole. The Miccosukee, who spoke the Mikasuki language, were located to the south, in an area cut through by completion of the Tamiami Trail in 1928.


title: Seminole Tribe of Florida

text: The Cow Creek Seminole eventually received of reservation land in the 1930s, beginning with Brighton Reservation. At first, few Seminoles had any interest in relocating to reservations, preferring their traditional lifestyle to a more sedentary reservation life. Following the efforts of Creek Christian missionaries, more Seminole moved to reservations in the 1940s to form their own churches. Other factors in the move include Florida's drainage of the wetlands and shift toward wide-scale agriculture. This contributed to the depletion of game and other resources by the state's expanding population, reducing the tribal people's ability to live in traditional ways.


title: Seminole Tribe of Florida

text: During the 1920–1940 period many changes took place in the habitat which the Seminole had lived. Settlers and developers wanting to convert wetlands to farms and residential communities had built drainage projects, which altered the wetlands ecosystem and damaged many species that it supported. As early as 1916, Royal Palm State Park, which would be incorporated into the Everglades National Park in 1947, was set aside as a conservation area. Construction of the Tamiami Trail across the center of the Everglades, the Civilian Conservation Corps projects from 1933 to 1934, and the eventual opening of the National Park, all served to displace many Seminole families who had lived throughout the area.


title: Seminole Tribe of Florida

text: In the 1930s, the US government established a reservation at Brighton and tried to recruit Seminole to resettle there. The government fenced in the reservation and introduced cattle, which had been part of Seminole culture for three centuries. The first government shipment of cattle arrived from Arizona in 1934 and, by the late 1930s, the cattle business was a way of life for many Seminole.


title: Seminole Tribe of Florida

text: With the introduction of cattle to Brighton, the Seminoles were introduced to democratic ideas and tribal organization. The trust agreement established by the Commissioner of Indian Affairs, on 12 September 1939, required that the tribe elect three trustees to transact the business of the cattle program. The first "election" was largely guided by the Florida Agricultural Extension Agent, Fred Montsdeoca, and a local missionary. They promoted men who knew English and were good at white-Native cooperation, as opposed to allowing the tribe to select those most skilled in animal husbandry. Montsdeoca was extremely influential in making decisions regarding the cattle program and, next to the Indian Affairs official at the reservation, was the most important local white man for the Seminole.


title: Seminole Tribe of Florida

text: Given their success at Brighton, in 1941, the Seminole acquired 150 head of cattle from Florida for the Big Cypress Reservation. By 1944, the Big Cypress Seminole wanted their own trustees and drafted an agreement with the government. Approved by the Commissioner of BIA on 8 August 1945, this agreement called for the establishment of the Brighton Agricultural and Livestock Enterprise and the Big Cypress Agricultural and Livestock Enterprise, each with their own 3-trustee cattle managers. It said that the tribal trustees would be appointed, with each of the cattle trustee groups and the BIA agent to appoint a tribal trustee. The three appointees on each reservation would also serve as tribal representatives. In essence, this requirement ensured that those adept at navigating between the Native American and white worlds would gain the positions. According to Covington, men who were adept at developing consensus decisions and had converted to Christianity were most likely to be selected.


title: Seminole Tribe of Florida

text: Although such tribal organization was relatively weak, the tribe used it as a basis for their team to file a land claim with the Indian Claims Commission, seeking compensation for lands taken by the federal government.


title: Seminole Tribe of Florida

text: In October 1948, the two livestock associations met with the Bureau of Indian Affairs superintendent to discuss pursuing a land claim against the U.S. Government through the newly formed Indian Claims Commission. They contacted Jacksonville attorney Roger J. Waybright, who initially was reluctant to take the case because the tribe had limited funding and the government dictated the amounts the attorneys could charge. Waybright was soon persuaded of the merits of the case and agreed to represent the tribe, signing a contract with his partner John O. Jackson on 15 October 1949. The 12 representatives who made the claim were the 6 trustees for the livestock associations and the 6 tribal representatives: Josie Billie, Jimmy Cypress, John Cypress, Junior Cypress, John Henry Gopher, Little Charlie Micco, Bill Osceola, Frank Shore, Jack Smith, Morgan Smith, Ben Tommie, and Sammy Tommie.


title: Seminole Tribe of Florida

text: The claim was filed 14 August 1950 and represented land taken under the Treaty of Moultrie Creek in 1823, land taken under the Treaty of Payne's Landing in 1832, land taken in the Macomb Treaty of 1839, and land taken in 1944 for the Everglades National Park —– in all totaling nearly $48,000,000. In July, 1951 the Seminole Nation of Oklahoma had also filed a petition before the Indian Claims Commission for claims involving their removal to Oklahoma and substantially the same land takings under Moultrie and Payne's Landing as the Florida Seminoles. Because of the overlapping of claims, the commission split the Florida claim into 2 cases, one sharing the Oklahoma claims in the treaties and the other, dealing with Florida's sole claim to land taken for the Everglades National Park.


title: Seminole Tribe of Florida

text: Government delays; tribal re-organization, which caused Waybright to resign from the case; resignation of the female replacement for Waybright, Effie Knowles, who felt the tribe would be happier with male representation; the hiring of Roy Struble of Miami and Charles Bragman of Washington, DC; and the death of attorney John Jackson all contributed to the claim dragging into the 1960s. Then in 1962, the Miccosukee Tribe of Indians of Florida organized their tribe and gained federal recognition. They sought to intervene in the case in 1968, but were not allowed. Finally on 13 May 1970, the Claims Commission awarded $12,262,780, which was promptly appealed by both the Oklahoma and Florida Seminoles. In 1975, in a compromise settlement to prevent further delays, the two groups agreed to $16,000,000 as a final settlement, but were required to have general meetings with their tribes to confirm the amount.


title: Seminole Tribe of Florida

text: In January 1976, the Florida Seminole were presented with the terms of settlement; it was translated into both the Mikasuki language and Muscogee language. Only seven tribemembers opposed accepting the agreement. In March 1976, the unorganized Traditionals in Florida filed an injunction to stop the award. On 11 March 1977 the Traditionals' complaint was dismissed. On 20 April 1977 the Macomb claim was disallowed, but an additional $50,000 was awarded for land in the Everglades. With those final decisions the awards were completed, but it took another fourteen years before the funds were distributed. The Claims Commission gave no direction as to how the judgment was to be split between the tribes of Oklahoma and Florida Seminoles, the Miccosukee and Traditionals.


title: Seminole Tribe of Florida

text: The groups had to negotiate as to how the settlement would be apportioned, leading to the most contact among them in a century. During this period, the money was put in trust and earning interest. In 1990, the groups finally agreed to the Seminole Nation of Oklahoma receiving three-quarters of the settlement, based on early population records from 1906 to 1914, when members had blood quantum; and the Florida Seminole in total to receive one-quarter, based on reconstructed early 20th-century censuses. At the time of the settlement, the two Florida tribes and Traditionals had a higher percentage of full-bloods due to their endogamous marriage practices. They also had blood quantum requirements for tribal membership. By 1990, the total value of the trust had reached $46 million.