1.
Royal Tunbridge Wells
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Royal Tunbridge Wells is a large affluent town in western Kent, England, about 40 miles south-east of central London by road,34.5 miles by rail. The town is close to the border of the county of East Sussex and it is situated at the northern edge of the High Weald, the sandstone geology of which is exemplified by the rock formations at the Wellington Rocks and High Rocks. Though its popularity waned with the advent of sea bathing, the town remains popular, the town has a population of around 56,500 and is the administrative centre of Tunbridge Wells Borough and the UK parliamentary constituency of Tunbridge Wells. The area which is now Tunbridge Wells was part of the parish of Speldhurst for hundreds of years, but the origin of the town as it is today, however, came in the seventeenth century. In 1606 Dudley, Lord North, a courtier to James I who was staying at a lodge in Eridge in the hope that the country air might improve his ailing constitution. He drank from the spring and, when his health improved and he persuaded his rich friends in London to try it, and by the time Queen Henrietta Maria, wife of King Charles I, visited in 1630 it had established itself as a spa retreat. Also in 1676 a subscription for a chapel of ease was opened, and in 1684 the Church of King Charles the Martyr was duly built and the town began to develop around it. Tradesmen in the town dealt in the luxury goods demanded by their patrons, which would certainly have included Tunbridge ware, a kind of decoratively inlaid woodwork. They have made the very commodious by the many good building all about it. All the people buy their own provisions at the market, which is just by the wells and is furnished with great plenty of all sorts of fish and fowl. and two rooms for the lottery and hazard board. He remained in position until his death in 1762. By the early nineteenth century Tunbridge Wells experienced growth as a place for the well-to-do to visit, during this time Decimus Burton developed John Wards Calverley Park estate. In 1889 the town was awarded the status of a Borough,1902 saw the opening of an Opera House, and in 1909 the town received its Royal prefix. The Second World War affected Tunbridge Wells in a different way—it became so swollen with refugees from London that accommodation was severely strained, over 3,800 buildings were damaged by bombing, but only 15 people lost their lives. Royal Tunbridge Wells is one of three towns in England to have been granted this. Although Wells has a form, it refers to the principal source. Royal Tunbridge Wells is the centre for both Tunbridge Wells Borough and the parliamentary constituency of Tunbridge Wells. The Borough is governed by 48 Councillors, representing 20 wards, elections are held for 16 Council seats each year on a rotational basis, with elections to Kent County Council taking place in the fourth year of the cycle
2.
Kent
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Kent /ˈkɛnt/ is a county in South East England and one of the home counties. It borders Greater London to the north west, Surrey to the west and East Sussex to the south west, the county also shares borders with Essex via the Dartford Crossing and the French department of Pas-de-Calais through the Channel Tunnel. France can be clearly in fine weather from Folkestone and the White Cliffs of Dover. Hills in the form of the North Downs and the Greensand Ridge span the length of the county, because of its relative abundance of fruit-growing and hop gardens, Kent is known as The Garden of England. The title was defended in 2006 when a survey of counties by the UKTV Style Gardens channel put Kent in fifth place, behind North Yorkshire, Devon. Haulage, logistics, and tourism are industries, major industries in north-west Kent include aggregate building materials, printing. Coal mining has played its part in Kents industrial heritage. Large parts of Kent are within the London commuter belt and its transport connections to the capital. Twenty-eight per cent of the county forms part of two Areas of Outstanding Natural Beauty, the North Downs and The High Weald, the area has been occupied since the Palaeolithic era, as attested by finds from the quarries at Swanscombe. The Medway megaliths were built during the Neolithic era, There is a rich sequence of Bronze Age, Iron Age, and Roman era occupation, as indicated by finds and features such as the Ringlemere gold cup and the Roman villas of the Darent valley. The modern name of Kent is derived from the Brythonic word Cantus meaning rim or border and this describes the eastern part of the current county area as a border land or coastal district. Julius Caesar had described the area as Cantium, or home of the Cantiaci in 51 BC, the extreme west of the modern county was by the time of Roman Britain occupied by Iron Age tribes, known as the Regnenses. East Kent became a kingdom of the Jutes during the 5th century and was known as Cantia from about 730, the early medieval inhabitants of the county were known as the Cantwara, or Kent people. These people regarded the city of Canterbury as their capital, in 597, Pope Gregory I appointed the religious missionary as the first Archbishop of Canterbury. In the previous year, Augustine successfully converted the pagan King Æthelberht of Kent to Christianity, the Diocese of Canterbury became Britains first Episcopal See with first cathedral and has since remained Englands centre of Christianity. The second designated English cathedral was in Kent at Rochester Cathedral, in the 11th century, the people of Kent adopted the motto Invicta, meaning undefeated. This naming followed the invasion of Britain by William of Normandy, the Kent peoples continued resistance against the Normans led to Kents designation as a semi-autonomous county palatine in 1067. Under the nominal rule of Williams half-brother Odo of Bayeux, the county was granted powers to those granted in the areas bordering Wales
3.
University of Edinburgh
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The University of Edinburgh, founded in 1582, is the sixth oldest university in the English-speaking world and one of Scotlands ancient universities. The university is deeply embedded in the fabric of the city of Edinburgh, the University of Edinburgh was ranked 17th and 21st in the world by the 2014–15 and 2015-16 QS rankings. It is now ranked 19th in the according to 2016-17 QS Rankings. It is ranked 16th in the world in arts and humanities by the 2015–16 Times Higher Education Ranking and it is ranked the 23rd most employable university in the world by the 2015 Global Employability University Ranking. It is ranked as the 6th best university in Europe by the U. S. News Best Global Universities Ranking and it is a member of both the Russell Group, and the League of European Research Universities, a consortium of 21 research universities in Europe. It has the third largest endowment of any university in the United Kingdom, after the universities of Cambridge and it continues to have links to the British Royal Family, having had the Duke of Edinburgh as its Chancellor from 1953 to 2010 and Princess Anne since 2011. Edinburgh receives approximately 50,000 applications every year, making it the fourth most popular university in the UK by volume of applicants, after St Andrews, it is the most difficult university to gain admission into in Scotland, and 9th overall in the UK. This was a move at the time, as most universities were established through Papal bulls. Established as the Tounis College, it opened its doors to students in October 1583, instruction began under the charge of another St Andrews graduate Robert Rollock. It was the fourth Scottish university in a period when the more populous. It was renamed King Jamess College in 1617, by the 18th century, the university was a leading centre of the Scottish Enlightenment. The universitys first custom-built building was the Old College, now Edinburgh Law School and its first forte in teaching was anatomy and the developing science of surgery, from which it expanded into many other subjects. From the basement of a nearby house ran the anatomy tunnel corridor and it went under what was then North College Street, and under the university buildings until it reached the universitys anatomy lecture theatre, delivering bodies for dissection. It was from this tunnel the body of William Burke was taken after he had been hanged, towards the end of the 19th century, Old College was becoming overcrowded and Robert Rowand Anderson was commissioned to design new Medical School premises in 1875. The medical school was more or less built to his design and was completed by the addition of the McEwan Hall in the 1880s. The building now known as New College was originally built as a Free Church college in the 1840s and has been the home of divinity at the university since the 1920s. The two oldest schools – law and divinity – are both well-esteemed, with law being based in Old College and divinity in New College on the Mound and they are also represented by the Edinburgh University Sports Union which was founded in 1866. The medical school is renowned throughout the world and it was widely considered the best medical school in the English-speaking world throughout the 18th century and first half of the 19th century
4.
Bayes' theorem
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In probability theory and statistics, Bayes’ theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. One of the applications of Bayes’ theorem is Bayesian inference. When applied, the involved in Bayes’ theorem may have different probability interpretations. With the Bayesian probability interpretation the theorem expresses how a subjective degree of belief should rationally change to account for availability of related evidence, Bayesian inference is fundamental to Bayesian statistics. Bayes’ theorem is named after Rev. Thomas Bayes, who first provided an equation that allows new evidence to update beliefs. It was further developed by Pierre-Simon Laplace, who first published the modern formulation in his 1812 “Théorie analytique des probabilités. ”Sir Harold Jeffreys put Bayes’ algorithm and Laplaces formulation on an axiomatic basis. Jeffreys wrote that Bayes’ theorem “is to the theory of probability what the Pythagorean theorem is to geometry. ”Bayes theorem is stated mathematically as the equation, P = P P P. P and P are the probabilities of observing A and B without regard to each other, P, a conditional probability, is the probability of observing event A given that B is true. P is the probability of observing event B given that A is true, Bayes’ theorem was named after the Reverend Thomas Bayes, who studied how to compute a distribution for the probability parameter of a binomial distribution. Bayes’ unpublished manuscript was edited by Richard Price before it was posthumously read at the Royal Society. Price edited Bayes’ major work “An Essay towards solving a Problem in the Doctrine of Chances”, Price wrote an introduction to the paper which provides some of the philosophical basis of Bayesian statistics. In 1765 he was elected a Fellow of the Royal Society in recognition of his work on the legacy of Bayes, the French mathematician Pierre-Simon Laplace reproduced and extended Bayes’ results in 1774, apparently quite unaware of Bayes’ work. The Bayesian interpretation of probability was developed mainly by Laplace, stephen Stigler suggested in 1983 that Bayes’ theorem was discovered by Nicholas Saunderson, a blind English mathematician, some time before Bayes, that interpretation, however, has been disputed. Martyn Hooper and Sharon McGrayne have argued that Richard Prices contribution was substantial, By modern standards, Price discovered Bayes’ work, recognized its importance, corrected it, contributed to the article, and found a use for it. The modern convention of employing Bayes’ name alone is unfair but so entrenched that anything else makes little sense, suppose a drug test is 99% sensitive and 99% specific. That is, the test will produce 99% true positive results for drug users, suppose that 0. 5% of people are users of the drug. If a randomly selected individual tests positive, what is the probability that he is a user and this surprising result arises because the number of non-users is very large compared to the number of users, thus the number of false positives outweighs the number of true positives. To use concrete numbers, if 1000 individuals are tested, there are expected to be 995 non-users and 5 users, from the 995 non-users,0.01 ×995 ≃10 false positives are expected
5.
Statistics
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Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, e. g. a scientific, industrial, or social problem, populations can be diverse topics such as all people living in a country or every atom composing a crystal. Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys, statistician Sir Arthur Lyon Bowley defines statistics as Numerical statements of facts in any department of inquiry placed in relation to each other. When census data cannot be collected, statisticians collect data by developing specific experiment designs, representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole. In contrast, an observational study does not involve experimental manipulation, inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena. A standard statistical procedure involves the test of the relationship between two data sets, or a data set and a synthetic data drawn from idealized model. A hypothesis is proposed for the relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the hypothesis is done using statistical tests that quantify the sense in which the null can be proven false. Working from a hypothesis, two basic forms of error are recognized, Type I errors and Type II errors. Multiple problems have come to be associated with this framework, ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis, measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random or systematic, the presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems. Statistics continues to be an area of research, for example on the problem of how to analyze Big data. Statistics is a body of science that pertains to the collection, analysis, interpretation or explanation. Some consider statistics to be a mathematical science rather than a branch of mathematics. While many scientific investigations make use of data, statistics is concerned with the use of data in the context of uncertainty, mathematical techniques used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory. In applying statistics to a problem, it is practice to start with a population or process to be studied. Populations can be diverse topics such as all living in a country or every atom composing a crystal. Ideally, statisticians compile data about the entire population and this may be organized by governmental statistical institutes
6.
Presbyterianism
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Presbyterianism is a part of the Reformed tradition within Protestantism which traces its origins to the British Isles, particularly Scotland. Presbyterian churches derive their name from the form of church government. Presbyterian theology typically emphasizes the sovereignty of God, the authority of the Scriptures, Presbyterian church government was ensured in Scotland by the Acts of Union in 1707 which created the Kingdom of Great Britain. In fact, most Presbyterians found in England can trace a Scottish connection, the Presbyterian denominations in Scotland hold to the theology of John Calvin and his immediate successors, although there are a range of theological views within contemporary Presbyterianism. The roots of Presbyterianism lie in the Protestant Reformation of the 16th century, most Reformed churches which trace their history back to Scotland are either presbyterian or congregationalist in government. In the twentieth century, some Presbyterians played an important role in the ecumenical movement, many Presbyterian denominations have found ways of working together with other Reformed denominations and Christians of other traditions, especially in the World Communion of Reformed Churches. Some Presbyterian churches have entered into unions with other churches, such as Congregationalists, Lutherans, Anglicans, Presbyterian history is part of the history of Christianity, but the beginning of Presbyterianism as a distinct movement occurred during the 16th-century Protestant Reformation. As the Catholic Church resisted the reformers, several different theological movements splintered from the Church, the Presbyterian church traces its ancestry back primarily to England and Scotland. In August 1560 the Parliament of Scotland adopted the Scots Confession as the creed of the Scottish Kingdom, Presbyterians distinguish themselves from other denominations by doctrine, institutional organization and worship, often using a Book of Order to regulate common practice and order. The origins of the Presbyterian churches are in Calvinism, many branches of Presbyterianism are remnants of previous splits from larger groups. Presbyterians place great importance upon education and lifelong learning, Presbyterian government is by councils of elders. Teaching and ruling elders are ordained and convene in the lowest council known as a session or consistory responsible for the discipline, nurture, teaching elders have responsibility for teaching, worship, and performing sacraments. Pastors are called by individual congregations, a congregation issues a call for the pastors service, but this call must be ratified by the local presbytery. Ruling elders are usually laymen who are elected by the congregation and ordained to serve with the elders, assuming responsibility for nurture. Often, especially in larger congregations, the elders delegate the practicalities of buildings, finance and this group may variously be known as a Deacon Board, Board of Deacons Diaconate, or Deacons Court. These are sometimes known as presbyters to the full congregation, above the sessions exist presbyteries, which have area responsibilities. These are composed of teaching elders and ruling elders from each of the constituent congregations, the presbytery sends representatives to a broader regional or national assembly, generally known as the General Assembly, although an intermediate level of a synod sometimes exists. The Church of Scotland abolished the Synod in 1993, Presbyterian governance is practised by Presbyterian denominations and also by many other Reformed churches
7.
Richard Price
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Richard Price was a Welsh moral philosopher, preacher and mathematician. He was a nonconformist, meaning that he was a Protestant Christian who did not conform to the governance and he was also a political pamphleteer, active in radical, republican, and liberal causes such as the American Revolution. He was well-connected and fostered communication between a number of people, including several of the Founding Fathers of the United States. Price spent most of his life as minister of Newington Green Unitarian Church. He also wrote on issues of demography and finance, and was a Fellow of the Royal Society, Richard Price was the son of Rhys Price, a dissenting minister. His mother was Catherine Richards, his fathers second wife, Richard was born at Tyn Ton, a farmhouse in the village of Llangeinor, Glamorgan, Wales. He was educated privately, then at Neath and Pen-twyn and he studied under Vavasor Griffiths at Chancefield, Talgarth. He then left Wales for England, where he spent the rest of his life and he studied with John Eames and the dissenting academy in Moorfields, London. Leaving the academy in 1744, Price became chaplain and companion to George Streatfield at Stoke Newington and he also held the lectureship at Old Jewry, where Samuel Chandler was minister. Streatfields death and that of an uncle in 1757 improved his circumstances, in 1758 Price moved to Newington Green, and took up residence in No.54 the Green, in the middle of a terrace even then a hundred years old. Price became minister to the Newington Green meeting-house, a church that continues today, among the congregation were Samuel Vaughan and his family. Price had Thomas Amory as preaching colleague from 1770, when, in 1770, Price became morning preacher at the Gravel Pit Chapel in Hackney, he continued his afternoon sermons at Newington Green. He also accepted duties at the house in Old Jewry. A close friend of Price was Thomas Rogers, father of Samuel Rogers, more than once, Price and the elder Rogers rode on horseback to Wales. Another was the Rev. James Burgh, author of The Dignity of Human Nature and Thoughts on Education, Price, Rogers, and Burgh formed a dining club, eating at each others houses in rotation. Price and Rogers joined the Society for Constitutional Information, the Bowood circle was a group of liberal intellectuals around Lord Shelburne, and named after Bowood House, his seat in Wiltshire. In 1771 Price had Shelburne employ Thomas Jervis, another member of the circle was Benjamin Vaughan. In 1772 Price recruited Joseph Priestley, who came to work for Shelburne as librarian from 1773, the group that Benjamin Franklin christened the Club of Honest Whigs was an informal dining group around John Canton
8.
Joshua Bayes
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Joshua Bayes, was an English nonconformist minister. Bayes was son of the Rev. Samuel Bayes, who was ejected by the Act of Uniformity of 1662 from a living in Derbyshire, believed to be born in 1671, he received his entire secular education in the grammar school of his native town, Manchester. Being dedicated from his birth to the nonconformist ministry, he was placed under the tuition of Richard Frankland, of Attercliffe in Yorkshire, on 15 Nov.1686. On the conclusion of his course he proceeded to London, and was admitted for examination by a number of the elder ministers according to the practice of the times and he was ordained preacher of the gospel and minister on 22 June 1694. This—the first public ordination amongst dissenters in the city after the Act of Uniformity—took place in the meeting-house of Samuel Annesley in Little St. Helens, there were six candidates, one of whom was Edmund Calamy. It appears that young Bayes served the churches around London as a kind of itinerant or evangelist for some years, but about 1706 he settled at St. Thomass meeting-house, Southwark, as assistant to John Sheffield, one of the most original of the later puritan writers. This engagement requiring his attendance only in the morning of each Sunday, the continuation has never secured the unique acceptance of Matthew Henrys own writing, but the Galatians is among the best of the supplements. With Taylor of Leather Lane dying in 1723, Bayes, his assistant, was invited to succeed him, accordingly he resigned the morning service at St. Thomass. Subsequently he himself appointed ‘assistants, ’ first John Cornish, and next his own son, Dr. Calamys death in 1732 caused a vacancy in the Merchants lectureship at Salters Hall, and Bayes was chosen to succeed him. In 1735 he associated himself with a number of divines in a course of lectures—also delivered at Salters Hall—against popery and his own subject was The Church of Romes Doctrine and Practice with relation to the Worship of God in an unknown tongue. He died on 24 April 1746, and was buried in Bunhill Fields, besides the publications already named, he published several occasional sermons. There is a fine portrait of him in Dr. Williamss library, engraved in Wilsons History
9.
Hertfordshire
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Hertfordshire is a county in southern England, bordered by Bedfordshire to the north, Cambridgeshire to the north-east, Essex to the east, Buckinghamshire to the west and Greater London to the south. For government statistical purposes, it is placed in the East of England region, in 2013, the county had a population of 1,140,700 living in an area of 634 square miles. Four towns have between 50,000 and 100,000 residents, Hemel Hempstead, Stevenage, Watford and St Albans. Hertford, once the market town for the medieval agricultural county derives its name from a hart. Elevations are high for the region in the north and west and these reach over 240m in the western projection around Tring which is in the Chilterns. The countys borders are approximately the watersheds of the Colne and Lea, hertfordshires undeveloped land is mainly agricultural and much is protected by green belt. The countys landmarks span many centuries, ranging from the Six Hills in the new town of Stevenage built by local inhabitants during the Roman period, Leavesden filmed much of the UK-based $7.7 Bn box office Harry Potter film series and has the countrys studio tour. Saint Alban, a Romano-British soldier, took the place of a Christian priest and was beheaded on Holywell Hill and his martyrs cross of a yellow saltire on a blue background is reflected in the flag and coat of arms of Hertfordshire. Hertfordshire is well-served with motorways and railways, providing access to London. The largest sector of the economy of the county is in services, Hertfordshire was the area assigned to a fortress constructed at Hertford under the rule of Edward the Elder in 913. Hertford is derived from the Anglo-Saxon heort ford, meaning deer crossing, the name Hertfordshire is first recorded in the Anglo-Saxon Chronicle in 1011. Deer feature in many county emblems, there is evidence of humans living in Hertfordshire from the Mesolithic period. It was first farmed during the Neolithic period and permanent habitation appeared at the beginning of the Bronze Age and this was followed by tribes settling in the area during the Iron Age. 293 the first recorded British martyrdom is believed to have taken place. Saint Alban, a Romano-British soldier, took the place of a Christian priest and was beheaded on Holywell Hill. His martyrs cross of a saltire on a blue background is reflected in the flag. He is the Patron Saint of Hertfordshire, with the departure of the Roman Legions in the early 5th century, the now unprotected territory was invaded and colonised by the Anglo-Saxons. By the 6th century the majority of the county was part of the East Saxon kingdom
10.
Nonconformist
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In English church history, a nonconformist was a Protestant Christian who did not conform to the governance and usages of the established Church of England. Broad use of the term was precipitated after the Restoration of the British monarchy in 1660, by the late 19th-century the term specifically included the Reformed Christians, plus the Baptists and Methodists. The English Dissenters such as the Puritans who violated the Act of Uniformity 1559 — typically by practising radical, sometimes separatist, in England and Wales in the late 19th century the new terms free churchman and Free Church started to replace dissenter or Nonconformist. One influential nonconformist minister is Matthew Henry, who beginning in 1710 published his multi-volume Commentary that is still used, issac Watts is an equally recognized nonconformist minister whose hymns are still sung by Christians worldwide. The Act of Uniformity of 1662 required churchmen to use all rites and ceremonies as prescribed in the Book of Common Prayer. Consequently, nearly 2,000 clergymen were ejected from the church for refusing to comply with the provisions of the act. The Great Ejection created an abiding public consciousness of non-conformity, thereafter, a Nonconformist was any English subject belonging to a non-Anglican church or a non-Christian religion. More broadly, any person who advocated religious liberty was typically called out as Nonconformist, culturally, in England and Wales, discrimination against Nonconformists endured even longer. Presbyterians, Congregationalists, Baptists, Calvinists, other reformed groups, following the act, other groups, including Methodists, Unitarians, Quakers, Plymouth Brethren, and the English Moravians were officially labelled as Nonconformists as they became established. A religious census in 1851 revealed Nonconformist comprised about half that of the people who attended services on Sundays. In the larger manufacturing areas, Nonconformists clearly outnumbered members of the Church of England, in Wales in 1850, Nonconformist chapel attendance significantly outnumbered Anglican church attendance. Historians distinguish two categories of Dissenters, or Nonconformists, in addition to the evangelicals or Low Church element in the Church of England, Old Dissenters, dating from the 16th and 17th centuries, included Baptists, Congregationalists, Quakers, Unitarians, and Presbyterians outside Scotland. New Dissenters emerged in the 18th century and were mainly Methodists, the Nonconformist Conscience was their moral sensibility which they tried to implement in British politics. The Nonconformist conscience of the Old group emphasized religious freedom and equality, pursuit of justice, and opposition to discrimination, compulsion, the New Dissenters stressed personal morality issues, including sexuality, temperance, family values, and Sabbath-keeping. Both factions were active, but until mid-19th century the Old group supported mostly Whigs and Liberals in politics. In the late 19th the New Dissenters mostly switched to the Liberal Party, the result was a merging of the two groups, strengthening their great weight as a political pressure group. The joined together on new issues especially regarding schools and temperance, by 1914 the linkage was weakening and by the 1920s it was virtually dead. Dissenters demanded removal of political and civil disabilities that applied to them, the Anglican establishment strongly resisted until 1828
11.
Sheffield
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Sheffield is a city and metropolitan borough in South Yorkshire, England. Historically part of the West Riding of Yorkshire, its derives from the River Sheaf. With some of its southern suburbs annexed from Derbyshire, the city has grown from its industrial roots to encompass a wider economic base. The population of the City of Sheffield is 569,700, Sheffield is the third largest English district by population. The metropolitan population of Sheffield is 1,569,000, in the 19th century, Sheffield gained an international reputation for steel production. Known as the Steel City, many innovations were developed locally, including crucible and stainless steel, Sheffield received its municipal charter in 1843, becoming the City of Sheffield in 1893. International competition in iron and steel caused a decline in these industries in the 1970s and 1980s, the 21st century has seen extensive redevelopment in Sheffield along with other British cities. Sheffields gross value added has increased by 60% since 1997, standing at £9.2 billion in 2007, the economy has experienced steady growth averaging around 5% annually, greater than that of the broader region of Yorkshire and the Humber. The city is in the foothills of the Pennines, and the valleys of the River Don and its four tributaries, the Loxley, the Porter Brook, the Rivelin. 61% of Sheffields entire area is space, and a third of the city lies within the Peak District national park. The area now occupied by the City of Sheffield is believed to have inhabited since at least the late Upper Palaeolithic period. The earliest evidence of occupation in the Sheffield area was found at Creswell Crags to the east of the city. In the Iron Age the area became the southernmost territory of the Pennine tribe called the Brigantes and it is this tribe who are thought to have constructed several hill forts in and around Sheffield. Gradually, Anglian settlers pushed west from the kingdom of Deira, a Celtic presence within the Sheffield area is evidenced by two settlements called Wales and Waleswood close to Sheffield. The settlements that grew and merged to form Sheffield, however, date from the half of the first millennium. In Anglo-Saxon times, the Sheffield area straddled the border between the kingdoms of Mercia and Northumbria, after the Norman conquest, Sheffield Castle was built to protect the local settlements, and a small town developed that is the nucleus of the modern city. By 1296, a market had been established at what is now known as Castle Square, from 1570 to 1584, Mary, Queen of Scots, was imprisoned in Sheffield Castle and Sheffield Manor. During the 1740s, a form of the steel process was discovered that allowed the manufacture of a better quality of steel than had previously been possible
12.
Logic
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Logic, originally meaning the word or what is spoken, is generally held to consist of the systematic study of the form of arguments. A valid argument is one where there is a relation of logical support between the assumptions of the argument and its conclusion. Historically, logic has been studied in philosophy and mathematics, and recently logic has been studied in science, linguistics, psychology. The concept of form is central to logic. The validity of an argument is determined by its logical form, traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logic. Informal logic is the study of natural language arguments, the study of fallacies is an important branch of informal logic. Since much informal argument is not strictly speaking deductive, on some conceptions of logic, formal logic is the study of inference with purely formal content. An inference possesses a purely formal content if it can be expressed as an application of a wholly abstract rule, that is. The works of Aristotle contain the earliest known study of logic. Modern formal logic follows and expands on Aristotle, in many definitions of logic, logical inference and inference with purely formal content are the same. This does not render the notion of informal logic vacuous, because no formal logic captures all of the nuances of natural language, Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference. Symbolic logic is divided into two main branches, propositional logic and predicate logic. Mathematical logic is an extension of logic into other areas, in particular to the study of model theory, proof theory, set theory. Logic is generally considered formal when it analyzes and represents the form of any valid argument type, the form of an argument is displayed by representing its sentences in the formal grammar and symbolism of a logical language to make its content usable in formal inference. Simply put, formalising simply means translating English sentences into the language of logic and this is called showing the logical form of the argument. It is necessary because indicative sentences of ordinary language show a variety of form. Second, certain parts of the sentence must be replaced with schematic letters, thus, for example, the expression all Ps are Qs shows the logical form common to the sentences all men are mortals, all cats are carnivores, all Greeks are philosophers, and so on. The schema can further be condensed into the formula A, where the letter A indicates the judgement all - are -, the importance of form was recognised from ancient times
13.
Isaac Newton
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His book Philosophiæ Naturalis Principia Mathematica, first published in 1687, laid the foundations of classical mechanics. Newton also made contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus. Newtons Principia formulated the laws of motion and universal gravitation that dominated scientists view of the universe for the next three centuries. Newtons work on light was collected in his influential book Opticks. He also formulated a law of cooling, made the first theoretical calculation of the speed of sound. Newton was a fellow of Trinity College and the second Lucasian Professor of Mathematics at the University of Cambridge, politically and personally tied to the Whig party, Newton served two brief terms as Member of Parliament for the University of Cambridge, in 1689–90 and 1701–02. He was knighted by Queen Anne in 1705 and he spent the last three decades of his life in London, serving as Warden and Master of the Royal Mint and his father, also named Isaac Newton, had died three months before. Born prematurely, he was a child, his mother Hannah Ayscough reportedly said that he could have fit inside a quart mug. When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabas Smith, leaving her son in the care of his maternal grandmother, Newtons mother had three children from her second marriage. From the age of twelve until he was seventeen, Newton was educated at The Kings School, Grantham which taught Latin and Greek. He was removed from school, and by October 1659, he was to be found at Woolsthorpe-by-Colsterworth, Henry Stokes, master at the Kings School, persuaded his mother to send him back to school so that he might complete his education. Motivated partly by a desire for revenge against a bully, he became the top-ranked student. In June 1661, he was admitted to Trinity College, Cambridge and he started as a subsizar—paying his way by performing valets duties—until he was awarded a scholarship in 1664, which guaranteed him four more years until he would get his M. A. He set down in his notebook a series of Quaestiones about mechanical philosophy as he found it, in 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became calculus. Soon after Newton had obtained his B. A. degree in August 1665, in April 1667, he returned to Cambridge and in October was elected as a fellow of Trinity. Fellows were required to become ordained priests, although this was not enforced in the restoration years, however, by 1675 the issue could not be avoided and by then his unconventional views stood in the way. Nevertheless, Newton managed to avoid it by means of a special permission from Charles II. A and he was elected a Fellow of the Royal Society in 1672. Newtons work has been said to distinctly advance every branch of mathematics then studied and his work on the subject usually referred to as fluxions or calculus, seen in a manuscript of October 1666, is now published among Newtons mathematical papers
14.
Calculus
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Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. It has two branches, differential calculus, and integral calculus, these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the notions of convergence of infinite sequences. Generally, modern calculus is considered to have developed in the 17th century by Isaac Newton. Today, calculus has widespread uses in science, engineering and economics, Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, Calculus has historically been called the calculus of infinitesimals, or infinitesimal calculus. Calculus is also used for naming some methods of calculation or theories of computation, such as calculus, calculus of variations, lambda calculus. The ancient period introduced some of the ideas that led to integral calculus, the method of exhaustion was later discovered independently in China by Liu Hui in the 3rd century AD in order to find the area of a circle. In the 5th century AD, Zu Gengzhi, son of Zu Chongzhi, indian mathematicians gave a non-rigorous method of a sort of differentiation of some trigonometric functions. In the Middle East, Alhazen derived a formula for the sum of fourth powers. He used the results to carry out what would now be called an integration, Cavalieris work was not well respected since his methods could lead to erroneous results, and the infinitesimal quantities he introduced were disreputable at first. The formal study of calculus brought together Cavalieris infinitesimals with the calculus of finite differences developed in Europe at around the same time, pierre de Fermat, claiming that he borrowed from Diophantus, introduced the concept of adequality, which represented equality up to an infinitesimal error term. The combination was achieved by John Wallis, Isaac Barrow, and James Gregory, in other work, he developed series expansions for functions, including fractional and irrational powers, and it was clear that he understood the principles of the Taylor series. He did not publish all these discoveries, and at this time infinitesimal methods were considered disreputable. These ideas were arranged into a calculus of infinitesimals by Gottfried Wilhelm Leibniz. He is now regarded as an independent inventor of and contributor to calculus, unlike Newton, Leibniz paid a lot of attention to the formalism, often spending days determining appropriate symbols for concepts. Leibniz and Newton are usually credited with the invention of calculus. Newton was the first to apply calculus to general physics and Leibniz developed much of the used in calculus today
15.
George Berkeley
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George Berkeley — known as Bishop Berkeley — was an Irish philosopher whose primary achievement was the advancement of a theory he called immaterialism. Berkeley is also known for his critique of abstraction, an important premise in his argument for immaterialism, in this book, Berkeleys views were represented by Philonous, while Hylas embodies the Irish thinkers opponents, in particular John Locke. Berkeley argued against Sir Isaac Newtons doctrine of space, time and motion in De Motu. His arguments were a precursor to the views of Mach and Einstein and his last major philosophical work, Siris, begins by advocating the medicinal use of tar water and then continues to discuss a wide range of topics, including science, philosophy, and theology. Berkeley was born at his home, Dysart Castle, near Thomastown, County Kilkenny, Ireland, the eldest son of William Berkeley. He was educated at Kilkenny College and attended Trinity College, Dublin, earning a degree in 1704. He remained at Trinity College after completion of his degree as a tutor and his earliest publication was on mathematics, but the first that brought him notice was his An Essay towards a New Theory of Vision, first published in 1709. In the essay, Berkeley examines visual distance, magnitude, position and problems of sight, while this work raised much controversy at the time, its conclusions are now accepted as an established part of the theory of optics. For this theory, the Principles gives the exposition and the Dialogues the defence, one of his main objectives was to combat the prevailing materialism of his time. Shortly afterwards, Berkeley visited England and was received into the circle of Addison, Pope and Steele. In 1721, he took Holy Orders in the Church of Ireland, earning his doctorate in divinity, in 1721/2 he was made Dean of Dromore and, in 1724, Dean of Derry. Swift said generously that he did not grudge Berkeley his inheritance, a story that Berkeley and Marshall disregarded a condition of the inheritance that they must publish the correspondence between Swift and Vanessa is probably untrue. In 1725, he began the project of founding a college in Bermuda for training ministers and missionaries in the colony, in 1728, he married Anne Forster, daughter of John Forster, Chief Justice of the Irish Common Pleas. He then went to America on a salary of £100 per annum and he landed near Newport, Rhode Island, where he bought a plantation at Middletown – the famous Whitehall. It has been claimed that he introduced Palladianism into America by borrowing a design from Kents Designs of Inigo Jones for the door-case of his house in Rhode Island, Whitehall. He also brought to New England John Smibert, the British artist he discovered in Italy, meanwhile, he drew up plans for the ideal city he planned to build on Bermuda. He lived at the plantation while he waited for funds for his college to arrive, the funds, however, were not forthcoming, and in 1732 he left America and returned to London. While living in Londons Saville Street, he took part in efforts to create a home for the abandoned children
16.
Fellow of the Royal Society
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As of 2016, there are around 1600 living Fellows, Foreign and Honorary Members. Fellowship of the Royal Society has been described by The Guardian newspaper as “the equivalent of a lifetime achievement Oscar” with several institutions celebrating their announcement each year. Up to 60 new Fellows, honorary and foreign members are elected annually usually in May, each candidate is considered on their merits and can be proposed from any sector of the scientific community. Fellows are elected for life on the basis of excellence in science and are entitled to use the post-nominal letters FRS, see Category, Fellows of the Royal Society and Category, Female Fellows of the Royal Society. Every year, Fellows elect up to ten new Foreign Members, like Fellows, Foreign Members are elected for life through peer review on the basis of excellence in science. As of 2016 there are around 165 Foreign Members, who are entitled to use the post-nominal ForMemRS, see Category, Foreign Members of the Royal Society. Honorary Fellows include Bill Bryson, Melvyn Bragg, Robin Saxby, David Sainsbury, Baron Sainsbury of Turville, Honorary Fellows are entitled to use the post nominal letters HonFRS. Others including John Maddox, Patrick Moore and Lisa Jardine were elected as honorary fellows, statute 12 is a legacy mechanism for electing members before official honorary membership existed in 1997. Fellows elected under statute 12 include David Attenborough and John Palmer, prime Ministers of the United Kingdom such as Margaret Thatcher, Neville Chamberlain, H. H. Asquith were elected under statute 12, see Category, Fellows of the Royal Society. The Council of the Royal Society can recommend members of the British Royal Family for election as Royal Fellows of the Royal Society. As of 2016 there are five royal fellows, Charles, Prince of Wales, Anne, Princess Royal, Prince Edward, Duke of Kent, Prince William, Duke of Cambridge and Prince Andrew, Duke of York. Her Majesty the Queen, Elizabeth II is not a Royal Fellow, Prince Philip, Duke of Edinburgh was elected under statute 12, not as a Royal Fellow. The election of new fellows is announced annually in May, after their nomination, each candidate for Fellowship or Foreign Membership is nominated by two Fellows of the Royal Society, who sign a certificate of proposal. Previously, nominations required at least five fellows to support each nomination by the proposer, the certificate of election includes a statement of the principal grounds on which the proposal is being made. There is no limit on the number of nominations each year. In 2015, there were 654 candidates for election as Fellows and 106 candidates for Foreign Membership. The final list of up to 52 Fellowship candidates and up to 10 Foreign Membership candidates is confirmed by the Council in April, a candidate is elected if he or she secures two-thirds of votes of those Fellows present and voting. A further maximum of six can be ‘Honorary’, ‘General’ or ‘Royal’ Fellows, nominations for Fellowship are peer reviewed by sectional committees, each with fifteen members and a chair
17.
Thomas Simpson
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Thomas Simpson FRS was a British mathematician, inventor and eponym of Simpsons rule to approximate definite integrals. The attribution, as often in mathematics, can be debated, this rule had been found 100 years earlier by Johannes Kepler, Simpson was born in Market Bosworth, Leicestershire. The son of a weaver, Simpson taught himself mathematics, at the age of nineteen, he married a fifty-year old widow with two children. As a youth he became interested in astrology after seeing a solar eclipse and he also dabbled in divination and caused fits in a girl after raising a devil from her. After this incident, he and his wife had to flee to Derby and he moved with his wife and children to London at age twenty-five, where he supported his family by weaving during the day and teaching mathematics at night. From 1743, he taught mathematics at the Royal Military Academy, Simpson was a fellow of the Royal Society. In 1758, Simpson was elected a member of the Royal Swedish Academy of Sciences. He died in Market Bosworth, and was laid to rest in Sutton Cheney, a plaque inside the church commemorates him. In both works, Simpson cited De Moivres work and did not claim originality beyond the presentation of some more accurate data, who Doubtless Hath Solved the Same Otherwise, Philosophical Transactions of the Royal Society of London,6, pp. 2093–2096. Of further related interest are problems posed in the early 1750s by J. Orchard, in The British Palladium and this type of generalization was later popularized by Alfred Weber in 1909. In 1971, Luc-Normand Tellier found the first direct numerical solution of the Fermat, long before Von Thünen’s contributions, which go back to 1818, the Fermat point problem can be seen as the very beginning of space economy. In 1985, Luc-Normand Tellier formulated an all-new problem called the “attraction-repulsion problem” and that problem was later further analyzed by mathematicians like Chen, Hansen, Jaumard and Tuy, and Jalal and Krarup. Containing a Number of New Improvements on the Theory, robertson, Edmund F. Thomas Simpson, MacTutor History of Mathematics archive, University of St Andrews
18.
Abraham de Moivre
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Abraham de Moivre was a French mathematician known for de Moivres formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory. He was a friend of Isaac Newton, Edmond Halley, even though he faced religious persecution he remained a steadfast Christian throughout his life. Among his fellow Huguenot exiles in England, he was a colleague of the editor and translator Pierre des Maizeaux, De Moivre wrote a book on probability theory, The Doctrine of Chances, said to have been prized by gamblers. De Moivre first discovered Binets formula, the expression for Fibonacci numbers linking the nth power of the golden ratio φ to the nth Fibonacci number. He also was the first to postulate the central limit theorem, Abraham de Moivre was born in Vitry-le-François in Champagne on May 26,1667. His father, Daniel de Moivre, was a surgeon who believed in the value of education, though Abraham de Moivres parents were Protestant, he first attended Christian Brothers Catholic school in Vitry, which was unusually tolerant given religious tensions in France at the time. When he was eleven, his parents sent him to the Protestant Academy at Sedan, the Protestant Academy of Sedan had been founded in 1579 at the initiative of Françoise de Bourbon, the widow of Henri-Robert de la Marck. In 1682 the Protestant Academy at Sedan was suppressed, and de Moivre enrolled to study logic at Saumur for two years, in 1684, de Moivre moved to Paris to study physics, and for the first time had formal mathematics training with private lessons from Jacques Ozanam. It forbade Protestant worship and required all children be baptized by Catholic priests. De Moivre was sent to the Prieure de Saint-Martin, a school that the authorities sent Protestant children to for indoctrination into Catholicism, by the time he arrived in London, de Moivre was a competent mathematician with a good knowledge of many of the standard texts. To make a living, de Moivre became a tutor of mathematics. De Moivre continued his studies of mathematics after visiting the Earl of Devonshire and seeing Newtons recent book, looking through the book, he realized that it was far deeper than the books that he had studied previously, and he became determined to read and understand it. By 1692, de Moivre became friends with Edmond Halley and soon after with Isaac Newton himself, in 1695, Halley communicated de Moivres first mathematics paper, which arose from his study of fluxions in the Principia Mathematica, to the Royal Society. This paper was published in the Philosophical Transactions that same year, shortly after publishing this paper, de Moivre also generalized Newtons noteworthy binomial theorem into the multinomial theorem. The Royal Society became apprised of this method in 1697, after de Moivre had been accepted, Halley encouraged him to turn his attention to astronomy. The mathematician Johann Bernoulli proved this formula in 1710, at least a part of the reason was a bias against his French origins. In November 1697 he was elected a Fellow of the Royal Society and in 1712 was appointed to a set up by the society. Arbuthnot, Hill, Halley, Jones, Machin, Burnet, Robarts, Bonet, Aston, the full details of the controversy can be found in the Leibniz and Newton calculus controversy article
19.
David Hume
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David Hume was a Scottish philosopher, historian, economist, and essayist, who is best known today for his highly influential system of radical philosophical empiricism, skepticism, and naturalism. Humes empiricist approach to philosophy places him with John Locke, Francis Bacon, beginning with his A Treatise of Human Nature, Hume strove to create a total naturalistic science of man that examined the psychological basis of human nature. Humes compatibilist theory of free will takes causal determinism as fully compatible with human freedom, Kant himself credited Hume as the spur to his philosophical thought who had awakened him from his dogmatic slumbers. Arthur Schopenhauer once declared there is more to be learned from each page of David Hume than from the collected philosophical works of Hegel, Herbart. Hume is thus regarded as a pivotal figure in the history of philosophical thought. David Hume was the second of two born to Joseph Home of Ninewells, an advocate, and his wife The Hon. Katherine. He was born on 26 April 1711 in a tenement on the side of the Lawnmarket in Edinburgh. Humes father died when Hume was a child, just after his birthday, and he was raised by his mother. He changed the spelling of his name in 1734, because of the fact that his surname Home, throughout his life Hume, who never married, spent time occasionally at his family home at Ninewells in Berwickshire, which had belonged to his family since the sixteenth century. His finances as a man were very slender. His family was not rich and, as a younger son and he was therefore forced to make a living somehow. Hume attended the University of Edinburgh at the early age of twelve at a time when fourteen was normal. He had little respect for the professors of his time, telling a friend in 1735 that there is nothing to be learnt from a Professor, which is not to be met with in Books. Aged around 18, he made a discovery that opened up to him a new Scene of Thought. He did not recount what this scene was, and commentators have offered a variety of speculations, due to this inspiration, Hume set out to spend a minimum of ten years reading and writing. He soon came to the verge of a breakdown, suffering from what a doctor diagnosed as the Disease of the Learned. Hume wrote that it started with a coldness, which he attributed to a Laziness of Temper, later, some scurvy spots broke out on his fingers. This was what persuaded Humes physician to make his diagnosis, Hume wrote that he went under a Course of Bitters and Anti-Hysteric Pills, taken along with a pint of claret every day
20.
An Enquiry Concerning Human Understanding
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An Enquiry Concerning Human Understanding is a book by the Scottish empiricist philosopher David Hume, published in English in 1748. It was a revision of an effort, Humes A Treatise of Human Nature. The end product of his labours was the Enquiry, the Enquiry dispensed with much of the material from the Treatise, in favor of clarifying and emphasizing its most important aspects. For example, Humes views on personal identity do not appear, however, more vital propositions, such as Humes argument for the role of habit in a theory of knowledge, are retained. This book has proven influential, both in the years that would immediately follow and today. Immanuel Kant points to it as the book which woke him from his dogmatic slumber. The Enquiry is widely regarded as a classic in modern philosophical literature, the argument of the Enquiry proceeds by a series of incremental steps, separated into chapters which logically succeed one another. After expounding his epistemology, Hume explains how to apply his principles to specific topics, in the first section of the Enquiry, Hume provides a rough introduction to philosophy as a whole. For Hume, philosophy can be split into two parts, natural philosophy and the philosophy of human nature. The latter investigates both actions and thoughts and he emphasizes in this section, by way of warning, that philosophers with nuanced thoughts will likely be cast aside in favor of those whose conclusions more intuitively match popular opinion. However, he insists, precision helps art and craft of all kinds, next, Hume discusses the distinction between impressions and ideas. By impressions, he means sensations, while by ideas, he means memories, according to Hume, the difference between the two is that ideas are less vivacious than impressions. For example, the idea of the taste of an orange is far inferior to the impression of actually eating one, writing within the tradition of empiricism, he argues that impressions are the source of all ideas. Hume accepts that ideas may be either the product of mere sensation, according to Hume, the creative faculty makes use of four mental operations which produce imaginings out of sense-impressions. These operations are compounding, transposing, augmenting, and diminishing, in a later chapter, he also mentions the operations of mixing, separating, and dividing. However, Hume admits that there is one objection to his account, in this thought-experiment, he asks us to imagine a man who has experienced every shade of blue except for one. He predicts that this man will be able to divide the color of this shade of blue. In this chapter, Hume discusses how thoughts tend to come in sequences and he explains that there are at least three kinds of associations between ideas, resemblance, contiguity in space-time, and cause-and-effect
21.
Bunhill Fields
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Bunhill Fields is a former burial ground in the London Borough of Islington, north of the City of London, now managed as a public garden by the City of London Corporation. It is about 1.6 hectares in extent, although historically it was much larger and it was in use as a burial ground from 1665 until 1854, by which date approximately 123,000 interments were estimated to have taken place. Nearby was a separate Quaker burial ground, sometimes known by the name Bunhill Fields. George Fox, one of the founders of the Quaker movement, was among those buried here and its remains are also now a public garden, Quaker Gardens, managed by the London Borough of Islington. Bunhill Fields was part of the Manor of Finsbury, which has its origins as the prebend of Halliwell and Finsbury, belonging to St Pauls Cathedral, in 1315 the prebendary manor was granted by Robert Baldock to the Mayor and commonalty of London. This act enabled more general public access to an area of fen or moor stretching from the City of Londons boundary. In 1498 part of the otherwise unenclosed landscape was set aside to form a field for military exercises of archers and others. This part of the manor still bears the name Artillery Ground, next to this lies Bunhill Fields. The dried bones were deposited on the moor and capped with a layer of soil. This built up a hill across the damp, flat fens. Although enclosing walls for the ground were completed, Church of England officials never consecrated the ground or used it for burials. A Mr Tindal took over the lease and it appears on Rocques Map of London of 1746, and elsewhere, as Tindals Burying Ground. Anno Domini 1665, and afterwards the gates thereof were built and finished in the mayoralty of Sir Thomas Bloudworth, the present gates and inscription date from 1868, but the wording follows that of an original 17th-century inscription at the western entrance, now lost. The earliest recorded monumental inscription was that to Grace, daughter of T. Cloudesly, the earliest surviving monument is believed to be the headstone to Theophilus Gale, the inscription reads Theophilus Gale MA / Born 1628 / Died 1678. In 1769 an Act of Parliament gave the City of London Corporation the right to continue to lease the ground from the estate for 99 years. The City authorities continued to let the ground to their tenant as a burial ground and this term was also later applied to its daughter cemetery established at Abney Park in Stoke Newington. In 1852 the Burial Act was passed which enabled burial grounds to be closed once they became full, an Order for Closure for Bunhill Fields was made in December 1853, and the final burial took place on 5 January 1854. Occasional interments continued to be permitted in existing vaults or graves, by this date approximately 123,000 interments had taken place in the burial ground
22.
Inverse probability
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In probability theory, inverse probability is an obsolete term for the probability distribution of an unobserved variable. The development of the field and terminology from inverse probability to Bayesian probability is described by Fienberg, the term inverse probability appears in an 1837 paper of De Morgan, in reference to Laplaces method of probability, though the term inverse probability does not occur in these. Later Jeffreys uses the term in his defense of the methods of Bayes and Laplace, the term Bayesian, which displaced inverse probability, was introduced by Ronald Fisher around 1950. Inverse probability, variously interpreted, was the dominant approach to statistics until the development of frequentism in the early 20th century by Ronald Fisher, Jerzy Neyman and Egon Pearson. Following the development of frequentism, the terms frequentist and Bayesian developed to contrast these approaches, the distribution p itself is called the direct probability. The inverse probability problem was the problem of estimating a parameter from experimental data in the sciences, especially astronomy. A simple example would be the problem of estimating the position of a star in the sky for purposes of navigation, given the data, one must estimate the true position. This problem would now be considered one of inferential statistics, the terms direct probability and inverse probability were in use until the middle part of the 20th century, when the terms likelihood function and posterior distribution became prevalent
23.
Probability
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Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1, the higher the probability of an event, the more certain that the event will occur. A simple example is the tossing of a fair coin, since the coin is unbiased, the two outcomes are both equally probable, the probability of head equals the probability of tail. Since no other outcomes are possible, the probability is 1/2 and this type of probability is also called a priori probability. Probability theory is used to describe the underlying mechanics and regularities of complex systems. For example, tossing a coin twice will yield head-head, head-tail, tail-head. The probability of getting an outcome of head-head is 1 out of 4 outcomes or 1/4 or 0.25 and this interpretation considers probability to be the relative frequency in the long run of outcomes. A modification of this is propensity probability, which interprets probability as the tendency of some experiment to yield a certain outcome, subjectivists assign numbers per subjective probability, i. e. as a degree of belief. The degree of belief has been interpreted as, the price at which you would buy or sell a bet that pays 1 unit of utility if E,0 if not E. The most popular version of subjective probability is Bayesian probability, which includes expert knowledge as well as data to produce probabilities. The expert knowledge is represented by some prior probability distribution and these data are incorporated in a likelihood function. The product of the prior and the likelihood, normalized, results in a probability distribution that incorporates all the information known to date. The scientific study of probability is a development of mathematics. Gambling shows that there has been an interest in quantifying the ideas of probability for millennia, there are reasons of course, for the slow development of the mathematics of probability. Whereas games of chance provided the impetus for the study of probability. According to Richard Jeffrey, Before the middle of the century, the term probable meant approvable. A probable action or opinion was one such as people would undertake or hold. However, in legal contexts especially, probable could also apply to propositions for which there was good evidence, the sixteenth century Italian polymath Gerolamo Cardano demonstrated the efficacy of defining odds as the ratio of favourable to unfavourable outcomes
24.
Markov chain Monte Carlo
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The state of the chain after a number of steps is then used as a sample of the desired distribution. The quality of the sample improves as a function of the number of steps, random walk Monte Carlo methods make up a large subclass of MCMC methods. They are also used for generating samples that gradually populate the rare failure region in rare event sampling, when an MCMC method is used for approximating a multi-dimensional integral, an ensemble of walkers move around randomly. At each point where a walker steps, the value at that point is counted towards the integral. The walker then may make a number of steps around the area. Random walk Monte Carlo methods are a kind of random simulation or Monte Carlo method, however, whereas the random samples of the integrand used in a conventional Monte Carlo integration are statistically independent, those used in MCMC methods are correlated. A Markov chain is constructed in such a way as to have the integrand as its equilibrium distribution, Gibbs sampling, This method requires all the conditional distributions of the target distribution to be sampled exactly. When drawing from the distributions is not straightforward other samplers-within-Gibbs are used. Gibbs sampling is popular partly because it not require any tuning. Slice sampling, This method depends on the principle one can sample from a distribution by sampling uniformly from the region under the plot of its density function. It alternates uniform sampling in the direction with uniform sampling from the horizontal slice defined by the current vertical position. Multiple-try Metropolis, This method is a variation of the Metropolis–Hastings algorithm that allows multiple trials at each point, by making it possible to take larger steps at each iteration, it helps address the curse of dimensionality. Reversible-jump, This method is a variant of the Metropolis–Hastings algorithm that allows proposals that change the dimensionality of the space, MCMC methods that change dimensionality have long been used in statistical physics applications, where for some problems a distribution that is a grand canonical ensemble is used. Is automatically inferred from the data, unlike most of the current MCMC methods that ignore the previous trials, using a new algorithm the MCMC algorithm is able to use the previous steps and generate the next candidate. This training-based algorithm is able to speed-up the MCMC algorithm by an order of magnitude, interacting MCMC methodologies are a class of mean field particle methods for obtaining random samples from a sequence of probability distributions with an increasing level of sampling complexity. These probabilistic models include path space state models with increasing time horizon, sequence of partial observations, increasing constraint level sets for conditional distributions, decreasing temperature schedules associated with some Boltzmann-Gibbs distributions, and many others. In principle, any MCMC sampler can be turned into an interacting MCMC sampler and these interacting MCMC samplers can be interpreted as a way to run in parallel a sequence of MCMC samplers. For instance, interacting simulated annealing algorithms are based on independent Metropolis-Hastings moves interacting sequentially with a selection-resampling type mechanism, in contrast to traditional MCMC methods, the precision parameter of this class of interacting MCMC samplers is only related to the number of interacting MCMC samplers
25.
Pierre-Simon Laplace
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Pierre-Simon, marquis de Laplace was an influential French scholar whose work was important to the development of mathematics, statistics, physics and astronomy. He summarized and extended the work of his predecessors in his five-volume Mécanique Céleste and this work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. In statistics, the Bayesian interpretation of probability was developed mainly by Laplace, Laplace formulated Laplaces equation, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. The Laplacian differential operator, widely used in mathematics, is named after him. Laplace is remembered as one of the greatest scientists of all time, sometimes referred to as the French Newton or Newton of France, he has been described as possessing a phenomenal natural mathematical faculty superior to that of any of his contemporaries. Laplace became a count of the Empire in 1806 and was named a marquis in 1817, Laplace was born in Beaumont-en-Auge, Normandy on 23 March 1749, a village four miles west of Pont lEveque in Normandy. According to W. W. Rouse Ball, His father, Pierre de Laplace and his great-uncle, Maitre Oliver de Laplace, had held the title of Chirurgien Royal. It would seem that from a pupil he became an usher in the school at Beaumont, however, Karl Pearson is scathing about the inaccuracies in Rouse Balls account and states, Indeed Caen was probably in Laplaces day the most intellectually active of all the towns of Normandy. It was here that Laplace was educated and was provisionally a professor and it was here he wrote his first paper published in the Mélanges of the Royal Society of Turin, Tome iv. 1766–1769, at least two years before he went at 22 or 23 to Paris in 1771, thus before he was 20 he was in touch with Lagrange in Turin. He did not go to Paris a raw self-taught country lad with only a peasant background, the École Militaire of Beaumont did not replace the old school until 1776. His parents were from comfortable families and his father was Pierre Laplace, and his mother was Marie-Anne Sochon. The Laplace family was involved in agriculture until at least 1750, Pierre Simon Laplace attended a school in the village run at a Benedictine priory, his father intending that he be ordained in the Roman Catholic Church. At sixteen, to further his fathers intention, he was sent to the University of Caen to read theology, at the university, he was mentored by two enthusiastic teachers of mathematics, Christophe Gadbled and Pierre Le Canu, who awoke his zeal for the subject. Here Laplaces brilliance as a mathematician was recognised and while still at Caen he wrote a memoir Sur le Calcul integral aux differences infiniment petites et aux differences finies. About this time, recognizing that he had no vocation for the priesthood, in this connection reference may perhaps be made to the statement, which has appeared in some notices of him, that he broke altogether with the church and became an atheist. Laplace did not graduate in theology but left for Paris with a letter of introduction from Le Canu to Jean le Rond dAlembert who at time was supreme in scientific circles. According to his great-great-grandson, dAlembert received him rather poorly, and to get rid of him gave him a mathematics book
26.
Bayesian inference
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Bayesian inference is a method of statistical inference in which Bayes theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics, Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a range of activities, including science, engineering, philosophy, medicine, sport. In the philosophy of theory, Bayesian inference is closely related to subjective probability. Bayesian inference derives the probability as a consequence of two antecedents, a prior probability and a likelihood function derived from a statistical model for the observed data. Bayesian inference computes the probability according to Bayes theorem, P = P ⋅ P P where ∣ means event conditional on. H stands for any hypothesis whose probability may be affected by data, often there are competing hypotheses, and the task is to determine which is the most probable. The evidence E corresponds to new data that were not used in computing the prior probability, P, the prior probability, is the estimate of the probability of the hypothesis H before the data E, the current evidence, is observed. P, the probability, is the probability of H given E, i. e. after E is observed. This is what we want to know, the probability of a hypothesis given the observed evidence, P is the probability of observing E given H. As a function of E with H fixed, this is the likelihood – it indicates the compatibility of the evidence with the given hypothesis. The likelihood function is a function of the evidence, E, while the probability is a function of the hypothesis. This factor is the same for all possible hypotheses being considered, Bayes rule can also be written as follows, P = P P ⋅ P where the factor P P can be interpreted as the impact of E on the probability of H. If the evidence does not match up with a hypothesis, one should reject the hypothesis, but if a hypothesis is extremely unlikely a priori, one should also reject it, even if the evidence does appear to match up. The critical point about Bayesian inference, then, is that it provides a way of combining new evidence with prior beliefs. This allows for Bayesian principles to be applied to various kinds of evidence and this procedure is termed Bayesian updating. Bayesian updating is widely used and computationally convenient, however, it is not the only updating rule that might be considered rational. Ian Hacking noted that traditional Dutch book arguments did not specify Bayesian updating, Hacking wrote And neither the Dutch book argument, nor any other in the personalist arsenal of proofs of the probability axioms, entails the dynamic assumption
27.
Royal Society
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Founded in November 1660, it was granted a royal charter by King Charles II as The Royal Society. The society is governed by its Council, which is chaired by the Societys President, according to a set of statutes and standing orders. The members of Council and the President are elected from and by its Fellows, the members of the society. As of 2016, there are about 1,600 fellows, allowed to use the postnominal title FRS, there are also royal fellows, honorary fellows and foreign members, the last of which are allowed to use the postnominal title ForMemRS. The Royal Society President is Venkatraman Ramakrishnan, who took up the post on 30 November 2015, since 1967, the society has been based at 6–9 Carlton House Terrace, a Grade I listed building in central London which was previously used by the Embassy of Germany, London. The Royal Society started from groups of physicians and natural philosophers, meeting at variety of locations and they were influenced by the new science, as promoted by Francis Bacon in his New Atlantis, from approximately 1645 onwards. A group known as The Philosophical Society of Oxford was run under a set of rules still retained by the Bodleian Library, after the English Restoration, there were regular meetings at Gresham College. It is widely held that these groups were the inspiration for the foundation of the Royal Society, I will not say, that Mr Oldenburg did rather inspire the French to follow the English, or, at least, did help them, and hinder us. But tis well known who were the men that began and promoted that design. This initial royal favour has continued and, since then, every monarch has been the patron of the society, the societys early meetings included experiments performed first by Hooke and then by Denis Papin, who was appointed in 1684. These experiments varied in their area, and were both important in some cases and trivial in others. The Society returned to Gresham in 1673, there had been an attempt in 1667 to establish a permanent college for the society. Michael Hunter argues that this was influenced by Solomons House in Bacons New Atlantis and, to a lesser extent, by J. V. The first proposal was given by John Evelyn to Robert Boyle in a letter dated 3 September 1659, he suggested a scheme, with apartments for members. The societys ideas were simpler and only included residences for a handful of staff and these plans were progressing by November 1667, but never came to anything, given the lack of contributions from members and the unrealised—perhaps unrealistic—aspirations of the society. During the 18th century, the gusto that had characterised the early years of the society faded, with a number of scientific greats compared to other periods. The pointed lightning conductor had been invented by Benjamin Franklin in 1749, during the same time period, it became customary to appoint society fellows to serve on government committees where science was concerned, something that still continues. The 18th century featured remedies to many of the early problems
28.
Philip Stanhope, 2nd Earl Stanhope
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Philip Stanhope, 2nd Earl Stanhope FRS was a British peer. The son of James Stanhope, 1st Earl Stanhope and Lucy Pitt and he was a Fellow of the Royal Society from 1735, and had a lifelong interest in mathematics. As a patron of various mathematicians, he came into contact with Thomas Bayes, on 25 July 1745, he married Grizel Hamilton, daughter of Charles Hamilton, Lord Binning. Sharon McGrayne The Theory That Would Not Die Ch 1
29.
Martin Folkes
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Martin Folkes, was an English antiquary, numismatist, mathematician, and astronomer. Folkes was born in Westminster on 29 October 1690, the eldest son of Martin Folkes, educated at Clare College, Cambridge, he so distinguished himself in mathematics that when only twenty-three years of age he was chosen a fellow of the Royal Society. He was elected one of the council in 1716, and in 1723 Sir Isaac Newton, president of the society, Folkes was a prominent Freemason, being appointed Deputy Grand Master of the Premier Grand Lodge of England during the year 1724-1725. In 1733 he set out on a tour through Italy, in the course of which he composed his Dissertations on the weights, in 1745 he printed the latter with another on the history of silver coinage. He also contributed both to the Society of Antiquaries and to the Royal Society other papers, chiefly on Roman antiquities, in 1739 he was elected one of the founding vice-presidents of Londons charitable Foundling Hospital for abandoned children, a position he maintained until 1747. Folkes was married in 1714 to Lucretia Bradshaw, an actress who had appeared at the Haymarket and his portrait was painted and etched by William Hogarth. Folkes was a noted atheist, and abhorred racial prejudice, some of his public statements have been interpreted as evidence of a Darwinian viewpoint. For Sir John Hills attack on Folkes, see Isaac DIsraeli, Calamities and Quarrels of Authors and this article incorporates text from a publication now in the public domain, Chisholm, Hugh, ed. article name needed. Works by or about Martin Folkes in libraries
30.
James Burrow
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Sir James Burrow PRS FSA, was a Legal Reporter at Inner Temple, London, and was Vice President and twice briefly President of the Royal Society. He was elected a Fellow of the Royal Society on 7 April 1737 and he served as a member of the Royal Society Council from 1752 until 1782, initially as a Vice President from 1752, and then as a Council member. He twice served briefly as a President of the Royal Society, from October to November 1768 following the death of The Earl of Morton, as a legal reporter, he wrote and published reports of the decisions of significant cases of English legal system. Quoted in His work is cited in law courses. James Burrow,1732, The Decisions of Kings Bench upon Settlement Cases from the Death of Lord Raymond, serious Reflections on the Present State of Domestic and Foreign Affairs. Together with some remarks on lotteries, etc. A few Anecdotes and Observations relating to Oliver Cromwell and his family, serving to rectify several errors concerning him, padopoli in his Historia Gymnasii Patavini. De usu et ratione interpungendi, an essay on the use of pointing, reports of Cases Argued and Adjudged in the Court of Kings Bench, During the Time Lord Mansfield Presided in That Court, from Michaelmas Term,30 Geo. 1756, to Easter Term,12 Geo, Record of Election Certificate, reference EC/1737/02, from the Royal Society Archive Catalogue, accessed via 17 December 2005 Record of James Burrow in the Royal Society Fellows Catalogue. Oxford Dictionary of National Biography, Online ed
31.
Google Books
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Books are provided either by publishers and authors, through the Google Books Partner Program, or by Googles library partners, through the Library Project. Additionally, Google has partnered with a number of publishers to digitize their archives. The Publisher Program was first known as Google Print when it was introduced at the Frankfurt Book Fair in October 2004, the Google Books Library Project, which scans works in the collections of library partners and adds them to the digital inventory, was announced in December 2004. But it has also criticized for potential copyright violations. As of October 2015, the number of scanned book titles was over 25 million, Google estimated in 2010 that there were about 130 million distinct titles in the world, and stated that it intended to scan all of them. Results from Google Books show up in both the universal Google Search as well as in the dedicated Google Books search website, if Google believes the book is still under copyright, a user sees snippets of text around the queried search terms. All instances of the terms in the book text appear with a yellow highlight. The four access levels used on Google Books are, Full view, Books in the domain are available for full view. In-print books acquired through the Partner Program are also available for full view if the publisher has given permission, usually, the publisher can set the percentage of the book available for preview. Users are restricted from copying, downloading or printing book previews, a watermark reading Copyrighted material appears at the bottom of pages. All books acquired through the Partner Program are available for preview and this could be because Google cannot identify the owner or the owner declined permission. If a search term appears many times in a book, Google displays no more than three snippets, thus preventing the user from viewing too much of the book. Also, Google does not display any snippets for certain reference books, such as dictionaries, Google maintains that no permission is required under copyright law to display the snippet view. No preview, Google also displays search results for books that have not been digitized, in effect, this is similar to an online library card catalog. Google also stated that it would not scan any in-copyright books between August and 1 November 2005, to provide the owners with the opportunity to decide which books to exclude from the Project. It can let Google scan the book under the Library Project and it can opt out of the Library Project, in which case Google will not scan the book. If the book has already been scanned, Google will reset its access level as No preview and this information is collated through automated methods, and sometimes data from third-party sources is used. This information provides an insight into the book, particularly useful when only a view is available
32.
Dictionary of National Biography
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The Dictionary of National Biography is a standard work of reference on notable figures from British history, published from 1885. The updated Oxford Dictionary of National Biography was published on 23 September 2004 in 60 volumes and he approached Leslie Stephen, then editor of the Cornhill Magazine, owned by Smith, to become editor. Stephen persuaded Smith that the work should focus on subjects from the UK and its present, an early working title was the Biographia Britannica, the name of an earlier eighteenth-century reference work. The first volume of the Dictionary of National Biography appeared on 1 January 1885, in May 1891 Leslie Stephen resigned and Sidney Lee, Stephens assistant editor from the beginning of the project, succeeded him as editor. While much of the dictionary was written in-house, the DNB also relied on external contributors, by 1900, more than 700 individuals had contributed to the work. Successive volumes appeared quarterly with complete punctuality until midsummer 1900, when the series closed with volume 63, the year of publication, the editor and the range of names in each volume is given below. The supplements brought the work up to the death of Queen Victoria on 22 January 1901. The dictionary was transferred from its original publishers, Smith, Elder & Co. to Oxford University Press in 1917, until 1996, Oxford University Press continued to add further supplements featuring articles on subjects who had died during the twentieth century. The supplements published between 1912 and 1996 added about 6,000 lives of people who died in the century to the 29,120 in the 63 volumes of the original DNB. In 1993 a volume containing missing biographies was published and this had an additional 1,000 lives, selected from over 100,000 suggestions. Consequently, the dictionary was becoming less and less useful as a reference work, in 1966, the University of London published a volume of corrections, cumulated from the Bulletin of the Institute of Historical Research. There were various versions of the Concise Dictionary of National Biography, the last edition, in three volumes, covered everyone who died before 1986. In the early 1990s Oxford University Press committed itself to overhauling the DNB, the new dictionary would cover British history, broadly defined, up to 31 December 2000. The research project was conceived as a one, with in-house staff co-ordinating the work of nearly 10,000 contributors internationally. Following Matthews death in October 1999, he was succeeded as editor by another Oxford historian, Professor Brian Harrison, in January 2000. The new dictionary, now known as the Oxford Dictionary of National Biography, was published on 23 September 2004 in 60 volumes in print at a price of £7500, most UK holders of a current library card can access it online free of charge. In subsequent years, the print edition has been able to be obtained new for a lower price. At publication, the 2004 edition had 50,113 biographical articles covering 54,922 lives, a small permanent staff remain in Oxford to update and extend the coverage of the online edition
33.
Harvard University Press
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Harvard University Press is a publishing house established on January 13,1913, as a division of Harvard University, and focused on academic publishing. In 2005, it published 220 new titles and it is a member of the Association of American University Presses. Its current director is William P. Sisler and the editor-in-chief is Susan Wallace Boehmer, the press maintains offices in Cambridge, Massachusetts, near Harvard Square, in New York City, and in London, England. The Display Room in Harvard Square, dedicated to selling HUP publications, HUP owns the Belknap Press imprint, which it inaugurated in May 1954 with the publication of the Harvard Guide to American History. The John Harvard Library book series is published under the Belknap imprint, Harvard University Press distributes the Loeb Classical Library and is the publisher of the I Tatti Renaissance Library, the Dumbarton Oaks Medieval Library, and the Murty Classical Library of India. It is distinct from Harvard Business Press, which is part of Harvard Business Publishing, category, Harvard University Press books Hall, Max. Official website Blog of Harvard University Press
34.
International Standard Book Number
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The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, however, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay. The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, the United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978, an SBN may be converted to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces. Separating the parts of a 10-digit ISBN is also done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker
"Bayes, Joshua". Dictionary of National Biography. London: Smith, Elder & Co. 1885–1900.
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