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What is a generator function in Python? Here's a regular function: def negate_all(iterable): print("Start") negatives = for n in iterable: print("Negating", n) negatives.append(-n) print("End") return negatives What do you think we'll see when we call this function? What do you think we'll get back? >>> negatives = negate_all([2, 1, 3]) When we call this function, we see a number of things printed out: >>> negatives = negate_all([2, 1, 3]) Start Negating 2 Negating 1 Negating 3 End And we get back the return value of this function: >>> negatives [-2, -1, -3] This function is very similar to a regular function: def negate_all(iterable): print("Start") for n in iterable: print("Negating", n) yield -n print("End") But it's not a normal Python function: it's a generator function. We can only tell it's a generator function by the presence of a yield statement turns a regular function into a generator function. What do you think we'll see when we call this generator function? What do you think it'll give us back? What will it return to us? >>> negatives = negate_all([2, 1, 3]) When we call this generator function, we don't see anything printed out. And the thing we get back is a generator object: >>> negatives = negate_all([2, 1, 3]) >>> negatives <generator object negate_all at 0x7f5d85fd49e0> One thing we can do with a generator object is pass it to the built-in Passing a generator object to next will start running the generator function that created it: >>> negatives = negate_all([2, 1, 3]) >>> x = next(negatives) Start Negating 2 The generator function printed out Start and then Negating 2, and then it stopped. It stopped because it hit a -2 to us: >>> x -2 If we call next again (passing in the same generator object) we'll see Negating 1 printed out: >>> x = next(negatives) Negating 1 And the generator yielded >>> x -1 Each time we pass this generator object to next, the generator function that created it will start up again from where it left off. Generator objects put themselves on pause to yield an item. Then when you ask them for another item, they'll start running their generator function again until they hit another The next item we get is >>> x = next(negatives) Negating 3 >>> x -3 But then if we pass this generator object to next again, it will hit the end of the function, which will raise a >>> x = next(negatives) End Traceback (most recent call last): File "<stdin>", line 1, in <module> StopIteration It's a little bit unusual to see a generator object passed to the built-in Normally, we loop over generator objects the same way we loop over any other iterable, with a >>> negatives = negate_all([2, 1, 3]) >>> for n in negatives: ... print("Got", n) ... When we loop over this generator object, we'll see that our generator function is being called in-between our for loop being run: >>> negatives = negate_all([2, 1, 3]) >>> for n in negatives: ... print("Got", n) ... Start Negating 2 Got -2 Negating 1 Got -1 Negating 3 Got -3 End So when we ask for the first item, it starts running our generator function. Start Negating 2 Then our generator function puts itself on pause to yield that first item to our for loop, which then prints out Got -2 (the first item is for loop asks the generator for another item, which causes the generator function to start running again (unpausing itself). The generator function then prints out Negating 1, and yields -1 to our for loop, which prints out Negating 1 Got -1 And the same thing happens with Our generator function prints out Negating 3, and then we move back to our for loop body, which prints out Negating 3 Got -3 Then finally, when our generator function returns, our for loop ends as well: Once we've consumed all the items in a generator object, we say that it's been exhausted (meaning it doesn't have anything left in it). So if we loop over our generator object a second time, we'll see that it's empty now: >>> for n in negatives: ... print("Got", n) ... >>> A generator function is a function with one or more yield statements in it. Unlike regular functions, generator functions return generator objects. Meaning, when you call a generator function, it doesn't run the function. Instead, it gives you back a generator object. If you loop over that generator object, it will run the function until a yield statement is reached. At that point the generator object will put itself on pause, and yield the next item. This process will continue over and over until you've consumed all the items within the generator. Need to fill-in gaps in your Python skills? I send regular emails designed to do just that. Sign up for my Python tips emails and I'll share my favorite Python insights with you every couple weeks. Generator functions look like regular functions but they have one or more yield statements within them. Unlike regular functions, the code within a generator function isn't run when you call it! Calling a generator function returns a generator object, which is a lazy iterable. Need to fill-in gaps in your Python skills? I send weekly emails designed to do just that.
In scientific research, it is required to calculate predicted values. Because in market research or data science, prediction is usually more significant. Therefore, the INTERCEPT function is more important here. The INTERCEPT function in Excel is a built-in function that is categorized as a Statistical Function. Using existing x- and y-values, the INTERCEPT function calculates the location at which a line will intersect the y-axis. By plotting a best-fit regression line through known x- and y-values determines the intercept point. In this tutorial, we will discuss the INTERCEPT function in Microsoft Excel along with its formula syntax and usage. In addition, we will plot a regression line using the INTERCEPT function to make it visualized. Download Practice Workbook Download this practice workbook to exercise while you are reading this article. Introduction to the INTERCEPT Function in Excel Based on known x and y values, the INTERCEPT function in Excel determines the location where a regression line will intersect the y-axis. \|Known_y’s\|\|Required\|\|The dependent set of observations or data.\| \|Known_x’s\|\|Required\|\|The independent set of observations or data.\| The INTERCEPT function gives you a number. It will return the #N/A error if the known y values and known x values arguments have different numbers of items. In a regression model, interpreting the intercept isn’t always as simple as it appears. When all X=0, the intercept is the predicted mean value of Y. So, let’s start with a single predictor, X, in a regression equation. If X equals 0 on occasion, the intercept is simply Y’s expected mean value at that point. That’s significant. The intercept has no intrinsic value if X never equals 0. Both of these instances occur frequently in real-world data. The Intercept Function uses the following equation to calculate the intercept of the linear regression line through a set of given points: where the slope, b is given by the equation: and the values of x and y are the sample means (the averages) of the known x- and y-values. Read More: How to calculate Average, Median, & Mode in Excel - How to Use MODE Function in Excel (4 Examples) - Use VAR Function in Excel (4 Examples) - How to Use PROB Function in Excel (3 Examples) - Use Excel STDEV Function (3 Easy Examples) - How to Use Excel GROWTH Function (4 Easy Methods) INTERCEPT Function: Basic Use and Regression Analysis In this section, we will demonstrate the basic use of the INTERCEPT function and Regression analysis Basic Use of the INTERCEPT Function in Excel Consider the following scenario: You have a data set of some independent values (X) and some dependent values of (Y). But there is no linear relationship between X and Y like a straight line. Therefore, we will use the INTERCEPT function to calculate the value of a dependent variable when the independent variable is zero (0). The following formula is used here, - Type the INTERCEPT function in the cell C14 - Select the range B5:B13 for the dependent variable known_ys. - Select the range C5:C13 for Independent variable known_xs. - Press Enter to see the Result. In the spreadsheet below, we will find the point where the linear regression line through the known x’s and known y’s crosses the y-axis. Generally, the objective of a regression model is to figure out how predictors and responses are related. If this is the case, and X is never equal to 0, the intercept is of no use. It doesn’t tell you anything about X and Y’s relationship. Consider centering X when X never equals 0 but you want a meaningful intercept. The intercept now has relevance if you rescale X so that the mean or any other relevant value = 0 (simply remove a constant from X). It’s the average value of Y at the specified X value. From the regression line, we have found that, the intercept point from the regression analysis is relatable to the intercept point found from using the INTERCEPT function. Read More: How to Use AVERAGE Function in Excel (5 Examples) ✍ Things to Remember ✎ Numbers or names, arrays, or references containing numbers should be used as parameters. ✎ Text, logical values, and empty cells in an array or reference argument are ignored; however, cells with the value zero are included. ✎ INTERCEPT returns the #N/A error value if known ys and known xs have different numbers of data points or no data points. To conclude, I hope this article has given you some useful information about how to apply the INTERCEPT function in Excel. You should learn at first and then apply all of these procedures. Take a look at the practice workbook and put these skills to the test. Your valuable support keep motivating us to make tutorials like this If you have any questions – Feel free to ask us. Also, feel free to leave comments in the section below. We, The ExcelDemy Team, are always responsive to your queries. Stay with us & keep learning.
This page uses content from Wikipedia and is licensed under CC BY-SA. Catholic Church in the 20th century The Roman Catholic Church in the 20th century had to respond to the challenge of increasing secularization of Western society and persecution resulting from great social unrest and revolutions in several countries. It instituted many reforms, particularly in the 1970s under the Vatican II Council, in order to modernize practices and positions. In this period, Catholic missionaries in the Far East worked to improve education and health care, while evangelizing peoples and attracting numerous followers in China, Taiwan, Korea, and Japan. In Rerum novarum, Leo set out the Catholic Church's response to the social instability and labor conflict that had arisen in the wake of industrialization and had led to the rise of socialism. The Pope taught that the role of the State is to promote social justice through the protection of rights, while the Church must speak out on social issues in order to teach correct social principles and ensure class harmony. He restated the Church's long-standing teaching regarding the crucial importance of private property rights, but recognised, in one of the best-known passages of the encyclical, that the free operation of market forces must be tempered by moral considerations: Let the working man and the employer make free agreements, and in particular let them agree freely as to the wages; nevertheless, there underlies a dictate of natural justice more imperious and ancient than any bargain between man and man, namely, that wages ought not to be insufficient to support a frugal and well-behaved wage-earner. If through necessity or fear of a worse evil the workman accept harder conditions because an employer or contractor will afford him no better, he is made the victim of force and injustice. Rerum novarum is remarkable for its vivid depiction of the plight of the late 19th-century urban poor and for its condemnation of unrestricted capitalism. Among the remedies it prescribed were the formation of trade unions and the introduction of collective bargaining, particularly as an alternative to state intervention. Rerum novarum also recognized that the poor have a special status in consideration of social issues: the modern Catholic principle of the "preferential option for the poor" and the notion that God is on the side of the poor found their first expression in this document. Forty years after Rerum novarum, and more than a year into the Great Depression, Pope Pius XI issued Quadragesimo anno, subtitled "On Reconstruction of the Social Order". Released on 15 May 1931, this encyclical expanded on Rerum novarum, noting the positive effect of the earlier document but pointing out that the world had changed significantly since Pope Leo's time. Unlike Leo, who addressed mainly the condition of workers, Pius XI concentrated on the ethical implications of the social and economic order. He called for the reconstruction of the social order based on the principle of solidarity and subsidiarity. He also noted major dangers for human freedom and dignity, arising from both unrestrained capitalism and totalitarian communism. Pius XI reiterated Leo's defence of private property rights and collective bargaining, and repeated his contention that blind economic forces cannot create a just society on their own: Just as the unity of human society cannot be founded on an opposition of classes, so also the right ordering of economic life cannot be left to a free competition of forces. For from this source, as from a poisoned spring, have originated and spread all the errors of individualist economic teaching. Destroying through forgetfulness or ignorance the social and moral character of economic life, it held that economic life must be considered and treated as altogether free from and independent of public authority, because in the market, i.e., in the free struggle of competitors, it would have a principle of self direction which governs it much more perfectly than would the intervention of any created intellect. But free competition, while justified and certainly useful provided it is kept within certain limits, clearly cannot direct economic life...' Quadragesimo Anno also supported state intervention to mediate labor-management conflicts (a reference to the economic system which Mussolini was attempting to establish in Italy at the time), and introduced the concept of subsidiarity into Catholic thought. Prior to Quadragesimo anno, some Catholics had wondered whether Leo XIII's condemnation of radical left-wing politics in Rerum novarum extended only to outright communism or whether it included milder forms of socialism as well. Pius made it clear that non-communistic Socialism was included in the condemnation. The Catholic Church defined a distinctive position for itself between free-marketcapitalism on the right and statist socialism on the left. The social teachings of Pope Pius XII repeat these teachings, and apply them in greater detail not only to workers and owners of capital, but also to other professions, such as politicians, educators, housewives, farmersbookkeepers, international organizations, and all aspects of life including the military. Going beyond Pius XI, he also defined social teachings in the areas of medicine, psychology, sport, TV, science, law and education. There is virtually no social issue, which Pius XII did not address and relate to the Christian faith. He was called "the Pope of Technology," for his willingness and ability to examine the social implications of technological advances. The dominant concern was the continued rights and dignity of the individual. With the beginning of the space age at the end of his pontificate, Pius XII explored the social implications of space exploration and satellites on the social fabric of humanity, asking for a new sense of community and solidarity in light of existing papal teachings on subsidiarity. The Catholic Church exercised a prominent role in shaping America's labor movement. In 1933, two American Catholics, Dorothy Day and Peter Maurin, founded a new Catholic peace group, the Catholic Worker that would embody their ideals of pacifism, commitment to the poor, and to fundamental change in American society. They published a newspaper of the same name for years. In Latin America, a succession of anti-clerical regimes came to power beginning in the 1830s. In the 1920s and 1930s, the Catholic Church was subjected to unprecedented persecution in Mexico, as well as in Europe in Spain and the Soviet Union. Pope Pius XI called this the "terrible triangle". The "harsh persecution short of total annihilation of the clergy, monks, and nuns and other people associated with the Church", began in 1918 and continued well into the 1930s. The Civil War in Spain started in 1936, during which thousands of churches were destroyed, thirteen bishops and some 6,832 clergy and religious Spaniards were assassinated. In Mexico, the Calles Law eventually led to the "worst guerilla war in Latin American History", the Cristero War. Between 1926 and 1934, over 3,000 priests were exiled or assassinated. In an effort to prove that "God would not defend the Church", Calles ordered Church desecrations in which services were mocked, nuns were raped, and captured priests were shot. Calles was eventually deposed. Despite the persecution, the Church in Mexico continued to grow. A 2000 census reported that 88 percent of Mexicans identify as Catholic. During the Spanish Civil War, Spanish republicans and anarchists targeted priests and nuns as symbols of conservatism, murdering large numbers of them. Confiscation of Church properties and restrictions on people's religious freedoms have generally accompanied secularist and Marxist-leaning governmental reforms. Worried by the persecution of Christians in the Soviet Union, Pius XI mandated Berlin nuncio Eugenio Pacelli to work secretly on diplomatic arrangements between the Vatican and the Soviet Union. Pacelli negotiated food shipments for Russia, and met with Soviet representatives including Foreign Minister Georgi Chicherin, who rejected any kind of religious education, or the ordination of priests and bishops, but offered agreements without the points vital to the Vatican. Despite Vatican pessimism and a lack of visible progress, Pacelli continued the secret negotiations. Pius XI ordered them to be discontinued in 1927, because they generated no results and he believed they would be dangerous to the Church's standing, if made public. The harsh persecution continued well into the 1930s. The Soviet government executed and exiled many clerics, monks and laymen, confiscating Church implements "for victims of famine", and closing many churches. Yet according to an official report based on the census of 1936, some 55% of Soviet citizens identified themselves openly as religious, while others possibly concealed their belief. In other countries Following the Soviet doctrine regarding the exercise of religion, postwar Communist governments in Eastern Europe severely restricted religious freedoms. Even though some clerics collaborated with the Communist regimes during their decades of power, from the late 1980s the Church's resistance and the leadership of Pope John Paul II have been credited with hastening the downfall in 1991 of communist governments across Europe. The rise to power of the Communists in China of 1949 led to the expulsion of all foreign missionaries, "often after cruel and farcical 'public trials'." In an effort to further isolate Chinese Catholics, the new government created the Patriotic Church whose unilaterally appointed bishops were initially rejected by Rome but subsequently many were accepted. The Cultural Revolution of the 1960s encouraged gangs of teenagers to eliminate all religious establishments and convert their occupants into labourers. When Chinese churches eventually reopened, they remained under the control of the Communist party's Patriotic Church, and many Catholic pastors and priests continued to be sent to prison for refusing to renounce allegiance to Rome. In 1954, under the regime of General Juan Perón, Argentina saw extensive destruction of churches, denunciations of clergy and confiscation of Catholic schools as Perón attempted to extend state control over national institutions. Cuba, under atheist Fidel Castro, succeeded in reducing the Church's ability to work by deporting the archbishop and 150 Spanish priests, discriminating against Catholics in public life and education and refusing to accept them as members of the Communist Party. The subsequent flight of 300,000 people from the island also helped to diminish the Church there. Response to authoritarianism Authoritarianism or Fascism describes certain related political regimes in 20th-century Europe, especially the Nazi Germany of Hitler, the authoritarian Soviet Union, the Fascist Italy of Mussolini and the falangist Spain of Franco. In the 1937 encyclical Mit brennender Sorge, drafted by the future Pope Pius XII,Pope Pius XI warned Catholics that antisemitism is incompatible with Christianity. Read from the pulpits of all German Catholic churches, it described Hitler as an insane and arrogant prophet and was the first official denunciation of Nazism made by any major organization. Nazi persecution of the Church in Germany then began by "outright repression" and "staged prosecutions of monks for homosexuality, with the maximum of publicity." When Dutch bishops protested against deportation of Jews in the Netherlands, the Nazi's responded with even more severe measures. Despite a number of condemnations of atrocities committed during World War II, Pope Pius XII has been criticized for not having explicitly spoken out against the Holocaust. Although he never defended himself against such criticism, there is evidence that he chose to keep his public pronouncements circumspect while acting covertly to assist Jews seeking refuge from the Holocaust. Although Pius XII was exhorted by the British government and the Polish government-in-exile to condemn Nazi atrocities directly, he declined to do so out of concern that such pronouncements would only instigate further persecution by the Nazis. These sentiments were based on opinions expressed to him by bishops in Germany and Poland. When Dutch bishops protested against the wartime deportation of Jews, the Nazis responded by increasing deportations rounding up 92 converts including Edith Stein who were then deported and murdered. "The brutality of the retaliation made an enormous impression on Pius XII." In Poland, the Nazis murdered over 2,500 monks and priests and even more were imprisoned. In the Soviet Union, an even more severe persecution occurred. After the war, Pius XII's efforts to protect their people were recognised by prominent Jews including Albert Einstein and Rabbi Isaac Herzog. However, the Church has also been accused by some of encouraging centuries of antisemitism and Pius himself of not doing enough to stop Nazi atrocities. Prominent members of the Jewish community have contradicted these criticisms. The Israeli historian Pinchas Lapide interviewed war survivors and concluded that Pius XII "was instrumental in saving at least 700,000, but probably as many as 860,000 Jews from certain death at Nazi hands". Some historians dispute this estimate while others consider Pinchas Lapide's work to be "the definitive work by a Jewish scholar" on the holocaust. Even so, in 2000 Pope John Paul II on behalf of all people, apologized to Jews by inserting a prayer at the Western Wall that read "We're deeply saddened by the behavior of those in the course of history who have caused the children of God to suffer, and asking your forgiveness, we wish to commit ourselves to genuine brotherhood with the people of the Covenant." This papal apology, one of many issued by Pope John Paul II for past human and Church failings throughout history, was especially significant because John Paul II emphasized Church guilt for, and the Second Vatican Council's condemnation of, anti-Semitism. The papal letter We Remember: A Reflection on the Shoah, urged Catholics to repent "of past errors and infidelities" and "renew the awareness of the Hebrew roots of their faith." In Poland, the Nazis murdered over 2500 monks and priests while even more were sent to concentration camps. The Priester-Block (priests barracks) in Dachau concentration camp lists 2600 Roman Catholic priests. Stalin staged an even more severe persecution at almost the same time. After World War II historians such as David Kertzer accused the Church of encouraging centuries of anti-Semitism, and Pope Pius XII of not doing enough to stop Nazi atrocities. Regarding the matter, historian Derek Holmes wrote, "There is no doubt that the Catholic districts, resisted the lure of National Socialism Nazism far better than the Protestant ones."Pope Pius XI declared - Mit brennender Sorge - that Fascist governments had hidden "pagan intentions" and expressed the irreconcilability of the Catholic position and Totalitarian Fascist State Worship, which placed the nation above God and fundamental human rights and dignity. His declaration that "Spiritually, [Christians] are all Semites" prompted the Nazis to give him the title "Chief Rabbi of the Christian World." Catholic priests were executed in concentration camps alongside Jews; for example, 2,600 Catholic Priests were imprisoned in Dachau, and 2,000 of them were executed. A further 2,700 Polish priests were executed (a quarter of all Polish priests), and 5,350 Polish nuns were either displaced, imprisoned, or executed. Many Catholic laypeople and clergy played notable roles in sheltering Jews during the Holocaust, including Pope Pius XII (1876–1958). The head rabbi of Rome became a Catholic in 1945 and, in honour of the actions the Pope undertook to save Jewish lives, he took the name Eugenio (the pope's first name). A former Israeli consul in Italy claimed: "The Catholic Church saved more Jewish lives during the war than all the other churches, religious institutions, and rescue organisations put together." South America, historically Catholic, has experienced a large Evangelical and Pentecostal infusion in the 20th century due to the influx of Christian missionaries from abroad. For example: Brazil, South America's largest country, is the largest Catholic country in the world, and at the same time is the largest Evangelical country in the world (based on population). Some of the largest Christian congregations in the world are found in Brazil. In 1939, Pope Pius XII, within weeks of his coronation, reverted the 250-year-old Vatican policy and permitted Catholics to practice Confucianism. The Church began to flourish again with twenty new arch-dioceses, seventy-nine dioceses and thirty-eight apostolic prefects, but only until 1949, when the Communist revolution took over the country. The Catholic Church engaged in a comprehensive process of reform following the Second Vatican Council (1962–65). Intended as a continuation of Vatican I, under Pope John XXIII the council developed into an engine of modernisation. It was tasked with making the historical teachings of the Church clear to a modern world, and made pronouncements on topics including the nature of the church, the mission of the laity and religious freedom. The council approved a revision of the liturgy and permitted the Latin liturgical rites to use vernacular languages as well as Latin during mass and other sacraments. Efforts by the Church to improve Christian unity became a priority. In addition to finding common ground on certain issues with Protestant churches, the Catholic Church has discussed the possibility of unity with the Eastern Orthodox Church. On 11 October 1962 Pope John XXIII opened the Second Vatican Council, the 21st ecumenical council of the Catholic Church. The council was "pastoral" in nature, emphasising and clarifying already defined dogma, revising liturgical practices, and providing guidance for articulating traditional Church teachings in contemporary times. The council is perhaps best known for its instructions that the Mass may be celebrated in the vernacular as well as in Latin. At the Second Vatican Council (1962–1965) the debate on papal primacy and authority re-emerged, and in the Dogmatic Constitution on the Church Lumen gentium, the Roman Catholic Church's teaching on the authority of the Pope, bishops and councils was further elaborated. Vatican II sought to correct the unbalanced ecclesiology left behind by Vatican I. The result is the body of teaching about the papacy and episcopacy contained in the Dogmatic Constitution on the Church, Lumen gentium. Vatican II reaffirmed everything Vatican I taught about papal primacy and infallibility, but it added important points about bishops. Bishops, it says, are not "vicars of the Roman Pontiff." Rather, in governing their local churches they are "vicars and legates of Christ". Together, they form a body, a "college," whose head is the pope. This episcopal college is responsible for the well-being of the Universal Church. Here in a nutshell are the basic elements of the Council's much-discussed communio ecclesiology, which affirms the importance of local churches and the doctrine of collegiality. In a key passage about collegiality, Vatican II teaches: "The order of bishops is the successor to the college of the apostles in their role as teachers and pastors, and in it the apostolic college is perpetuated. Together with their head, the Supreme Pontiff, and never apart from him, they have supreme and full authority over the Universal Church; but this power cannot be exercised without the agreement of the Roman Pontiff". Much of the present discussion of papal primacy is concerned with exploring the implications of this passage. Chapter 3 of the dogmatic constitution on the Church of Vatican Council I (Pastor aeternus) is the principal document of the Magisterium about the content and nature of the primatial power of the Roman Pontiff. Chapter 4 is a development and defining of one particular characteristic of this primatial power, namely the Pope's supreme teaching authority, i.e. when the Pope speaks ex cathedra he teaches the doctrine of the faith infallibly. Changes to old rites and ceremonies following Vatican II produced a variety of responses. Some stopped going to church, while others tried to preserve the old liturgy with the help of sympathetic priests. These formed the basis of today's Traditionalist Catholic groups, which believe that the reforms of Vatican II have gone too far. Liberal Catholics form another dissenting group who feel that the Vatican II reforms did not go far enough. The liberal views of theologians such as Hans Küng and Charles Curran, led to Church withdrawal of their authorization to teach as Catholics. According to Professor Thomas Bokenkotter, most Catholics "accepted the changes more or less gracefully." In 2007, Benedict XVI reinstated the old mass as an option, to be celebrated upon request by the faithful. A new Codex Juris Canonici - Canon Law called for by John XXIII, was promulgated by Pope John Paul II on 25 January 1983. It includes numerous reforms and alterations in Church law and Church discipline for the Latin Church. It replaced the 1917 version issued by Benedict XV. The Catholic Church initiated a comprehensive process of reform under Pope John XXIII. Intended as a continuation of the First Vatican Council, the Second Vatican Council (1962–1965), developed into an engine of modernisation, making pronouncements on religious freedom, the nature of the Church and the mission of the laity. The role of the bishops of the Church was brought into renewed prominence, especially when seen collectively, as a college that has succeeded to that of the Apostles in teaching and governing the Church. This college does not exist without its head, the successor of St. Peter. It also permitted the Latin liturgical rites to use vernacular languages as well as Latin during Mass and other sacraments.Christian unity became a greater priority. In addition to finding more common ground with Protestant Churches, the Catholic Church has reopened discussions regarding the possibility of unity with the Eastern Orthodox churches. In the 1960s, growing social awareness and politicization in the Church in Latin America gave birth to liberation theology. The Peruvian priest, Gustavo Gutiérrez, became a primary theorist and, in 1979, the bishops' conference in Mexico officially declared the Latin American Church's "preferential option for the poor". Archbishop Óscar Romero, a supporter of the movement, became the region's most famous contemporary martyr in 1980, when he was murdered by forces allied with the government of El Salvador while saying Mass. Both Pope John Paul II and Pope Benedict XVI (as Cardinal Ratzinger) denounced the movement. The Brazilian theologian-priest Leonardo Boff was twice ordered to cease publishing and teaching. Pope John Paul II was criticized for his severity in dealing with proponents of the movement, but he maintained that the Church, in its efforts to champion the poor, should not do so by advocating violence or engaging in partisan politics. The movement is still alive in Latin America today, although the Church now faces the challenge of Pentecostal revival in much of the region. Efforts to lead the Church to consider the ordination of women led Pope John Paul II to issue two documents to explain Church teaching. Mulieris Dignitatem was issued in 1988 to clarify women's equally important and complementary role in the work of the Church. Then in 1994, Ordinatio Sacerdotalis explained that the Church extends ordination only to men in order to follow the example of Jesus, who chose only men for this specific duty. The sexual revolution of the 1960s precipitated Pope Paul VI's 1968 encyclical Humanae vitae (On Human Life), which rejected the use of contraception, including sterilization, claiming these work against the intimate relationship and moral order of husband and wife by directly opposing God's will. It approved Natural Family Planning as a legitimate means to limit family size.Abortion was condemned by the Church as early as the 1st century, again in the 14th century and again in 1995 with Pope John Paul II's encyclical Evangelium vitae (Gospel of Life). This encyclical condemned the "culture of death" which the pope often used to describe the societal embrace of contraception, abortion, euthanasia, suicide, capital punishment, and genocide. The Church's rejection of the use of condoms has provoked criticism, especially with respect to countries where the incidence of AIDS and HIV has reached epidemic proportions. The Church maintains that in countries like Kenya and Uganda, where behavioral changes are encouraged alongside condom use, greater progress in controlling the disease has been made than in those countries solely promoting condoms.Feminists disagreed with these and other Church teachings and worked together with a coalition of American nuns to lead the Church to consider the ordination of women. They stated that many of the major Church documents were supposedly full of anti-female prejudice and a number of studies were conducted to discover how this supposed prejudice developed when it was deemed contrary to the openness of Jesus. These events led Pope John Paul II to issue the 1988 encyclical Mulieris dignitatem (On the Dignity of Women), which declared that women had a different, yet equally important role in the Church. In 1994 the encyclical Ordinatio sacerdotalis (On Ordination to the Priesthood) further explained that the Church follows the example of Jesus, who chose only men for the specific priestly duty. Modern response to Protestantism Well into the 20th century, Catholics—even if no longer resorting to persecution—still defined Protestants as heretics. Thus, Hilaire Belloc - in his time one of the most conspicuous speakers for Catholicism in Britain - was outspoken about the "Protestant heresy". He also defined Islam as "A Christian heresy", on the grounds that Muslims accept many of the tenets of Christianity but deny the godhood of Jesus (see Hilaire Belloc#On Islam). In the second half of the century - and especially in the wake of Vatican II - the Catholic Church, in the spirit of ecumenism, no longer referred to Protestantism as a heresy, even if the teachings of Protestantism are heretical from a Catholic perspective. Modern usage favors referring to Protestants as "separated brethren" rather than "heretics". The latter term is occasionally applied to Catholics who abandon their Church to join a Protestant denomination. Many Catholics consider most Protestants to be material rather than formal heretics, and thus non-culpable. Among the doctrines of Protestantism that the Catholic Church considers heretical are the beliefs that: the Bible is the only source and rule of faith ("sola scriptura"), faith alone can lead to salvation ("sola fide"), and no sacramental, ministerial priesthood is attained by ordination, but there is a universal priesthood of all believers. Ecumenism broadly refers to movements between Christian groups to establish a degree of unity through dialogue. "Ecumenism" is derived from Greekοἰκουμένη (oikoumene), which means "the inhabited world", but more figuratively something like "universal oneness." The movement can be distinguished into Catholic and Protestant movements, with the latter characterised by a redefined ecclesiology of "denominationalism" (which the Catholic Church, among others, rejects). Some of the most difficult questions in relations with the ancient Eastern Churches concern some doctrine (i.e. Filioque, Scholasticism, functional purposes of asceticism, the essence of God, Hesychasm, Fourth Crusade, establishment of the Latin Empire, Uniatism to note but a few) as well as practical matters, such as the concrete exercise of the claim to papal primacy and how to ensure that ecclesiastical union would not result in absorption of the smaller Churches by the Latin component of the much larger Catholic Church (the most numerous single religious denomination in the world). Both parties wanted to avoid the stifling or abandonment of the other churches' rich theological, liturgical and cultural heritage. In June 1995, Patriarch Bartholomew I, who was elected as the 273rd Ecumenical Patriarch of Constantinople in October 1991, visited the Vatican for the first time, when he joined in the historic inter-religious day of prayer for peace at Assisi. Pope John Paul II and the Patriarch explicitly stated their mutual "desire to relegate the excommunications of the past to oblivion and to set out on the way to re-establishing full communion." In May 1999, John Paul II traveled to Romania: the first pope since the Great Schism to visit an Eastern Orthodox country. Upon greeting John Paul II, the Romanian Patriarch Teoctist stated: "The second millennium of Christian history began with a painful wounding of the unity of the Church; the end of this millennium has seen a real commitment to restoring Christian unity." Pope John Paul II visited other strongly Orthodox areas such as Ukraine, despite lack of welcome at times. He said that healing the divisions between Western and Eastern Christianity was one of his fondest wishes. 1901 - Nazarene John Diaz goes to Cape Verde Islands; Maude Cary sails for Morocco; Oriental Missionary Society founded by Charles Cowman (his wife is the compiler of popular devotional book Streams in the Desert); Missionary James Chalmers killed and eaten by cannibals in Papua New Guinea 1907 - Massive revival meetings in Korea; Harmon Schmelzenbach sails for Africa; Presbyterians and Methodists open Union Theological Seminary in Manila, Philippines; Bolivian Indian Mission founded by George Allen 1914–1918 World War I numerous missionaries in Africa and Asia in British, French, German and Belgian colonies are expelled or detained for the duration of the war, if their nation was at war with the colonial authority 1916 - Rhenish missionaries are forced to leave Ondjiva in southern Angola under pressure from the Portuguese authorities and Chief Mandume of the Kwanyama. By then, four congregations existed with a confessing membership of 800. 1926–1929 Cristero War in Mexico, the Constitution of 1917 brought persecution of Christian practices and anti-clerical laws - approximately 4,000 Catholic Priests were expelled, assassinated or executed 1927 - East African revival movement (Balokole) emerges in Rwanda and moves across several other countries 1928 - Cuba Bible Institute (West Indies Mission) opens; Jerusalem Conference of International Missionary Council; foundation of Borneo Evangelical Mission by Hudson Southwell, Frank Davidson and Carey Tolley. 1936 - With the outbreak of civil war in Spain, missionaries are forced to leave that country. 1937 - After expulsion of missionaries from Ethiopia by Italian invaders, widespread revival erupts among Protestant (SIM) churches in south; Child Evangelism Fellowship (CEF ) founded by Jesse Irvin Overholzer 1948 - Alfredo del Rosso merges his Italian Holiness Mission with the Church of the Nazarene, thus opening Nazarene work on the European continent; Southern Baptist Convention adopts program calling for the tripling of the number of missionaries. 1951 The Last Temptation a fictional account of the life of Jesus written by Nikos Kazantzakis, wherein Christ's divinity is juxtaposed with his humanity, is published, and promptly banned in many countries. 1960 - Kenneth Strachan starts Evangelism-in-Depth in Central America; 18,000 people in Morocco reply to newspaper ad by Gospel Missionary Union offering free correspondence course on Christianity;Loren Cunningham founds Youth with a Mission; The Asia Evangelistic Fellowship (AEF), one of the largest Asian indigenous missionary organisations, is launched in Singapore by G. D. James 1961 - International Christian radio stations now number 30 1962–1965 Catholic Second Vatican Council, announced by Pope John XXIII in 1959, produced 16 documents which became official Roman Catholic teaching after approval by the Pope, purpose to renew "ourselves and the flocks committed to us" 1963 - Theological Education by Extension movement launched in Guatemala by Ralph Winter and James Emery 1963 campaign by Madalyn Murray O'Hair results in U.S. Supreme Court ruling prohibiting reading of Bible in public schools 1964 - In separate incidents, rebels in the Congo kill missionaries Paul Carlson and Irene Ferrel as well as brutalizing missionary doctor Helen Roseveare; Carlson is featured on 4 December TIME magazine cover; Hans von Staden of the Dorothea Mission proposes to Patrick Johnstone that he write the book now titled Operation World 1968 Zeitoun, Egypt, a bright image of the Virgin Mary as Our Lady of Zeitoun was seen over the Coptic Orthodox Church of Saint Demiana for over a 3-year period. Over six million Egyptians and foreigners saw the image, including Copts, Eastern Orthodox, Roman Catholic, Protestants, Muslims, Jews and people of no particular faith. 1983 - Missionary Athletes International, a global soccer ministry, founded by Tim Conrad 1984 - Founding of The Mission Society for United Methodists, a voluntary missionary sending agency within the United Methodist Church; rebranded in 2006 to The Mission Society; Founding of STEM (Short Term Evangelical Mission teams) ministry by Roger Petersen signals the rising importance of Short-term missions groups 1985 - Howard Foltz founds Accelerating International Mission Strategies (AIMS) 1999 - Trans World Radio goes on the air from Grigoriopol (Moldova) using a 1-million-watt AM transmitter; Veteran Australian missionary Graham Stuart Staines and his two sons are burned alive by Hindu extremists as they are sleeping in a car in eastern India. 1999 Gospel of Jesus Christ - An Evangelical Celebration; a consensus Gospel endorsed by various evangelical leaders including J.I. Packer, John Ankerberg, Jerry Falwell, Thomas C. Oden, R.C. Sproul, Wayne Grudem, Charles Swindoll, et al. 2000 - Asia College of Ministry (ACOM), a ministry of Asia Evangelistic Fellowship (AEF), was launched by Jonathan James, to train national missionaries in Asia. 2000 Our Lady appears in Assiut, Upper Egypt; phenomena associated to Our Lady reported again, in 2006, in a Church at the same location during the Mass. Local Coptic priests and then the Coptic Orthodox Church of Assiut issue statements in 2000 and 2006, respectively ^ abcNorman, The Roman Catholic Church an Illustrated History (2007), pp. 167–8 ^ abcChadwick, A History of Christianity (1995), p. 266 ^Pham, Heirs of the Fisherman: Behind the Scenes of Papal Death and Succession (2005), p. 45, quote: "When Pius XI was complimented on the publication, in 1937, of his encyclical denouncing Nazism, Mit Brennender Sorge, his response was to point to his Secretary of State and say bluntly, 'The credit is his.' " ^ abcVidmar, The Catholic Church Through the Ages (2005), pp. 327–333, quote: "Mark well that in the Catholic Mass, Abraham is our Patriarch and forefather. Anti-Semitism is incompatible with the lofty thought which that fact expresses. It is a movement with which we Christians can have nothing to do. No, no, I say to you it is impossible for a Christian to take part in anti-Semitism. It is inadmissible. Through Christ and in Christ we are the spiritual progeny of Abraham. Spiritually, we are all Semites." ^ abcdefgBokenkotter, A Concise History of the Catholic Church (2004), p. 389–92 ^Rhodes, pp. 182–183 quote "His contention seemed confirmed in a speech by Staatsminister Wagner in Munich on the 31st March 1934, only nine months after the signature of the Concordat. Wagner said if the Church had not signed a concordat with Germany, the National Socialist government would have abolished the Catholic Youth organisations altogether, and placed them in the same 'anti-state' category as the Marxist groups. ... If the maintenance of Catholic education and of the Catholic Youth associations was, as we have seen often enough before, the principal aim of Papal diplomacy, then his phrase, 'the Concordat prevented greater evils' seems justified. ... "The German episcopate considered that neither the Concordats up to then negotiated with individual German States (Lander), nor the Weimar Constitution gave adequate guarantees or assurance to the faithful of respect for their convictions, rights or liberty of action. In such conditions the guarantees could not be secured except through a settlement having the solemn form of a concordat with the central government of the Reich, I would add that since it was the German government which made the proposal, the responsibility for all the regrettable consequences would have fallen on the Holy See if it had refused the proposed Concordat. Although the Church had few illusions about National Socialism, it must be recognized that the Concordat in the years that followed brought some advantages, or at least prevented worse evils. In fact, in spite of all the violations to which it was subjected, it gave German Catholics a juridical basis for their defence, a stronghold behind which to shield themselves in their oppositions to the ever-growing campaign of religious persecution." ^Rhodes, p. 197 quote "Violence had been used against a Catholic leader as early as June 1934, in the 'Night of the Long Knives' ... by the end of 1936 physical violence was being used openly and blatantly against the Catholic Church. The real issue was not, as the Nazis contended, a struggle with 'political Catholicism', but that the regime would tolerate the Church only if it adapted its religious and moral teaching to the materialist dogma of blood and race - that is, if it ceased to be Christian." ^Shirer, p. 235 quote "On July 25, five days after the ratification of the concordat, the German government promulgated a sterilization law, which particularly offended the Catholic Church. Five days later the first steps were taken to dissolve the Catholic Youth League. During the next years, thousands of Catholic priests, nuns and lay leaders were arrested, many of them on trumped-up charges of 'immorality' or 'smuggling foreign currency'. Erich Klausener, leader of Catholic Action, was, as we have seen, murdered in the June 30, 1934, purge. Scores of Catholic publications were suppressed, and even the sanctity of the confessional was violated by Gestapo agents. By the spring of 1937, the Catholic hierarchy, in Germany, which, like most of the Protestant clergy, had tried to co-operate with the new regime, was thoroughly disillusioned. ^ abcdMcGonigle, p. 172 quote "Hitler, of course flagrantly violated the rights of Catholics and others whenever it pleased him. Catholic Action groups were attacked by Hitler's police and Catholic schools were closed. Priests were persecuted and sent to concentration camps. ... On Palm Sunday, 21 March 1937, the encyclical Mit Brennender Sorge was read in Catholic Churches in Germany. In effect it taught that the racial ideas of the leader (fuhrer) and totalitarianism stood in opposition to the Catholic faith. The letter let the world, and especially German Catholics, know clearly that the Church was harassed and persecuted, and that it clearly opposed the doctrines of Nazism." ^Pham, p. 45, quote: "When Pius XI was complimented on the publication, in 1937, of his encyclical denouncing Nazism, Mit Brennender Sorge, his response was to point to his Secretary of State and say bluntly, 'The credit is his.'" ^Vidmar, p. 327 quote "Pius XI's greatest coup was in writing the encyclical Mit Brennender Sorge ("With Burning Desire") in 1936, and having it distributed secretly and ingeniously by an army of motorcyclists, and read from the pulpit on Palm Sunday before the Nazis obtained a single copy. It stated (in German and not in the traditional Latin) that the Concordat with the Nazis was agreed to despite serious misgivings about Nazi integrity. It then went on to condemn the persecution of the church, the neopaganism of the Nazi ideology-especially its theory of racial superiority-and Hitler himself, calling him 'a mad prophet possessed of repulsive arrogance.'" ^ abcdRhodes, p. 204-205 quote "Mit brennender Sorge did not prevaricate. Although it began mildly enough with an account of the broad aims of the Church, it went on to become one of the greatest condemnations of a national regime ever pronounced by the Vatican. Its vigorous language is in sharp contrast to the involved style in which encyclicals were normally written. The education question was fully and critically examined, and a long section devoted to disproving the Nazi theory of Blood and Soil (Blut und Boden) and the Nazi claim that faith in Germany was equivalent to faith in God. There were scathing references to Rosenberg's Myth of the Twentieth Century and its neo-paganism. The pressure exercised by the Nazi party on Catholic officials to betray their faith was lambasted as 'base, illegal and inhuman'. The document spoke of "a condition of spiritual oppression in Germany such as has never been seen before", of 'the open fight against the Confessional schools and the suppression of liberty of choice for those who desire a Catholic education'. 'With pressure veiled and open,' it went on, 'with intimidation, with promises of economic, professional, civil, and other advantages, the attachment of Catholics to the Faith, particularly those in government employment, is exposed to a violence as illegal as it is inhuman.' 'The calvary of the Church': 'The war of annihilation against the Catholic Faith'; 'The cult of idols'. The fulminations thundered down from the pulpits to the delighted congregations. Nor was the Fuhrer himself spared, for his 'aspirations to divinity', 'placing himself on the same level as Christ': 'a mad prophet possessed of repulsive arrogance' (widerliche Hochmut)." ^ abCourtois, p. 29 quote "... Pope Pius XI condemned Nazism and Communism respectively in the encyclicals Mit Brennender Sorge ... and Divini redemptoris ... ." ^Norman, p. 167 quote "But violations began almost at once by Nazi Party officials, and in 1937 the papacy issued a Letter to the German bishops to be read in the churches. Mit Brennender Sorge ... denounced the violations as contrary to Natural Law and to the term of the Concordat. The Letter, in fact, amounted to a condemnation of Nazi ideology: 'In political life within the state, since it confuses considerations of utility with those of right, it mistakes the basic fact that man as a person possesses God-given rights which must be preserved from all attacks aimed at denying, suppressing, or disregarding them.' The Letter also rejected absolutely the concept of a German National Church." ^Bokenkotter, pp. 389–392, quote "And when Hitler showed increasing belligerence toward the Church, Pius met the challenge with a decisiveness that astonished the world. His encyclical Mit Brennender Sorge was the 'first great official public document to dare to confront and criticize Nazism' and 'one of the greatest such condemnations ever issued by the Vatican.' Smuggled into Germany, it was read from all the Catholic pulpits on Palm Sunday in March 1937. It denounced the Nazi "myth of blood and soil" and decried its neopaganism, its war of annihilation against the Church, and even described the Fuhrer himself as a 'mad prophet possessed of repulsive arrogance'. The Nazis were infuriated, and in retaliation closed and sealed all the presses that had printed it and took numerous vindictive measures against the Church, including staging a long series of immorality trials of Catholic clergy." ^ abcDuffy, (paperback edition) p. 343 quote "In a triumphant security operation, the encyclical was smuggled into Germany, locally printed, and read from Catholic pulpits on Palm Sunday 1937. Mit Brennender Sorge ('With Burning Anxiety') denounced both specific government actions against the Church in breach of the concordat and Nazi racial theory more generally. There was a striking and deliberate emphasis on the permanent validity of the Jewish scriptures, and the Pope denounced the 'idolatrous cult' which replaced belief in the true God with a 'national religion' and the 'myth of race and blood'. He contrasted this perverted ideology with the teaching of the Church in which there was a home 'for all peoples and all nations'. The impact of the encyclical was immense, and it dispelled at once all suspicion of a Fascist Pope. While the world was still reacting, however, Pius issued five days later another encyclical, Divini Redemptoris denouncing Communism, declaring its principles 'intrinsically hostile to religion in any form whatever', detailing the attacks on the Church which had followed the establishment of Communist regimes in Russia, Mexico and Spain, and calling for the implementation of Catholic social teaching to offset both Communism and 'amoral liberalism'. The language of Divini Redemptoris was stronger than that of Mit Brennender Sorge, its condemnation of Communism even more absolute than the attack on Nazism. The difference in tone undoubtedly reflected the Pope's own loathing of Communism as the ultimate enemy. The last year of his life, however, left no one any doubt of his total repudiation of the right-wing tyrannies in Germany and, despite his instinctive sympathy with some aspects of Fascism, increasingly in Italy also. His speeches and conversations were blunt, filled with phrases like 'stupid racialism', 'barbaric Hitlerism'." ^Chadwick, Owen p. 254 quote "The encyclical was smuggled into Germany and read from the pulpits on Palm Sunday. It made the repression far worse; but it too was necessary to Christian honour." ^Vidmar, pp. 327–333, quote: "Mark well that in the Catholic Mass, Abraham is our Patriarch and forefather. Anti-Semitism is incompatible with the lofty thought which that fact expresses. It is a movement with which we Christians can have nothing to do. No, no, I say to you it is impossible for a Christian to take part in anti-Semitism. It is inadmissible. Through Christ and in Christ we are the spiritual progeny of Abraham. Spiritually, we are all Semites." ^Duffy, (paperback edition) p. 348 quote "It is clear from Maglione's intervention that Papa Pacelli cared about and sought to avert the deportation of the Roman Jews. but he did not denounce: a denunciation, the Pope believed, would do nothing to help the Jews, and would only extend Nazi persecution to yet more Catholics. It was the Church as well as the Jews in Germany, Poland and the rest of occupied Europe who would pay the price for any papal gesture. There was some weight in this argument: when the Dutch Catholic hierarchy denounced measures against Jews there, the German authorities retaliated by extending the persecution to baptized Jews who had formerly been protected by their Catholicism." ^Bokenkotter p. 192 quote "The end of the war saw the prestige of the papacy at an all-time high. Many nations had ambassadors accredited with the Vatican. The President of the United States sent his personal representative, while a constant stream of the world's celebrities moved through its portals. The Holy Year of 1950 brought millions of more humble pilgrims to the tomb of Peter. The pope gave daily addresses on every conceivable subject and was widely quoted around the world. The number of Catholic dioceses increased during his reign from 1,696 to 2,048. ... Einstein, for instance, in an article in Time, paid tribute to Pius and noted that the Church alone 'stood squarely across the path of Hitler's campaign.' ... 'Rabbi Herzog, the chief rabbi of Israel, sent a message in February 1944 declaring "the people of Israel will never forget what His Holiness ... (is) doing for our unfortunate brothers and sisters in the most tragic hour of our history."' David Dalin cites these tributes as recognition of the work of the Holy See in saving hundreds of thousands of Jews." ^Bokenkotter, pp. 480–481, quote:"A recent article by American rabbi, David G. Dalin, challenges this judgement. He calls making Pius XII a target of moral outrage a failure of historical understanding, and he thinks Jews should reject any 'attempt to usurp the Holocaust' for the partisan purposes at work in this debate. Dalin surmises that well-known Jews such as Albert Einstein, Golda Meir, Moshe Sharett, and Rabbi Isaac Herzog would likely have been shocked at these attacks on Pope Pius. ... Dalin points out that Rabbi Herzog, the chief rabbi of Israel, sent a message in February 1944 declaring 'the people of Israel will never forget what His Holiness ... (is) doing for our unfortunate brothers and sisters in the most tragic hour of our history.'" Dalin cites these tributes as recognition of the work of the Holy See in saving hundreds of thousands of Jews." ^Bokenkotter, A Concise History of the Catholic Church (2004), pp. 480–1, quote:"A recent article by American rabbi, David G. Dalin, challenges this judgement. He calls making Pius XII a target of moral outrage a failure of historical understanding, and he thinks Jews should reject any 'attempt to usurp the Holocaust' for the partisan purposes at work in this debate. Dalin surmises that well–known Jews such as Albert Einstein, Golda Meir, Moshe Sharett, and Rabbi Isaac Herzog would likely have been shocked at these attacks on Pope Pius. Einstein, for instance, in an article in Time, paid tribute to Pius and noted that the Church alone 'stood squarely across the path of Hitler's campaign.' Dalin points out that 'Rabbi Herzog, the chief rabbi of Israel, sent a message in February 1944 declaring "the people of Israel will never forget what His Holiness ... (is) doing for our unfortunate brothers and sisters in the most tragic hour of our history." ' Dalin cites these tributes as recognition of the work of the Holy See in saving hundreds of thousands of Jews." ^Bokenkotter, A Concise History of the Catholic Church (2004), p. 467 ^ abPope Benedict XVI, Jesus of Nazareth (2008), pp. 180–1, quote: "The difference between the discipleship of the Twelve and the discipleship of the women is obvious; the tasks assigned to each group are quite different. Yet Luke makes clear—and the other Gospels also show this in all sorts of ways—that 'many' women belonged to the more intimate community of believers and that their faith—filled following of Jesus was an essential element of that community, as would be vividly illustrated at the foot of the Cross and the Resurrection."
How climate change models could get better, thanks to NASA NASA is set to launch satellite Glory early Wednesday. It will measure incoming sunlight and atmospheric particles, both key to crafting better climate models. In the dark of night, scientists expect to launch a satellite they hope will provide new insights into the energy the sun provides for Earth's climate in the light of day. At 2:09 a.m. Pacific Standard Time Wednesday, NASA is launching Glory on a mission that will give the most accurate measurements yet of incoming sunlight, as well as highly accurate measurements of the size, distribution, and effects of tiny particles in the atmosphere known as aerosols, planners say. The satellite's data should help atmospheric scientists improve climate models. Better models not only would increase scientists' knowledge of how the climate system operates, but also would help them make more accurate projections of the effects of global warming – even as atmospheric concentrations of greenhouse gases continue to rise, as a result of burning fossil fuels and land-use changes. Direct and indirect effects of aerosols and black-carbon soot represent "the greatest uncertainty in our ability to predict climate," says Hal Maring, the Glory program scientist at NASA headquarters in Washington. Aerosols reflect sunlight or absorb it, cooling or heating the atmosphere depending on the particles' size and composition. Aerosols also can have indirect effects on climate by serving as tiny platforms on which atmospheric water vapor can condense to form cloud droplets. These tiny particles can vary widely in size, composition, and sources. Aerosols in the atmosphere have natural sources, such as volcanic eruptions, or can result from human activities, such as burning fossils fuels or using wood for cooking and heating. Aerosols from different sources and with different compositions can occupy the same parcel of air. Numerous field studies have monitored aerosols and black-carbon soot in individual regions. But until now, no project has provided a global view. As a result, the uncertainty in the estimates of aerosols' effects are thought to be as large as the effects being estimated. The human-caused change in Earth's climate, from the addition of greenhouse gases to the atmosphere, Dr. Mishchenko adds, "also has an uncertainty comparable to the estimate – and almost all of this uncertainty comes from the poor knowledge of aerosols." Glory will provide real-world aerosol measurements to help reduce these uncertainties, during a mission slated to last up to five years, depending on how well the spacecraft and instruments hold up. Glory is designed to make more than 10,000 measurements at 600,000 locations around the world, comparing incoming sunlight with the solar radiation reflected back into space over those locations. In addition, the satellite carries an instrument that can calculate aerosols' sizes and composition from the polarization of the light that they reflect back into space. Of particular interest to some scientists will be the data on black-carbon soot. Within the past few years, researchers have conducted field measurements suggesting that black-carbon soot's warming effect on the atmosphere is as much as half that of carbon dioxide. Yet climate models produce only one-third to half of the observed warming from black carbon, explains Veerabhadran Ramanathan, an atmospheric scientist at the Scripps Institution of Oceanography in La Jolla, Calif., and a pioneer in the study of black-carbon soot's impact on climate. "The only thing that beats my excitement for this mission is spending time with my grandchildren," he says. Over the next couple of years, two phenomena he studies – black-carbon soot's impact on cloud formation over the Arabian Sea, and the impact of dust from the western US and abroad on the timing of snow melt in the Rockies – would benefit greatly from having Glory in orbit and operating, says Dr. Ramanathan. Indeed, the Glory science team notes that the satellite will become the sixth orbiter to join the so-called A-Train – a constellation of Earth-observing satellites launched during the past decade by the US, Canada, and France. The spacecraft focus on clouds, precipitation, ice and snow cover, and other climate-related phenomena. All pass over the same spot within minutes of one another each afternoon, allowing scientists to track the interaction of different contributors to climate under virtually the same conditions. "The value of Glory goes up substantially because it's in the A-Train," says NASA's Dr. Maring.
An equator of a rotating spheroid is its zeroth circle of latitude. It is the imaginary line on the spheroid, equidistant from its poles, dividing it into northern and southern hemispheres. In other words, it is the intersection of the spheroid with the plane perpendicular to its axis of rotation and midway between its geographical poles. On Earth, the Equator is 21.3 % over land. Indonesia is the country straddling the greatest length of the equatorial line across both land and sea; the name is derived from medieval Latin word aequator, in the phrase circulus aequator diei et noctis, meaning ‘circle equalizing day and night’, from the Latin word aequare meaning ‘make equal’. The latitude of the Earth's equator is, by definition, 0° of arc; the Equator is one of the five notable circles of latitude on Earth. The Equator is the only line of latitude, a great circle — that is, one whose plane passes through the center of the globe; the plane of Earth's equator, when projected outwards to the celestial sphere, defines the celestial equator. In the cycle of Earth's seasons, the equatorial plane runs through the Sun twice per year: on the equinoxes in March and September. To a person on Earth, the Sun appears to travel above the Equator at these times. Light rays from the Sun's center are perpendicular to Earth's surface at the point of solar noon on the Equator. Locations on the Equator experience the shortest sunrises and sunsets because the Sun's daily path is nearly perpendicular to the horizon for most of the year; the length of daylight is constant throughout the year. Earth bulges at the Equator. Sites near the Equator, such as the Guiana Space Centre in Kourou, French Guiana, are good locations for spaceports as they have a faster rotational speed than other latitudes. Since Earth rotates eastward, spacecraft must be launched eastward to take advantage of this Earth-boost of speed; the precise location of the Equator is not fixed. This effect must be accounted for in detailed geophysical measurements; the International Association of Geodesy and the International Astronomical Union have chosen to use an equatorial radius of 6,378.1366 kilometres. This equatorial radius is in the 2003 and 2010 IERS Conventions. It is the equatorial radius used for the IERS 2003 ellipsoid. If it were circular, the length of the Equator would be 2π times the radius, namely 40,075.0142 kilometres. The GRS 80 as approved and adopted by the IUGG at its Canberra, Australia meeting of 1979 has an equatorial radius of 6,378.137 kilometres. The WGS 84, a standard for use in cartography and satellite navigation including GPS has an equatorial radius of 6,378.137 kilometres. For both GRS 80 and WGS 84, this results in a length for the Equator of 40,075.0167 km. The geographical mile is defined as one arc-minute of the Equator, so it has different values depending on which radius is assumed. For example, by WSG-84, the distance is 1,855.3248 metres, while by IAU-2000, it is 1,855.3257 metres. This is a difference of less than one millimetre over the total distance; the earth is modeled as a sphere flattened 0.336% along its axis. This makes the Equator 0.16% longer than a meridian. The IUGG standard meridian is, to the nearest millimetre, 40,007.862917 kilometres, one arc-minute of, 1,852.216 metres, explaining the SI standardization of the nautical mile as 1,852 metres, more than 3 metres less than the geographical mile. The sea-level surface of the Earth is irregular, so the actual length of the Equator is not so easy to determine. Aviation Week and Space Technology on 9 October 1961 reported that measurements using the Transit IV-A satellite had shown the equatorial "diameter" from longitude 11° West to 169° East to be 1,000 feet greater than its "diameter" ninety degrees away; the Equator passes through the land of 11 countries. Starting at the Prime Meridian and heading eastwards, the Equator passes through: Despite its name, no part of Equatorial Guinea lies on the Equator. However, its island of Annobón is 155 km south of the Equator, the rest of the country lies to the north. Seasons result from the tilt of the Earth's axis compared to the plane of its revolution around the Sun. Throughout the year the northern and southern hemispheres are alternately turned either toward or away from the sun depending on Earth's position in its orbit. The hemisphere turned toward the sun receives more sunlight and is in summer, while the other hemisphere receives less sun and is in winter. At the equinoxes, the Earth's axis Latin America is a group of countries and dependencies in the Western Hemisphere where Romance languages such as Spanish and French are predominantly spoken. The term "Latin America" was first used in an 1856 conference with the title "Initiative of the America. Idea for a Federal Congress of the Republics", by the Chilean politician Francisco Bilbao; the term was used by Napoleon III's French government in the 1860s as Amérique latine to consider French-speaking territories in the Americas, along with the larger group of countries where Spanish and Portuguese languages prevailed, including the Spanish-speaking portions of the United States Today, areas of Canada and the United States where Spanish and French are predominant are not included in definitions of Latin America. Latin America consists of 13 dependencies and 20 countries which cover an area that stretches from the northern border of Mexico to the southern tip of South America, including the Caribbean, it has an area of 19,197,000 km2 13% of the Earth's land surface area. As of 2016, its population was estimated at more than 639 million and in 2014, Latin America had a combined nominal GDP of US$5,573,397 million and a GDP PPP of 7,531,585 million USD. The idea that a part of the Americas has a linguistic affinity with the Romance cultures as a whole can be traced back to the 1830s, in the writing of the French Saint-Simonian Michel Chevalier, who postulated that this part of the Americas was inhabited by people of a "Latin race", that it could, ally itself with "Latin Europe" overlapping the Latin Church, in a struggle with "Teutonic Europe", "Anglo-Saxon America" and "Slavic Europe". Further investigations of the concept of Latin America are by Michel Gobat in the American Historical Review, the studies of Leslie Bethell, the monograph by Mauricio Tenorio-Trillo, Latin America: The Allure and Power of an Idea. Historian John Leddy Phelan (located the origins of “Latin America” in the French occupation of Mexico, his argument is that French imperialists used the concept of "Latin" America as a way to counter British imperialism, as well as to challenge the German threat to France. The idea of a "Latin race" was taken up by Latin American intellectuals and political leaders of the mid- and late-nineteenth century, who no longer looked to Spain or Portugal as cultural models, but rather to France. French ruler Napoleon III had a strong interest in extending French commercial and political power in the region he and his business promoter Felix Belly called “Latin America” to emphasize the shared Latin background of France with the former colonies of Spain and Portugal; this led to Napoleon's failed attempt to take military control of Mexico in the 1860s. However, though Phelan thesis is still mentioned in the U. S. academy, two Latin American historians, the Uruguayan Arturo Ardao and the Chilean Miguel Rojas Mix proved decades ago that the term "Latin America" was used earlier than Phelan claimed, the first use of the term was opposite to support imperialist projects in the Americas. Ardao wrote about this subject in his book Génesis de la idea y el nombre de América latina, Miguel Rojas Mix in his article "Bilbao y el hallazgo de América latina: Unión continental, socialista y libertaria". As Michel Gobat reminds in his article "The Invention of Latin America: A Transnational History of Anti-Imperialism and Race", "Arturo Ardao, Miguel Rojas Mix, Aims McGuinness have revealed the term'Latin America' had been used in 1856 by Central and South Americans protesting U. S. expansion into the Southern Hemisphere". Edward Shawcross summarizes Ardao's and Rojas Mix's findings in the following way: "Ardao identified the term in a poem by a Colombian diplomat and intellectual resident in France, José María Torres Caicedo, published on 15 February 1857 in a French based Spanish-language newspaper, while Rojas Mix located it in a speech delivered in France by the radical liberal Chilean politician Francisco Bilbao in June 1856". So, regarding when the words "Latin" and "America" were combined for the first time in a printed work, the term "Latin America" was first used in 1856 in a conference by the Chilean politician Francisco Bilbao in Paris; the conference had the title "Initiative of the America. Idea for a Federal Congress of Republics." The following year the Colombian writer José María Torres Caicedo used the term in his poem "The Two Americas". Two events related with the U. S. played a central role in both works. The first event happened less than a decade before the publication of Bilbao's and Torres Caicedo works: the Mexican–American War, after which Mexico lost a third of its territory; the second event, the Walker affair, happened the same year both works were written: the decision by U. S. president Franklin Pierce to recognize the regime established in Nicaragua by American William Walker and his band of filibusters who ruled Nicaragua for nearly a year and attempted to reinstate slavery there, where it had been abolished for three decades In both Bilbao's and Torres Caicedo's works, the Mexican-American War and Walker's expedition to Nicaragua are explicitly mentioned as examples of dangers for the region. For Bilbao, "Latin America" w Goiás is a state of Brazil, located in the Center-West region of the country. The name Goiás comes from the name of an indigenous community; the original word seems to have been guaiá, a compound of gua e iá, meaning "the same person" or "people of the same origin." It borders the Federal District and the states of Tocantins, Minas Gerais, Mato Grosso do Sul and Mato Grosso. The most populous state of its region, Goiás is characterized by a landscape of chapadões. In the height of the drought season, from June to September, the lack of rain makes the level of the Araguaia River go down and exposes 2 kilometres of beaches, making it the main attraction of the State. At the Emas National Park in the municipality of Mineiros, it is possible to observe the typical fauna and flora from the region. At the Chapada dos Veadeiros the attractions are the canyons, valleys and waterfalls. Other attractions are the historical city of Goiás, 132 km from Goiânia, established in the beginning of 18th Century, Caldas Novas, with its hot water wells attracting more than one million tourists per year. In Brazil's geoeconomic division, Goiás belongs to the Centro-Sul, being the northernmost state of the southern portion of Brazil. Located in the east of the Center-West region, adjacent to Brazil's Southeastern region, Goiás lies on the southern portion of the Brazilian Highlands, which are located in the center of the country, it occupies a large plateau, the vast level surface of which stands between 750 and 900 m above sea level and forms the divide between three of Brazil's largest river systems: to the south. Goiás is drained by a tributary of the Paraná River. Other major rivers in the state are the Meia Ponte, Aporé, São Marcos, Corumbá River, Maranhão, Paranã and Preto. None of these rivers is navigable except for short distances by small craft; the state's highest point is Pouso Alto, at 1,676 metres above sea level, in the Chapada dos Veadeiros. Goiás is covered with a woodland savanna known in Brazil as campo cerrado, although there are still tropical forests along the rivers; this cerrado has been diminished in recent years due to cattle raising and soybean farming with great loss of animal life and forest cover. The climate of the plateau is tropical. Average monthly temperatures vary from 26 °C in the warmest month to 22 °C in the coldest; the year is divided into a dry season. Average annual rainfall is about 1,700 millimetres, but this varies due to elevation and microclimate; some parts of the state, have small remnants of tropical Atlantic forest, that appears around rivers and valleys. The Great Central West Region, consisting of the states of Goiás, Mato Grosso, Mato Grosso do Sul, the Federal District, is among the fastest-growing regions of Brazil; the population of Goiás state tripled in size in the period from 1950 to 1980 and is still growing quickly. However, outside the Federal District and the Goiânia metropolitan region most of Goiás is thinly populated; the chief concentration of settlement is in the southeast, in the area of Goiânia, across the border from Minas Gerais, around the Federal District. See also: History of Goiás The first European exploration of this interior part of Brazil was carried out by expeditions from São Paulo in the 17th century. Gold was discovered in the gravel of a tributary of the Araguaia River by the bandeirante Bartolomeu Bueno da Silva in 1682. The settlement he founded there, called Santa Anna, became the colonial town of Goiás Velho, the former state capital. In 1744 the large inland area, much of it still unexplored by Europeans, was made a Captaincy General, in 1822 it became a province of the empire of Brazil, it became a state in 1889. The Brazilian constitution of 1891 specified that the nation's capital should be moved to the Brazilian Highlands, in 1956 Goiás was selected as the site for the federal district and capital national, Brasília; the seat of the federal government was moved to Brasília in 1960. Goiânia, the largest city and capital was planned in 1933 to replace the old, inaccessible former state capital of Goiás, 110 kilometres northwest. In 1937 the state government moved there, in 1942 the official inauguration was held. Goiânia is now one of the fastest growing cities in Brazil and one of the most livable cities in the country.. It stands out as both an industrial center and as a cultural center for country culture and music, known as Sertanejo. Due to the large territory of the state, over 600,000 square kilometres, communications were very difficult; the northern part of the state began to feel abandoned by the southern government and began a movement for separation. Local political leaders, many of whom were large landowners and were eager to gain important positions such as governor or senator and financial gain with the construction of a new capital encouraged the movement. In 1989 the northern half of Goiás became. According to the IBGE of 2010, there were 6,004,045 people residing in the state; the population density was 16.9 inh./km2. Ur Fernando de Noronha Fernando de Noronha is an archipelago of 21 islands and islets in the Atlantic Ocean, 354 km offshore from the Brazilian coast. The archipelago's name is a corruption of the name of the Portuguese merchant Fernão de Loronha, to whom it was given by the Portuguese crown for services rendered regarding wood imported from Brazil. Only the homonymous main island is inhabited; the archipelago's total area is 26 km2. Administratively the islands are a unique case in Brazil of a special "state district", not part of any municipality and is administered directly by the government of the state of Pernambuco; the state district's jurisdiction includes the remote Saint Peter and Saint Paul Archipelago, located 625 kilometres northeast of Fernando de Noronha. 70% of the islands area were established in 1988 as a national maritime park. In 2001, UNESCO designated it as a World Heritage Site because of the importance of its environment, its time zone is UTC−02:00 all year round. The local population and travelers can get to Noronha by plane from Natal. An "environmental preservation" daily fee is charged from tourists upon arrival by Pernambuco State administration, while another fee is paid once to have access to the National Park attractions. The islands of this archipelago are the visible parts of a range of submerged mountains, it consists of 21 islands and rocks of volcanic origin. The main island has an area of 18 km2, being 3.5 km wide at its maximum. The base of this enormous volcanic formation is 756 metres below the surface; the volcanic rocks are of variable though silica-undersaturated character with basanite and phonolite among the lava types found. The main island, from which the group gets its name, makes up 91% of the total area; the central upland of the main island is called the Quixaba. The United Nations Environment Programme lists 15 possible endemic plant species, including species of the genera Capparis noronhae, Ceratosanthes noronhae, Cayaponia noronhae, Moriordica noronhae, Cereus noronhae, Palicourea noronhae, Guettarda noronhae, Bumelia noronhae, Physalis noronhae, Ficus noronhae. The islands have two endemic birds -- the Noronha vireo. Both are present on the main island. In addition there is an endemic subspecies of Zenaida auriculata noronha. Subfossil remains of an extinct endemic rail have been found; the archipelago is an important site for breeding seabirds. An endemic sigmodontine rodent, Noronhomys vespuccii, mentioned by Amerigo Vespucci, is now extinct; the islands have two endemic reptiles, the Noronha wormlizard, Amphisbaena ridleyi, the Noronha skink, Trachylepis atlantica. The life above and below sea is the main attraction of the island. Sea turtles, cetaceans and many other species are observed; the climate is tropical, with two well-defined seasons for rainfall, if not temperature. The rainy season lasts from February to July; the temperature ranges, both diurnal and monthly, are unusually slight. Many controversies mark the discovery of the archipelago by Europeans. At least three names – São Lourenço, São João, Quaresma – have been associated with the island around the time of its discovery. Based on the written record, Fernando de Noronha island was discovered on August 10, 1503, by a Portuguese expedition and financed by a private commercial consortium headed by the Lisbon merchant Fernão de Loronha. The expedition was under the overall command of captain Gonçalo Coelho and carried the Italian adventurer Amerigo Vespucci aboard, who wrote an account of it; the flagship of the expedition hit a reef and foundered near the island, the crew and contents had to be salvaged. On Coelho's orders, Vespucci anchored at the island, spent a week there, while the rest of the Coelho fleet went on south. In his letter to Soderini, Vespucci describes the uninhabited island and reports its name as the "island of St. Lawrence", its existence was reported to Lisbon sometime between and January 16, 1504, when King Manuel I of Portugal issued a charter granting the "island of St. John" as a hereditary captaincy to Fernão de Loronha; the date and new name in the charter has presented historians with a puzzle. As Vespucci did not return to Lisbon until September 1504, the discovery must have been earlier. Historians have hypothesized that a stray ship of the Coelho fleet, under an unknown captain, may have returned to the island to collect Vespucci, did not find him or anyone else there, went back to Lisbon by itself with the news; the captain who returned to Lisbon with the n International rankings of Brazil The following are international rankings of Brazil. International Monetary Fund: GDP 2012, ranked 7 out of 181 countries International Monetary Fund: GDP per capita 2011, ranked 53 out of 183 countries The Wall Street Journal and the Heritage Foundation: Index of Economic Freedom 2006, ranked 81 out of 157 countries World Economic Forum: Global Competitiveness Index 2011-2012, ranked 53 out of 142 countries Motor Vehicle Production: ranked 6 Yale University and Columbia University: 2012 Environmental Performance Index, ranked 30 out of 132 2010 KOF Index of Globalization ranked 75 out of 181 Institute for Economics and Peace Global Peace Index ranked 85 out of 144 Transparency International: 2011 Corruption Perceptions Index, ranked 73 out of 182 countries Reporters Without Borders: 2011-2012 Press Freedom Index, ranked 99 out of 179 countries Economist Intelligence Unit: E-readiness 2008, ranked 41 out of 70 countries Futron: Space Competitiveness Index 2010, ranked 10th in the world United Nations: 2011 Human Development Index, ranked 84 out of 187 countries Rio de Janeiro (state) Rio de Janeiro is one of the 27 federative units of Brazil. It has the second largest economy of Brazil, with the largest being that of the state of São Paulo; the state of Rio de Janeiro is located within the Brazilian geopolitical region classified as the Southeast. Rio de Janeiro shares borders with all the other states in the same Southeast macroregion: Minas Gerais, Espírito Santo and São Paulo, it is bounded on the south by the South Atlantic Ocean. Rio de Janeiro has an area of 43,653 km2, its capital is the city of Rio de Janeiro, the capital of the Portuguese Colony of Brazil from 1763 to 1815, of the following United Kingdom of Portugal and the Algarves from 1815 to 1822, of independent Brazil as a kingdom and republic from 1822 to 1960. The archaic demonym meaning for the Rio de Janeiro State is "fluminense", taken from the Latin word flumen, meaning "river". Despite the fact "carioca" is a most ancient demonym of Rio de Janeiro's inhabitants, it was replaced by "fluminense" in 1783, when it was sanctioned as the official demonym of the Royal Captaincy of Rio de Janeiro, a few years after the City of São Sebastião do Rio de Janeiro has become the capital city of the Brazilian colonies. From 1783 and during the Imperial Regime, "carioca" remained only as a nickname by which other Brazilians called the inhabitants of Rio. During the first years of the Brazilian Republic, "carioca" was the name given to those who lived in the slums or a pejorative way to refer the bureaucratic elite of the Federal District. Only when the City of Rio lost its status as Federal District and became a Brazilian State when the capital was moved to Brasília earlier in 1960, "carioca" was made a co-official demonym with "guanabarino". In 1975, the Guanabara State was ended and extinct by President Ernesto Geisel becoming the present City of Rio de Janeiro and "carioca" was made the demonym of its municipality. Although "carioca" is not recognized as an official demonym of Rio de Janeiro State, Brazilians call the inhabitants of Rio de Janeiro in general as "cariocas", most of its inhabitants claim to be "cariocas". Nowadays, social movements like "Somos Todos Cariocas" have tried to achieve the official recognition of "carioca" as a co-official demonym of the Rio de Janeiro State. The state's 22 largest cities are Rio de Janeiro, São Gonçalo, Duque de Caxias, Nova Iguaçu, Niterói, Campos dos Goytacazes, Belford Roxo, São João de Meriti, Petrópolis, Volta Redonda, Magé, Macaé, Itaboraí, Cabo Frio, Armação dos Búzios, Angra dos Reis, Nova Friburgo, Barra Mansa, Barra do Piraí, Teresópolis and Nilópolis. Rio de Janeiro is one of the smallest in Brazil, it is, the third most populous Brazilian state, with a population of 16 million of people in 2011 and has the third longest coastline in the country. In the Brazilian flag, the state is represented by the beta star in the Southern Cross. European presence in Rio de Janeiro is as old as Brazil itself, dating back to 1502. Rio de Janeiro originated from parts of the captainships of São Vicente. Between 1555 and 1567, the territory was occupied by the French, who intended to install a colony, France Antarctique. Aiming to prevent the occupation of the Frenchmen, in March 1565, the city of Rio de Janeiro was established by Estácio de Sá. In the 17th century, cattle raising and sugar cane cultivation stimulated the city's progress, definitively assured when the port started to export gold extracted from Minas Gerais in the 18th century. In 1763, Rio de Janeiro became the capital of Colonial Brazil. With the flight of the Portuguese royal family from Portugal to Brazil in 1808, the region soon benefited from urban reforms to house the Portuguese. Chief among the promoted changes were: the transformation of agencies of public administration and justice, the creation of new churches, hospitals, the foundation of the first bank of the country - the Banco do Brasil - and the Royal Press, with the Gazette do Rio of Janeiro; the following years witnessed the creation of the Academia Real Militar. There followed a process of cultural enhancement influenced not only by the arrival of the Royal Family, but by the presence of European graphic artists who were hired to record the society and Brazilian natural features. During this same time, the Escola Real de Ciências, Artes e Ofícios was founded as well. In 1834, the city of Rio de Janeiro was transformed into a "neutral city", remaining as capital of the state, while the captainships became provinces, with headquarters in Niterói, a neighboring city. In 1889, the city became the capital of the Republic, the neutral city became the federal district and the province a state. In 1894, Petrópolis became the capital of Rio de Janeiro, until 1902 when Niterói recovered its capital status. With the relocation of the federal capital to Brasília in 1960, the city of Rio de Janeiro became Guanabara State. Niterói remained the state capital for Rio de Janeiro state, while Rio de Janeiro served the same status for Guanabara. In 1975, the states of Guanabara and Rio de Janeiro were merged under the name of Rio de Janeiro, with the city of Rio de Janeiro as state capital; the symbols of the former State of Rio de Janeiro were preserved, while the symbols of Guanabara were kept by the city of Rio de Janeir Flag of Brazil The flag of Brazil, known in Portuguese as Verde e amarela, or less usually'Auriverde, is a blue disc depicting a starry sky spanned by a curved band inscribed with the national motto "Ordem e Progresso", within a yellow rhombus, on a green field. Brazil adopted this design for its national flag on November 19, 1889 — four days after the Proclamation of the Republic, to replace the flag of the Empire of Brazil; the concept was the work of Raimundo Teixeira Mendes, with the collaboration of Miguel Lemos, Manuel Pereira Reis and Décio Villares. The green field and the yellow rhombus from the previous imperial flag, though modified in hue and shape, were preserved — the green represented the House of Braganza of Pedro I, the first Emperor of Brazil, while the yellow represented the House of Habsburg of his wife, Empress Maria Leopoldina. A blue circle with white five-pointed stars replaced the arms of the Empire of Brazil — its position in the flag reflects the sky over the city of Rio de Janeiro on November 15, 1889. The motto Ordem e Progresso is inspired by Auguste Comte's motto of positivism: "L'amour pour principe et l'ordre pour base. Each star corresponds to a Brazilian Federative Unit and, according to Brazilian Law, the flag must be updated in case of creation or extinction of a state. At the time the flag was first adopted in 1889, it held 21 stars, it received one more star in 1960 another in 1968, four more stars in 1992, totalling 27 stars in its current version. The Portuguese territories in the Americas, corresponding to what is now Brazil, never had their own official flag, since Portuguese tradition encouraged hoisting the flag of the Kingdom of Portugal in all territories of the Portuguese Crown; the first Brazilian vexillological symbols were private maritime flags used by Portuguese merchant ships that sailed to Brazil. A flag with green and white stripes was used until 1692; the green and white colors represented the national colours of Portugal. In 1692, that flag was no longer used by ships that sailed to Brazil and became the flag of the merchant vessels in coastal Portugal. In 1692, a new flag was introduced for merchant vessels sailing to Brazil. The new flag had a white field with a golden armillary sphere; the armillary sphere had served as the personal emblem of King Manuel I of Portugal. During his reign Portuguese ships used it and it became a national emblem of Portugal and, more of the Portuguese empire. A similar flag was introduced for the Portuguese ships that sailed to India, but with a red armillary sphere. Despite representing the entire Portuguese empire, the armillary sphere began to be used more extensively in Brazil — the largest and most developed colony at the time — not only in maritime flags, but on coins and other media, it became the unofficial ensign of Brazil. In 1815, Brazil was elevated to the rank of kingdom, the kingdoms of Portugal and the Algarves were united as a single state--the United Kingdom of Portugal and the Algarves; the Charter Act of 1816 established the insignia of the new kingdom. It specified that the arms of the Kingdom of Brazil was to be composed of a gold armillary sphere on a blue field. During this time, the flag of Brazil was the flag of the United Kingdom of Portugal and the Algarves. The imperial flag of Brazil was designed by Jean-Baptiste Debret as the Royal Standard of the Prince Royal of the United Kingdom of Portugal and the Algarves, Pedro I. After the Brazilian Declaration of Independence, with the coronation of Pedro I as Emperor of Brazil, the Royal Standard was modified to become the flag of the Empire of Brazil; the new flag featured the imperial coat of arms on a green field. The green and yellow colors represented the dynastic houses of Pedro I and his consort Maria Leopoldina of Austria; the imperial flag was modified during the reign of Pedro II, when an extra star was added to the imperial arms to conform to the new territorial organization of the country. Upon the proclamation of the Republic, one of the civilian leaders of the movement, the lawyer Ruy Barbosa, proposed a design for the nation's new flag inspired by the flag of the United States, it was flown from 15 November 1889, until 19 November 1889, when Marshal Deodoro da Fonseca vetoed the design, citing concerns that it looked too similar to the flag of another state. Fonseca suggested. This was intended to underscore continuity of national unity during the transition from a constitutional monarchy to a republic. Raimundo Teixeira Mendes presented a project in which the imperial coat of arms was replaced by a blue celestial globe and the positivist motto, it was presented to Fonseca. The flag was designed by a group formed by Raimundo Teixeira Mendes, Miguel Lemos, Manuel Pereira Reis and Décio Villares, it was adopted on 19 November 1889. The flag has been modified on three occasions to add additional stars intended to reflect newly created states: 1960, 1968 and 1992. In contrast to many other national flags with elements representing political subdivisions, modifications to the flag of Brazil were not always made promptly upon political reorganisation, resulting in multi-year periods of history wh
Sheet to be used as a prompt to help the process of math problem solving. Aligned with Common Core State Standards: 1.OA.1, Operations and Algebraic Thinking; 2.OA.2, Operations and Algebraic Thinking; 3.OA.8, Operations and Algebraic Thinking; 4.OA.1, 4.OA.3, Operations and Algebraic Thinking; 5.NF.2. Problem solving review sheet Subject Math — Fractions, Operations and Algebraic Thinking Grade Level Grades K-5 Resource Type Handout Common Core State Standards Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Really liked this as a thinking skill linked activity to get the children understanding how they actually come to the conclusions they do mathematically. Could be used in any using and applying setting for any area of math. More from this Contributor Addition and Subtraction Facts to Five Study Cards Handout, Lesson Plan \| Grades K-2
There are two main types of topology. Network topologies may be physical or logical. Physical topology means the physical design of a network including the devices, locations and cables. Logical topology is about how data is actually moved around in a network, not its physical design. The names used - such as ring or star - are only rough descriptions. The computers on a home network can be arranged in a circle but it does not necessarily mean that it represents a ring network. Basic topology types[change \| change source] There are seven basic topologies: - Point-to-point topology - Bus (point) topology - Star topology - Ring topology - Tree topology - Full/partial Mesh topology - Hybrid topology Which of these is chosen depends on what devices need to be connected, how reliable it has to be, and the cost associated with cabling. Physical topology[change \| change source] The shape of the cabling layout used to link devices is called the physical topology of the network. This refers to how the cables are laid out to connect many computers to one network. The physical topology you choose for your network depends on: - Office Layout - Troubleshooting Techniques - Cost of Installation - Type of cable used Types of Physical topologies[change \| change source] The mapping of the nodes of the network and the physical connections between them – the layout of wiring, cables, the locations of nodes, and the interconnections between the nodes and the cabling or wiring system. Point-to-point[change \| change source] The simplest topology is a permanent link between two endpoints (the line in the illustration above). Switched point-to-point topologies are the basic model of conventional telephony. The value of a permanent point-to-point network is the value of guaranteed, or nearly so, communications between the two endpoints. The value of an on-demand point-to-point connection is proportional to the number of potential pairs of subscribers, and has been expressed as Metcalfe's Law. - Permanent (dedicated) - Easiest to understand, of the variations of point-to-point topology, is a point-to-point communications channel that appears, to the user, to be permanently associated with the two endpoints. A children's "tin-can telephone" is one example, with a microphone to a single public address speaker is another. These are examples of physical dedicated channels. - Within many switched telecommunications systems, it is possible to establish a permanent circuit. One example might be a telephone in the lobby of a public building, which is programmed to ring only the number of a telephone dispatcher. "Nailing down" a switched connection saves the cost of running a physical circuit between the two points. The resources in such a connection can be released when no longer needed, for example, a television circuit from a parade route back to the studio. Bus[change \| change source] - In local area networks where bus topology is used, each machine is connected to a single cable. Each computer or server is connected to the single bus cable through some kind of connector. A terminator is required at each end of the bus cable to prevent the signal from bouncing back and forth on the bus cable. A signal from the source travels in both directions to all machines connected on the bus cable until it finds the MAC address or IP address on the network that is the intended recipient. If the machine address does not match the intended address for the data, the machine ignores the data. Alternatively, if the data does match the machine address, the data is accepted. Since the bus topology consists of only one wire, it is cheap to implement compared to other topologies. However, there is a higher cost of managing the network. Additionally, since only one cable is used, if the network cable breaks, the whole network will be shutdown Star[change \| change source] - In local area networks with a star topology, each network host (for example a PC) is connected to a central hub with a point-to-point connection. All traffic on the network passes through the central hub. The hub acts as a signal booster or repeater. The star topology is considered the easiest topology to design and implement. An advantage of the star topology is the simplicity of adding additional nodes. The primary disadvantage of the star topology is that it may need a lot more cables, and if the hub breaks everything will stop working. Ring[change \| change source] - A network topology that is set up in a circular fashion in which data travels around the ring in one direction and each device on the right acts as a repeater to keep the signal strong as it travels. Each device incorporates a receiver for the incoming signal and a transmitter to send the data on to the next device in the ring. The network is dependent on the ability of the signal to travel around the ring. Mesh[change \| change source] - Fully connected mesh topology - The number of connections in a full mesh network of n nodes is = n(n - 1) / 2. The fully connected mesh topology is generally too costly and complex for practical networks. It has been used on networks with only a small number of nodes. - Partially connected mesh topology - The type of network topology in which some of the nodes of the network are connected to more than one other node in the network with a point-to-point link – this makes it possible to take advantage of some of the redundancy that is provided by a physical fully connected mesh topology without the expense and complexity required for a connection between every node in the network. In most practical networks that are based upon the partially connected mesh topology, all of the data that is transmitted between nodes in the network takes the shortest path between nodes. The network used a longer alternative path in the case of a failure or break in one of the links. This requires that the nodes of the network possess some type of logical 'routing' algorithm to determine the correct path to use at any particular time. Tree[change \| change source] Also known as a hierarchy network. The type of network topology in which a central 'root' node (the top level of the hierarchy) is connected to one or more other nodes that are one level lower in the hierarchy (i.e., the second level) with a point-to-point link between each of the second level nodes and the top level central 'root' node. Each of the second level nodes that are connected to the top level central 'root' node will also have one or more other nodes that are one level lower in the hierarchy (i.e., the third level) connected to it, also with a point-to-point link, the top level central 'root' node being the only node that has no other node above it in the hierarchy (The hierarchy of the tree is symmetrical.) Each node in the network having a specific fixed number, of nodes connected to it at the next lower level in the hierarchy, the number, being referred to as the 'branching factor' of the hierarchical tree. This tree has individual peripheral nodes. Logical topology[change \| change source] Logical topology describes the way in which a network transmits information from network/computer to another and not the way the network looks or how it is laid out. The logical layout also describes the different speeds of the cables being used from one network to another. The logical topology, in contrast to the "physical", is the way that the signals act on the network media, or the way that the data passes through the network from one device to the next without regard to the physical interconnection of the devices. A network's logical topology is not necessarily the same as its physical topology. For example, twisted pair Ethernet is a logical bus topology in a physical star topology layout. While IBM's Token Ring is a logical ring topology, it is physically set up in a star topology. The logical classification of network topologies generally follows the same classifications as those in the physical classifications of network topologies but describes the path that the data takes between nodes being used as opposed to the actual physical connections between nodes. - Logical topologies are often closely associated with Media Access Control methods and protocols. - The logical topologies are generally determined by network protocols as opposed to being determined by the physical layout of cables, wires, and network devices or by the flow of the electrical signals, although in many cases the paths that the electrical signals take between nodes may closely match the logical flow of data, hence the convention of using the terms logical topology and signal topology interchangeably. - Logical topologies are able to be dynamically reconfigured by special types of equipment such as routers and switches. Daisy chains[change \| change source] Except for star-based networks, the easiest way to add more computers into a network is by daisy-chaining, or connecting each computer in series to the next. If a message is intended for a computer partway down the line, each system bounces it along in sequence until it reaches the destination. A daisy-chained network can take two basic forms: linear and ring. Centralization[change \| change source] The star topology reduces the probability of a network failure by connecting all of the peripheral nodes (computers, etc.) to a central node. When the physical star topology is applied to a logical bus network such as Ethernet, this central node (traditionally a hub) rebroadcasts all transmissions received from any peripheral node to all peripheral nodes on the network, sometimes including the originating node. All peripheral nodes may thus communicate with all others by transmitting to, and receiving from, the central node only. The failure of a transmission line linking any peripheral node to the central node will result in the isolation of that peripheral node from all others, but the remaining peripheral nodes will be unaffected. However, the disadvantage is that the failure of the central node will cause the failure of all of the peripheral nodes also, If the central node is passive, the originating node must be able to tolerate the reception of an echo of its own transmission, delayed by the two-way round trip transmission time (i.e. to and from the central node) plus any delay generated in the central node. An active star network has an active central node that usually has the means to prevent echo-related problems. A tree topology (a.k.a. hierarchical topology) can be viewed as a collection of star networks arranged in a hierarchy. This tree has individual peripheral nodes (e.g. leaves) which are required to transmit to and receive from one other node only and are not required to act as repeaters or regenerators. Unlike the star network, the functionality of the central node may be distributed. As in the conventional star network, individual nodes may thus still be isolated from the network by a single-point failure of a transmission path to the node. If a link connecting a leaf fails, that leaf is isolated; if a connection to a non-leaf node fails, an entire section of the network becomes isolated from the rest. In order to alleviate the amount of network traffic that comes from broadcasting all signals to all nodes, more advanced central nodes were developed that are able to keep track of the identities of the nodes that are connected to the network. These network switches will "learn" the layout of the network by "listening" on each port during normal data transmission, examining the data packets and recording the address/identifier of each connected node and which port it's connected to in a lookup table held in memory. This lookup table then allows future transmissions to be forwarded to the intended destination only. Decentralization[change \| change source] In a mesh topology (i.e., a partially connected mesh topology), there are at least two nodes with two or more paths between them to provide redundant paths to be used in case the link providing one of the paths fails. This decentralization is often used to advantage to compensate for the single-point-failure disadvantage that is present when using a single device as a central node (e.g., in star and tree networks). A special kind of mesh, limiting the number of hops between two nodes, is a hypercube. The number of arbitrary forks in mesh networks makes them more difficult to design and implement, but their decentralized nature makes them very useful. This is similar in some ways to a grid network, where a linear or ring topology is used to connect systems in multiple directions. A multi-dimensional ring has a toroidal topology, for instance. A fully connected network, complete topology or full mesh topology is a network topology in which there is a direct link between all pairs of nodes. In a fully connected network with n nodes, there are n(n-1)/2 direct links. Networks designed with this topology are usually very expensive to set up, but provide a high degree of reliability due to the multiple paths for data that are provided by the large number of redundant links between nodes. This topology is mostly seen in military applications. However, it can also be seen in the file sharing protocol BitTorrent in which users connect to other users in the "swarm" by allowing each user sharing the file to connect to other users also involved. Often in actual usage of BitTorrent any given individual node is rarely connected to every single other node as in a true fully connected network but the protocol does allow for the possibility for any one node to connect to any other node when sharing files. Hybrids[change \| change source] Hybrid networks use a combination of any two or more topologies in such a way that the resulting network does not exhibit one of the standard topologies (e.g., bus, star, ring, etc.). For example, a tree network connected to a tree network is still a tree network, but two star networks connected together exhibit a hybrid network topology. A hybrid topology is always produced when two different basic network topologies are connected. Two common examples for Hybrid network are: star ring network and star bus network - A Star ring network consists of two or more star topologies connected using a multistation access unit (MAU) as a centralized hub. - A Star Bus network consists of two or more star topologies connected using a bus trunk (the bus trunk serves as the network's backbone). References[change \| change source] - Groth, David; Toby Skandier (2005). Network+ Study Guide, Fourth Edition'. Sybex, Inc.. ISBN 0-7821-4406-3. - ATIS committee PRQC. "network topology". ATIS Telecom Glossary 2007. Alliance for Telecommunications Industry Solutions. Retrieved 2008-10-10. - Inc, S., (2002). Networking Complete. Third Edition. San Francisco: Sybex - Bicsi, B., (2002). Network Design Basics for Cabling Professionals. City: McGraw-Hill Professional Tendaishe Sigauke, (2007: 46) Explaining networking terms Other websites[change \| change source] \|Wikimedia Commons has media related to Topology (Network).\| - A Guide to Network Topology - Research network topology - Types of topology - Logical Topology Example - 8 Common Network Topologies & How to Use Tendaishe Sigauke, (2007: 46) Explaining networking terms
\|The Moon is not robed in a smooth and polished surface but is ... rough and uneven, covered everywhere, just like the earth's surface, with huge prominences, deep valleys, and chasms.\| \|-- Galileo, c. 1610\| Everyone is familiar with the fact that as the sun gets lower in the sky, shadows get progressively longer. Just before sunset your shadow can be significantly longer than you are tall. The same thing happens on the moon, and we can actually use this effect to determine how tall features on the surface of the moon are. The bright part of the moon is where it is "day time" and the dark part is where it is "night time". So the line between these two regions, called the "terminator" corresponds to where the sun is setting on the moon. Thus, it is here that the shadows will be the longest, so this is where it is easiest to find the heights of the features. Astronomers used this very technique to determine the topography of the moon, which was critical in being able to safely land the Eagle on the moon in 1969. Measuring the size of the shadows is fairly straightforward. But how do you convert these distances into heights of the features? Figure 1 shows you a schematic diagram of the moon. The sunlight is coming from the right side of the picture. M is the location of some mountain on the moon. T is the location of the terminator. And O is the center of the moon. Since the light is coming from the right, you can imagine horizontal lines representing sun rays. Thus, if you extend a horizontal line from the top of the mountain to the left, the place it hits the surface of the moon is where the end of the shadow will be. Figure 2 shows this more explicitly. We've added a few points to the diagram: P is the peak of the mountain, and S is the end of the shadow. So the shadow is line SP. (Not SM, since the peak also casts a shadow on the mountain itself.) Now the geometry. (If you want, you can skip all this and just use the result, but if you remember some basic geometry, you might want to follow it. It's not really that bad.) There are two similar triangles in Figure 2: OTM and SMP. Thus, we can setup ratios of corresponding sides: TM / OM = MP / SP OK, so what are each of these really? OM is the radius of the moon (Know it -- 1738 km). TM is the distance of the mountain from the terminator (We can measure it). SP is the size of the shadow (We can measure it, too). MP is the height of the feature (This is what we want). So let's rearrange that equation and rename things for what they are: height = (shadow length) x (distance to terminator) / (radius of moon) . Step One: Callibrating the Eyepiece In order to measure the sizes of the shadows, we will need to callibrate the tick marks in an eyepiece. That is, we need to know how to covert the size of a shadow in ticks to something more physical like arcseconds or even kilometers. So this callibration is the first step. The easiest way to do this is to use the Earth's rotation to move an object across the field of view and time how long it takes. Since we know how fast the Earth is turning, we can use the old distance = rate x time equation to figure out the spacing. To do this we need the rate, though. At the celestial equator, objects move through the sky at the rate of 360 degrees every 24 hours, which is 15 degrees per hour or 15 arcminutes per minute or 15 arcseconds per second. But this is only at the equator. For instance, Polaris moves at the rate of 0 arcseconds per second (that is, it doesn't move). So what about stuff in between? Basically it just depends on the cosine of the declination: rate = 15 * cos(dec) arcsec/sec . So, we are ready to do the callibration. First find the moon in your telescope. The callibration lines are easiest to see when backlit by the moon, so pick some easy to recognize feature on the moon somewhere. Before doing the timing run, you need to figure out which way the moon moves when you turn off the tracking. So watch the moon in the eyepiece as you unplug the tracking motor, and see which way it moves. (Then plug the tracking back in to set up for the real run.) You want the feature you picked to move from one end of the callibration marker to the other, so reposition the object on the appropriate side of the field of view and turn the eyepiece so the callibration marks extend in this direction. When you think you have it set, you should unplug the tracking again to make sure. The feature should move right along the line of tick marks. Then reposition the feature again for the timing run. Now, time how long it takes from the time you unplug the tracking for the feature to reach the other end of the callibration line. The angle between tick marks is then scale = (rate x time) / (# tick marks traversed) . (Hint: Don't count the mark where you started.) Step Two: Find the height of a mountain There are two things we need to measure: the size of the shadow and the distance of the shadow from the terminator. But first we need to pick a feature to work with. Any crater or mountain with a measurable shadow will work. You don't want one right next to the terminator, since the shadows often disappear off the edge of the terminator. Nor do you want something far from the terminator, since then the shadow will be too small. So pick something in between where you can measure the shadow, but you won't get confused about where the end of it is. Now just line up the callibration marks over your shadow and measure how many ticks (plus fractions of a tick) it is. Be as precise as you can. Also measure how many ticks it is from the terminator to the far side of your shadow. Granted, the terminator is not very well defined, since there are shadows all over the place, but do your best. Use your scale factor from step one to convert to arcsec. Then we want to convert this to kilometers. To do this we need to use the small angle formula. Let X be the linear size of either the shadow or the distance to the terminator, A be the angular size, and d be the distance to the moon. Then: X / (2 * pi * d) = A / (360-degrees) or, X = (d) * (A [in arcsec]) / 206265 . d = 384,400 km on average (which is good enough for us), so d / 206265 = 1.864 km. Thus, X = (1.864 * A [in arcsec]) km . Actually, this is not exactly right. The equation we started with is only accurate if we are looking at something straight on -- that is, if it's pointed perpendicular to the direction we are looking. If you look at Figure 1 again, you'll see that shadows near the terminator are only perpendicular to us if it is exactly first (or third) quarter moon, when the suns light is coming exactly from the side. If it's not exactly first quarter, the shadows will be at a bit of an angle to us. What this means is that a shadow will appear smaller than it really is. If you hold a pen at arm's length and turn it a bit, the angular size will get smaller, even though the pen is still the same length. If you know some trig, you can convince yourself that the apparent size of the pen is smaller by the cosine of the angle that you turned it. (If you don't know trig or don't want to bother, you can take my word for it.) So, we have to correct for this projection effect by dividing the observed angular size by the cosine of this angle. Let's call it T (since we already used A and this angle is based on the time from first quarter). Then, since there are 29.5 days between new moons, T = (360 degrees) * (# days from first quarter) / 29.5 . And our complete formula for X is X = 1.864 * A[in arcsec] / cos(T) km . Now you can find the height of the mountain using the equation given in the introduction.
The weather satellite is a type of satellite that is primarily used to monitor the weather and climate of the Earth. Satellites can be polar orbiting, covering the entire Earth asynchronously, or geostationary, hovering over the same spot on the equator. Meteorological satellites see more than clouds and cloud systems. City lights, fires, effects of pollution, auroras, sand and dust storms, snow cover, ice mapping, boundaries of ocean currents, energy flows, etc., and other types of environmental information are collected using weather satellites. Weather satellite images helped in monitoring the volcanic ash cloud from Mount St. Helens and activity from other volcanoes such as Mount Etna. Smoke from fires in the western United States such as Colorado and Utah have also been monitored. Other environmental satellites can detect changes in the Earth's vegetation, sea state, ocean color, and ice fields. For example, the 2002 Prestige oil spill off the northwest coast of Spain was watched carefully by the European ENVISAT, which, though not a weather satellite, flies an instrument (ASAR) which can see changes in the sea surface. El Niño and its effects on weather are monitored daily from satellite images. The Antarctic ozone hole is mapped from weather satellite data. Collectively, weather satellites flown by the U.S., Europe, India, China, Russia, and Japan provide nearly continuous observations for a global weather watch. As early as 1946, the idea of cameras in orbit to observe the weather was being developed. This was due to sparse data observation coverage and the expense of using cloud cameras on rockets. By 1958, the early prototypes for TIROS and Vanguard (developed by the Army Signal Corps) were created. The first weather satellite, Vanguard 2, was launched on February 17, 1959. It was designed to measure cloud cover and resistance, but a poor axis of rotation and its elliptical orbit kept it from collecting a notable amount of useful data. The Explorer VI and VII satellites also contained weather-related experiments. The first weather satellite to be considered a success was TIROS-1, launched by NASA on April 1, 1960. TIROS operated for 78 days and proved to be much more successful than Vanguard 2. TIROS paved the way for the Nimbus program, whose technology and findings are the heritage of most of the Earth-observing satellites NASA and NOAA have launched since then. Beginning with the Nimbus 3 satellite in 1969, temperature information through the tropospheric column began to be retrieved by satellites from the eastern Atlantic and most of the Pacific ocean, which led to significant improvements to weather forecasts. The ESSA and NOAA polar orbiting satellites followed suit from the late 1960s onward. Geostationary satellites followed, beginning with the ATS and SMS series in the late 1960s and early 1970s, then continuing with the GOES series from the 1970s onward. Polar orbiting satellites such as QuikScat and TRMM began to relay wind information near the ocean's surface starting in the late 1970s, with microwave imagery which resembled radar displays, which significantly improved the diagnoses of tropical cyclone strength, intensification, and location during the 2000s and 2010s. Some of these channels include - Visible and Near Infrared: 0.6 μm – 1.6 μm – For recording cloud cover during the day - Infrared: 3.9 μm – 7.3 μm (Water Vapor), 8.7 μm, – 13.4 μm (Thermal imaging) Visible-light images from weather satellites during local daylight hours are easy to interpret even by the average person; clouds, cloud systems such as fronts and tropical storms, lakes, forests, mountains, snow ice, fires, and pollution such as smoke, smog, dust and haze are readily apparent. Even wind can be determined by cloud patterns, alignments and movement from successive photos. The thermal or infrared images recorded by sensors called scanning radiometers enable a trained analyst to determine cloud heights and types, to calculate land and surface water temperatures, and to locate ocean surface features. Infrared satellite imagery can be used effectively for tropical cyclones with a visible eye pattern, using the Dvorak technique, where the difference between the temperature of the warm eye and the surrounding cold cloud tops can be used to determine its intensity (colder cloud tops generally indicate a more intense storm). Infrared pictures depict ocean eddies or vortices and map currents such as the Gulf Stream which are valuable to the shipping industry. Fishermen and farmers are interested in knowing land and water temperatures to protect their crops against frost or increase their catch from the sea. Even El Niño phenomena can be spotted. Using color-digitized techniques, the gray shaded thermal images can be converted to color for easier identification of desired information. Geostationary weather satellites orbit the Earth above the equator at altitudes of 35,880 km (22,300 miles). Because of this orbit, they remain stationary with respect to the rotating Earth and thus can record or transmit images of the entire hemisphere below continuously with their visible-light and infrared sensors. The news media use the geostationary photos in their daily weather presentation as single images or made into movie loops. These are also available on the city forecast pages of noaa.gov (example Dallas, TX). Several geostationary meteorological spacecraft are in operation. The United States has three in operation; GOES-12, GOES-13, and GOES-15. GOES-12, previously designated GOES-East and now used for South America, is located at 60 degrees west. GOES-13 took over the role of GOES-East on April 14, 2010 and is located at 75 degrees west. GOES-11 was GOES-West over the eastern Pacific Ocean until it was decommissioned December 2011 and replaced by GOES-15. Russia's new-generation weather satellite Elektro-L No.1 operates at 76°E over the Indian Ocean. The Japanese have the MTSAT-2 located over the mid Pacific at 145°E and the Himawari 8 at 140°E. The Europeans have four in operation, Meteosat-8 (3.5°W) and Meteosat-9 (0°) over the Atlantic Ocean and have Meteosat-6 (63°E) and Meteosat-7 (57.5°E) over the Indian Ocean. China currently has three Fengyun (风云) geostationary satellites (FY-2E at 86.5°E, FY-2F at 123.5°E, and FY-2G at 105°E) operated. India also operates geostationary satellites called INSAT which carry instruments for meteorological purposes. Polar orbiting weather satellites circle the Earth at a typical altitude of 850 km (530 miles) in a north to south (or vice versa) path, passing over the poles in their continuous flight. Polar satellites are in sun-synchronous orbits, which means they are able to observe any place on Earth and will view every location twice each day with the same general lighting conditions due to the near-constant local solar time. Polar orbiting weather satellites offer a much better resolution than their geostationary counterparts due their closeness to the Earth. The United States has the NOAA series of polar orbiting meteorological satellites, presently NOAA 17 and NOAA 18 as primary spacecraft, NOAA 15 and NOAA 16 as secondary spacecraft, NOAA 14 in standby, and NOAA 12. Europe has the Metop-A and Metop-B satellites operated by EUMETSAT. Russia has the Meteor and RESURS series of satellites. China has FY-3A, 3B and 3C. India has polar orbiting satellites as well. The United States Department of Defense's Meteorological Satellite (DMSP) can "see" the best of all weather vehicles with its ability to detect objects almost as 'small' as a huge oil tanker. In addition, of all the weather satellites in orbit, only DMSP can "see" at night in the visual. Some of the most spectacular photos have been recorded by the night visual sensor; city lights, volcanoes, fires, lightning, meteors, oil field burn-offs, as well as the Aurora Borealis and Aurora Australis have been captured by this 450-mile-high space vehicle's low moonlight sensor. At the same time, energy use and city growth can be monitored since both major and even minor cities, as well as highway lights, are conspicuous. This informs astronomers of light pollution. The New York City Blackout of 1977 was captured by one of the night orbiter DMSP space vehicles. In addition to monitoring city lights, these photos are a life saving asset in the detection and monitoring of fires. Not only do the satellites see the fires visually day and night, but the thermal and infrared scanners on board these weather satellites detect potential fire sources below the surface of the Earth where smoldering occurs. Once the fire is detected, the same weather satellites provide vital information about wind that could fan or spread the fires. These same cloud photos from space tell the firefighter when it will rain. Some of the most dramatic photos showed the 600 Kuwaiti oil fires that the fleeing Army of Iraq started on February 23, 1991. The night photos showed huge flashes, far outstripping the glow of large populated areas. The fires consumed millions of gallons of oil; the last was doused on November 6, 1991. Snowfield monitoring, especially in the Sierra Nevada, can be helpful to the hydrologist keeping track of available snowpack for runoff vital to the watersheds of the western United States. This information is gleaned from existing satellites of all agencies of the U.S. government (in addition to local, on-the-ground measurements). Ice floes, packs and bergs can also be located and tracked from weather space craft. Even pollution whether it is nature-made or man-made can be pinpointed. The visual and infrared photos show effects of pollution from their respective areas over the entire earth. Aircraft and rocket pollution, as well as condensation trails, can also be spotted. The ocean current and low level wind information gleaned from the space photos can help predict oceanic oil spill coverage and movement. Almost every summer, sand and dust from the Sahara Desert in Africa drifts across the equatorial regions of the Atlantic Ocean. GOES-EAST photos enable meteorologists to observe, track and forecast this sand cloud. In addition to reducing visibilities and causing respiratory problems, sand clouds suppress hurricane formation by modifying the solar radiation balance of the tropics. Other dust storms in Asia and mainland China are common and easy to spot and monitor, with recent examples of dust moving across the Pacific Ocean and reaching North America. In remote areas of the world with few local observers, fires could rage out of control for days or even weeks and consume millions of acres before authorities are alerted. Weather satellites can be a tremendous asset in such situations. Nighttime photos also show the burn-off in gas and oil fields. Atmospheric temperature and moisture profiles have been taken by weather satellites since 1969. - Earth observation satellite - Geostationary orbit - Low Earth orbit - Satellite temperature measurements - NESDIS. Satellites. Retrieved on July 4, 2008. - NOAA. NOAA Satellites, Scientists Monitor Mt. St. Helens for Possible Eruption. Retrieved on July 4, 2008. - Janice Hill (1991). Weather From Above: America's Meteorological Satellites. Smithsonian Institution. pp. 4–7. ISBN 0-87474-394-X. - "VANGUARD - A HISTORY, CHAPTER 12, SUCCESS - AND AFTER". NASA. Archived from the original on 2008-05-09. - "U.S. Launches Camera Weather Satellite". The Fresno Bee. AP and UPI. April 1, 1960. pp. 1a, 4a. - National Environmental Satellite Center (January 1970). "SIRS and the Improved Marine Weather Forecast". Mariners Weather Log. Environmental Science Services Administration. 14 (1): 12–15. - EUMETSAT – MSG Spectrum (PDF) - EUMETSAT – MFG Payload - A. F. Hasler, K. Palaniappan, C. Kambhammetu, P. Black, E. Uhlhorn, and D. Chesters. High-Resolution Wind Fields within the Inner Core and Eye of a Mature Tropical Cyclone from GOES 1-min Images. Retrieved on 2008-07-04. - Chris Landsea. Subject: H1) What is the Dvorak technique and how is it used? Retrieved on January 3, 2009. - "GOES 12 Spacecraft Status Summary". NOAA Satellite and Information Service. Retrieved December 13, 2010. - "GOES 13 Spacecraft Status Summary". NOAA Satellite and Information Service. Retrieved February 15, 2012. - "GOES 15 Spacecraft Status Summary". NOAA Satellite and Information Service. Retrieved February 15, 2012. - National Satellite Meteorological Center of CMA (in Chinese) http://www.nsmc.cma.gov.cn/NSMC/Channels/100003.html. Missing or empty - Ann K. Cook (July 1969). "The Breakthrough Team" (PDF). ESSA World. Environmental Satellite Services Administration: 28–31. Retrieved 2012-04-21. \|Wikimedia Commons has media related to Meteorological satellites.\| - Ralph E. Taggard (1994). Weather satellite handbook (5th edition). Newington, CT: American Radio Relay League. ISBN 0-87259-448-3. - Cooperative Institute for Meteorological Satellite Studies - Dr. Verner Suomi ("father of the geostationary satellite") biography - Physical Characteristics of Geostationary and Polar-Orbiting weather satellites - Near realtime composite of satellite image of the Earth by Intellicast - International weather satellite viewer Online geostationary weather satellite viewer with 2 months of archived data. - Earth at night by NASA - EUMETSAT – the European Organisation for the Exploitation of Meteorological Satellites - NASA Langley Cloud and Radiation Research Near real-time and archived satellite imagery and cloud products. - Government policy - Geostationary Weather Satellites: Progress Made, but Weaknesses in Scheduling, Contingency Planning, and Communicating with Users Need To Be Addressed: Report to the Committee on Science, Space, and Technology, House of Representatives Government Accountability Office - Polar Weather Satellites: NOAA Identified Ways to Mitigate Data Gaps, but Contingency Plans and Schedules Require Further Attention: Report to the Committee on Science, Space, and Technology, House of Representatives Government Accountability Office
The first thing one must know to understand quadratic equations is the term "quadratic". A quadratic equation is an algebraic equation in which the highest power of the variable is 2. For example x^2+2x+3=0 is a quadratic equation, whereas 2x+4=0, x^3+2x^2+x+5=0 are not. Generally speaking the standard form of a quadratic equation is ax^2+bx+c=0, where a,b, c are integers. To solve quadratic equations there are several methods one can use. I will discuss these methods below. Suppose you wish to multiply (x + 5) and (x - 3). This is done by a process known as FOIL. Multiply the first term in the set of parentheses, (x)(x). Then multiply the outer term in each set of parentheses, (x)(-3). Then multiply the inner terms (5)(x). Finally, multiply the last terms (5)(-3). When combining like terms we get x^2 -3x + 5x -15 = x^2 + 2x -15. Suppose now that we wish to take the quadratic equation, x^2 + 2x - 15 and factor it. The factored form is (x + 5)(x - 3). So the process I am going to introduce is basically a reverse FOIL. You will set up two sets of parentheses ( )( ). In each set you will have 2 terms, with an addition or subtraction sign between each term. First you have to think of what two terms multiplied together gives the first term in the quadratic equation. That would be x and x, since x times x is x^2. Put them in the first location in each parenthesis. So you have (x )(x ). Next you want to see what multiplies together to give you the last term of -15, but ADDS to give you the middle term coefficient of 2. That would be 5 and -3 since 5 times -3 equals -15 and 5 plus -3 equals 2.. Those numbers go in the remaining two spots in the parenthesis to give you (x + 5)(x- 3). Suppose the quadratic equation used in the example above is set equal to zero. How do we solve such an equation? We simply factor it and set each factor equal to zero and solve. For example, (x + 5)(x - 3) = 0, so we have 2 equations to solve: (x + 5) = 0 and (x - 3) = 0 Solving each equation gives us x = -5 or x = 3. Note that in some quadratic equations, you must factor out the greatest common factor first to make factoring easier. For example, if the equation is 4x^2 + 20x + 16, it's easier to factor out a 4 first to get 4(x^2 + 5x + 4). From here, we can factor x^2 + 5x + 4 like we did above. The factored form is 4(x + 4)(x + 1). The next way to factor is a method called completing the square. The idea is when factoring to get a perfect square trinomial on the left side of the equation equaling a number on the right side and taking square root of both sides to solve for x. A perfect square trinomial is a trinomial that is factored into a single term squared. For example x^2 + 6x + 9 is a perfect square trinomial because it is factored to (x +3)(x+ 3). Suppose we have the problem x^2 + 4x + 3 = 0. First thing we do is make sure the coefficient (number in front of the variable) of the squared term is 1, if it isn't you must divide by that coefficient to get that to be 1. Subtract 3 from both sides of the equation to get x^2 + 4x = -3 We want to turn x^2 + 4x into a perfect square trinomial. To do that we take half the middle term coefficient, square it and add to both sides. This gives us x^2 + 4x + 4 = -3 + 4 Notice now that the left side of the equation is a perfect square trinomial. Factor this and add terms on the right side to get (x + 2)(x + 2) = 1 or (x + 2)^2 = 1 Now we take the square root of both sides to eliminate the exponent of 2 from the left side of the equation. (x + 2) = +/-1 When we solve this for x, we get x = -3 and x = -1. Generally speaking if you can factor by the reverse FOIL method, do so because this is a bit more complex, as is the next method. The final method used to factor quadratic equations is by the quadratic formula. The basis of this is using the standard form of ax^2+bx+c=0 and using the a,b,c in a formula to solve for x. The formula is x=-b +/ - square root of b^2-4ac, all divided by 2a. In our example of x^2+4x+3=0, a is 1, b is 4 and c is 3. By substituting those numbers into that formula you get x = -[4 +/- square root(4^2 - 4(1)(3))]/2(1) x =[ -4 +/- square root(16 - 12)]/2 x =[ -4 +/- square root(4)]/2 x = (-4 +/- 2)/2 x = (-4 + 2)/2 or (-4 - 2)/2 x = -1 or x = -3. Notice that all 3 methods give the same answer. You can use any of the methods you wish to factor a quadratic equation. This example has solutions for x that are real numbers and 2 answers. There is also a possibility that there is only 1 solution when there is a square, ( (x+2)^2=0, would give x= -2, which is called a double root) . You could also get an imaginary number as the solution if the square root part of the quadratic formula is negative. The graphs of quadratic equations such as y = ax^2 + bx + c are parabolas which open upward. If a is negative it opens downward. IF the equation is in the form x = ay^2 + by + c, then the parabola opens left. If a is negative, the parabola opens to the left. One can graph quadratic equations by setting up an x, y chart and choose a few numbers for x, solve for y and plot on a rectangular coordinate system. If the equation is y = ax^2 + bx + c, it is wise to use 0 for y and find the x intercepts. The vertex is then halfway between the intercepts. For example, if the intercepts are where the x coordinates are 0 and 4, you know the vertex is where x = 2. The axis of symmetry for a parabola opening up or down is always the line the goes vertically through the vertex. Likewise, graphing a parabola in the form x = ay^2 + by + c is easy if you find the y-intercepts first. This is done by putting 0 in for x and solving for y. The vertex will be halfway in between the intercepts and the axis of symmetry is the horizontal line through the vertex. I have tutored algebra for 12 years and these are the methods I teach students all the time when trying to factor quadratic equations. I hope anyone that needs help has gotten a better understanding how to do this with my article.
A meteoroid (/ˈmiːtiərɔɪd/) is a small rocky or metallic body in outer space. Meteoroids are significantly smaller than asteroids, and range in size from small grains to 1 meter-wide objects. Objects smaller than this are classified as micrometeoroids or space dust. Most are fragments from comets or asteroids, whereas others are collision impact debris ejected from bodies such as the Moon or Mars. When a meteoroid, comet, or asteroid enters Earth's atmosphere at a speed typically in excess of 20 km/s (72,000 km/h; 45,000 mph), aerodynamic heating of that object produces a streak of light, both from the glowing object and the trail of glowing particles that it leaves in its wake. This phenomenon is called a meteor or "shooting star". A series of many meteors appearing seconds or minutes apart and appearing to originate from the same fixed point in the sky is called a meteor shower. If that object withstands ablation from its passage through the atmosphere as a meteor and impacts with the ground, it is then called a meteorite. An estimated 15,000 tonnes of meteoroids, micrometeoroids and different forms of space dust enter Earth's atmosphere each year. In 1961, the International Astronomical Union defined a meteoroid as "a solid object moving in interplanetary space, of a size considerably smaller than an asteroid and considerably larger than an atom". In 1995, Beech and Steel, writing in the Quarterly Journal of the Royal Astronomical Society, proposed a new definition where a meteoroid would be between 100 µm and 10 meters across. In 2010, following the discovery of asteroids below 10 m in size, Rubin and Grossman revised the previous definition of meteoroid to objects between 10 µm and 1 m in diameter in order to maintain the distinction. According to Rubin and Grossman, the minimum size of an asteroid is given by what can be discovered from Earth-bound telescopes, so the distinction between meteoroid and asteroid is fuzzy. Some of the smallest asteroids discovered (based on absolute magnitude H) are 2008 TS26 with H = 33.2 and 2011 CQ1 with H = 32.1 both with an estimated size of 1 meter. Objects smaller than meteoroids are classified as micrometeoroids and cosmic dust. The Minor Planet Center does not use the term "meteoroid". Almost all meteoroids contain extraterrestrial nickel and iron. They have three main classifications: iron, stone, and stony-iron. Some stone meteoroids contain grain-like inclusions known as chondrules and are called chondrites. Stoney meteoroids without these features are called "achondrites", which are typically formed from extraterrestrial igneous activity; they contain little or no extraterrestrial iron. The composition of meteoroids can be inferred as they pass through Earth's atmosphere from their trajectories and the light spectra of the resulting meteor. Their effects on radio signals also give information, especially useful for daytime meteors, which are otherwise very difficult to observe. From these trajectory measurements, meteoroids have been found to have many different orbits, some clustering in streams (see meteor showers) often associated with a parent comet, others apparently sporadic. Debris from meteoroid streams may eventually be scattered into other orbits. The light spectra, combined with trajectory and light curve measurements, have yielded various compositions and densities, ranging from fragile snowball-like objects with density about a quarter that of ice, to nickel-iron rich dense rocks. The study of meteorites also gives insights into the composition of non-ephemeral meteoroids. Most meteoroids come from the asteroid belt, having been perturbed by the gravitational influences of planets, but others are particles from comets, giving rise to meteor showers. Some meteoroids are fragments from bodies such as Mars or our moon, that have been thrown into space by an impact. Meteoroids travel around the Sun in a variety of orbits and at various velocities. The fastest move at about 42 kilometers per second through space in the vicinity of Earth's orbit. This is escape velocity from the sun, equal to the square root of 2 times Earth's speed, and is the upper speed limit of objects in the vicinity of Earth, unless they come from interstellar space. Earth travels at about 29.6 kilometers per second, so when meteoroids meet the atmosphere head-on (which only occurs when meteors are in a retrograde orbit such as the Eta Aquarids, which are associated with the retrograde Halley's Comet) the combined speed may reach about 71 kilometers per second. Meteoroids moving through Earth's orbital space average about 20 km/s. On January 17, 2013 at 05:21 PST, a 1 meter-sized comet from the Oort cloud entered Earth atmosphere over a wide area in California and Nevada. The object had a retrograde orbit with perihelion at 0.98 ± 0.03 AU. It approached from the direction of the constellation Virgo, and collided head-on with Earth atmosphere at 72 ± 6 km/s vapourising more than 100 km above ground over a period of several seconds. When meteoroids intersect with Earth's atmosphere at night, they are likely to become visible as meteors. If meteoroids survive the entry through the atmosphere and reach Earth's surface, they are called meteorites. Meteorites are transformed in structure and chemistry by the heat of entry and force of impact. A noted 4-meter asteroid, 2008 TC3, was observed in space on a collision course with Earth on 6 October 2008 and entered Earth's atmosphere the next day, striking a remote area of northern Sudan. It was the first time that a meteoroid had been observed in space and tracked prior to impacting Earth. NASA has produced a map showing the most notable asteroid collisions with Earth and its atmosphere from 1994 to 2013 from data gathered by U.S. government sensors (see below). A meteor, known colloquially as a "shooting star" or "falling star", is the visible passage of a glowing meteoroid, micrometeoroid, comet or asteroid through Earth's atmosphere, after being heated to incandescence by collisions with air molecules in the upper atmosphere, creating a streak of light via its rapid motion and sometimes also by shedding glowing material in its wake. Meteors typically occur in the mesosphere at altitudes from 76 to 100 km (47 to 62 mi). The root word meteor comes from the Greek meteōros, meaning "high in the air". Millions of meteors occur in Earth's atmosphere daily. Most meteoroids that cause meteors are about the size of a grain of sand. Meteors may occur in showers, which arise when Earth passes through a stream of debris left by a comet, or as "random" or "sporadic" meteors, not associated with a specific stream of space debris. A number of specific meteors have been observed, largely by members of the public and largely by accident, but with enough detail that orbits of the meteoroids producing the meteors have been calculated. All of the orbits passed through the asteroid belt. The atmospheric velocities of meteors result from the movement of Earth around the Sun at about 30 km/s (18 miles/second), the orbital speeds of meteoroids, and the gravity well of Earth. Meteors become visible between about 75 to 120 km (47 to 75 mi) above Earth. They usually disintegrate at altitudes of 50 to 95 km (31 to 59 mi). Meteors have roughly a fifty percent chance of a daylight (or near daylight) collision with Earth. Most meteors are, however, observed at night, when darkness allows fainter objects to be recognized. For bodies with a size scale larger than 10 cm to several meters meteor visibility is due to the atmospheric ram pressure (not friction) that heats the meteoroid so that it glows and creates a shining trail of gases and melted meteoroid particles. The gases include vaporised meteoroid material and atmospheric gases that heat up when the meteoroid passes through the atmosphere. Most meteors glow for about a second. Although meteors have been known since ancient times, they were not known to be an astronomical phenomenon until early in the 19th century. Prior to that, they were seen in the West as an atmospheric phenomenon, like lightning, and were not connected with strange stories of rocks falling from the sky. In 1807, Yale University chemistry professor Benjamin Silliman investigated a meteorite that fell in Weston, Connecticut. Silliman believed the meteor had a cosmic origin, but meteors did not attract much attention from astronomers until the spectacular meteor storm of November 1833. People all across the eastern United States saw thousands of meteors, radiating from a single point in the sky. Astute observers noticed that the radiant, as the point is now called, moved with the stars, staying in the constellation Leo. The astronomer Denison Olmsted made an extensive study of this storm, and concluded that it had a cosmic origin. After reviewing historical records, Heinrich Wilhelm Matthias Olbers predicted the storm's return in 1867, which drew the attention of other astronomers to the phenomenon. Hubert A. Newton's more thorough historical work led to a refined prediction of 1866, which proved to be correct. With Giovanni Schiaparelli's success in connecting the Leonids (as they are now called) with comet Tempel-Tuttle, the cosmic origin of meteors was now firmly established. Still, they remain an atmospheric phenomenon, and retain their name "meteor" from the Greek word for "atmospheric". A fireball is a brighter-than-usual meteor. The International Astronomical Union (IAU) defines a fireball as "a meteor brighter than any of the planets" (apparent magnitude −4 or greater). The International Meteor Organization (an amateur organization that studies meteors) has a more rigid definition. It defines a fireball as a meteor that would have a magnitude of −3 or brighter if seen at zenith. This definition corrects for the greater distance between an observer and a meteor near the horizon. For example, a meteor of magnitude −1 at 5 degrees above the horizon would be classified as a fireball because, if the observer had been directly below the meteor, it would have appeared as magnitude −6. Fireballs reaching apparent magnitude −14 or brighter are called bolides. The IAU has no official definition of "bolide", and generally considers the term synonymous with "fireball". Astronomers often use "bolide" to identify an exceptionally bright fireball, particularly one that explodes. They are sometimes called detonating fireballs (also see List of meteor air bursts). It may also be used to mean a fireball which creates audible sounds. In the late twentieth century, bolide has also come to mean any object that hits Earth and explodes, with no regard to its composition (asteroid or comet). The word bolide comes from the Greek βολίς (bolis) which can mean a missile or to flash. If the magnitude of a bolide reaches −17 or brighter it is known as a superbolide. A relatively small percentage of fireballs hit Earth's atmosphere and then pass out again: these are termed Earth-grazing fireballs. Such an event happened in broad daylight over North America in 1972. Another rare phenomena is a meteor procession, where the meteor breaks up into several fireballs traveling nearly parallel to the surface of Earth. A steadily growing number of fireballs are recorded at the American Meteor Society every year. There are probably more than 500,000 fireballs a year, but most will go unnoticed because most will occur over the ocean and half will occur during daytime. The entry of meteoroids into Earth's atmosphere produces three main effects: ionization of atmospheric molecules, dust that the meteoroid sheds, and the sound of passage. During the entry of a meteoroid or asteroid into the upper atmosphere, an ionization trail is created, where the air molecules are ionized by the passage of the meteor. Such ionization trails can last up to 45 minutes at a time. Small, sand-grain sized meteoroids are entering the atmosphere constantly, essentially every few seconds in any given region of the atmosphere, and thus ionization trails can be found in the upper atmosphere more or less continuously. When radio waves are bounced off these trails, it is called meteor burst communications. Meteor radars can measure atmospheric density and winds by measuring the decay rate and Doppler shift of a meteor trail. Most meteoroids burn up when they enter the atmosphere. The left-over debris is called meteoric dust or just meteor dust. Meteor dust particles can persist in the atmosphere for up to several months. These particles might affect climate, both by scattering electromagnetic radiation and by catalyzing chemical reactions in the upper atmosphere. Meteoroids or their fragments may achieve dark flight after deceleration to terminal velocity. Dark flight starts when they decelerate to about 2–4 km/s (4,500–8,900 mph). Larger fragments will fall further down the strewn field. The visible light produced by a meteor may take on various hues, depending on the chemical composition of the meteoroid, and the speed of its movement through the atmosphere. As layers of the meteoroid abrade and ionize, the colour of the light emitted may change according to the layering of minerals. Colours of meteors depend on the relative influence of the metallic content of the meteoroid versus the superheated air plasma, which its passage engenders: Sound generated by a meteor in the upper atmosphere, such as a sonic boom, typically arrives many seconds after the visual light from a meteor disappears. Occasionally, as with the Leonid meteor shower of 2001,"crackling", "swishing", or "hissing" sounds have been reported, occurring at the same instant as a meteor flare. Similar sounds have also been reported during intense displays of Earth's auroras. Theories on the generation of these sounds may partially explain them. For example, scientists at NASA suggested that the turbulent ionized wake of a meteor interacts with Earth's magnetic field, generating pulses of radio waves. As the trail dissipates, megawatts of electromagnetic power could be released, with a peak in the power spectrum at audio frequencies. Physical vibrations induced by the electromagnetic impulses would then be heard if they are powerful enough to make grasses, plants, eyeglass frames, and other conductive materials vibrate. This proposed mechanism, although proven to be plausible by laboratory work, remains unsupported by corresponding measurements in the field. Sound recordings made under controlled conditions in Mongolia in 1998 support the contention that the sounds are real. (Also see Bolide.) A meteor shower is the result of an interaction between a planet, such as Earth, and streams of debris from a comet or other source. The passage of Earth through cosmic debris from comets and other sources is a recurring event in many cases. Comets can produce debris by water vapor drag, as demonstrated by Fred Whipple in 1951, and by breakup. Each time a comet swings by the Sun in its orbit, some of its ice vaporizes and a certain amount of meteoroids will be shed. The meteoroids spread out along the entire orbit of the comet to form a meteoroid stream, also known as a "dust trail" (as opposed to a comet's "dust tail" caused by the very small particles that are quickly blown away by solar radiation pressure). The frequency of fireball sightings increases by about 10-30% during the weeks of vernal equinox. Even meteorite falls are more common during the northern hemisphere's spring season. Although this phenomenon has been known for quite some time, the reason behind the anomaly is not fully understood by scientists. Some researchers attribute this to an intrinsic variation in the meteoroid population along Earth's orbit, with a peak in big fireball-producing debris around spring and early summer. Others have pointed out that during this period the ecliptic is (in the northern hemisphere) high in the sky in the late afternoon and early evening. This means that fireball radiants with an asteroidal source are high in the sky (facilitating relatively high rates) at the moment the meteoroids "catch up" with Earth, coming from behind going in the same direction as Earth. This causes relatively low relative speeds and from this low entry speeds, which facilitates survival of meteorites. It also generates high fireball rates in the early evening, increasing chances of eye witness reports. This explains a part, but perhaps not all of the seasonal variation. Research is in progress for mapping the orbits of the meteors to gain a better understanding of the phenomenon. A meteorite is a portion of a meteoroid or asteroid that survives its passage through the atmosphere and hits the ground without being destroyed. Meteorites are sometimes, but not always, found in association with hypervelocity impact craters; during energetic collisions, the entire impactor may be vaporized, leaving no meteorites. Geologists use the term, "bolide", in a different sense from astronomers to indicate a very large impactor. For example, the USGS uses the term to mean a generic large crater-forming projectile in a manner "to imply that we do not know the precise nature of the impacting body ... whether it is a rocky or metallic asteroid, or an icy comet for example". The diameter of the largest impactor to hit Earth on any given day is likely to be about 40 centimeters (16 inches), in a given year about 4 meters, and in a given century about 20 meters. These statistics are obtained by the following: Over at least the range from 5 centimeters (2.0 inches) to roughly 300 meters (980 feet), the rate at which Earth receives meteors obeys a power-law distribution as follows: where N (>D) is the expected number of objects larger than a diameter of D meters to hit Earth in a year. This is based on observations of bright meteors seen from the ground and space, combined with surveys of near-Earth asteroids. Above 300 meters in diameter, the predicted rate is somewhat higher, with a two-kilometer asteroid (one million-megaton TNT equivalent) every couple of million years — about 10 times as often as the power-law extrapolation would predict. Meteoroid collisions with solid Solar System objects, including the Moon, Mercury, Callisto, Ganymede and most small moons and asteroids, create impact craters, which are the dominant geographic features of many of those objects. On other planets and moons with active surface geological processes, such as Earth, Venus, Mars, Europa, Io and Titan, visible impact craters may become eroded, buried or transformed by tectonics over time. In early literature, before the significance of impact cratering was widely recognised, the terms cryptoexplosion or cryptovolcanic structure were often used to describe what are now recognised as impact-related features on Earth. Molten terrestrial material ejected from a meteorite impact crater can cool and solidify into an object known as a tektite. These are often mistaken for meteorites. Content from Wikipedia
Mathematics and art - perspective \|Alphabetical list of History Topics\|\|History Topics Index\| There is little doubt that a study of the development of ideas relating to perspective would be expected to begin with classical times, and in particular with the ancient Greeks who used some notion of perspective in their architecture and design of stage sets. However, although Hellenistic painters could create an illusion of depth in their works, there is no evidence that they understood the precise mathematical laws which govern correct representation. We chose to begin this article, therefore, with the developments in the understanding of perspective which took place during the Renaissance. First let us state the problem: how does one represent the three-dimensional world on a two-dimensional canvass? There are two aspects to the problem, namely how does one use mathematics to make realistic paintings and secondly what is the impact of the ideas for the study of geometry. By the 13th Century Giotto was painting scenes in which he was able to create the impression of depth by using certain rules which he followed. He inclined lines above eye-level downwards as they moved away from the observer, lines below eye-level were inclined upwards as they moved away from the observer, and similarly lines to the left or right would be inclined towards the centre. Although not a precise mathematical formulation, Giotto clearly worked hard on how to represent depth in space and examining his pictures chronologically shows how his ideas developed. Some of his last works suggest that he may have come close to the correct understanding of linear perspective near the end of his life. The person who is credited with the first correct formulation of linear perspective is Brunelleschi. He appears to have made the discovery in about 1413. He understood that there should be a single vanishing point to which all parallel lines in a plane, other than the plane of the canvas, converge. Also important was his understanding of scale, and he correctly computed the relation between the actual length of an object and its length in the picture depending on its distance behind the plane of the canvas. Using these mathematical principles, he drew two demonstration pictures of Florence on wooden panels with correct perspective. One was of the octagonal baptistery of St John, the other of the Palazzo de Signori. To give a more vivid demonstration of the accuracy of his painting, he bored a small hole in the panel with the baptistery painting at the vanishing point. A spectator was asked to look through the hole from behind the panel at a mirror which reflected the panel. In this way Brunelleschi controlled precisely the position of the spectator so that the geometry was guaranteed to be correct. These perspective paintings by Brunelleschi have since been lost but a "Trinity" fresco by Masaccio from this same period still exists which uses Brunelleschi's mathematical principles. Here is a picture of Masaccio's Holy Trinity It is reasonable to think about how Brunelleschi came to understand the geometry which underlies perspective. Certainly he was trained in the principles of geometry and surveying methods and, since he had a fascination with instruments, it is reasonable to suppose that he may have used instruments to help him survey buildings. He had made drawing of the ancient buildings of Rome before he came to understand perspective and this must have played an important role. Now although it is clear that Brunelleschi understood the mathematical rules involving the vanishing point that we have described above, he did not write down an explanation of how the rules of perspective work. The first person to do that was Alberti in his treatise On painting. Now in fact Alberti wrote two treatises, the first was written in Latin in 1435 and entitled De pictura while the second, dedicated to Brunelleschi, was an Italian work written in the following year entitled Della pittura. Certainly these books are not simply the same work translated into two different languages. Rather Alberti addresses the books to different audiences, the Latin book is much more technical and addressed to scholars while his Italian version is aimed at a general audience. De pictura is in three parts, the first of which gives the mathematical description of perspective which Alberti considers necessary to a proper understanding of painting. It is, Alberti writes:- ... completely mathematical, concerning the roots in nature from which arise this graceful and noble art.In fact he gives a definition of a painting which shows just how fundamental he considers the notion of perspective to be:- A painting is the intersection of a visual pyramid at a given distance, with a fixed centre and a defined position of light, represented by art with lines and colours on a given surface.Alberti gives background on the principles of geometry, and on the science of optics. He then sets up a system of triangles between the eye and the object viewed which define the visual pyramid referred to above. He gives a precise concept of proportionality which determines the apparent size of an object in the picture relative to its actual size and distance from the observer. One of the most famous examples used by Alberti in his text was that of a floor covered with square tiles. For simplicity we take the centric point, as Alberti calls it (today it is called the vanishing point), in the centre of the square picture. Here is a Alberti's construction of perspective for a tiled floor In our diagram the centric point is C. The square tiles are assumed to have one edge parallel to the bottom of the picture. The other edges which in reality are perpendicular to these edges, will appear in the picture to converge to the centric point C. The diagonals of the squares will all converge to a point D on a line through the centric point parallel to the bottom of the picture. The length of CD determines the correct viewing distance, that is the distance the observer has to be from the picture to obtain the correct perspective effect. Alberti chooses not to give mathematical proofs, however, writing:- We have talked as much as seems necessary about the pyramid, the triangle, the intersection. I usually explain these things to my friends with certain tedious geometrical proofs, which in this commentary it seems to me better to omit for the sake of brevity.Pictures from this period which include a square tiled floor are called pavimento (Italian for floor) pictures. There are many examples of such pictures in the years following Alberti's book which had a huge influence on painting. Of course the pavimento provides a type of Cartesian coordinate system. Alberti shows how to use the grid to obtain the correct shape for a circle. Place a circle on a square grid and mark where the squares cut the circle. Construct the perspective view of the square grid as above and reconstruct the circle by seeing the positions of the points of intersection in the projected view. The circle will project into an ellipse, but it would be a long time before the importance of projecting conic sections was realised. Next we should mention Lorenzo Ghiberti who was born in Pelago, Italy around 1378. He is famed as a sculptor and his most famous work is the bronze doors on the east side of the baptistery in Florence. He created two sets of doors and before he designed the second set he had become familiar with the new ideas on perspective as set out by Alberti. The doors contain ten panels which, Ghiberti wrote, exhibit:- ... architectural settings in the relation with which the eye measures them, and real to such a degree that ... one sees the figures which are near appear larger, and those that are far off smaller, as reality shows it.Ghiberti is also important for his treatise I Commentarii, written around 1447, in three volumes. The work contains a history of art in ancient times, a history of thirteenth century artists, an autobiography, and a compilation of medieval texts on the theory of vision such as that by al-Haytham. This was important since, as we mentioned at the beginning of this article, al-Haytham and others had studied optics and vision without relating the ideas to painting, while now Ghiberti showed the relevance of the earlier ideas on optics to art. The most mathematical of all the works on perspective written by the Italian Renaissance artists in the middle of the 15th century was by Piero della Francesca. In some sense this is not surprising since as well as being one of the leading artists of the period, he was also the leading mathematician writing some fine mathematical texts. In Trattato d'abaco which he probably wrote around 1450, Piero includes material on arithmetic and algebra and a long section on geometry which was very unusual for such texts at the time. It also contains original mathematical results which again is very unusual in a book written in the style of a teaching text (although in the introduction Piero does say that he wrote the book at the request of his patron and friends and not as a school book). Is there a connection with perspective? Yes there is, for Piero illustrates the text with diagrams of solid figures drawn in perspective. Here is Piero's illustration of a dodecahedron Continuing the theme of the regular solids, we note that a later text by Piero is Short book on the five regular solids. However, it is his three volume treatise On perspective for painting (some believe written in the mid 1470s, others believe written in the 1460s) which is of most interest to us in this article. His book begins with a description of painting:- Painting has three principal parts, which we say are drawing, proportion and colouring. Drawing we understand as meaning outlines and contours contained in thing. Proportion we say is these outlines and contours positioned in proportion in their places. Colouring we mean as giving the colours as shown in the things, light and dark according as the light makes them vary. Of the three parts I intend to deal only with proportion, which we call perspective, mixing in with it some part of drawing, because without this perspective cannot be shown in action; colouring we shall leave out, and we shall deal with that part which can be shown by means of lines, angles and proportion, speaking of points, lines, surfaces and bodies.We see from this introduction that Piero intends to concentrate on the mathematical principles. Perhaps it is most accurate to say that he is studying the geometry of vision which he later makes clearer:- First is sight, that is to say the eye; second is the form of the thing seen; third is the distance from the eye to the thing seen; fourth are the lines which leave the boundaries of the object and come to the eye; fifth is the intersection, which comes between the eye and the thing seen, and on which it is intended to record the object.Piero begins by establishing geometric theorems in the style of Euclid but, unlike Euclid, he also gives numerical examples to illustrate them. He then goes on to give theorems which relate to the perspective of plane figures. In the second of the three volumes Piero examines how to draw prisms in perspective. Although less interesting mathematically than the first volume, the examples he chooses to examine in the volume are clearly important to him since they appear frequently in his own paintings. The third volume deals with more complicated objects such as the human head, the decoration on the top of columns, and other "more difficult shapes". For this Piero uses a method which involves a very large amount of tedious calculation. He uses two rulers, one to determine width, the other to determine height. In fact he is using a coordinate system and computing the correct perspective position of many points of the "difficult shape" from which the correct perspective of the whole can be filled in. Piero della Francesca's works were heavily relied on by Luca Pacioli for his own publications. In fact the third book of Pacioli's Divina proportione is an Italian translation of Piero's Short book on the five regular solids. The illustrations in Pacioli's work were by Leonardo da Vinci and include some fine perspective drawings of regular solids. Here is a Leonardo's illustration Now in Leonardo's early writings we find him echoing the precise theory of perspective as set out by Alberti and Piero. He writes:- ... Perspective is a rational demonstration by which experience confirms that the images of all things are transmitted to the eye by pyramidal lines. Those bodies of equal size will make greater or lesser angles in their pyramids according to the different distances between the one and the other. by a pyramid of lines I mean those which depart from the superficial edges of bodies and converge over a distance to be drawn together in a single point.He developed mathematical formulas to compute the relationship between the distance from the eye to the object and its size on the intersecting plane, that is the canvas on which the picture will be painted:- If you place the intersection one metre from the eye, the first object, being four metres from the eye, will diminish by three-quarters of its height on the intersection; and if it is eight metres from the eye it will diminish by seven-eighths and if it is sixteen metres away it will diminish by fifteen-sixteenths, and so on. As the distance doubles so the diminution will double.Not only did Leonardo study the geometry of perspective but he also studied the optical principles of the eye in his attempts to create reality as seen by the eye. By around 1490 Leonardo had moved forward in his thinking about perspective. He was one of the first people to study the converse problem of perspective: given a picture drawn in correct linear perspective compute where the eye must be placed to see this correct perspective. Now he was led to realise that a picture painted in correct linear perspective only looked right if viewed from one exact location. Brunelleschi had been well aware of this when he arranged his demonstration of perspective through a hole. However for a painting on a wall, say, many people would not view it from the correct position, indeed for many paintings it would be impossible for someone viewing them to have their eye in this correct point, as it may have been well above their heads. Leonardo distinguished two different types of perspective: artificial perspective which was the way that the painter projects onto a plane which itself may be seen foreshortened by an observer viewing at an angle; and natural perspective which reproduces faithfully the relative size of objects depending on their distance. In natural perspective, Leonardo correctly claims, objects will be the same size if they lie on a circle centred on the observer. Then Leonardo looked at compound perspective where the natural perspective is combined with a perspective produced by viewing at an angle. Perhaps in Leonardo, more than any other person we mention in this article, mathematics and art were fused in a single concept. The story we have told up to this point has been very much an understanding of perspective in Italy by artists and mathematicians learning personally from each other. By 1500, however, Dürer took the development of the topic into Germany. He did so only after learning much from trips to Italy where he learned at first hand from mathematicians such as Pacioli. He published Unterweisung der Messung mit dem Zirkel und Richtscheit in 1525, the fourth book of which contains his theory of shadows and perspective. Geometrically his theory is similar to that of Piero but he made an important addition stressing the importance of light and shade in depicting correct perspective. An excellent example of this is in the geometrical shape he sketched in 1524. Here is a Dürer's shaded geometrical design Another contribution to perspective made by Dürer in his 1525 treatise was the description of a variety of mechanical aids which could be used to draw images in correct perspective. Let us consider a number of other contributions to the study of perspective over the following 200 years. We mention first Federico Commandino who published Commentarius in planisphaerium Ptolemaei in 1558. In this work he gave an account of Ptolemy's stereographic projection of the celestial sphere, but its importance for perspective is that he broadened the study of that topic which had up until then been concerned almost exclusively with painting. Commandino was more interested in the use of perspective in the making of stage scenery principally because his main interest was in classic texts and, unlike many earlier treatises he was writing for mathematicians rather than artists. Wentzel Jamnitzer wrote a beautiful book on the Platonic solids in 1568 called Perspectiva corporum regularium. This is not a book designed to teach perspective drawing but, nevertheless, contains many illustrations superbly drawn in perspective. He is clear in his intention:- All superfluity will be avoided and, in contrast to the old fashioned way of teaching, no line or point will be drawn needlessly.Daniele Barbaro's La Practica della perspectiva published in 1569, the year after Jamnitzer's treatise, complained that painters had stopped using perspective. Taken at face value this is not true, but what he undoubtedly meant was that painters were not painting architectural scenes. Barbaro was interested in perspective in stage sets mainly because he had published an Italian translation of Vitruvius's On architecture in 1556 and his interest had been aroused by this work. His 1569 treatise shows that he had studied the work of Piero and Dürer carefully and the methods he gave for perspective constructions were variations on their methods. Egnatio Danti, like so many of the others we have mentioned in this article, was both an excellent mathematician and artist. His preface to Le due regole della prospettiva pratica di M Iacomo Barozzi da Vignola was published in 1583, three years before his death. In his introduction to this work Danti wrote a brief history of perspective:- ... we know of no book or written document which has come down to us from ancient practitioners, although they were mot excellent, as is convincingly shown by the descriptions of the stage scenery they made, which was much prized both in Athens among the Greeks and in Rome among the Latins. But in our own time, among those who have left something of note in this art, the earliest, and one who wrote with best method and form, was Messer Pietro della Francesca dal Borgo Sansepolcro, from whom we have today three books in manuscript, most excellently illustrated; and whoever wants to know how excellent they are should look to Daniele Barbaro, who has transcribed a great part of them in his book on Perspective.Not only did Danti write an introduction to his edition of Vignola's treatise, but he also added considerably to its content by giving mathematical justification where Vignola simply states a rule to be applied. The next contributor we mention is Giovanni Battista Benedetti who was a pupil of Tartaglia. He produced a work entitled A book containing various studies of mathematics and physics in 1585 which contains a treatise on arithmetic, some other short works and letters on various scientific topics, as well as a short treatise on perspective De rationibus operationum perspectivae. In his perspective treatise Benedetti was concerned not just with rules for artists working in two dimensions but with the underlying three-dimensional reasons for the rules. We mentioned Commandino above and the next person who we want to note for his contribution to perspective, Guidobaldo del Monte, was a pupil of Commandino. Del Monte's six books on perspective Perspectivae libri sex (1600) contain theorems which he deduces with frequent references to Euclid's Elements. The most important result in del Monte's treatise is that any set of parallel lines, not parallel to the plane of the picture, will converge to a vanishing point. This treatise represents a major step forward in understanding the geometry of perspective and it was a major contribution towards the development of projective geometry. In 1636 Desargues published the short treatise La perspective which only contains 12 pages. In this treatise, which consists of a single worked example, Desargues sets out a method for constructing a perspective image without using any point lying outside the picture field. He considers the representation in the picture plane of lines which meet at a point and also of lines which are parallel to each another. In the last paragraph of the work he considered the problem of finding the perspective image of a conic section. Three years later, in 1639, Desargues wrote his treatise on projective geometry Brouillon project d'une atteinte aux evenemens des rencontres du cone avec un plan. One can see the influence of the work from three years earlier, but Desargues himself gives no motivation for the ideas he introduced. The first part of this treatise deals with the properties of sets of straight lines meeting at a point and ranges of points lying on a straight line. In the second part, the properties of conics are investigated in terms of properties of ranges of points on straight lines. The modern term "point at infinity" appears for the first time in this treatise and pencils of lines are introduced, although that name is not used. In this treatise Desargues shows that he had completely understood the connection between conics and perspective; in fact he treats the fact that any conic can be projected into any other conic as obvious. Although a "cone of vision" had been considered by earlier authors, the significance of this and the way that a study of conics could thus be unified had not been appreciated before. Following Desargues' innovative work it may be surprising that the subject was not developed rapidly in the following years. That it was not may in part have been due to mathematicians failing to recognise the power in what had been put forward. On the other hand the algebraic approach to geometry put forward by Descartes at almost exactly the same time (1637) may have diverted attention from Desargues' projective methods. The first person to really carry forward Desargues' ideas was Philippe de la Hire. He had written a work on conics in 1673 before he discovered Desargues' Brouillon project. In 1679 he made a copy of Desargues' book writing:- In the month of July of the year 1679, I first read this little book by M. Desargues, and copied it out so as to get to know it better. This was more than six years after I had published my first work on conic sections. And I do not doubt that, if I had known anything of this treatise, I should not have discovered the method that I used, for I should never have believed it possible to find any simpler procedure which was also general in application.In fact la Hire had treated conics from a projective point of view in his 1673 treatise New method of geometry for sections of conics and cylindrical surfaces and there he had introduced the cross ratio of four points before meeting Desargues' approach. In 1685 la Hire published Conic sections which is a projective approach to conics which combines the best of the ideas from his earlier work and also those of Desargues. Before discussing the work of Brook Taylor, with which we will end our article, let us mention that of Humphry Ditton who wrote A treatise on perspective, demonstrative and practical in 1712. This is relevant to Taylor's work since it influenced him. Ditton's book is not particularly original but he did present a geometrical approach to perspective which is carefully constructed and well written. In many ways Brook Taylor's Linear perspective: or a new method of representing justly all manners of objects which appeared three years later in 1715, is similar to Ditton's work in its quality. One notable aspect of Taylor's work was that he stated the incidence properties as axioms, making him the first to do so. In 1719 Taylor published a much modified second edition New principles of linear perspective. The work gives the first general treatment of vanishing points. Taylor had a highly mathematical approach to the subject and, despite being an accomplished amateur artist himself, made no concessions to artists who should have found the ideas of fundamental importance to them. At times this highly condensed work is very difficult for even a mathematician to understand, and Taylor makes it clear that he is interested in the underlying principles rather than their application. The phrase "linear perspective" was invented by Taylor in this work and he defined the vanishing point of a line, not parallel to the plane of the picture, as the point where a line through the eye parallel to the given line intersects the plane of the picture. He also defined the vanishing line to a given plane, not parallel to the plane of the picture, as the intersection of the plane through the eye parallel to the given plane. As we have shown above the term vanishing point was invented long before Taylor's time, but he was one of the first to stress the mathematical importance of the vanishing point and vanishing line. The main theorem in Taylor's theory of linear perspective is that the projection of a straight line not parallel to the plane of the picture passes through its intersection and its vanishing point. There is also the interesting inverse problem which is to find the position of the eye in order to see the picture from the viewpoint that the artist intended. Taylor was not the first to discuss this inverse problem as we saw above, one of the first to examining it had been Leonardo nearly 250 years earlier, but Taylor did make innovative contributions to the theory of such perspective problems. One could certainly consider this work as being an important step towards the theory of descriptive and projective geometry as developed by Monge, Chasles and Poncelet. Let us end by giving examples of artists having fun with the deliberate misuse of perspective. The first is by the famous English artist William Hogarth (1697-1764) whose Perspective absurdities formed the frontispiece to J J Kirby's book Dr Brook Taylor's method of perspective made easy in both theory and practice (1754). Here is Hogarth's Perspective absurdities The second examples are by Maurits Escher who is famous for producing impossible pictures using perspective tricks. Here are Waterfall and Up and down [All M C Escher works © 2001 Cordon Art - Baarn - Holland. All rights reserved. Used by permission.] Article by: J J O'Connor and E F Robertson \|History Topics Index\|\|Alphabetical list of History Topics\| \|Main index\|\|Biographies Index\| The URL of this page is:
Hubble Space Telescope images of four of the galaxies found to contain growing intermediate-mass black holes inside nuclear star clusters (indicated inside the squares). (Image credit: X-ray: NASA/CXC/Washington State Univ./V. Baldassare et al.; Optical: NASA/ESA/STScI) A new survey of over 100 galaxies by NASA’s Chandra X-ray Observatory has uncovered signs that black holes are demolishing thousands of stars in a quest to pack on weight. The four galaxies shown in this graphic are among 29 galaxies in the sample that showed evidence for growing black holes near their centers. X-rays from Chandra (blue) have been overlaid on optical images from NASA’s Hubble Space Telescope of the galaxies NGC 1385, NGC 1566, NGC 3344, and NGC 6503. The boxes that appear in the roll-over outline the location of the burgeoning black holes. These new results suggest a somewhat violent path for at least some of these black holes to reach their present size — stellar destruction on a scale that has rarely if ever been seen before. Astronomers have made detailed studies of two distinct classes of black holes. The smaller variety are “stellar-mass” black holes that typically weigh 5 to 30 times the mass of the Sun. On the other end of the spectrum are the supermassive black holes that live in the middle of most large galaxies, which weigh millions or even billions of solar masses. In recent years, there has also been evidence that an in-between class called “intermediate-mass black holes” (IMBHs) exists. The new study with Chandra could explain how such IMBHs are made through the runaway growth of stellar-mass black holes. One key to making IMBHs may be their environment. This latest research looked at very dense clusters of stars in the centers of galaxies. With stars in such close proximity, many stars will pass within the gravitational pull of black holes in the centers of the clusters. Theoretical work by the team implies that if the density of stars in a cluster — the number packed into a given volume — is above a threshold value, a stellar-mass black hole at the center of the cluster will undergo rapid growth as it pulls in, shreds and ingests the abundant neighboring stars in close proximity.
When working with Integromat, you most likely also work with dates, or you have to work with dates and dates can be really confusing. In this blog, you will learn how you can calculate the difference between two dates to know the days in between or even the days, the hours, the minutes and the seconds. We look at it using an example, and I will explain to you all the functions that you will need and how to set it up. I've prepared this sample scenario. We have Date 1, which is the 8th of September, and we have Date 2, which is the 9th of April. We want to see the difference between these two dates. You could theoretically do ‘Date 1 minus Date 2’. But when you run this once, you see the time difference, it's just empty. Why is that? Because it understands this as a text string. And for a text string, you can't make a calculation. You can't say day one minus day two. We have to parse the date first. So we use the parseDate function. The parseDate function basically transforms the string into an actual date, and then you can do more things with it. Add the parseDate function in the variable value on both dates. If we run it once again, we see it still looks exactly the same. But the output of this function is now actually, time, that is, in milliseconds. That's basically the time difference between these two dates in milliseconds. But how do we show the time difference between these two dates in seconds? Let’s format them into seconds. We can do this using the formatDate function. As the value for the format, we use the uppercase X, which means seconds. You could also use the lowercase x, which is milliseconds, and that will give the same output as if you calculated the difference right away. Run it once and below are the results in milliseconds and seconds. With seconds, you can easily calculate everything. You could also do it in milliseconds. You just have to divide it by 1000, and then you get the actual seconds. The next would be to calculate the days. How many days are there between two dates? There's this handy function called the round function. We have date one minus date two. Then we divide it by 1000. Divide it by 60, divide it by 60 again, and lastly, divide it by 24. Why is that? Because we have 24 hours a day, 60 minutes an hour, 60 seconds a minute, and 1000 milliseconds a second. Since the output is in milliseconds, we have to divide by 1000 to get the value in seconds. Then we divide it by 60 to get the value in minutes. Then we divide it by 60 again to get the value in hours, and then we divide it by 24 to get the actual number of days. So the output is 152, as you can see here. Check the results over on Google and see. How to calculate for hours, minutes, and seconds. Now we want to get hours, minutes and seconds split up. Divide the date difference first by 3600 to get the hours, and we use the floor function to round it down to the full hour, because we don't want, like, 3600.57 hours because that doesn't make sense. So we divide by 3600. For the minutes, we have the floor function as well. We use the value that we had before this same variable. Then we use modulus 3600, which means it is divided by 3600 and then give back the rest. Divide that value by 60. That gives us the minutes. Do the same for seconds. Use modulus 3600, which gives the rest of the first function of the hours. Then again, modulus 60, which gives the rest of the minutes. And that is the second. So now running that again, it is 3656 hours, 47 minutes and 45 seconds. Now, let’s make this a bit more complicated, shall we? Let’s add in the days. The main difference is we divide it by 86,400, because 86,400 is how many seconds one day has. Divide the time difference in seconds by 86,400, then use the floor function to round it down to the full number to get the number of days. Use the modulus function again to get the rest of it and divide it by 3600 like we did before to get the hours. Use the modulus two times again, with 86,400 to get the days, then 3600 to get the hours and then divided by 60 to have it in minutes. Last but not the least, do the same with modulus 86,400, modulus 3,600 and modulus 60 to get the seconds. The output is 152 days, 8 hours, 47 minutes and 45 seconds. That's exactly what the time difference is between these two dates. You can use this however you want to, and however you need it. If you want to say okay, time difference needs to be exactly 30 days and 50 seconds, then you can set up a filter that the days and the seconds should be above that value or the total seconds should be above that value. You can also save the result into a custom field and use it further. I hope the explanation was helpful for you because I know times are quite hard to grasp. I will provide more blogs about times, working with times and timestamps and working with different time zones in the future. If you think that these Integromat functions that I've used here look cool but you have no idea how they work, then I suggest you look into the Integromat functions cheat sheet where I have over 45 pages of Integromat functions explained. You can download it. It's in PDF and it's fully searchable. You can just type whatever keyword you want, and it will search through the whole PDF and guide you directly to the correct place. You will have copy and paste ready functions in there with an explanation and some examples that you can use inside your scenarios. Integromat functions are super helpful. They provide a lot of value, as I have just recently demonstrated, and they enhance your automation without using any kind of operation. Operation costs money, and you save massive operations using Integromat functions. The thing about using Integromat is that you can have a high degree of control over your processes and have them perform without any intervention from you. Consider the many areas where integrating your business processes can lead to significant benefits. You can use Integromat when handling & automating tasks for operations management, human resources and delivery services, to name a few. Learn more about what else you can automate in Integromat by taking the Integromasters course. It's an interactive course where you will be able to learn the basics of Integromat and get to know it's most used features. There will be several lessons for you to learn, along with some quizzes to help you understand the information. It's an affordable way to learn what you have always wanted to know about Integromat! In Part 03 you'll learn a HACK how to keep formulas alive when adding new rows to Google Sheets using Integromat as well as how to batch update multiple rows... Integromat webhooks are a great way to connect any service to start your automations on Make instantly when something happens on the other platform. This FREE guide will help you and your clients to find out what your biggest time wasters are that you could automate right now to free up your time and enjoy work again.Download Now
Reporting: The Pillar of Journalism In a world inundated with information, the role of reporting has become more vital than ever before. Reporting serves as the foundation of journalism, providing the public with accurate and reliable information about events, issues, and developments that shape our society. It is through reporting that journalists fulfill their duty to inform and empower citizens. At its core, reporting involves gathering facts, verifying their authenticity, and presenting them in a clear and concise manner. A skilled reporter possesses a keen eye for detail, an ability to ask probing questions, and a commitment to uncovering the truth. The process of reporting requires thorough research, interviews with relevant sources, and a dedication to unbiased storytelling. One of the fundamental principles of reporting is objectivity. Reporters strive to present information without personal bias or opinion. They aim to provide readers with a fair representation of events so that they can form their own opinions based on accurate information. Objectivity ensures that reporting remains trustworthy and credible in the eyes of the public. Another crucial aspect of reporting is transparency. Journalists have an ethical responsibility to disclose any potential conflicts of interest or biases that may influence their work. By being transparent about their sources, methods, and perspectives, reporters maintain the integrity of their reporting and uphold public trust. In today’s fast-paced digital age, where news spreads rapidly through social media platforms, responsible reporting becomes even more critical. Misinformation and fake news can easily circulate online, misleading readers and distorting public discourse. It is the duty of reporters to counteract this by adhering to rigorous fact-checking processes and providing well-sourced information. Reporting also plays a vital role in holding those in power accountable. Through investigative journalism, reporters dig deep into complex issues and expose wrongdoing or corruption. By shining a light on such matters, they act as watchdogs for society, ensuring transparency within institutions and promoting justice. Moreover, reporting serves as a platform for marginalized voices to be heard. It provides an opportunity to highlight stories and perspectives that might otherwise go unnoticed. By giving a voice to the voiceless, reporting contributes to a more inclusive and democratic society. In conclusion, reporting is the cornerstone of journalism. It upholds the principles of objectivity, transparency, and accountability. Through accurate and reliable reporting, journalists empower citizens with the knowledge they need to navigate an increasingly complex world. In an era where information is abundant but accuracy is often compromised, responsible reporting remains essential in preserving the integrity of journalism and fostering an informed society. The Benefits of Reporting: Enhancing Understanding, Identifying Opportunities, Tracking Progress, Informing Decisions, Ensuring Compliance, and Fostering Collaboration - Reports provide structure and organization to data, making it easier to understand. - Reports can help identify areas of improvement or success within an organization. - Reports can be used to track progress over time and measure performance against goals. - Reports can help inform decisions by providing accurate information quickly and efficiently. - Reporting helps ensure compliance with laws and regulations by providing a consistent source of information for auditing purposes. - Reporting allows for better communication between departments, which can lead to increased productivity and collaboration across teams. The 7 Cons of Reporting: Time Consumption, Errors, Cost, Skill Requirements, Confidentiality Risks, Maintenance Demands, and Interpretation Challenges - Reports can be time consuming to write and review. - Reports may contain errors or inaccuracies due to lack of data or insufficient analysis. - Reports can be costly to produce, requiring resources such as personnel and technology. - Report writing may require specialized skills that not all employees possess. - Reports may contain confidential information that needs to be protected from unauthorized access or disclosure. - Reports often require frequent updating in order to remain accurate and relevant over time, which can lead to additional costs and resources being devoted towards maintenance activities. - If reports are not written clearly, they can be difficult for readers to understand or interpret correctly, leading to confusion and misinterpretation of the data presented in the report Reports provide structure and organization to data, making it easier to understand. Reports: Unveiling Clarity through Structure and Organization In the realm of information overload, the power of reporting lies in its ability to bring structure and organization to data. Reports serve as valuable tools that transform raw information into a comprehensible format, making it easier for readers to understand and extract meaningful insights. When faced with a deluge of data, it can be overwhelming to make sense of it all. This is where reporting steps in, providing a framework that arranges facts, figures, and findings into a coherent narrative. By presenting information in a structured manner, reports help readers navigate complex topics with clarity and ease. The process of creating a report involves careful analysis and synthesis of data. Reporters sift through vast amounts of information, identify key elements, and distill them into concise summaries or visual representations. This condensation of data eliminates unnecessary noise and allows readers to focus on the most important aspects. By organizing information logically, reports enable readers to grasp the big picture while also understanding the finer details. They provide context by presenting data within a framework that highlights relationships, patterns, or trends. This contextualization aids comprehension by giving readers a roadmap to follow as they navigate through the report. Moreover, reports often include visual elements such as charts, graphs, or infographics that enhance understanding. These visual representations offer an intuitive way to interpret complex data at a glance. By visually summarizing large datasets or illustrating comparisons, visuals within reports facilitate quicker comprehension and aid in retaining information. Another advantage of structured reporting is its potential for customization. Different audiences have varying levels of familiarity with specific topics or industries. Reports can be tailored to meet the needs of different readerships by adjusting the level of detail provided or incorporating relevant background information. This customization ensures that reports cater to both experts seeking in-depth analysis and general readers looking for an overview. Furthermore, organized reporting promotes accountability and transparency. When information is presented systematically within a report, it becomes easier to trace its sources and verify its accuracy. This not only enhances the credibility of the report but also allows readers to evaluate the reliability of the data and conclusions presented. In conclusion, reports play a crucial role in making data more accessible and understandable. By providing structure and organization, reports transform complex information into digestible formats that facilitate comprehension. Through thoughtful analysis, synthesis, and visual representation, they guide readers through a wealth of data, helping them extract valuable insights. In an era where information overload is prevalent, well-structured reporting serves as a beacon of clarity amidst the noise, empowering readers to make informed decisions based on reliable information. Reports can help identify areas of improvement or success within an organization. Reports: The Key to Identifying Organizational Growth Reporting plays a crucial role in organizations by providing valuable insights into their performance, strengths, and areas for improvement. Through comprehensive reports, businesses can gain a deeper understanding of their operations and make informed decisions to drive growth and success. One significant advantage of reporting is its ability to identify areas of improvement within an organization. By analyzing data and trends, reports can pinpoint inefficiencies, bottlenecks, or gaps in processes. This information allows businesses to take corrective measures and streamline their operations. Whether it’s identifying workflow issues, optimizing resource allocation, or improving communication channels, reports provide the necessary data to address these challenges effectively. Moreover, reports also shed light on successes within an organization. They highlight achievements and milestones that may have gone unnoticed amidst the day-to-day activities. Celebrating these successes not only boosts morale but also provides valuable insights into what strategies or practices are working well. By recognizing and replicating these successful initiatives, organizations can further enhance their performance and build upon their strengths. Reports offer a comprehensive overview of various metrics such as sales figures, customer satisfaction ratings, productivity levels, financial performance, and more. These metrics provide quantifiable data that allows organizations to set benchmarks and track progress over time. By comparing current performance against historical data or industry standards, businesses can gauge their success objectively. Furthermore, reporting enables organizations to make data-driven decisions. Instead of relying on assumptions or gut feelings, leaders can base their choices on concrete evidence provided by reports. This ensures that strategies and initiatives are aligned with the organization’s goals and supported by reliable information. In addition to internal improvements, reporting can also help organizations communicate their achievements externally. Whether it’s sharing quarterly financial results with shareholders or showcasing positive environmental impact to stakeholders, reports serve as a tool for transparency and accountability. They provide evidence of an organization’s commitment to responsible practices while instilling confidence in investors and partners. In conclusion, reporting is a powerful tool that helps organizations identify areas of improvement and success. By analyzing data and trends, businesses can optimize their operations, celebrate achievements, and make informed decisions. Reports provide a comprehensive overview of performance metrics, allowing organizations to set benchmarks and track progress over time. With accurate and reliable reporting, businesses can drive growth, enhance efficiency, and build a solid foundation for long-term success. Reports can be used to track progress over time and measure performance against goals. Reports: Tracking Progress and Measuring Performance One of the significant advantages of reporting is its ability to track progress over time and measure performance against goals. Whether in business, education, or any other field, reports provide valuable insights into the effectiveness of strategies, initiatives, and actions taken. By systematically documenting data and information, reports offer a comprehensive view of an organization’s or individual’s journey towards their objectives. They serve as a roadmap that highlights milestones achieved, challenges faced, and areas that require improvement. This tracking mechanism enables stakeholders to assess progress objectively and make informed decisions based on concrete evidence. Reports act as a reliable record of accomplishments and setbacks. They allow individuals or teams to reflect on their past performance and identify patterns or trends that may impact future outcomes. By analyzing the data presented in reports, it becomes possible to recognize areas of strength that can be further capitalized on and areas that need attention or modification. Furthermore, reports facilitate effective communication among stakeholders by providing a common platform for sharing information. They enable individuals or teams to present their achievements in a structured manner, making it easier for others to understand the context and significance of their efforts. Reports also foster transparency by ensuring that progress is documented accurately and shared with all relevant parties. Measuring performance against goals is essential for organizations seeking growth and improvement. Reports enable businesses to evaluate whether they are meeting their targets or falling short. By comparing actual results with predetermined benchmarks or key performance indicators (KPIs), organizations can identify gaps and take corrective actions accordingly. Reports also play a crucial role in accountability. When individuals or teams are held responsible for achieving specific objectives, reports provide an objective means of assessing their performance. This accountability fosters a culture of responsibility where individuals strive to meet expectations and contribute effectively towards organizational success. In addition to tracking progress internally within an organization, reports can also be used externally to demonstrate achievements to stakeholders such as investors, clients, or regulatory bodies. A well-prepared report showcasing progress and performance can enhance credibility, build trust, and attract further support or investment. In conclusion, the ability of reports to track progress over time and measure performance against goals is a valuable pro of reporting. By providing a comprehensive overview of accomplishments, setbacks, and areas for improvement, reports enable individuals and organizations to make data-driven decisions. They foster transparency, accountability, and effective communication among stakeholders. Ultimately, reports serve as a powerful tool in driving growth, facilitating improvement, and ensuring that goals are met in various spheres of life. Reports can help inform decisions by providing accurate information quickly and efficiently. Reports: Empowering Decision-Making with Accurate Information In a world where decisions need to be made swiftly and effectively, the role of reports cannot be overstated. Reports serve as valuable tools that provide accurate information in a concise and timely manner, empowering individuals and organizations to make informed choices. One of the key advantages of reports is their ability to deliver information quickly. In today’s fast-paced society, time is of the essence, and decision-makers often require up-to-date data to evaluate situations and take appropriate action. Reports offer a streamlined format that presents relevant facts, figures, and analysis in a digestible way, enabling decision-makers to access essential information without sifting through vast amounts of data. Accuracy is another crucial aspect of reporting. Reports are based on thorough research, reliable sources, and rigorous fact-checking processes. By presenting verified information, reports help decision-makers avoid the pitfalls of misinformation or incomplete data that can lead to poor judgments. Accurate reports provide a solid foundation upon which decisions can be made confidently. Moreover, reports allow decision-makers to access comprehensive insights on specific topics or issues. They provide a holistic view by consolidating relevant data from various sources into one document. This comprehensive approach enables decision-makers to understand the broader context surrounding their choices and consider multiple perspectives before reaching conclusions. Reports also contribute to efficient decision-making by organizing information in a structured manner. They present key findings, analysis, and recommendations in a logical sequence, facilitating clarity and understanding. Decision-makers can quickly grasp the main points without getting lost in unnecessary details or ambiguity. Furthermore, reports have the advantage of being easily shareable among stakeholders involved in the decision-making process. Whether it is within an organization or across different sectors, reports serve as effective communication tools that disseminate crucial information uniformly. This facilitates collaboration and ensures that all parties are working from the same factual basis when making decisions. In conclusion, reports play an indispensable role in informing decisions by providing accurate information quickly and efficiently. Their ability to deliver timely, reliable, and comprehensive insights empowers decision-makers to evaluate situations, weigh options, and take appropriate action. By harnessing the power of reports, individuals and organizations can navigate complex challenges with confidence, knowing that their choices are grounded in accurate knowledge. Reporting helps ensure compliance with laws and regulations by providing a consistent source of information for auditing purposes. Reporting: Ensuring Compliance and Accountability One significant advantage of reporting is its role in ensuring compliance with laws and regulations. By providing a consistent source of information for auditing purposes, reporting becomes a valuable tool in maintaining transparency, accountability, and adherence to legal requirements. In various industries and sectors, organizations must comply with a myriad of laws, regulations, and standards. These can range from financial reporting requirements to environmental regulations or data protection laws. Compliance is not only essential for legal reasons but also for maintaining the trust of stakeholders and the public. Reporting plays a crucial role in this process by providing a structured framework for organizations to document their activities and demonstrate compliance. By regularly reporting on their operations, organizations can track their adherence to relevant laws and regulations, ensuring that they are operating within the prescribed boundaries. Consistent reporting helps establish an audit trail that can be reviewed internally or by external auditors to assess compliance. This documentation provides evidence of an organization’s commitment to following applicable rules and regulations. It helps identify any potential areas of non-compliance or gaps in processes, allowing corrective actions to be taken promptly. Moreover, reporting ensures that organizations have accurate records readily available for regulatory authorities or governing bodies when required. These reports serve as a reliable source of information during audits or investigations, facilitating transparency and accountability. The act of reporting also fosters a culture of responsibility within organizations. When employees are aware that their actions will be documented and reported on, it encourages them to adhere to established policies and procedures. Reporting acts as a deterrent against non-compliance by creating accountability at all levels of an organization. Furthermore, consistent reporting enables organizations to identify trends or patterns that may require attention or improvement. By analyzing the data captured in reports over time, organizations can proactively address potential risks or issues before they escalate into major problems. This proactive approach not only ensures compliance but also enhances overall operational efficiency. In conclusion, one significant advantage of reporting is its contribution to ensuring compliance with laws and regulations. By providing a consistent source of information for auditing purposes, reporting promotes transparency, accountability, and adherence to legal requirements. It enables organizations to demonstrate their commitment to compliance, identify areas for improvement, and maintain the trust of stakeholders. Reporting serves as a powerful tool in promoting responsible business practices and upholding the integrity of operations within organizations. Reporting allows for better communication between departments, which can lead to increased productivity and collaboration across teams. Reporting: Fostering Collaboration and Productivity In any organization, effective communication is key to achieving success. Reporting serves as a powerful tool that enables better communication between departments, leading to increased productivity and collaboration across teams. By providing valuable insights and data, reporting facilitates informed decision-making and promotes a cohesive work environment. When departments have access to accurate and up-to-date reports, they gain a comprehensive understanding of the organization’s goals, challenges, and progress. This shared knowledge fosters collaboration as teams can align their efforts towards common objectives. By breaking down silos and encouraging cross-departmental communication, reporting enables employees to work together more efficiently. Through reporting, departments can identify areas that require improvement or optimization. Whether it’s analyzing sales figures, tracking project timelines, or monitoring customer feedback, reporting provides valuable metrics that help identify bottlenecks or inefficiencies. Armed with this information, teams can collaborate on finding solutions and implementing necessary changes to enhance productivity. Moreover, reporting allows for the identification of trends and patterns that may not be immediately apparent. By analyzing data over time, organizations can uncover insights that contribute to strategic decision-making. This shared knowledge empowers departments to anticipate challenges or opportunities proactively and adjust their strategies accordingly. Regular reporting also encourages accountability within an organization. When teams are aware that their performance will be measured and reported on regularly, it creates a sense of responsibility and motivation to meet targets or exceed expectations. This accountability fosters a culture of continuous improvement and drives individuals to strive for excellence in their work. Furthermore, reporting serves as a means of recognition for individual achievements or team milestones. Celebrating successes through reports not only boosts morale but also encourages collaboration by highlighting effective strategies or practices that can be shared with other teams. This recognition creates an environment where employees feel valued for their contributions and are motivated to support one another’s efforts. In conclusion, the power of reporting lies in its ability to enhance communication between departments, leading to increased productivity and collaboration across teams. By providing valuable insights, data, and metrics, reporting enables informed decision-making and facilitates a cohesive work environment. With improved communication and shared knowledge, organizations can identify areas for improvement, anticipate challenges, and celebrate successes. Embracing reporting as a vital tool within an organization can drive efficiency, foster collaboration, and ultimately contribute to overall success. Reports can be time consuming to write and review. The Conundrum of Time: Reporting’s Time-Consuming Nature Reporting, while essential in the realm of journalism, comes with its fair share of challenges. One such con is the time-consuming nature of writing and reviewing reports. Journalists invest significant amounts of time and effort into crafting accurate and well-rounded reports, ensuring that every detail is thoroughly researched and verified. The process begins with gathering information from various sources, conducting interviews, and sifting through data. This initial stage alone can be time-intensive, as reporters strive to collect all relevant facts and perspectives. Once the information is gathered, the task of organizing it into a coherent narrative begins. Writing a comprehensive report requires careful consideration of structure, clarity, and language. Reporters must present complex information in a manner that is accessible to readers without compromising accuracy or depth. This endeavor demands meticulous attention to detail and extensive revision to ensure the report’s quality. However, the time investment does not end with writing alone. The reviewing process is equally crucial but can be equally time-consuming. Editors meticulously scrutinize each report for factual accuracy, grammar, style, and adherence to journalistic standards. This iterative process may involve multiple rounds of revisions before a report is deemed ready for publication. While this dedication to thoroughness ensures high-quality reporting, it also poses challenges within tight deadlines or when covering breaking news stories. Journalists often face pressure to deliver reports promptly while maintaining their commitment to accuracy and integrity. Furthermore, the time-consuming nature of reporting can limit journalists’ ability to cover a broad range of topics comprehensively. With limited resources and competing demands for their attention, reporters must prioritize certain stories over others. Consequently, some important issues may receive less coverage or be overlooked entirely due to time constraints. Despite these challenges, it is crucial not to compromise on the quality and accuracy of reporting. The time invested in writing and reviewing reports helps uphold journalistic standards and ensures that readers receive reliable information. Journalists remain committed to their duty of providing well-researched and verified content, even if it means grappling with the time-consuming nature of the process. In conclusion, the time-consuming nature of writing and reviewing reports is an inherent con of reporting. However, it is a necessary investment to uphold the integrity of journalism. While it may pose challenges within tight deadlines and resource limitations, journalists persist in their commitment to deliver accurate, well-crafted reports that inform and empower readers. Reports may contain errors or inaccuracies due to lack of data or insufficient analysis. The Pitfall of Reporting: Errors and Inaccuracies While reporting serves as a crucial pillar of journalism, it is not without its flaws. One significant con of reporting is the potential for errors or inaccuracies to arise due to a lack of data or insufficient analysis. This issue highlights the challenges journalists face in their quest to provide accurate and reliable information. In today’s fast-paced news environment, reporters often work under tight deadlines, leaving limited time for thorough research and analysis. As a result, there may be instances where reporters must rely on incomplete or insufficient data to construct their reports. This can lead to gaps in understanding and potentially inaccurate conclusions being drawn. Furthermore, the complexity of certain topics can make it challenging to obtain all the necessary information. In-depth analysis requires access to multiple sources, expert opinions, and relevant data sets. However, these resources may not always be readily available or easily accessible to journalists. Consequently, reports may lack the depth needed for a comprehensive understanding of complex issues. Another factor contributing to errors or inaccuracies in reporting is the inherent subjectivity that journalists must grapple with. Even with diligent fact-checking processes in place, personal biases can unintentionally influence the interpretation and presentation of information. These biases might lead to subtle distortions or omissions that impact the accuracy of a report. It is important for both journalists and readers alike to recognize that no report is entirely immune from errors. However, responsible news organizations are committed to minimizing these mistakes by implementing rigorous editorial standards and fact-checking procedures. Corrections and retractions are issued promptly when errors are identified. To mitigate the risk of errors or inaccuracies, it is essential for reporters to prioritize transparency and accountability in their work. By clearly stating their sources, methodologies, and limitations within their reports, journalists can provide readers with a more nuanced understanding of the information presented. As consumers of news, it is crucial that we approach reported information critically and engage in media literacy. Cross-referencing multiple sources, seeking expert opinions, and evaluating the credibility of the reporting organization can help to identify potential inaccuracies or biases. In conclusion, while reporting is a vital component of journalism, it is not infallible. Errors and inaccuracies can occur due to factors such as limited data availability or insufficient analysis. However, responsible journalists and news organizations strive to uphold high standards of accuracy and transparency. By remaining vigilant as consumers of news, we can navigate the complexities of reported information and make informed judgments. Reports can be costly to produce, requiring resources such as personnel and technology. The Costly Conundrum of Reporting While reporting serves as a vital pillar of journalism, it is not without its challenges. One such drawback is the cost associated with producing reports. The process of gathering, verifying, and presenting information requires significant resources, including personnel and technology. This financial burden poses a conundrum for news organizations striving to deliver accurate and comprehensive reporting. Personnel expenses are a major factor in the cost of reporting. Skilled journalists and reporters are essential for conducting thorough research, interviewing sources, and crafting compelling narratives. These professionals dedicate their time and expertise to uncovering the truth behind complex issues. However, employing a talented team comes with substantial financial implications for news organizations. Furthermore, technology plays a crucial role in modern reporting. From digital tools for data analysis to sophisticated equipment for capturing visuals and audio, technological advancements have become integral to the reporting process. However, acquiring and maintaining these technologies can be expensive. News organizations must invest in up-to-date equipment and software to ensure their reporters have access to the necessary tools for effective reporting. Additionally, there are costs associated with fact-checking processes and ensuring accuracy in reporting. Verifying information through multiple sources requires time and effort from reporters and editors alike. Organizations may need to allocate funds specifically for fact-checkers or invest in training their staff on proper verification techniques. The financial strain of producing reports can be particularly challenging for smaller news outlets or independent journalists who may lack the resources available to larger media organizations. Limited budgets can hinder their ability to cover certain stories or conduct in-depth investigations. However, despite these challenges, news organizations recognize the importance of investing in quality reporting. They understand that accurate information is essential for an informed society and that cutting corners on resources can compromise journalistic integrity. To mitigate these costs, news outlets often explore various strategies such as partnerships with other organizations or crowdfunding initiatives to secure additional funding for specific projects or investigative journalism endeavors. In conclusion, the cost of producing reports is a significant conundrum for news organizations. The expenses associated with personnel, technology, and fact-checking pose financial challenges. However, the commitment to delivering accurate and comprehensive reporting remains paramount. Striking a balance between allocating resources effectively and finding innovative ways to secure funding is crucial to ensure the continuation of high-quality journalism in an ever-evolving media landscape. Report writing may require specialized skills that not all employees possess. The Conundrum of Specialized Skills in Report Writing Reporting is an essential aspect of journalism and communication, but it is not without its challenges. One notable con of reporting is that report writing may require specialized skills that not all employees possess. This poses a conundrum for organizations and individuals who rely on accurate and well-structured reports. Effective report writing demands a unique set of skills that go beyond basic writing abilities. It requires the ability to gather information, analyze data, and present findings in a coherent and concise manner. A well-written report should be clear, organized, and accessible to its intended audience. Unfortunately, not everyone possesses these specialized skills naturally. Many employees may excel in their respective fields but struggle when it comes to articulating their thoughts and findings in a written format. This can lead to reports that lack clarity or fail to communicate the intended message effectively. Moreover, producing high-quality reports often requires knowledge of specific formats, such as technical reports or research papers. Understanding the conventions and requirements of these formats can be challenging for individuals who are not trained in academic or technical writing. The lack of specialized report writing skills can hinder productivity and efficiency within organizations. It may result in delays as employees struggle to produce reports that meet the required standards. Inaccurate or poorly written reports can also lead to misunderstandings or misinterpretations, potentially impacting decision-making processes. To address this conundrum, organizations can invest in training programs or workshops focused on developing report writing skills. By providing employees with the necessary tools and guidance, organizations can enhance their overall communication capabilities and ensure consistent quality in their reports. Additionally, seeking external expertise through professional writers or editors can be a viable solution for individuals or organizations facing challenges with report writing. These experts possess the necessary skills to transform complex information into clear and compelling reports. In conclusion, while reporting is an integral part of effective communication, it does come with its share of challenges. The need for specialized skills in report writing can be a conundrum for individuals and organizations alike. However, through training, guidance, and leveraging external expertise, it is possible to overcome this obstacle and produce high-quality reports that effectively convey information to their intended audience. By recognizing the importance of report writing skills and taking proactive steps to address any deficiencies, organizations can ensure that their reports are accurate, well-structured, and impactful. Reports may contain confidential information that needs to be protected from unauthorized access or disclosure. The Conundrum of Confidentiality in Reporting While reporting serves as a vital tool for disseminating information, it also presents a conundrum when it comes to handling confidential information. Reports often contain sensitive details that must be protected from unauthorized access or disclosure. This challenge highlights the delicate balance between the public’s right to know and the need to safeguard private or classified information. In the pursuit of uncovering truth, journalists sometimes encounter confidential documents, sources, or data that shed light on significant issues. These materials may include classified government documents, trade secrets, personal medical records, or sensitive corporate information. The responsibility lies with reporters to handle such information with utmost care and respect for privacy. Confidentiality is crucial for several reasons. First and foremost, protecting confidential information ensures the safety and security of individuals involved. Whistleblowers who provide sensitive documents or sources who share insider knowledge often rely on journalists to maintain their anonymity. Breaching confidentiality can have severe consequences for these individuals, including threats to their personal safety or legal repercussions. Secondly, confidentiality helps maintain trust between journalists and their sources. By assuring sources that their identities will be protected and their information kept confidential, reporters encourage transparency and enable individuals to come forward with valuable insights. This trust is essential for investigative journalism and uncovering stories that would otherwise remain hidden. However, maintaining confidentiality poses challenges in an era of digital communication and surveillance. Journalists must adopt secure communication practices to protect sensitive information from interception or hacking attempts. Encryption tools, secure file-sharing platforms, and anonymous communication channels are some measures employed by reporters to safeguard confidential data. Additionally, news organizations often have internal protocols in place to ensure the proper handling of confidential information. Ethical guidelines dictate that reporters should weigh the public interest against potential harm before publishing sensitive details. Responsible journalists consult with legal experts or engage in discussions within their organizations to determine how best to handle such cases. Nevertheless, there are instances where confidentiality conflicts with the public’s right to know. Journalists face ethical dilemmas when deciding whether to publish information that may be in the public interest but could also harm individuals or compromise national security. These situations require careful consideration and a balancing act between transparency and responsible reporting. In conclusion, protecting confidential information is a critical aspect of reporting. Journalists must navigate the delicate balance between the public’s right to know and the need to safeguard sensitive data. Upholding confidentiality is essential for ensuring source protection, maintaining trust, and encouraging whistleblowers to come forward. However, it also presents challenges in an era of digital surveillance and requires journalists to adopt secure communication practices. Striking the right balance between transparency and privacy is an ongoing challenge for reporters as they strive to fulfill their duty of informing the public while respecting confidentiality. Reports often require frequent updating in order to remain accurate and relevant over time, which can lead to additional costs and resources being devoted towards maintenance activities. The Challenge of Maintenance: The Cost of Keeping Reports Accurate Reporting is a dynamic process that demands constant updates to ensure accuracy and relevance over time. While this dedication to maintaining the integrity of information is commendable, it also presents a conundrum for news organizations: the need for additional costs and resources to support ongoing maintenance activities. In an ever-changing world, new developments, emerging facts, and evolving perspectives can reshape the narrative surrounding a reported event. To provide readers with up-to-date and reliable information, reporters must diligently monitor and verify these changes. This process often involves reaching out to sources, conducting further research, and revising previously published reports. However, this commitment to accuracy comes at a price. News organizations must allocate resources for the continuous monitoring and updating of reports. Journalists may need to invest additional time in fact-checking and reevaluating information. Editors must oversee these maintenance activities while ensuring that other pressing stories are not neglected. Financially, the need for ongoing updates can strain the budgets of news organizations. Allocating resources for regular maintenance may divert funds from other crucial areas such as investigative reporting or hiring specialized journalists. This challenge becomes even more pronounced for smaller news outlets with limited budgets. Moreover, frequent updates can pose logistical challenges. Ensuring seamless transitions between versions of reports can be complex, particularly when readers refer back to earlier versions or when multiple platforms are involved. News organizations must develop efficient systems to manage these updates effectively without causing confusion or disrupting user experience. Despite these challenges, the commitment to accuracy remains paramount in responsible journalism. The investment in maintenance activities is necessary to uphold journalistic standards and provide readers with reliable information they can trust. It is through these efforts that news organizations demonstrate their dedication to truthfulness and accountability. In conclusion, while the need for frequent updates in reporting presents financial and logistical challenges, it is an essential aspect of responsible journalism. Maintaining accurate and relevant reports over time ensures that readers receive reliable information. News organizations must strike a balance between allocating resources for maintenance activities and pursuing new stories, all in the pursuit of providing the public with up-to-date and trustworthy reporting. If reports are not written clearly, they can be difficult for readers to understand or interpret correctly, leading to confusion and misinterpretation of the data presented in the report The Pitfall of Unclear Reporting: Navigating the Maze of Misinterpretation In the realm of reporting, clarity is paramount. When reports are not written clearly, they run the risk of becoming a source of confusion and misinterpretation for readers. This pitfall can have far-reaching consequences, as it hampers the accurate understanding and analysis of the data presented within the report. Reports serve as a means to communicate information, findings, and insights to a wide range of audiences. However, if the language used is convoluted, technical jargon dominates, or key points are buried under layers of unnecessary detail, readers may struggle to grasp the intended message. As a result, important information can be lost or misunderstood. One common consequence of unclear reporting is confusion. Readers may find themselves grappling with complex sentences or struggling to decipher intricate concepts. This confusion can lead to frustration and disengagement from the report’s content altogether. When readers are unable to comprehend what is being conveyed, they may miss out on valuable insights or make incorrect assumptions based on their own interpretations. Misinterpretation is another significant risk associated with unclear reporting. When information is not presented in a clear and concise manner, readers may draw inaccurate conclusions or misread data trends. This can have serious implications when decisions or actions are based on these misinterpretations. In fields such as finance, healthcare, or policy-making, where precise understanding is crucial for informed choices, misinterpreting data due to unclear reporting can lead to costly errors or ineffective strategies. Moreover, unclear reporting can erode trust in the credibility of both the report and its authors. Readers may question the accuracy and reliability of information when it is poorly communicated. The lack of clarity raises doubts about whether the report was thoroughly researched or if biases have influenced its content. As trust diminishes, so does the impact and influence that reporting should ideally have on decision-making processes. To mitigate the conundrum of unclear reporting, it is essential for writers to prioritize clarity and simplicity in their communication. Using plain language, avoiding unnecessary jargon, and organizing information in a logical manner can greatly enhance reader comprehension. Additionally, providing clear explanations of complex concepts or using visual aids such as charts and graphs can further aid understanding. Editors also play a crucial role in ensuring clarity in reporting. They should review reports with a critical eye, identifying areas where language can be simplified or sections that may require further explanation. By working collaboratively with writers, editors can help bridge the gap between technical information and reader comprehension. In conclusion, the con of unclear reporting is a significant challenge that compromises the effectiveness of reports. When readers struggle to understand or interpret data due to unclear writing, confusion and misinterpretation arise. This not only hampers decision-making processes but also erodes trust in the report’s credibility. By prioritizing clarity and simplicity in reporting, writers and editors can overcome this pitfall, enabling readers to accurately comprehend and utilize the valuable insights presented within reports.
RUTH DOYLE MIDDLE SCHOOL Observe. Wonder. Question “Week in Review” September 5 - 9 Tuesday and Wednesday we learned about RESEARCH in the scientific method and why variables are so important. Variables are factors or conditions that can change in an experiment. There are usually 3 types of variables, 2 of which are interrelated. The Independent and Dependent variables work together and the Controlled Variables are kept separate. Below you will find definitions for each… This is the day we conducted the RB experiment to help the students better understand this concept. We also spent a large portion of our time learning how to PROPERLY graph our data using a Line Graph. I taught the students the 4 steps to Graphing as outlined below: Thursday and Friday we learned about step 4 of the scientific method “Experiment”. The number one, most important things about experiments are that they have to be REPEATABLE!!! In order to achieve this you need two things (A) step-by-step procedures (B) materials list. In order to do this we had to “Save Sam”! The goal of the lab is to practice writing procedural steps in an experiment. They had to not only save same but also provide a step-by-step set of procedures, complete with a materials list and illustrated instructions. They also had to walk me through their procedure to ensure that it could be repeated! If you have any questions or concerns please email me at firstname.lastname@example.org or call the school at (501) 450-6675. Thank you and have a great weekend! – Mr. Lowe Assignments turned in this week - RB Lab (15 points) and Variable Worksheet (15 points)
Honors Geometry Chapter 1 Points, Lines, Planes, and Angles Vocabulary Terms in this set (23) simplest figure studied in geometry a figure with no thickness that extends in two directions without ending a figure with no thickness or edges, yet extends without ending the set of all points all the points in one line points all in one plane the set of points in both figures where the two meet collinear, falling on the same line, and somewhere on the line between the two points two objects that have the same size and shape, symbol is a = with a ~ over the top midpoint of a segment the point that divides a line segment into TWO CONGRUENT line segments. bisector of a segment the line, segment, ray, or plane that INTERSECTS the segment at its MIDPOINT. figure formed by 2 rays that share a common endpoint that common endpoint 2 rays of the angle tool used to measure the degree of an angle ° angles of equal measure 2 angles in a plane that have a common vertex and a common side Bisector of an Angle ray that divides an angle into 2 congruent , adjacent angles The points on a line can be corresponded to real numbers anyhow to a way where two points can be 0 and 1. Once a coordinate system is set up that way, the distance between any two points is the absolute value of the difference of their coordinates/points. Segment Addition Postulate On line segment ABC, if B is between A and C, then AB + BC = AC You can measure an angle from any angle. Angle Addition Postulate <ABC = <ABD + <DBC YOU MIGHT ALSO LIKE... The Slope Formula \| Algebra Study Guide Geometry; Chapter 1 10th geometry - 1.2, 1.3, 1.4, 1.5 OTHER SETS BY THIS CREATOR Spanish I The Body Spanish I The Classroom Spanish I Commands Spanish 1 Dates THIS SET IS OFTEN IN FOLDERS WITH... Properties of Equality Properties of Congruence
Presentation on theme: "Triangle Fundamentals"— Presentation transcript: 1 Triangle Fundamentals Intro to G.10TriangleFundamentalsModified by Lisa Palen 2 Triangle What’s a polygon? Definition: A triangle is a three-sided polygon.What’s a polygon? 3 PolygonsDefinition:A closed figure formed by a finite number of coplanar segments so that each segment intersects exactly two others, but only at their endpoints.These figures are not polygonsThese figures are polygons 4 Definition of a Polygon A polygon is a closed figure in a plane formed by a finite number of segments that intersect only at their endpoints. 5 Triangles can be classified by: Their sidesScaleneIsoscelesEquilateralTheir anglesAcuteRightObtuseEquiangular 6 Classifying Triangles by Sides Scalene:A triangle in which no sides are congruent.BC=5.16cmBCABC=3.55cmABCAB = 3.47 cmAC = 3.47 cmAB = 3.02 cmAC = 3.15 cmIsosceles:A triangle in which at least 2 sides are congruent.HI=3.70cmGHIEquilateral:A triangle in which all 3 sides are congruent.GI = 3.70 cmGH = 3.70 cm 7 Classifying Triangles by Angles Obtuse:1084428BCAA triangle in which one angle is....obtuse.Right:A triangle in which one angle is...right. 8 Classifying Triangles by Angles Acute:574776GHIA triangle in which all three angles are....acute.Equiangular:A triangle in which all three angles are...congruent. 10 Classification by Sides polygonsPolygontrianglesTrianglescaleneisoscelesScaleneIsoscelesequilateralEquilateral 11 Classification by Angles polygonsPolygontrianglesTrianglerightacuteequiangularRightObtuseAcuteobtuseEquiangular 12 Naming Triangles We name a triangle using its vertices. For example, we can call this triangle:∆ABC∆ACBReview: What is ABC?∆BAC∆BCA∆CAB∆CBA 13 Parts of Triangles Every triangle has three sides and three angles. For example, ∆ABC hasSides: Angles: CAB ABC ACB 14 Opposite Sides and Angles Side opposite of BAC :Side opposite of ABC :Side opposite of ACB :Opposite Angles:Angle opposite of : BACAngle opposite of : ABCAngle opposite of : ACB 15 Interior Angle of a Triangle An interior angle of a triangle (or any polygon) is an angle inside the triangle (or polygon), formed by two adjacent sides.For example, ∆ABC has interior angles: ABC, BAC, BCA 16 Exterior AngleAn exterior angle of a triangle (or any polygon) is an angle that forms a linear pair with an interior angle. They are the angles outside the polygon formed by extending a side of the triangle (or polygon) into a ray.Exterior AngleInterior AnglesAFor example, ∆ABC has exterior angle ACD, because ACD forms a linear pair with ACB.DBC 17 Interior and Exterior Angles The remote interior angles of a triangle (or any polygon) are the two interior angles that are “far away from” a given exterior angle. They are the angles that do not form a linear pair with a given exterior angle.For example, ∆ABC has exterior angle:ACD andremote interior angles A and BExterior AngleRemote Interior AnglesADBC 19 m<A + m<B + m<C = 180 Triangle Sum TheoremThe sum of the measures of the interior angles in a triangle is 180˚.m<A + m<B + m<C = 180IGO GeoGebra Applet 20 Third Angle CorollaryIf two angles in one triangle are congruent to two angles in another triangle, then the third angles are congruent. 21 Third Angle Corollary Proof Given:The diagramProve:C Fstatementsreasons1. A D, B E2. mA = mD, mB = mE3. mA + mB + m C = 180ºmD + mE + m F = 180º4. m C = 180º – m A – mBm F = 180º – m D – mE5. m C = 180º – m D – mE6. mC = mF7. C F1. Given2. Definition: congruence3. Triangle Sum TheoremSubtraction Property of EqualityProperty: SubstitutionDefinition: congruenceQED 22 Corollary Each angle in an equiangular triangle measures 60˚. 60 60 23 CorollaryThere can be at most one right or obtuse angle in a triangle.ExampleTriangles??? 24 CorollaryAcute angles in a right triangle are complementary.Example 25 Exterior Angle Theorem The measure of the exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.Remote Interior AnglesAExterior AngleDExample:Find the mA.BC3x - 22 = x + 803x – x =2x = 102x = 51mA = x = 51° 26 Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.GeoGebra Applet (Theorem 1) 28 Introduction There are four segments associated with triangles: MediansAltitudesPerpendicular BisectorsAngle Bisectors 29 Median - Special Segment of Triangle Definition:A segment from the vertex of the triangle to the midpoint of the opposite side.BADECFSince there are three vertices, there are three medians.In the figure C, E and F are the midpoints of the sides of the triangle. 30 Altitude - Special Segment of Triangle The perpendicular segment from a vertex of the triangle to the segment that contains the opposite side.Definition:BADFIn a right triangle, two of the altitudes are the legs of the triangle.BADFIKIn an obtuse triangle, two of the altitudes are outside of the triangle. 31 Perpendicular Bisector – Special Segment of a triangle A line (or ray or segment) that is perpendicular to a segment at its midpoint.Definition:The perpendicular bisector does not have to start from a vertex!ROQPExample:MLNCDAEABBIn the isosceles ∆POQ, is the perpendicular bisector.In the scalene ∆CDE, is the perpendicular bisector.In the right ∆MLN, is the perpendicular bisector. 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So far in this course, you have learned the following about neural networks: - That they are composed of neurons - That each neuron uses an activation function applied to the weighted sum of the outputs from the preceding layer of the neural network - A broad, no-code overview of how neural networks make predictions We have not yet covered a very important part of the neural network engineering process: how neural networks are trained. In this tutorial, you will learn how neural networks are trained. We'll discuss data sets, algorithms, and broad principles used in training modern neural networks that solve real-world problems. You can skip to a specific section of this Python deep learning tutorial using the table of contents below: - Hard-Coding vs. Soft-Coding - Training A Neural Network Using A Cost Function - Modifying A Neural Network - Final Thoughts There are two main ways that you can develop computer applications. Before digging in to how neural networks are trained, it's important to make sure that you have an understanding of the difference between soft-coding computer programs. Hard-coding means that you explicitly specify input variables and your desired output variables. Said differently, hard-coding leaves no room for the computer to interpret the problem that you're trying to solve. Soft-coding is the complete opposite. It leaves room for the program to understand what is happening in the data set. Soft-coding allows the computer to develop its own problem-solving approaches. A specific example is helpful here. Here are two instances of how you might identify cats within a data set using soft-coding and hard-coding techniques. - Hard-coding: you use specific parameters to predict whether an animal is a cat. More specifically, you might say that if an animal's weight and length lie within certain - Soft-coding: you provide a data set that contains animals labelled with their species type and characteristics about those animals. Then you build a computer program to predict whether an animal is a cat or not based on the characteristics in the data set. As you might imagine, training neural networks falls into the category of soft-coding. Keep this in mind as you proceed through this course. Neural networks are trained using a cost function, which is an equation used to measure the error contained in a network's prediction. The formula for a deep learning cost function (of which there are many - this is just _one _example) is below: Note: this cost function is called the mean squared error, which is why there is an MSE on the left side of the equal sign. While there is plenty of formula mathematics in this equation, it is best summarized as follows: Take the difference between the predicted output value of an observation and the actual output value of that observation. Square that difference and divide it by 2. Note that this is simply one example of a cost function that could be used in machine learning (although it is admittedly the most popular choice). The choice of which cost function to use is a complex and interesting topic on its own. We'll learn more about why this choice of cost function is so popular in our next section when we begin discussing gradient descent. As mentioned, the goal of an artificial neural network is to minimize the value of the cost function. The cost function is minimized when your algorithm's predicted value is as close to the actual value as possible. Said differently, the goal of a neural network is to minimize the error it makes in its predictions! After an initial neural network is created and its cost function is imputed, changes are made to the neural network to see if they reduce the value of the cost function. More specifically, the actual component of the neural network that is modified is the weights of each neuron at its synapse that communicate to the next layer of the network. The mechanism through which the weights are modified to move the neural network to weights with less error is called gradient descent. Gradient descent is a complicated topic and will be discussed in more detail in the next section of the course. For now, it's enough for you to understand that the process of training neural networks looks like this: - Initial weights for the input values of each neuron are assigned - Predictions are calculated using these initial values - The predictions are fed into a cost function to measure the error of the neural network - A gradient descent algorithm changes the weights for each neuron's input values - This process is continued until the weights stop changing (or until the amount of their change at each iteration falls below a specified threshold) This may seem very abstract - and that's ok! You will learn more about how neural networks are trained in the next section of this course. In this tutorial, you received a basic, no-code introduction to how deep learning neural networks are built and trained. Here is a broad summary of what you learned in this article: - The difference between hard-coding and soft-coding in computer programming - The role of cost functions in building deep learning models - How cost functions and gradient descent are used to modify weights inside of a neural networks
ASCII (American Standard Code for Information Interchange) is a character set and a character encoding based on the Roman alphabet as used in modern English. It is most commonly used by computers and other communication equipment to represent text and by control devices that work with text. Like other codes, ASCII specifies a correspondence between integers that can be represented digitally and the symbols of a written language, thus allowing digital devices to communicate with each other and to process and store character-oriented information. The ASCII character encoding (or a compatible extension; see below) is used on nearly all common computers, especially personal computers and workstations. The preferred MIME name for this encoding is "US-ASCII". ASCII is a seven-bit code, meaning that it uses the integers representable with seven binary digits (a range of 0 to 127 decimal) to represent information. Even at the time that ASCII was introduced, most computers dealt with eight-bit bytes as the smallest unit of information; the eighth bit was commonly used for error checking on communication lines or other device-specific functions. ASCII does not specify any way to represent information about the structure or appearance of a piece of text. That requires other standards markup language. ASCII was first published as a standard in 1963 by the American Standards Association (ASA), which later became ANSI. There are many variations of ASCII, but its present, most widely-used form is ANSI X3.4-1967, also standardized as ECMA-6, ISO/IEC 646:1991 International Reference Version, and ITU-T Recommendation T.50 (09/92). It is embedded in page zero of its probable replacement, unicode. ASCII is generally considered the most successful software standard ever promulgated. Historically, ASCII developed from telegraphic codes. It started as a commercial 7-bit teleprinter code promoted by Bell data services. ASA reordered the code for sorting (alphabetization) of lists, and added features for devices other than teleprinters. Bell's code added punctuation and lower-case letter to the earlier 5-bit Baudot[?] teleprinter code. Baudot automated sending and receiving of telegraphic messages and took many features from Morse code. The first thirty-two codes (numbers 0-31 decimal) in ASCII are reserved for control characters: codes that may not themselves represent information, but that are used to control devices (such as printers) that make use of ASCII. For example, character 10 represents the "line feed" function (which causes a printer to advance its paper), and character 27 represents the "escape" key found on the top left of common keyboards. Code 127 (all seven bits on) is another special character known as "delete" or "rubout". Though its function is similar to that of other control characters, it was placed at this position so that it could be used to erase a section of paper tape, a popular storage medium at one time, by punching out all its holes. Code 0 (all bits off) is ignored by many computer systems. Many of the codes are to mark data packets, and control a data transmission protocol (i.e. enquiry (any stations out there?), acknowledge, negative acknowledge, start of header, start of text, end of text). Escape and substitute permit a protocol to mark binary data so that if it contains codes with the same values as protocol characters, the codes will be processed as data. The separator characters (record separator, etc.) were designed for use with magnetic tape systems. XON and XOFF are often sent from a slow device, such as a printer, to start and stop a flow of data so no data is lost. \|0000 0000\|\|0\|\|00\|\|NUL\|\|␀\|\|Null character\| \|0000 0001\|\|1\|\|01\|\|SOH\|\|␁\|\|Start of Header\| \|0000 0010\|\|2\|\|02\|\|STX\|\|␂\|\|Start of Text\| \|0000 0011\|\|3\|\|03\|\|ETX\|\|␃\|\|End of Text\| \|0000 0100\|\|4\|\|04\|\|EOT\|\|␄\|\|End of Transmission\| \|0000 1001\|\|9\|\|09\|\|HT\|\|␉\|\|Horizontal Tab\| \|0000 1010\|\|10\|\|0A\|\|LF\|\|␊\|\|Line Feed\| \|0000 1011\|\|11\|\|0B\|\|VT\|\|␋\|\|Vertical Tab\| \|0000 1100\|\|12\|\|0C\|\|FF\|\|␌\|\|Form Feed\| \|0000 1101\|\|13\|\|0D\|\|CR\|\|␍\|\|Carriage return\| \|0000 1110\|\|14\|\|0E\|\|SO\|\|␎\|\|Shift Out\| \|0000 1111\|\|15\|\|0F\|\|SI\|\|␏\|\|Shift In\| \|0001 0000\|\|16\|\|10\|\|DLE\|\|␐\|\|Data Link Escape\| \|0001 0001\|\|17\|\|11\|\|DC1\|\|␑\|\|XON Device Control 1\| \|0001 0010\|\|18\|\|12\|\|DC2\|\|␒\|\|Device Control 2\| \|0001 0011\|\|19\|\|13\|\|DC3\|\|␓\|\|XOFF Device Control 3\| \|0001 0100\|\|20\|\|14\|\|DC4\|\|␔\|\|Device Control 4\| \|0001 0101\|\|21\|\|15\|\|NAK\|\|␕\|\|Negative Acknowledgement\| \|0001 0110\|\|22\|\|16\|\|SYN\|\|␖\|\|Synchronous Idle\| \|0001 0111\|\|23\|\|17\|\|ETB\|\|␗\|\|End of Trans. Block\| \|0001 1001\|\|25\|\|19\|\|EM\|\|␙\|\|End of Medium\| \|0001 1100\|\|28\|\|1C\|\|FS\|\|␜\|\|File Separator\| \|0001 1101\|\|29\|\|1D\|\|GS\|\|␝\|\|Group Separator\| \|0001 1110\|\|30\|\|1E\|\|RS\|\|␞\|\|Record Separator\| \|0001 1111\|\|31\|\|1F\|\|US\|\|␟\|\|Unit Separator\| In the table above, the fifth column contains graphic characters that are reserved for representing the position of control codes in a data stream; your HTML user agent may require the installation of additional fonts in order to display them. See new line. Code 32 is the "space" character, denoting the space between words, which is produced by the large space bar of a keyboard. Codes 33 to 126 are called the printable characters, which represent letters, digits, punctuation marks, and a few miscellaneous symbols. ASCII provides some internationalization for French and Spanish (both spoken in the U.S.) by providing a backspace with the grave, accent (miscalled a "single quote"), tilde, and breath mark (inverted vel). Note how uppercase characters can be converted to lowercase by adding 32 to their ASCII value; in binary, this can be accomplished simply by setting the sixth-least significant bit to 1. The international spread of computer technology led to many variations and extensions to the ASCII character set, since ASCII does not include accented letters and other symbols necessary to write most languages besides English that use Roman-based alphabets. International standard ISO 646 (1972) was the first attempt to remedy this problem, although it regrettably created compatibility problems as well. ISO 646 was still a seven-bit character set, and since no additional codes were available, some were re-assigned in language-specific variants. See ISO 646 for details. Improved technology brought out-of-band means to represent the information formerly encoded in the eighth bit of each byte, freeing this bit to add another 128 additional character codes for new assignments. Eight-bit standards such as ISO 8859 enabled a broader range of languages to be represented, but were still plagued with incompatibilities and limitations. Still, ISO 8859-1 and original 7-bit ASCII are the most common character encodings in use today, though Unicode (with a much larger code set) is quickly becoming standard in many places. These newer codes are backward-compatible: that is, the first 127 code points of each code are the same as ASCII, and the first 256 code points of Unicode are the same as ISO 8859-1. The portmanteau word "ASCIIbetical" has evolved to describe the collation of data in ASCII code order rather than genuine alphabetical order (which requires some tricky computation, and varies with language). (See the Jargon File (http://www.catb.org/~esr/jargon/html/entry/ASCIIbetical-order).)
First Grade Math Worksheets Our first grade math worksheets are aligned directly with the Core Curriculum Standards for First Grade. Each standard is throughly covered. Each topic comes complete with homework sheets, practice worksheets, and quizzes. We also we add extra materials that are out of the scope of the standards that we find on all other testing for this grade level. Some extras would include our First Grade Math Posters. These math worksheets are tailored to first grade students at both math and reading levels. Also make sure to visit our First Grade Math Tests to gauge your level of achievement with this grade level. First Grade Operations and Hints of Algebra Worksheets - Addition and Subtraction Word Problems (OA.1)- These worksheets focus on problems that are in word form and require a single sum or difference calculation to be performed to solve a situation based exercise. - Single Digit Subtraction (1.OA.A.1)- We introduce students to the basic concept of a mathematical difference. - Simple Subtraction Word Problems (1.OA.A.1)- We take the concept differences and apply it to word problems. - Fixed Integer Subtraction to 12 (Related to 1.OA.A.1)- Students work on removing just a single specific number for various integers that are 12 and under. A great section for working on your basic first grade math facts. - Addition Word Problems (Up to 20) - (OA.2)- These worksheets present problems that are found in sentence form and involve sums that total twenty or less. - Simple Addition Word Problem (1.OA.A.2)- This is where you should start with the entire word problem set. - Properties of Operations as Strategies (OA.3)- These worksheets look at the common math properties for students at this level. The mainstay here is the associative and commutative properties. - The Commutative Property (OA.3) - This also looks at the concept of multiplying, but great for advanced learners. - Subtraction and Unknown Addends (to 20) (OA.4)- This is really a primer to get students ready for single step algebra. - Missing Operations (Add and Subtract) (1.OA.B.4)- Tell us what these problems are missing. Hint: It is an operator. - Subtracting Numbers with Figures (Related to 1.OA.4)- We start to make the transition from integers to pictures. - Relate Counting to Addition and Subtraction (1.OA.B.5)- When you think about it, both of these operations are exactly like counting. Moving in one direction or another. We make this obvious for students. - Adding and Subtracting Within 20 (1.OA.C.6)- We keep the sums and different just under the value of twenty. - Math Fact Families (1.OA.C.6, 1.OA.B, 3.OA.4)- Fact families are groups of numbers that are almost systematic in the way they can be rearranged to add and subtract. This really helps you master basic operations quickly. - Subtraction Mad Minutes (1.OA.C.6)- These are left to right sum problems. - Rapid Fire Horizontal Subtraction Math Facts (1.OA.C.6)- Same as above, but we subtract now. - Rapid Fire Vertical Addition Math Facts (1.OA.C.6)- These are awesome to keep up your level of practice. - Subtraction Math Facts (1.OA.C.6)- This is the format that most students are accustom to, but in the real world things are a bit more fluid. - Number Bonds (1.OA.C.6)- A fun way to reinforce this skill for students and teachers alike. - Working With Equals Signs ( OA.7)- This is the foundation of working with equations. - Unknown Numbers in Sums and Differences (OA.8)- This helps students make a nice transition to word problems. First Grade Numbers and Base Ten Worksheets - Counting (Up to 120) (1.NBT.1)- This really helps to make the transition to learning to form sums and differences. - One and Tens Place Values - 1.NBT.2)- Students begin to understand the meaning behind place holder and place value. - Compare Two-Digit Numbers (1.NBT.3)- This is where the greater than, less than, and equal values come. - Single Digit Addition (1.NBT.C.4)- Students start adding two single digit numbers together. - Addition of Numbers (Under 100) (1.NBT.4)- This section starts to piece together two and three pairs of numbers. - Ten More Or Ten Less - 1.NBT.5)- This is great for learning the powers of ten and eventually leap frogging over to exponents. - Visual Sum and Difference Word Problems (1.NBT.6)- This is where you have to balance multiple pieces: sentences, integers, and visuals that represent integers. First Grade Measurement and Data Worksheets - Indirect Length Word Problems (1.MD.1)- You will use other references available to find set measures. - Length Word Problems In Units (1.MD.2)- We use separate values to work with metric and U.S. standards units of length. - Hours and Half Hours of Time (1.MD.3)- The minute hand is either always at the twelve or the six, in this case. - Organizing and Understanding Data (1.MD.4)- Students learn how to make data more understandable for themselves and their audience. First Grade Geometry Worksheets - Attributes of Shapes (G.1)- Each shape has something very unique to it. - Making Two-Dimensional Shapes (G.2)- These are the standard shapes and we have you draw them from scratch. - Partitioning Circles and Rectangles (G.3)- You will break apart these geometric figures based on written directions. How To Use Our First Grade Math WorksheetsFor Teachers We have teachers take all types of different approaches with our work in their classes. Usually, the most difficult decision for teachers is not how to use this in teaching, but how should we order the topics in which we present them to students. Some teachers blindly follow the order in which the curriculum committee set up when they designed it. I find that more newer teachers do this because they were never really given any help with this when they were student teaching. Some staffs have a preset school district approach that is already setup for them. Many other teachers are left to decide by themselves. My best suggestion is to write a sample problem from each section on a 3 x 5 notecard. Some topics will have multiple looks at a topic but write a single fundamental problem. There are 30 topics here, so that would require you to make 30 notecards. When you are done arrange the problems in an order of logical sequence. This will give you your best logical approach to begin with. Also know that as you teach this, it might make more sense to reorder topics. Keep those notecards handy all year long. We would highly suggest that you consider using our math posters to post in your classroom. Our math tests are highly recommended to assess how your students are doing with all the different content areas. For Parents and Students We welcome you and think that every student should consider using our work year-round. If you add this work into addition of your classroom experience you are sure to have great success. Some students are looking either to get ahead, stay on task, or catch up with their math skills. This is the perfect place for you. For Those That Are Behind - Begin with the lesson, follow it up with the guided lesson and complete the work. Check your answers with the guided lesson explanation. Then move on to the worksheets. If you feel you are doing well, take a shot at a quiz. If you score north of 85%, you are in good shape. If not, go back and crack away at the practice sheets to get you in better standing. Always refer back to the original lesson, when in doubt. For Those That Are Staying on Task - All of our sections will be helpful to help you push on with each of these topics. We would encourage you start with the guided lessons. If they make sense, push on to a few practice worksheets and follow it up with a quiz. If they do not make sense, drop back to the original lesson. For Those That Are Reviewing - If you are reviewing a topic, we suggest that you start with a math quiz on that topic. You will find those at the bottom of every topic page. See how you do. If you do well, try a second quiz to make sure you have it down. If you do poorly, start at the lesson and follow through the entire topic. If you do satisfactorily, review the guided lesson and follow it up with a few worksheets. Then go back and take another quiz. What Do Students Learn In First Grade Math Class? In the first grade students are all about expanding their skills, which they have learned in kindergarten and preschool. The first-grade curriculum pays major emphasis on building the foundation of mathematics. Some of the things they learn in first-grade maths class are: - Counting to 100 into small number groups such as 2s, 5s, and 10s. It helps their learning towards recognizing and writing numbers to 100. - They learn the concept of "greater than" or "equal to" as well the basic mathematical operations such as addition, subtraction, division, and multiplication. - They learn the use of symbols while using basic math operations such as "+," "-," "=," <," ">." - Adding numbers all the way up to 100 in their head. - Learning to do simple subtraction. - Working addition and subtraction using coins. - Learning to identify simple patterns. - Learning basic measurement units such as length, weight, height. - Understanding and doing simple fractions (1/2, 1/3, 1/4). Learning to tell time on an analog clock and learning different terms for telling time. One thing to keep in mind when taking in the concepts behind a math curriculum is that it follows a spiral curriculum.What that means is that year after year we spiral around and build on old knowledge. So in the first grade you are building on skills that you initially learned in kindergarten. When you reach second grade, you will build on the skills that you learned in first grade.This means that if we do not quite master something, we will see it again.This gives us the chance to get it right this time. But it also indicates that if you have bad habits and do not fix them, they will be a problem in the future for you.
Professional Development Information - Para Academy Supplement instructions - How to register on the PDS Scheduler - Non-employee registration - Directions to Bartow Airbase State Tuition Program Support Acquiring and utilizing math vocabulary is an essential skill for students. Having a robust math vocabulary allows students to think about, talk about, and interact with their math environment. To increase math vocabulary development consider: - Pre-teaching mathematics vocabulary. - Modeling vocabulary when teaching new concepts. - Using appropriate labels clearly and consistently. - Integrating vocabulary knowledge in assessments. - Using graphic rich and interactive games that reinforce or teach vocabulary. Some examples include: A Maths Dictionary for Kids – Interactive math dictionary from A to Z with sample problems Math is Fun – Illustrated math dictionary Graphic Organizers – Collection of printable graphic organizers useful for planning, organizing, and solving Visuwords – Word relationship graphic organizer with dictionary and thesaurus Wordle – Online tool for creating word clouds Concrete Math Instruction Students that lack a firm foundation built on conceptual knowledge may experience barriers to learning and assimilating new math skills. One method to increase conceptual knowledge is to use the Concrete-Representational-Abstract sequence of instruction (CRA Instruction). In this method, students begin with multiple opportunities to explore, experiment, and solve problems with concrete objects. Objects might include chips, base-ten blocks, pattern blocks, or fraction tiles. Real world objects, like M & Ms, food cartons, and floor tiles also provide opportunities for students to explore concepts such as patterns and shapes, measurement, and more. During the representational phase, students approach and solve problems through drawings, pictures, or visual maps relative to the concrete items. In the Abstract phase, students solve problems using numbers and symbols associated with the concrete items and representations. More information and online resources: Strategies for Teaching Elementary Mathematics Concrete-Representational-Abstract Instructional Model YouTube Video Concrete-Representational-Abstract: An Instructional Strategy for Math Virtual Manipulatives and Simulations Virtual manipulatives and simulations can provide the platform for representational instruction in a CRA sequence of instruction as well as take the place of concrete objects when materials are not readily available in a classroom, when materials are not accessible by students with disabilities, or to increase student engagement. Virtual representations and simulations are often graphic-rich and interactive resources, can be customized by the user, such as size and color and can be paired with a student’s assistive technology such as alternative mouse controls. National Library of Virtual Manipulatives – Online math manipulatives and simulations for grades PK-12 Illuminations – Collection of online, standard-based virtual manipulatives and lessons Explore Learning – Interactive mathematic simulations for grades 3-12 MathBlaster – Interactive virtual world math games Algodoo – Physics sandbox that allows the user to create, explore, and experiment MathTV is an online site that provides over 10,000 video tutorials covering topics from basic math through calculus. In each video tutorial a student or adult math teacher explains, demonstrates, or solves a specific example. Multistep problems are written out step-by-step using traditional math logic. Most videos are a couple of minutes long and users are able to select which tutor they want for each individual lesson. Other features include: - Multiple videos by different tutors for each example. - Video tutorials available in closed captioning. - Video tutorials available in Spanish. Find more information and videos at MathTV. Calculators allow students to simplify tasks and spend more time on understanding concepts and solving problems. Calculators can also increase student engagement by serving as scaffolds for lost or deficient math skills in related topics, thus allowing students to focus their time on grade-level standards. Calculators available as mobile apps, software downloads, and as online versions often have features that can eliminate barriers such as voice output, customizable layouts, size, and color. Meta Calc – Online calculator with adjustable sizes, including full screen Calculatoria – Online basic and advanced calculators with printable paper tape display and comments Percentage Calculator – Online calculator for finding percent increase, percent decrease, and percent change Simplify Fractions – Online calculator that converts a fraction to lowest terms Improper Fractions to Mixed Numbers Conversion – Online calculator for improper fraction to mixed number conversion Alcula – An extensive array of free online calculators for a variety of purposes, including simple mathematics, statistics, science, and more More calculators including mobile apps and direct downloads: The Amazing Math Toolbox Handout, Calculators
Populists and Progressives After the Civil War, the challenges presented by a developing industrial economy helped to encourage the American populist and progressive movements of the late nineteenth and early twentieth centuries. The political and economic landscape had changed fundamentally, and many argued that industrialization, technological innovation, urbanization, big business, and large accumulations of wealth threatened equality of opportunity and the common good. Political corruption only added to the problem. Special interests were said to dominate the political process to the benefit of the few and the detriment of the many. Broadly understood, American populism and progressivism sought to respond to these perceived challenges. The organized populism of late-nineteenth-century America was predominantly an outgrowth of southern and midwestern agrarian movements during the 1870s and 1880s. Cooperative alliances emerged claiming to defend the interests of farmers in the face of railroad expansion, exploitative banking practices, and diminishing crop prices. Of key importance were groups such as the Farmers’ Alliance, the Agricultural Wheel, and the Grange. In the early 1890s, the Farmers’ Alliance and other groups reached out to northeastern labor to form the relatively short-lived Populist (or People’s) Party. Among other things, the new party advocated the regulation and possible public ownership of the railroads, the abolition of national banking, the graduated income tax, reduced tariffs, abandoning the gold standard and embracing free silver, the initiative and referendum, the direct election of U.S. senators, and the eight-hour workday. The Populist Party reached its zenith when it joined with the Democrats to nominate William Jennings Bryan for president in 1896. While the Democratic Party absorbed Jennings’ defeat and survived, the smaller Populist Party could not, especially when Bryan lost again in 1900. The Populist Party collapsed soon afterward. Various strands of the party were absorbed into other elements of the political landscape, among them an emerging movement we now call progressivism. The American progressive movement lasted roughly from the early 1890s to the early 1920s, encompassing much more than the political party that sprang up around Theodore Roosevelt in 1912. Yet, as with many such “movements,” it is difficult to reduce progressivism to a single defining concept or motivation. Among turn-of-the century progressives we find a hodgepodge of political and intellectual strains. Under the tent of progressivism one could find the remnants of the populist agrarians, a variety of Christian social activists, temperance advocates and suffragists, labor and industrial reformers, and university Ph.D.s in philosophy and the new behavioral and social sciences, just to name a few. Nevertheless, we might see in the movement some common themes, perhaps the most significant of which resides in the name attached to it—“progressivism.” It might seem obvious, but one key element uniting many of these reformers, politicians, and intellectuals was their shared embrace of the doctrine of Progress with a capital “P.” The particular engine of that progress, be it the internal dynamics of history itself or some notion of biological or social evolution, varied among thinkers. We might say, however, that a progressive is someone who likely adheres to some notion that the human condition, and the human being, are improving, developing, or evolving over time. Through social, political, and economic reform, we not only participate in that progress but might help speed it along. As the “ism” in the name suggests, progressivism is an ideology of progress. Distinguished from philosophy, which contemplates truth for its own sake, ideology tends to investigate and employ ideas for the expressed purpose of practical, political action, be it preservation or change. Whatever particular concerns might separate the various elements of the progressive movement, they were united in their dedication to changing American life in the name of progress. In general, the progressives sought to reinterpret the American political order by giving the people more direct power over legislation and elected politicians, and in turn, giving administrative experts in state and federal agencies more power to regulate social and economic life. Progressive political scientists such as Woodrow Wilson and Frank Goodnow distinguished politics from administration. Politics might determine the broad ends or purposes of government, but administration, they argued, deals with detailed policy and the particular, technical means by which we secure those ends. Many progressives argued that enlightened administration could be released from the restraints of elections, separation of powers, and checks and balances to help solve political and economic problems. This progressive vision was perhaps best realized a few years later in the form of Franklin Roosevelt’s New Deal. Political scientists sometimes refer to this as the rise of the “administrative state.” Key to the progressive project was the attempt to regulate certain sectors of the economy and redistribute wealth and private property in the name of “social and industrial justice.” But these policies, many progressives argued, would not be enacted as long as the political process was dominated by powerful special interests and as long as the Constitution presented supposedly antidemocratic obstacles to progressive reform (e.g., representation, a difficult method of constitutional amendment, federalism, separation of powers and checks and balances, and a cumbersome legislative process). For many, the progressive project required an explicit, direct criticism of the principles of the Declaration of Independence and the U.S. Constitution. Progressive thinkers understood that the natural rights and social contract thinking that informed the Declaration of Independence provided the basis for a limited government constitutionalism that often seemed to frustrate contemporary progressive reform. They often claimed that these founding principles had been swept aside in the march of progressive history or by the evolutionary science of Darwinism. Educated men, they asserted, now knew that there were no transhistorical truths or natural rights that applied to all human beings everywhere and always. Liberty ought not to be seen as natural to man, but as a product of history, a convention, or a dispensation of government. Moreover, if human nature and political wisdom can be improved through historical and scientific progress, perhaps limitations on government were no longer necessary. These admittedly abstract ideas had very practical consequences for America’s political development. This document volume deviates from more common “textbook” approaches to the study of populism and progressivism in American history, not only because it focuses on primary sources but because it takes ideas seriously. Indeed, the leaders in these movements asked Americans to think about the proper ends and means of American democracy. This is especially true of the progressive movement. Insofar as it is a reaction to the founding, any real understanding of progressivism requires that we place its ideas and institutions in conversation with those of the Founders. We must weigh, balance, and ultimately judge what among their opinions is most reasonable. Necessarily limited in its scope, the present volume can only contribute to part of that dialogue. The reader might begin to construct that dialogue, however, by pairing this volume with others in the Core Documents series, perhaps those on the American Founding and the Constitutional Convention. I thank David Tucker for editorial advice and assistance. I am also grateful for the advice provided by two anonymous readers. In closing, I should also note that this volume is in part the result of a progressivism course I sometimes teach as a visiting faculty member in Ashland University’s MAHG program (Master of Arts in American History and Government). I wish to thank the students in those classes—most of them teachers—for their conversation, insights, questions, and dedication to learning through primary source documents. I have also benefitted much from other faculty who have taught the course, among them Christopher Burkett, David Alvis, Ronald J. Pestritto, and William Atto. Pestritto and Atto’s excellent and frequently assigned reader on American progressivism originated in their iteration of the course. That volume should be required reading for anyone interested in the principles of American progressivism and is listed among the suggested readings in Appendix C. Jason R. Jividen Saint Vincent College American Populism and a Changing Economy Henry George, Introduction to Progress and Poverty, 1879 Nelson A. Dunning, “Introductory History,” 1891 James B. Weaver, Excerpts from A Call to Action, 1892 William A. Pefer, “The Mission of the Populist Party,” December 1893 William Jennings Bryan, The “Cross of Gold” Address, July 9, 1896 Marion Butler, Keynote Speech at the Populist National Convention, July 22, 1896 The Political Theory of American Progressivism Charles E. Merriam, “Recent Tendencies,” 1903 Herbert Croly, Excerpt from The Promise of American Life, 1909 Woodrow Wilson, “What Is Progress?” 1913 Frank J. Goodnow, “The American Conception of Liberty,” 1916 Carl L. Becker, “The Philosophy of the Declaration in the Nineteenth Century,” 1922/1942 John Dewey, “Te Crisis in Liberalism,” 1935 The Populist Party Platform, July 4, 1892 The Populist Party Platform, July 24, 1896 The Progressive Party Platform, August 7, 1912 J. Allen Smith, “The Constitution a Reactionary Document,” 1907 Theodore Roosevelt, “The Right of the People to Rule,” March 20, 1912 Herbert Croly, Progressive Democracy, 1914 The Administrative State Woodrow Wilson, “The Study of Administration,” June 1887 Woodrow Wilson, “Leaders of Men,” June 17, 1890 Theodore Roosevelt, “The New Nationalism,” August 31, 1910 Progressive Social Reform Richard T. Ely “The Inheritance of Property,” July 1891 Jane Addams, “The Subjective Necessity for Social Setlements,” 1893 W. E. B. Du Bois, The Niagara Movement’s “Address to the Country,” August 19, 1906 Walter Rauschenbusch, Christianity and the Social Crisis, 1907 Jane Addams, “Why Women Should Vote,” January 1910 W. E. B. Du Bois, Open Letters To Woodrow Wilson, March and For each of the Documents in this collection, we suggest below in section A questions relevant for that document alone and in section B questions that require comparison between documents. 1. Henry George, Progress and Poverty, 1879 A. How does George characterize the relationship between progress and poverty? George says we have based our political system (in which human beings are theoretically equal) on a foundation of social inequality. This, he writes, “is to stand a pyramid on its apex.” What do you take this to mean? B. George’s thought enjoyed wide influence on the populist and progressive movements. Do you especially see that influence in thinkers such as Ely, Weaver, and Rauschenbusch? What ideas or phrases would you point to in those documents to show George’s influence? 2. Woodrow Wilson, “The Study of Administration,” June 1887 A. What exactly is the difference between politics and administration, according to Wilson? According to Wilson, why are modern democratic governments especially in need of the science of administration? What is the relationship between administration and public opinion? B. In Wilson’s scheme, might administration require the use of “leaders of men” to shape public opinion, particularly in democratic governments (see Wilson)? 3. Woodrow Wilson, “Leaders of Men,” June 17, 1890 A. What are the key characteristics of a “leader of men,” according to Wilson? Is a true “leader” especially able to shape public opinion through political rhetoric and oratory? Do we routinely expect or demand this “leadership” from politicians today, especially American presidents? B. William Jennings Bryan and Theodore Roosevelt are often considered two of the more powerful orators in American history. Do they illustrate the sort of rhetorical talents Wilson attributes to “leaders” of men? Why/why not (see also Roosevelt)? 4. Nelson A. Dunning, “Introductory History,” 1891 A. According to Dunning, when and why did agricultural alliances, such as the Grange, begin to emerge in America? What purposes do they serve? Why does Dunning think it especially important, under modern conditions, for farming interests to organize? B. Both Dunning and Weaver criticize the U.S. Senate. What do they argue? 5. Richard T. Ely, “The Inheritance of Property,” July 1891 A. According to Ely, what general means are available to progressives who want to foster economic reform and a wider distribution of wealth? Of what particular use is the inheritance tax? According to Ely, why are property rights no obstacle to such reforms? B. To what extent does the inheritance tax find favor in Roosevelt’s New Nationalism and the 1912 Progressive Party Platform? 6. James B. Weaver, A Call to Action, 1892 A. Weaver suggests that a “plutocracy” is trying to control American political and economic life. What is “plutocracy” and what examples does Weaver offer to try to illustrate its existence in the United States? B. How are Weaver, Addams (See “The Subjective Necessity for Social Settlements” and “Why Women Should Vote“), and Rauschenbusch similar in their appeals to Christian duty as obligating progressive reform? 7. The Populist Party Platform, July 4, 1892 A. What would you identify as the most important ideas and proposals of the 1892 Populist Party Platform? What sorts of political and economic challenges does the party seek to address? B. In what respects does the 1892 Populist Party Platform anticipate or contribute to some of the features of the 1896 Populist Platform and the 1912 Progressive Party Platform? 8. Jane Addams, “The Subjective Necessity for Social Settlements,” 1893 A. What is the social settlement movement, as it is presented here? What are its purposes? Addams sometimes writes that the Progressive project is to make democracy social, not just political. What do you take this to mean? B. How are Addams (See “The Subjective Necessity for Social Settlements” and “Why Women Should Vote“), Weaver, and Rauschenbusch similar in their appeals to Christian duty as obligating progressive reform? 9. William A. Peffer, “The Mission of the Populist Party,” December 1893 A. According to Peffer, how is the Populist Party securing the purposes of the Declaration of Independence and the U.S. Constitution? Is he persuasive here? What are the four demands of the Populist Party, according to Peffer? B. Peffer suggests that “no man ever earned a million dollars.” Do Ely and Roosevelt agree, and how might this influence their ideas on the distribution of wealth? 10. William Jennings Bryan, The “Cross of Gold” Address, July 9, 1896 A. What is the “money question” to which Bryan refers in this speech? What is “bimetallism” and what is Bryan’s stance on it? What does Bryan mean when he insists that mankind shall not be crucified “upon a cross of gold”? B. Why would you say this speech helped Bryan, a Democrat, secure the Populist Party’s nomination for the presidency in 1896? Consider Butler and the 1896 Populist Party Platform. 11. Marion Butler, Keynote Speech at the Populist National Convention, July 22, 1896 A. According to Butler, how have the Democratic and Republican Parties failed America? What does he say is the “only way to build up” the People’s [Populist] Party for the future? B. How would you say Butler’s speech helped to convince Populists to back Bryan for the 1896 nomination? Why might Bryan be the most attractive candidate? 12. The Populist Party Platform, July 24, 1896 A. What would you identify as the most important ideas and proposals of the 1896 Populist Party Platform? What sorts of political and economic challenges does the party seek to address? At the end of the platform, what is described as the “pressing issue” of the campaign? B. In way ways does the 1896 Populist Party Platform build upon the 1892 Platform? Is the 1896 platform distinguished by its special focus on the “financial question” and interparty cooperation? 13. Charles E. Merriam, “Recent Tendencies,” 1903 A. Merriam suggests that progressive social science criticizes many of the political ideas associated with the American founding. Identify a few of those ideas and explain the critiques Merriam presents. How are some progressive theories of liberty indebted to the thinking of John C. Calhoun? B. How do Wilson (See “The Study of Administration” and “What is Progress?”) and Goodnow each exemplify some of the recent tendencies in progressive scholarship to which Merriam refers? Offer a few examples. 14. W. E. B. Du Bois, The Niagara Movement’s “Address to the Country,” August 19, 1906 A. What is the Niagara movement? What are its “demands,” or purposes? By what means will the movement pursue those ends, according to Du Bois? B. Of what special importance are the ideas of equal suffrage and black voting in the Niagara movement’s plan and in Du Bois’ letters to Woodrow Wilson? 15. J. Allen Smith, “The Constitution a Reactionary Document,” 1907 A. What does Smith mean in referring to the U.S. Constitution as a “reactionary” document? What is his evidence for this claim? According to Smith, how does this help to explain our frequent frustration with American politics? B. Compare Smith with Roosevelt. Although both are sympathetic to direct democratic reforms, Roosevelt the politician does not criticize the U.S. Constitution as overtly or strongly as Smith the academic. Why might that be? 16. Walter Rauschenbusch, Christianity and the Social Crisis, 1907 A. What does social and economic equality have to do with Christian morality, according to Rauschenbusch? Rauschenbusch says we have “one kind of constitution on paper, and another system of government in fact.” What does he mean and why does he think this is the case? B. Compare Rauschenbusch and Goodnow on the courts. According to each, how do the courts protect special privilege? 17. Herbert Croly, The Promise of American Life, 1909 A. Try to explain Croly’s Hamilton-Jefferson dichotomy (a.k.a. the difference between “the “national” and “democratic” traditions) in American political thought. How might this distinction help us understand American political development and the aims of progressivism, according to Croly? B. Is Croly’s account of the Jeffersonian tradition, and its supposed limitations, another way of criticizing the American individualism that Goodnow and Dewey reject? 18. Jane Addams, “Why Women Should Vote,” January 1910 A. For Addams, why ought women to vote? Who would you say her audience is in this piece and how might that affect the kind of argument she makes? B. Compare Addams on the role of young, reformist woman in the settlement houses and the role of a mother. How does each contribute to progressive ends? 19. Theodore Roosevelt, “The New Nationalism,” August 31, 1910 A. How would you describe Roosevelt’s New Nationalism? What are its ends? What are its means? Are you convinced that Roosevelt follows in the footsteps of Lincoln here? Why/why not? B. Do some of the administrative regulations of the New Nationalism serve as a good example of administration as envisioned by Wilson? What do Roosevelt and Ely have to say about property rights and the redistribution of wealth? 20. Theodore Roosevelt, “The Right of the People to Rule,” March 20, 1912 A. What kinds of problems does Roosevelt seek to remedy with methods of more “direct” democracy? What particular methods does he propose? B. Compare Roosevelt with Croly. Does either appear to believe in the danger of majority tyranny? Why/why not? 21. The Progressive Party Platform, August 7, 1912 A. What would you identify as the most important ideas and proposals of the 1912 Progressive Party Platform? What sorts of political and economic challenges does the party seek to address? B. In what ways is the Progressive Party Platform indebted to the Populist platforms of 1892 and 1896? 22. Woodrow Wilson, “What Is Progress?” 1913 A. Explain Wilson’s idea of the “Newtonian” and “Darwinian” worldviews. How does he use this distinction to critique the American Founders’ understanding of the Constitution? What does Wilson mean when he says the Declaration of Independence is a practical, rather than a theoretical, document? Why would he want to convince us of this? B. Compare Wilson with Becker. How does the idea of Darwinism shape their respective arguments? 23. W. E. B. Du Bois, Open Letters To Woodrow Wilson, March and September 1913 A. How would you describe the difference in tone between Du Bois’ March and September letters to President Wilson? Why does Du Bois approach Wilson with guarded optimism in the first letter and express his profound disappointment with the president in the second? B. What do the challenges described in these letters and in the Niagara Address suggest about the status of black civil rights in the progressive era? 24. Herbert Croly, Progressive Democracy, 1914 A. According to Croly, why is direct (as opposed to representative) democracy more feasible today than in the past? Was the only argument against direct democracy really one of size, technology, etc.? Are there any other reasonable arguments against direct democracy? B. Compare Croly and Smith. Why does each think the American regime did not originally embrace direct democracy? Are they persuasive? 25. Frank J. Goodnow, “The American Conception of Liberty,” 1916 A. Explain Goodnow’s critique of natural rights and social contract. What is the difference between contemporary American and European conceptions of liberty, according to Goodnow? How has the American conception of liberty affected the way U.S. courts think about property rights and due process? B. How are Goodnow and Dewey similar in their critique of earlier, Enlightenment Era notions of liberty? Offer a few examples of that similarity. 26. Carl L. Becker, “The Philosophy of the Declaration in the Nineteenth Century,” 1922/1942 A. According to Becker in 1922, to “ask whether the natural rights philosophy of the Declaration of Independence is true or false is essentially a meaningless question.” What is he suggesting here? What is the role of Darwinism in bringing him to this conclusion? In 1942, is the truth of natural rights a seemingly meaningful question once again? Why? B. Compare Becker and Dewey. Is Dewey’s claim that the truth of natural rights is “historically relative” essentially the same as Becker’s suggestion that it is meaningless to ask whether the natural right principles of the Declaration of Independence are true or false? 27. John Dewey, “The Crisis in Liberalism,” 1935 A. What do you think Dewey means when he refers to a “crisis in liberalism”? Dewey writes that earlier liberals “lacked historic sense and interest,” and failed to see that their own “interpretations of liberty” were “historically conditioned.” What does this mean and how does it supposedly lead to the “crisis” Dewey describes? B. Compare Dewey and Goodnow on the courts. According to each, how do the courts rely on outdated notions of liberty to protect property? Do they think this a good thing?
Spherical law of cosines In spherical trigonometry, the law of cosines (also called the cosine rule for sides) is a theorem relating the sides and angles of spherical triangles, analogous to the ordinary law of cosines from plane trigonometry. Given a unit sphere, a "spherical triangle" on the surface of the sphere is defined by the great circles connecting three points u, v, and w on the sphere (shown at right). If the lengths of these three sides are a (from u to v), b (from u to w), and c (from v to w), and the angle of the corner opposite c is C, then the (first) spherical law of cosines states: Since this is a unit sphere, the lengths a, b, and c are simply equal to the angles (in radians) subtended by those sides from the center of the sphere (for a non-unit sphere, they are the distances divided by the radius). As a special case, for , then and one obtains the spherical analogue of the Pythagorean theorem: where A and B are the angles of the corners opposite to sides a and b, respectively. It can be obtained from consideration of a spherical triangle dual to the given one. If the law of cosines is used to solve for c, the necessity of inverting the cosine magnifies rounding errors when c is small. In this case, the alternative formulation of the law of haversines is preferable. A proof of the law of cosines can be constructed as follows. Let u, v, and w denote the unit vectors from the center of the sphere to those corners of the triangle. Then, the lengths (angles) of the sides are given by the dot products: To get the angle C, we need the tangent vectors ta and tb at u along the directions of sides a and b, respectively. For example, the tangent vector ta is the unit vector perpendicular to u in the u-v plane, whose direction is given by the component of v perpendicular to u. This means: where for the denominator we have used the Pythagorean identity sin2(a) = 1 − cos2(a) and where \|\| \|\| denotes the length of the vector in the denominator. Similarly, Then, the angle C is given by: from which the law of cosines immediately follows. Proof without vectors To the diagram above, add a plane tangent to the sphere at u, and extend radii from the center of the sphere O through v and through w to meet the plane at points y and z. We then have two plane triangles with a side in common: the triangle containing u, y and z and the one containing O, y and z. Sides of the first triangle are tan a and tan b, with angle C between them; sides of the second triangle are sec a and sec b, with angle c between them. By the law of cosines for plane triangles (and remembering that sec2 of any angle is tan2 + 1), Multiply both sides by cos a cos b and rearrange. Planar limit: small angles For small spherical triangles, i.e. for small a, b, and c, the spherical law of cosines is approximately the same as the ordinary planar law of cosines, Substituting these expressions into the spherical law of cosines nets: or after simplifying: Remembering the properties of big O notation, we can discard summands where the lowest exponent for a or b is greater than 1, so finally, the error in this approximation is: - W. Gellert, S. Gottwald, M. Hellwich, H. Kästner, and H. Küstner, The VNR Concise Encyclopedia of Mathematics, 2nd ed., ch. 12 (Van Nostrand Reinhold: New York, 1989). - Romuald Ireneus 'Scibor-Marchocki, Spherical trigonometry, Elementary-Geometry Trigonometry web page (1997). - Reiman, István (1999). Geometria és határterületei. Szalay Könyvkiadó és Kereskedőház Kft. p. 83. - R. W. Sinnott, "Virtues of the Haversine", Sky and Telescope 68 (2), 159 (1984).
A History of the Fair Trade Movement Sunday, September 1, 2002 "It's tough to be ethical consumers in this age of sweatshops - both at home and abroad. Fair Trade coffee offers one good way to know with confidence that the products you purchase are made in just working conditions. All of us must do more to support fair trade alternatives." Kim Bobo, National Interfaith Committee for Worker Justice Sip a steaming brew at Starbucks, and you might associate coffee with prosperity. The image of carefree consumers enjoying $4 lattes seems totally unrelated to that of coffee-bean farmers and workers, who live with grinding poverty, illiteracy, and a long legacy of economic colonialism. But the two groups are part of an intricately related system that has existed for centuries, leaving coffee harvesters destitute and coffee drinkers mostly unaware of the suffering that goes into making their beverage. But a movement is growing among coffee consumers to demand justice for coffee workers and farmers. Consumer activists have been putting grassroots pressure on big coffee retailers such as Starbucks to buy directly from cooperative farmers and pay them a price that represents a living wage. This movement demands that corporations not just makeover their images as socially responsible businesses while maintaining their laser-beam focus on shareholder profit, but that they are accountable to all their stakeholders - including consumers, citizens, and, most importantly, the people who produce the goods that generate their revenue. The movement also encourages Americans to be as ethical in their behavior as consumers as they are in all aspects of their lives. But importantly, it demonstrates that when we act not only as consumers, but as citizens, we can become powerful enough to force large corporations to be accountable to basic principles of human rights and fairness. Because of the new movement, Starbucks -- and dozens of other companies - have begun offering millions of consumers a choice: between coffee produced under sweatshop conditions, and a product based on principles of fair trade. Indeed, Fair Trade is the name of the movement, and its time has come. Coffee is the world's second most valuable market commodity after petroleum, and U.S. consumers drink one fourth of the beans traded in the global market. Coffee is a significant source of foreign exchange for many Latin American and African countries and has played a major role in the political histories of nations such as Mexico, Colombia, Guatemala, Brazil, Indonesia, and Rwanda. It was traditionally developed as a colonial cash crop, planted and harvested by serfs or wage laborers on large plantations, then exported to imperial countries. In its natural, shaded habitat, coffee is a sustainable crop. In the mid-20th century, however, with the advent of the Green Revolution—an agribusiness-oriented scheme that pressed high technology on traditional farmers—varieties of high-yielding coffee were pursued. In the 1970s the United States Agency for International Development (USAID) gave over $80 million to coffee plantations in Latin America to "modernize"—to strip coffee of shade trees and purchase chemical pesticides and fertilizers. This has led to severe environmental problems, such as contamination of air and water through pesticide poisoning. Deforestation has also become a major threat to migratory songbirds because of habitat destruction. Such outcomes have led to consumer demand for organic and shade grown coffees. Farmers, many of them indigenous peoples, grow most of the world's coffee beans on plots of less than 10 acres. The prices they receive are often less than the costs of production, which pushes them into an endless cycle of poverty and debt. All over Latin America, farmers are forced to sell the future rights to their harvest to exploitative middlemen in exchange for the credit they need to pay for basic necessities. The world price is set on the New York "C market"—the section of Wall Street that deals in sugar, cocoa, and coffee. While severely volatile, the C market price for coffee hovered around $1 per pound since the collapse of the International Coffee Agreement in 1989 through the end of the 1990s. Farmers in over 50 nations are hostage to this speculative market. They generally receive less than half the C market price, or between 30 and 50 cents a pound for coffee that retails for as much as $10. That rate earns a family an average of only $600 a year. Coffee is also grown on large plantations worked by landless day laborers with low rates of unionization and extremely poor working conditions. In 1995, as a result of pressure from the US/Guatemala Labor Education Project, Starbucks drafted the first Code of Conduct for coffee suppliers, but they have yet to implement it. Starbucks refuses to disclose the location of the plantations from which it buys, making independent monitoring impossible. A study in 2000 by the Guatemalan Commission for the Verification of Corporate Codes of Conduct found half the workers on plantations in that country earning less than $3 per day for picking 100 pounds of coffee. Workers also were subject to forced overtime without compensation, and usually did not receive their legally-mandated benefits. Coffee workers are denied basic labor rights not just in Guatemala, but worldwide, and efforts to develop an industry-wide Code of Conduct are underway. Unfortunately, coffee prices have plummeted to all-time lows in the last two years and are currently less than $.50 per pound, with no increase in sight. Until 1989, the International Coffee Agreement (ICA) helped stabilize prices by regulating world supply. The US worked to abolish the ICA in 1989 in favor of a "free market" in the coffee trade -- knowing that importers' monopolistic control over the coffee trade would lead to lower prices for farmers in poor countries, and higher profits for multinationals. Many countries have since worked to expand their coffee exports to generate foreign revenues to help finance debt. The result is a worldwide coffee surplus that has led to a crash in market prices and huge profit growth for coffee companies at the expense of farmers around the world. "The drastic fall in coffee prices means, in two words, poverty and hunger for thousands of small producers in Latin America," says Merling Preza Ramos, director of PRODECOOP Fair Trade cooperative in Nicaragua. The crisis is causing a combustible brew of impoverishment, social dislocation, migration, and increased drug cultivation. Tens of thousands of Mexican coffee farmers have fled their fields in search of incomes to feed their families. According to the Associated Press, at least seven of the 14 men who died crossing the US/Mexico border in May of 2001 were coffee farmers from the Mexican state of Veracruz who were forced to leave their communities in search of higher wages in the US because they could no longer support their families. El Salvador recently acknowledged that over 30,000 jobs have been destroyed because of the price slump. Many of the 60,000 coffee producers in Nicaragua are facing losing their land because of mass indebtedness. Recent accounts reveal that farmers in traditionally coffee-growing areas in Colombia are uprooting coffee plants in favor of planting the more lucrative coca and opium poppies. Surely millions of Americans would be happy to pay a fair price for coffee if it meant less illegal drugs coming into the US. Why are US taxpayers forking over $1.3 billion a year for anti-drug efforts in Colombia while accepting an economic policy that encourages increased cultivation? Farmers in all these countries have taken to the streets to demand government support for farmers on the brink of starvation. Political unrest is brewing. In many countries the crisis has been exacerbated by "structural adjustment" programs imposed on local governments by the World Bank that have meant cuts in rural credit, technical assistance, health care, and educational infrastructures. In addition, trade liberalization has forced many countries to deregulate their coffee sectors, removing the state as a buffer between the farmers and the world market. According to the Washington Post, the collapse of world coffee prices is contributing to societal meltdowns affecting an estimated 125 million people. In countries such as Uganda and Burundi, which get 70 percent of their export earnings from coffee, the severe price drop has all but negated benefits from international debt relief. Even the World Bank recently acknowledged that approximately 500,000 people lost their jobs in Central America during the last crop cycle. The head of the International Coffee Organization, Nestor Osorio, acknowledged that a crisis is facing the industry. Importantly, however, he has noted the huge disparity in the price of retail sales of coffee compared to what producers in Africa, Asia, and Latin America actually receive. In the early 1990s, retail sales were around $30 billion, but have now more than doubled to $65 billion. However, producers' share of coffee sales has fallen from $12.5 billion to $5.5 billion. This is because coffee companies have not lowered consumer prices but are pocketing the difference. Procter & Gamble, the largest coffee retailer in the US, sells over 600 million pounds of coffee a year through their Folgers and Millstone labels. As the price of the raw commodity plummets, they have saved an estimated $2-300 million per year on the blood and sweat of coffee farmers. The crisis for Procter & Gamble is not a crisis of survival, but rather a profit bonanza. The Fair Trade Alternative Is a system that structurally impoverishes farmers and leaves consumers unwittingly contributing towards the exploitation of poor farmers the best the modern world can imagine? Fortunately, the answer is no. The coffee crisis gives new urgency to efforts to promote the alternative--Fair Trade. Fair Trade offers a mechanism for small farmers to receive higher prices as an alternative to the "tyranny of the C market". To have their coffee certified as Fair Trade, importers must satisfy strict international criteria and submit to independent monitoring by TransFair USA, the certification agency based in Oakland, California. The most important requirement is a minimum price of $1.26 per pound, paid directly to organized farmer cooperatives—not to middlemen. Fair Trade importers also must provide farmers with credit at fair terms and commit to long-term trade relationships. The recipients of fair trade benefits are some 550,000 farmers organized into 300 cooperatives in 21 countries in Central and South America, Africa, and Asia. One such group, PRODECOOP, is based in Esteli, Nicaragua. It was founded in 1993 and boasts over 2,420 families. PRODECOOP has undertaken projects such as building schools and healthcare centers as well as training in production techniques and legal matters. From sales to the fair trade market, farmers earned $600,000 over the regular market price for their coffee last year. The income is used to pay bank debt and thus avoid loss of land, to purchase the cooperative's own mill, and to increase the quality of the coffee. "With world market prices as low as they are right now, we see that a lot of farmers cannot maintain their families and their land anymore. We need Fair Trade now more than ever," says Jerónimo Bollen, Director of Manos Campesinas, a Fair Trade coffee cooperative in Guatemala. Another Fair Trade cooperative in Oaxaca, Mexico is the Union of Indigenous Communities of the Isthmus Region (UCIRI). Established in 1982, it has more than 5,000 families who farm roughly 15 acres each. UCIRI has helped create the region's only public bus line; a farm supply center; healthcare services; cooperative corn mills; an agricultural extension and training program; and the region's only secondary school. In contrast to the assumption that upping prices paid for cash crops might induce farmers to increase export dependence, experience has shown that farmers are more likely to use the additional incomes they gain from the Fair Trade market to invest in projects that increase food security. "We are happy that Fair Trade Certified coffee is finally becoming available in the United States," said Jorge Cuevas, a manager of a Fair Trade cooperative in Oaxaca, Mexico. "It will mean so much for our communities and our families. A fair price means the difference between poverty and success." Fair Trade History The idea of marketing fairly priced products from cooperatives is not entirely new, particularly for people who were sympathetic to Central America's revolutionary movements of the 1980s. At that time, solidarity activists and organizations, such as the Boston-based group Equal Exchange, were importing and selling small amounts of Nicaraguan coffee to support that country's Sandinista movement, and paying farmers fair prices. Their support made the difference in many cooperatives keeping rather than losing their land when the Sandinistas lost power in 1990. Equal Exchange is now the largest Fair Trade coffee importer in the US, purchasing 1.76 million pounds of green beans in 2001 and returning an unprecedented $960,000 in Fair Trade over-market premiums directly to farmer cooperatives. Now other organizations like Peace Coffee, Cloudforest Initiatives, and Café Campesino are working to spread the message of the importance of 100% commitment to Fair Trade. While coffee is the largest single product in the Fair Trade movement, it is not just about commodities. The Fair Trade Federation (FTF), the national association of fair trade retailers and wholesalers, boasts over a hundred business members that import or market crafts with the primary motive of supporting cooperative producers with fair prices. The FTF, and its sister organization the Fair Trade Resource Network, works to increase public awareness about Fair Trade and increase the sales of Fair Trade products in the US. FTF criteria include paying a fair wage in a local context; providing equal opportunities for all people, particularly the most disadvantaged; engaging in environmentally-sustainable practices; building long-term trading relationships; providing healthy and safe working conditions; and providing financial and technical assistance to workers whenever possible. Many FTF members have roots in religious organizations as well, such as the Mennonite-initiated Ten Thousand Villages network of Fair Trade stores, and SERRV, originally a program of the Church of the Brethren, that sells Fair Trade products to a network of over 3000 inter-denominational churches across the country. Many religious organizations find that Fair Trade is consistent with an ethical approach to purchasing, and make a commitment to buy only Fair Trade gifts, clothing, jewelry, housewares, and other items, because it respects the dignity inherent in the person producing what we purchase. These organizations had their roots in post-WWII Europe, helping to support refugees and war victims, and are now a major anchor in the Fair Trade movement. Later, the emphasis shifted to sustainable development for Third World artisans. Now a majority of the dozens of businesses that support Fair Trade are small family-owned operations with a strong dedication to working with a specific cooperative or region. For example, Maya Traditions is a small importer partnering with four rural women weavers' cooperatives in Guatemala. Participating in the cooperatives allows the women to gain a fair price for their high-quality products as well as access to a women's herbal health center and increased educational opportunities for their children. Ganesh Himal has a long-term relationship with the Dhukuti women's craft center in Nepal, which provides over 700 low income and abandoned women with employment and training in traditional skills, as well as access to health care, funds for female education, peer counseling services, a bonus program, and welfare and retirement funds. Prescraft is dedicated to preserving the rich cultural heritage of men and women from rural villages in Cameroon in West Africa. In addition to providing fair employment, Prescraft's goals are to stem the flow of peasants from the rural areas to the cities and to preserve traditional craft skills. The situation was similar in Europe, whose long, explicit history of colonialism has left more of the population aware of how their countries' economic policies have aggravated poverty in the Global South. European fair trade efforts originally focused on operating alternative retail stores that sold folk crafts. Currently, Europe has about 3500 such stores, whose efforts are coordinated through the Network of European World Shops. In addition, they work together through the European Fair Trade Association, based in Holland. Globally, Fair Trade efforts are coordinated through the International Federation for Alternative Trade, or IFAT, which focuses on Fair Trade producers. While Fair Trade sales in the US are small, it represents a huge potential for growth. The Fair Trade industry in North America made nearly $100 million in gross sales in the year 2000, according to a report in May of 2002 by the Fair Trade Federation. That marked a major increase over previous years, according to the FTF, which expects further increases for 2001 and 2002 primarily due to the rapidly growing market for Fair Trade coffee sold by retail outlets that are not themselves Fair Trade companies. The market is also growing for another reason. Many consumers have grown frustrated by US companies' lack of response to continuing exposes about sweatshops overseas. Nike claims that it pays Indonesian, Chinese, and Vietnamese workers fairly for stitching its outrageously expensive shoes. But an independent assessment three years after Nike made it first promise to clean up its act has shown that we are 'Still Waiting for Nike to Do It.' GAP Inc claims to be a 'socially responsible company', yet refuses to settle a three year old lawsuit with human rights and labor organizations for slave labor conditions on the US island of Saipan in the Pacific. After learning more about the exploitation many young women workers are subjected to by US companies operating overseas, many consumers want to be able to buy products without contributing to such abhorrent ills as child labor, indentured servitude, poverty wages, and forced 70- and 80-hour workweeks. "I support the principles of Fair Trade. A successful Fair Trade model would be a substantial step towards a more socially just society, in which the principles of decent wages and working conditions are seen not as an "alternative" model for business firms, but as the minimum standard for their operations. To this end, consumers should consider seriously the social and environmental realities behind the products they use and choose fairly traded items when they are available. Unfortunately, in many cases there simply are no alternative products to choose from--you can't find socially responsible sneakers or jeans. However, there is a choice with coffee. Consumers at the supermarket, cafe, and restaurant can make a conscious choice to support farming families all over the world by looking for the Fair Trade Certified label. Drinking Fair Trade Certified coffee can help change the world one cup at a time!" --Dr. Noam Chomsky Movement for Certification In 1988 fair trade advocates realized that producers of basic agricultural commodities faced tremendous disadvantages in the global market as their 'terms of trade' (the value of their products related to other goods) continued to decline -- and that developing a Fair Trade market could be a solution. The effort to bring the Fair Trade concept to mainstream commodities and markets originated in Europe through a Dutch organization called Max Havelaar, the original fair trade monitoring organization. The name comes from the title of a book about Dutch colonial exploitation of Indonesian coffee workers at the turn of the century, whose popularity garnered Dutch support for labor reforms. Fair Trade advocates pressured existing coffee companies to abide by Fair Trade criteria and carry the Max Havelaar label, which now enjoys wide recognition all over Holland. Max Havelaar later added sugar, cocoa, tea, honey, orange juice, and bananas—historically colonial cash crops—from cooperatives in former colonies. More countries took on the concept and changed the name to TransFair, and in 1997 incorporated into Fair Trade Labeling Organizations International (FLO), which now has branches in Canada, Japan, and 15 importing countries in Europe. The concept of "mainstreaming" fair trade took off in the United States in 1998, with the formation of Transfair USA, this country's branch of FLO. Paul Rice, TransFair's Executive Director, spent over ten years working with coffee cooperatives in Latin America and realized that building a Fair Trade market was more sustainable than other development projects. TransFair reasoned that it could appeal to 'specialty' coffee consumers: buyers who pay top dollar for top-quality Arabica beans. Arabica coffee retails for about $10 a pound and comprises 15 to 25 percent of the total coffee market. TransFair's research showed that people who pay $10 a pound for coffee would not mind adding a dollar more to guarantee a fair trade price to small coffee farmers. Transfair USA began its efforts in late 1998 - and as of 2002 there are over 130 roasters and coffee importers that have agreed to abide by Fair Trade criteria and submit to monitoring by TransFair USA. Campaigning for Fair Trade Global Exchange got involved with campaigning for Fair Trade as an outgrowth of the 10 years we have spent promoting Fair Trade through our Bay Area craft stores. We believe that as we criticize free trade and corporate globalization for its lack of democracy and exploitation of poor people around the world, we also need to promote our own vision of a global trade system based on economic justice. As this country's first product with an independent monitoring system to ensure against sweatshop-style labor abuses, coffee represents an important alternative model to the free trade practices advocated by the iron triangle of the global sweatshop economy: the World Bank, the International Monetary Fund (IMF), and the World Trade Organization. Global Exchange initiated a public education-for-action campaign in summer 1999, and since then we have built a network of activists, church groups, students, labor unions, and environmentalists to increase consumer demand for Fair Trade coffee in our own communities. We successfully lobbied city councils in San Francisco, Berkeley, and Oakland to limit those cities' coffee purchases to brands that are Fair Trade Certified and usually organic. The Santa Cruz city council later followed suit. We helped host a farmer from Esteli, Nicaragua—San Francisco's Sister City—for an event with San Francisco Board of Supervisors and living wage advocates. After many hours of volunteer public education efforts and solid media coverage, the Bay Area now boasts over 100 retail outlets for Fair Trade Certified coffee, up from four when we started in 1999. Branching out nationally, we laid the groundwork in fall 1999 to help community activists and college students coordinate Fair Trade coffee campaigns. We now have a network of over 130 groups, mostly on campuses such as University of Chicago and Columbia, where students are working to pass purchasing restrictions at those institutions for Fair Trade coffee. Efforts have already been successful at over 100 campuses including Stanford, Duke, American University, Boston University, and many others. Meanwhile, the Student Alliance to Reform Corporations, United Students Against Sweatshops, the Student Environmental Action Coalition, and Campus Greens have participated in Fair Trade Certified coffee activities across the country. In the fall of 2000, Oxfam America also got involved in helping to promote Fair Trade campaigns on college campuses across the US, adding to the movement for student leadership on global issues affecting poverty around the world. Some of these efforts have led to important developments with large companies. In February of 2000, students at Wesleyan University in Connecticut wrote letters to the coffee company that sells on campus, Green Mountain. They applauded Green Mountain's commitment to organic coffee, and asked them to extend that commitment to Fair Trade principles. Now Green Mountain is one of the largest roasters of Fair Trade coffee in the US, offering many roasts of Fair Trade, shade grown, organic varieties. That same spring, students at the University of California at Davis convinced Java City to go Fair Trade. And in the spring of 2001, students at the University of California at Los Angeles convinced Sara Lee, the third largest coffee company in the US, to adopt Fair Trade standards rather than lose the lucrative UCLA coffee account. This has had the important side effect of placing Fair Trade coffee in 250 Borders Books Cafes, as they purchase coffee from Sara Lee. Coordinated student activism had led directly to many hundreds of thousands of Fair Trade coffee sold in the US. Perhaps our most dramatic campaign has been focused on Starbucks. We chose Starbucks because it is the largest specialty coffee retailer, with a fifth of all cafes in the country. In the fall of 1999, Global Exchange approached then CEO Howard Schultz and requested that Starbucks offer Fair Trade Certified coffee in all its stores. The company was initially very hesitant, alleging the beans were of low quality. Shortly thereafter, we organized several peaceful demonstrations in front of Starbucks stores in Seattle during the mass protests against the World Trade Organization. While 50,000 trade unionists, environmentalists, church people and regular citizens demonstrated against 'free trade' corporate globalization, we also advocated for the Fair Trade alternative. In February 2000, an investigative report by San Francisco's ABC TV affiliate exposed child labor and scandalously low wages on Guatemalan coffee plantations, some of which sell coffee to Starbucks. Immediately after the program aired, we organized a local protest. We then petitioned Starbucks stockholders at their annual meeting in Seattle in February to offer Fair Trade Certified coffee. That same week, the company announced a one-time shipment of 75,000 pounds of Fair Trade coffee. We responded that for a firm as big as Starbucks, this represented a "Drop in the Cup"—an average of only about 30 pounds per store—and the coffee was not certified! We then circulated an Open Letter, signed by 84 student, environmental, church, and social justice organizations, again asking Starbucks to pay farmers a living wage and offer their customers Fair Trade Certified coffee. Hundreds of people faxed letters to Starbucks from our website or sent postcards asking the giant retailer to pay farmers fair prices. Meanwhile, we organized 30 demonstrations, scheduled for April 13, across the country at Starbucks shops. Our protests were planned right in the middle of a Week of Action for Global Justice organized to protest the International Monetary Fund and the World Bank's annual meeting -- the largest mass mobilization against global corporate rule and for Fair Trade since the Seattle protests against the WTO. Three days before our scheduled demonstrations, Starbucks announced an agreement with TransFair USA to offer Fair Trade Certified coffee at all its stores nationwide, which they did on October 4, 2000. This was a huge victory for farmers, whose incomes triple when they can sell their coffee at Fair Trade prices. It was also an important win for the corporate accountability movement. Starbucks' quick capitulation in the face of nationwide protest illustrates that grassroots organizing and education can indeed bring major results. We then gave Starbucks a fair amount of time to implement their commitments. Unfortunately, Starbucks has not adhered to all aspects of its commitments to seriously promote Fair Trade coffee. In the fall of 2001 we then joined with the Organic Consumers Association in demanding that Starbucks regularly brew and seriously promote Fair Trade coffee in all its stores. OCA also demanded that Starbucks offer rBGH-free milk that is safe for consumers in all its coffee drinks, and that it permanently commit to not purchasing genetically modified coffee or other food products. Their campaign mobilized thousands of new environmental and Fair Trade advocates. Starbucks' model of offering only one type of whole bean coffee, and not brewing it regularly in its coffee drinks, treated Fair Trade as a flavor, not a way of doing business. In addition, it leaves the responsibility for choosing Fair Trade up to the individual consumer, rather than the company taking responsibility for assuring that its supply chain is not exploiting farmers. As they continue to charge upwards of $4 for a coffee beverage for which the farmer received pennies, it is easy to see how much more Starbucks could be doing to promote Fair Trade as an integrated part of their business. In October of 2001 Starbucks announced new programs related to Fair Trade Certified coffee, including the commitment to purchase 1 million pounds of coffee over the next 18 months. Any increase in the amount of Fair Trade Certified coffee purchased in the United States means a direct and immediate improvement in the lives of farmers around the world. However, the announcement falls short of offering brewed Fair Trade coffee at least once a week at all store locations, a move that would prove a significant commitment to Fair Trade. The 1 million pound announcement still puts Starbucks, a company with over $3 billion in sales last year, far behind other industry leaders such as Equal Exchange, a $7 million company, which purchased close to 2 million pounds of Fair Trade Certified coffee in 2001. And Starbucks' volume as a percentage of sales is still far below the industry minimum standard of 5% Fair Trade shared by almost every other of the 130 companies offering Fair Trade Certified coffee. Close, but no cigar. Demanding fair trade coffee from your favorite vendor is a simple way of combating the economic slavery that is endemic to our world. Starbucks, for one, will specially prepare any of your latte drinks with fair trade espresso, but you have to ask. We need to be conscious of the role of slave labor in producing so many of the goods we enjoy. Let us raise our awareness with coffee, and then continue with other products. "If not now, when?" Rabbi Jonathan Singer, Temple Beth Am Religious groups have increased their support for Fair Trade immensely in the last three years. Groups such as Lutheran World Relief, the Presbyterian Church (USA), Maryknoll, Church of Christ, the Unitarian Universalists, the United Methodist Church, and others have endorsed Fair Trade efforts as being in line with their religious teachings on ethical consumerism. Over 4,500 of them serve Fair Trade coffee (through Equal Exchange's Interfaith Coffee Program) at their social hours. As Jonathan Fredrichs of Lutheran World Relief states, "That comforting cup of coffee is our closest link to the smallest players in the global economy. Coffee farmers do 90 percent of the work of getting that coffee into your hands, while sharing less than 10 percent of the proceeds of that very rich crop. Fair trade is genuinely concerned about the well-being of the farmer. We hold this (cup) in our hands every day. Either there is justice in the cup, or injustice in the cup." Many members of the Catholic Church agree. Melanie Piendak is the Social Justice Coordinator of the San Francisco Archdiocese Office of Public Policy and Social Concerns, and a Fair Trade advocate. She told Global Exchange that, "the Church is familiar with the dire situation of poverty in Central America and other areas; this is a project very much in line with the church's social teachings on promoting justice by being responsible for the moral implications of our consumer choices." In San Francisco, after one church heard about Fair Trade, they got three other local parishes involved. After educating themselves, they split up the city into quadrants -- and walked door-to-door to each coffee shop in town, asking that they offer Fair Trade coffee. Advocating for Fair Trade coffee has been one of the most important ways to bring home the issues of the global economy to parishioners -- and provide concrete activities that people can engage in on a local level that have a positive affect on the global economy. Global Exchange's motto is "building people-to-people ties." One of the reasons why consumers sometimes don't realize the impact their purchasing choices can have on people around the world is that they have never had the opportunity to meet a farmer or factory worker who toiled to produce the goods they purchase. To increase the direct connection between consumers and farmers, we have organized a series of speaking tours for farmers and Fair Trade activists to visit communities across the country to exchange experiences with consumers in the US. For example, Elvia Alvarado, a coffee farmer and long-time peasant activist from Honduras, spoke in cities across the US about the situation of coffee farmers in the global economy and the implications of the current crisis in coffee producing communities. In 1999 and 2000, Rosario Castellon, the founder of a successful Fair Trade cooperative in Nicaragua and Producer Relations director for Equal Exchange, spoke about the history of coffee in Nicaragua and the impact of Fair Trade on farmers there. We also continue to tour Jorge Cuevas, an eloquent speaker and director of a Fair Trade coffee cooperative from Oaxaca, Mexico. Many environmental organizations that have garnered significant support for shade-grown coffee have begun to join forces to promote Fair Trade, including the Smithsonian Migratory Bird Center and the Songbird Foundation. While some commentators think that consumers might suffer from 'label confusion' -- among Fair Trade, shade, and organic certification, we believe that consumers understand the importance of both labor and environmental concerns in production. Americans seem ready for this new way of doing business. In a recent BusinessWeek/Harris poll, 51 percent of Americans interviewed said they support fair trade rather than protectionism or "free trade". In addition, TransFair USA has been organizing regional campaigns to promote Fair Trade that have increased support in important coffee consumer cities such as Seattle, the Boston area, and now Washington, DC. Recently the US Congress -- and ironically the World Bank - began selling Fair Trade coffee in their cafes. There is even a resolution being put forward to require all coffee purchased by the federal government to be Fair Trade Certified. And in Berkeley, the city that passed the first divestment restriction against companies trading in South Africa during apartheid, a citizen ballot initiative is gaining popularity to restrict all sales of brewed coffee sold within the city to coffee that is Fair Trade, organic, or shade-grown. Even the Specialty Coffee Association of America (SCAA) recently officially endorsed Fair Trade Certification, and has formed a task force to determine ways to promote it. While some businesses initially resisted the idea, and most companies still only sell about 5% of their volume Fair Trade, many coffee business leaders are now actively promoting it. The quality of coffee worldwide is dropping precipitously because of the crisis, and they acknowledge farmers need to be paid fairly if they are going to be able to continue to produce specialty quality coffee. Fair Trade is a way to promote sustainability for quality in the coffee industry as well as for farmers and our shared environment. Businesses, like Thanksgiving Coffee, Dean's Beans, Sustainable Harvests, and the Santa Cruz Coffee Roasting Company, have seen that Fair Trade allows them to maintain their ethics and commitment to treating farmers fairly, and delight in developing personal relationships with the farmer cooperatives. It also helps their business by connecting consumers and farmers, and guaranteeing consumers the 'added value' of fairness to their brew. There is even a new importing cooperative of small Fair Trade roasters, Cooperatives Coffees, that is paving the way for more coffee companies to convert to 100% Fair Trade purchases. The majority of Fair Trade coffee consumer activism has focused on the specialty coffee industry. However, because of the catastrophe of the crisis, it has become necessary to intensify our efforts and focus on the largest purchaser of coffee in the country. Last year Fair Trade cooperatives produced over 165 million pounds of coffee - yet only 30 million were sold at Fair Trade terms. The other 135 million were sold to other exporters, or to importers at below Fair Trade prices. It is clear that the hole in the loop is not on the producer side -- there is plenty of availability of Fair Trade coffee from any country of origin -- but on the consumer side, because the large companies still refuse to buy Fair Trade. Folgers, owned by food and household products conglomerate Procter & Gamble, a public company based in Cincinnati, sells 600 million pounds of coffee annually. A shift of 5% of their total volume would double the amount of Fair Trade coffee sold worldwide. This would provide desperately needed relief for many of our coffee cooperative partners in Latin America. We have begun dialogue with the company, including presenting a petition at their recent shareholder's meeting in Cincinnati last November. However, they have not responded positively to our efforts at engagement. Therefore we are mobilizing consumers to pressure Folgers to proactively respond to the devastating affects of the coffee crisis. On December 12, 2001 we organized a National Day of Action, where consumer activists educated their communities to raise awareness about the coffee crisis and Fair Trade. We continuously encourage consumers -- and shareholders - to contact the company through letters, faxes, postcards, emails, and phone calls, to demand that Folgers pay farmers a fair price. It is because of consumer action like this that Starbucks decided not to become the 'Nike of the coffee industry' and adopt Fair Trade standards. It is now up to Folgers to see if they will respond to consumer demand and do the same. If coffee was the only crop Americans regularly consume that is produced under exploitative conditions, we could stop there. Unfortunately, this is far from true. When most people bite into a candy bar, it is unlikely that they take even a moment to consider where the chocolate they enjoy comes from. If they knew, it probably would not taste as sweet. In 1998, an investigation by the United Nations Children's Fund (UNICEF) uncovered a reemergence of child slavery in the cocoa fields of the Ivory Coast, where 43 percent of the world's cocoa comes from. Two years later, a report by the US State Department concluded that in recent years approximately 15,000 children aged 9 to 12 have been sold into forced labor on cotton, coffee, and cocoa plantations in the north of the country. A June 15, 2001 document released by the Geneva, Switzerland-based International Labor Organization (ILO) reported that trafficking in children is widespread in West Africa. Some of these children wind up as slaves on cocoa farms in the Ivory Coast. At the beginning of the 21st century, the children of West Africa are trapped in conditions that were supposed to have been eliminated in the 19th century. The reemergence of child slavery can be blamed, in part, by a downturn in the price of raw cocoa. Cocoa prices are currently in a slump, the casualty of global overproduction. The price drop has been exacerbated by deregulation of agriculture in West Africa, which abolished commodity boards across the region, leaving small farmers at the mercy of the market. With prices in the basement, cocoa farmers have been forced to cut their labor costs, and tragically that has meant relying on slave labor. The six largest cocoa producing countries are the Ivory Coast, Ghana, Indonesia, Nigeria, Brazil, and Cameroon. In these countries, cocoa has especially significant effects on the economy and the population. For example, in Ghana, cocoa accounts for 40% of total export revenues, and two million farmers are employed in cocoa production. In the Ivory Coast, much of the work of picking the cocoa pods, slicing them open, and then scooping out the cocoa beans is done by slaves. The child slaves come from countries such as Mali and Burkina Faso -- nations that are even more destitute than the impoverished Ivory Coast. Parents in these countries sell their children to traffickers believing that they will find honest work once they arrive in Ivory Coast and then send their earnings home. But as soon as they are separated from their families, the young boys are made to work for nothing. The child slaves work long and hard -- they head into the fields at 6:00 in the morning and often do not finish until 6:30 at night. Beatings by farm owners and managers are common. "The beatings were a part of my life," Aly Diabate, a freed slave, told reporters in 2001. "Anytime they loaded you with bags [of cocoa] and you fell while carrying them, nobody helped you. Instead, they beat you and beat you until you picked it up again." Though he had worked countless days harvesting cocoa pods -- 400 of which are needed to make a pound of chocolate -- Diabate has never tasted the finished product. "I don't know what chocolate is," he told the press. For years, US chocolate manufacturers have said they are not responsible for the conditions on cocoa plantations since they don't own them. But the $13 billion chocolate industry is heavily consolidated, with just two firms -- Hershey's and M&M/Mars -- controlling two-thirds of the US chocolate candy market. This means that if these global corporations really wanted to reform problems in the supply chain, they have the power and the ability to do so. This past year the chocolate industry finally stopped denying responsibility for the problems in West Africa after a string of media exposés and the threat of government action jeopardized their image and business-as-usual. Frightened by the thought of any sort of regulation, the chocolate industry said it would take steps to eliminate child slavery. On November 30, 2001 the US chocolate industry announced, in a Joint Statement with the International Union of Foodworkers, the ILO, Free the Slaves, and the Child Labor Coalition, to establish a joint foundation to oversee and sustain efforts to eliminate the worst forms of child labor (ILO Convention 182) and forced labor (ILO Convention 29) in the growing and processing of cocoa beans and their derivative products. However, the plan does not address the basic issue of prices for small farmers. Fortunately, there is a way to correct the economic imbalances of the cocoa system: Fair Trade. Similar to Fair Trade in the coffee industry, Fair Trade in cocoa is an international system of monitoring and certification to guarantee that poor producers are paid a fair price for their harvests. The Fair Trade system guarantees farmers a fair income to support their families with dignity. In the spring of 2002 Global Exchange launched a campaign targeting the US chocolate industry, focusing on global leader M&M/Mars as the largest US chocolate company in the world. While cocoa workers make approximately $100 per year, if they are paid at all, the three owners of M&M/Mars, the Mars siblings, are worth a combined $27 billion -- three of the richest people in the world. We demand that chocolate companies take immediate steps to end child slavery and poverty wages by committing to purchase at least five percent of their cocoa as Fair Trade Certified. Our campaign against M&M's hijacked their "Global Color Vote" promotion with our own campaign to collect write-in "votes for Fair Trade Certified - the color of dignity and freedom." This campaign was well received by the media and the public, involving grassroots organizers in over 120 cities across the US. Teachers across the country used the color voting kit as a tool for education about child labor in the classrooms. Parents wrote in, shocked and disgusted that their children are encouraged to sell chocolate as a fundraiser for their school -- chocolate that could have been made using child slave labor. Parents want -- and deserve -- to teach their children about fairness in the global economy, and our obligations as consumers to do the right thing. Fortunately, the campaign also provided a way parents and teachers could teach children about not only consumer responsibility but also about citizen action. They were able to demonstrate that we as citizens have the power, and the responsibility, to force companies to adhere to accepted principles of fairness and human rights in their business practices. In addition to this, we circulated a sign-on letter, asking groups to endorse the call for Fair Trade to M&M/Mars. The letter was endorsed by over 200 groups, including Amnesty International, Anti-Slavery International, Oxfam America, the National Family Farm Coalition, the Hotel Employees and Restaurant Employees Union, the International Longshore and Warehouse Union, the General Board of Global Ministries of the United Methodist Church, the Presbyterian Church (USA), the United Church of Christ, and many other organizations. As with Fair Trade coffee, many of these churches are now promoting Fair Trade in their own constituencies, including writing articles in their magazines, featuring Fair Trade at their conferences, and getting more and more churches to sell Fair Trade. Chocolate is often given as a sign of affection. Would your loved ones want a bittersweet flavor of chocolate stained with blood and sweat? Or would they rather savor the sweetness of fairness and dignity with their favorite confection? What Can You Do Fortunately, you can do something to ensure that your purchasing activities are in line with the rest of your ethical decisions as a human being. Thousands of consumers across the country have organized into hundreds of community groups to coordinate support for Fair Trade in their communities. We believe in simple, creative activities people can engage in their local communities to advocate for global economic justice. One of our activist consumers, Karen from a small town in California, told us that, "[I]t was wonderful to see people's faces light up as we explained how Fair Trade [Certification] can help plantation conditions. "Oh!" they would say, a half smile of new understanding on their faces, thrilled that someone had thought of a solution to these impossible faraway problems, a solution that they can contribute to personally! "Many people have been led to believe that the power to change things resides elsewhere, but the power resides in all of us, and in the networks we link with. Interacting with your neighbors is a delight that we don't often experience, and Fair Trade Day was a great way to address a global problem, while educating and becoming more connected with our own community." -You can send a free fax to the CEOs of Procter & Gamble and M&M/Mars from our website, http://www.globalexchange.org. -You can write a letter to the heads of these companies: Paul Michaels, President, M&M/Mars Inc., 6885 Elm St., McLean, VA 22101 and A. G. Lafley, President and CEO, Procter & Gamble, 1 Procter & Gamble Plaza, Cincinnati, Ohio 45201. -You can call M&M/Mars at 1-800-627-7852 and Procter & Gamble at (800) 937-9745 and demand that they offer a Fair Trade alternative. -You can host a Fair Trade speaker, show a Fair Trade video, and educate your community. -You can visit coffee shops and grocery stores in your neighborhood and tell them about the importance of Fair Trade. -You can travel with Global Exchange to witness farmer cooperatives producing coffee and chocolate firsthand on one of our Reality Tours. Last year, Fair Trade coffee sales in the US topped 7 million pounds, up from 4.2 in 2000 and 1.9 the year before. If you figure out the difference that farmers received from the Fair Trade price, as opposed to what they would have received had they sold their coffee in the 'free' market, adjusted to the dramatic changes in the market, Fair Trade efforts have delivered over $10 million in over-market premiums in the last three years -- as a result of consumer responsibility combined with citizen action for corporate accountability. The anti-sweatshop movement has struggled for years to answer to the consumer question, "I'd be happy to stop buying from Nike or GAP, but what should I buy instead?" It is clear from the recent scandals at major corporations like Enron, WorldCom, and Adelphia, that corporations cannot be let alone to act responsibly -- they must be held accountable to citizens and government regulation to ensure that they respect human rights and environmental conservation. As Fair Trade demonstrates, the key to success is to educate consumers that another way to trade exists, and to mobilize citizens to demand it. At least when it comes to our daily brew, an independently monitored alternative finally exists—one that sets a standard for Fair Trade in the global economy. For more information on how to locate stores and cafes that sell Fair Trade Certified coffee and chocolate; how to request that retailers stock Fair Trade; how to start a local Fair Trade campaign; or to learn about Global Exchange's upcoming Fair Trade Reality Tour, contact: Global Exchange 2017 Mission Street, Suite 303, San Francisco, CA 94110 email@example.com TransFairUSA 1611 Telegraph Ave., Oakland, CA 94612 510/663.5260 www.transfairusa.org TransFairUSA is the only certifying agency of Fair Trade Certified coffee in the US. It represents the US in the international Fair Trade Labeling Organizations. Equal Exchange 251 Revere Street, Canton, MA 02021 781/830.0303 www.equalexchange.com Equal Exchange is the oldest and largest fair trade coffee importer and distributor in the US, and has played an active role in the movement for Fair Trade for over 15 years. Fair Trade Federation 1612 K Street, Suite 600, Washington, DC 20006 202/872.5329 www.fairtradefederation.org The FTF is the national trade association of wholesalers and retailers involved in fair trade with artisans and farmers around the world. Fair Trade Resource Network PO Box 33772, Washington, DC 20033 202-302-0976 www.fairtraderesource.org The Fair Trade Resource Network raises consumer awareness about improving people's lives through Fair Trade alternatives. Oxfam America 26 West Street, Boston, MA 02111 617/482.1211 www.oxfamamerica.org Oxfam America supports a grassroots network of students promoting Fair Trade coffee, as well as maintains partnerships with several coffee producer cooperatives. Organic Consumers Association 6114 Hwy 61, Little Marais, MN 55614 218/226.4164 www.purefood.org The OCA is currently coordinating a campaign to pressure Starbucks to commit to not selling GMO coffee, to not using rBGH milk, and to seriously promoting and brewing Fair Trade coffee. US/Labor Education in the Americas Project PO Box 268-290, Chicago, IL 60626 773/262.6502 www.usleap.org/ US/LEAP is a labor advocacy organization that led a successful campaign to get Starbucks to adopt a Framework for Action or Improving the Lives of the People Who Grow, Harvest and Process Coffee. Smithsonian Migratory Bird Center 3000 Connecticut Ave. NW, Washington DC 20008 202/673.4908 www.si.edu/smbc Researches shade coffee as bird habitat and supports "bird friendly" certification. Convened first Sustainable Coffee Congress in 1996. Songbird Foundation 2367 Eastlake Avenue East, Seattle, WA 98102 206/374.3674 www.songbird.org The Songbird Foundation educates and motivates people to make sustainable choices to preserve migratory songbirds, focusing on promoting shade grown coffee.
Ocean acidification is a growing concern in the context of climate change, as it poses significant threats to marine ecosystems and biodiversity. The increasing concentration of carbon dioxide (CO2) emissions in the atmosphere has led to its absorption by the oceans, resulting in chemical changes that lower ocean pH levels. This phenomenon can have profound consequences for various marine organisms, including coral reefs, shellfish, and phytoplankton. For instance, consider the case study of coral reefs, which are highly vulnerable to ocean acidification. As carbon dioxide dissolves into seawater, it forms carbonic acid, reducing the availability of carbonate ions necessary for corals to build their calcium carbonate skeletons. Without these essential building blocks, coral growth and reef formation become severely compromised. Additionally, increased acidity can weaken existing coral structures, making them more susceptible to damage from storms and other stressors. Consequently, this jeopardizes not only the survival of corals but also the diverse array of species relying on these vital habitats for food and shelter. The impacts of ocean acidification extend beyond individual species’ survival; they have far-reaching implications for entire ecosystems and human societies dependent on them. Understanding these effects and finding effective mitigation strategies are crucial steps toward safeguarding our oceans’ health and preserving their preserving their invaluable ecological services, such as seafood production, carbon sequestration, and shoreline protection. Negative effects on marine life Ocean acidification is a growing concern in the context of climate change, with significant negative effects on marine life. One example illustrating these impacts is the case of coral reefs. As carbon dioxide levels increase in the atmosphere and subsequently dissolve into seawater, the pH level of ocean water decreases, making it more acidic. This increased acidity poses a threat to coral reef ecosystems worldwide. The detrimental effects of ocean acidification on marine life are vast and diverse. Firstly, many species of shell-building organisms such as corals, oysters, and mussels struggle to create or maintain their protective shells or exoskeletons under increasingly acidic conditions. The reduced availability of carbonate ions necessary for calcification hinders their ability to grow and develop properly. Consequently, weakened shells make these organisms more vulnerable to predation and environmental stressors. Furthermore, ocean acidification disrupts the delicate balance within marine food webs. A rise in acidity can interfere with the reproduction and survival rates of various species at different trophic levels. For instance, studies have shown that certain fish larvae experience impaired growth and sensory abilities when exposed to elevated CO2 levels found in acidified waters. Such disruptions not only affect individual species but also ripple throughout entire ecosystems by altering predator-prey dynamics and reducing overall biodiversity. - Loss of vibrant coral reefs due to bleaching events caused by stressed corals. - Declining populations of commercially important shellfish leading to economic losses for coastal communities. - Reduced availability of seafood resources impacting global food security. - Disruption of natural habitats affecting numerous other marine organisms dependent on healthy ecosystems. In addition to this emotive approach, a table can be utilized effectively: \|Effects of Ocean Acidification\|\|Examples\| \|Impaired growth\|\|Fish larvae\| \|Altered predator-prey dynamics\|\|Marine food webs\| The negative consequences of ocean acidification on marine life are alarming. As the subsequent section will discuss, one specific impact worth highlighting is the decline in shellfish populations. This decline not only affects individual species but also has broader implications for coastal communities and global ecosystems alike. Decline in shellfish populations Negative effects on marine life have been well-documented in relation to ocean acidification. However, the decline in shellfish populations further highlights the detrimental consequences of this phenomenon on marine ecosystems. One example that illustrates the impact of ocean acidification on shellfish is the case study conducted in a coastal region heavily reliant on oyster farming. In this hypothetical scenario, imagine an area known for its thriving oyster industry suddenly experiencing a significant decline in production. Oysters are highly susceptible to changes in water chemistry, particularly when it comes to pH levels. As ocean acidity increases due to absorption of carbon dioxide from the atmosphere, oyster larvae struggle to develop their protective shells. Consequently, there is a reduction in survival rates and overall reproductive success. The decline in shellfish populations due to ocean acidification can be attributed to several key factors: Impaired shell formation: Higher acidity inhibits calcification processes necessary for building and maintaining strong shells. This renders shellfish vulnerable to predation and limits their ability to withstand environmental stressors. Altered food availability: Ocean acidification disrupts the delicate balance of marine ecosystems, leading to shifts in primary productivity and changes in food availability for shellfish species. These alterations can negatively impact growth rates and overall health. Disrupted ecological interactions: Shellfish play crucial roles within their respective habitats by filtering water and providing substrate for other organisms. Their decline can disrupt intricate ecological relationships within these environments, potentially triggering cascading effects throughout entire ecosystems. Economic implications: The loss or decline of shellfish populations has far-reaching economic consequences for communities dependent on commercial fishing or aquaculture. Job losses, reduced income, and decreased seafood supply pose challenges not only for local economies but also global markets. It is evident that addressing the issue of declining shellfish populations requires urgent attention and concerted efforts at various levels—local, national, and international—to mitigate ocean acidification’s adverse impacts. This necessitates implementing measures to reduce carbon dioxide emissions, enhancing monitoring and research programs, and developing strategies to support the resilience of shellfish populations. Transitioning into the subsequent section on “Damage to coral reefs,” it becomes clear that ocean acidification poses a multi-faceted threat to marine ecosystems beyond just shellfish populations. Damage to coral reefs ocean acidification: Its Impact in the Context of Climate Change Decline in Shellfish Populations As highlighted in the previous section, ocean acidification poses a significant threat to marine ecosystems. However, it is not just shellfish populations that are experiencing adverse effects. Damage to coral reefs, another critical component of our oceans, has also been observed due to increased acidity levels. Coral reefs serve as vital habitats for numerous species and play a crucial role in providing food and livelihoods for coastal communities worldwide. To illustrate the impact of ocean acidification on coral reefs, let us consider a hypothetical scenario involving a reef located off the coast of Australia’s Great Barrier Reef – one of the most diverse and iconic reef systems globally. In this hypothetical case study: - The water surrounding the reef has become increasingly acidic over time. - The corals struggle to maintain their calcium carbonate structures due to reduced pH levels. - As a result, they experience difficulties in calcifying, leading to weakened skeletal growth. - This vulnerability makes them more susceptible to other stressors such as rising sea temperatures and pollution. This example highlights how ocean acidification can exacerbate existing threats faced by coral reefs, compounding their decline and endangering countless marine species dependent on these fragile ecosystems. - Loss of biodiversity: Ocean acidification disrupts the delicate balance within marine ecosystems, jeopardizing various species’ survival. - Economic consequences: Impacts on fisheries can have devastating economic implications for coastal communities reliant on seafood resources. - Food security at risk: Declines in fish populations could lead to challenges in meeting global demand for protein-rich food sources. - Ecological disruption: Changes within marine environments may trigger cascading effects throughout entire food webs, affecting multiple trophic levels simultaneously. Additionally, let us visualize the emotional impact through a three-column, four-row table: \|Declining fish stocks\|\|Loss of income for fishermen and reduced availability of seafood\| \|Diminished coastal beauty\|\|Negative impacts on tourism industry and local economies\| \|Threat to cultural heritage\|\|Disruption of traditional practices and loss of indigenous knowledge\| \|Increased vulnerability\|\|Weakening resilience against future environmental challenges\| In conclusion, ocean acidification poses not only a threat to shellfish populations but also has severe implications for coral reefs. The hypothetical case study presented here underscores the vulnerabilities these ecosystems face due to increased acidity levels. Additionally, our bullet point list highlights the wide-ranging consequences that extend beyond marine life alone. As we delve further into this discussion, it is crucial to explore another significant aspect affected by ocean acidification – reduction in oxygen levels. (Note: This paragraph serves as a transition into the subsequent section without explicitly stating “step”.) Reduction in oxygen levels Ocean Acidification: Its Impact in the Context of Climate Change Damage to Coral Reefs Coral reefs are invaluable ecosystems that support a diverse array of marine life. However, ocean acidification poses a significant threat to their survival. The increase in carbon dioxide (CO2) emissions from human activities has led to elevated levels of CO2 being absorbed by seawater, resulting in its increased acidity. This heightened acidity negatively impacts coral reef systems in several ways. One example illustrating the damaging effects of ocean acidification on coral reefs is the case study conducted in the Great Barrier Reef off the coast of Australia. Researchers found that an increase in ocean acidity due to rising CO2 levels significantly impairs the ability of corals to build their calcium carbonate skeletons, which serve as critical habitats for numerous species. As a result, coral growth rates decrease and can even be reversed, compromising the structural integrity and resilience of these vibrant underwater communities. The impact of ocean acidification on coral reefs can be further understood through considering specific consequences: - Reduced calcification: Elevated acidity inhibits the process of calcification, making it difficult for corals and other shell-forming organisms to extract or produce sufficient amounts of calcium carbonate needed for skeletal growth. - Increased vulnerability: Weakened coral structures become more susceptible to physical damage caused by storms, wave action, and predation. - Bleaching events: Ocean acidification exacerbates existing stressors on coral reefs such as rising sea temperatures, leading to more frequent and severe bleaching events where corals expel symbiotic algae living within them. - Loss of biodiversity: As coral reefs decline due to acidification-induced damage, entire ecosystems face disruption, leading to loss of habitat for countless marine species. To grasp the magnitude of this issue visually, consider Table 1 below highlighting some key impacts of ocean acidification on coral reefs: \|Reduced coral growth\|\|Weakened reef structures and limited habitat\| \|Increased bleaching\|\|Loss of symbiotic algae, leading to coral death\| \|Vulnerability to damage\|\|Heightened physical vulnerability to external forces\| \|Biodiversity loss\|\|Disruption of intricate food webs and marine ecosystems\| In light of the damaging consequences outlined above, immediate action is necessary to mitigate the effects of ocean acidification on coral reefs. Addressing climate change by reducing CO2 emissions is paramount in preserving these fragile ecosystems. Furthermore, targeted conservation efforts aimed at restoring damaged corals and enhancing their resilience are essential for safeguarding the biodiversity and ecological function provided by healthy coral reefs. The next section will delve into another critical aspect affected by ocean acidification: the disruption of the marine food chain. It highlights how changes in acidity levels impact various trophic levels within aquatic systems, ultimately affecting entire marine communities. Disruption of the marine food chain Reduction in oxygen levels is just one of the many consequences of ocean acidification. Another significant impact is the disruption it causes in the marine food chain, which can have far-reaching ecological and economic implications. The decline in pH levels due to increased carbon dioxide absorption by seawater directly affects various organisms lower down the food chain. For instance, shell-forming species such as planktonic calcifiers rely on dissolved carbonate ions to build their protective shells or skeletons. As acidity increases, these ions become scarcer, making it increasingly difficult for these organisms to form and maintain their structures. This has a cascading effect on other marine life that depend on them for sustenance. One hypothetical example illustrating this disruption involves an ecosystem centered around coral reefs. Coral polyps provide habitat and food sources for countless species, creating a vibrant ecosystem teeming with biodiversity. However, when exposed to acidic conditions, corals experience reduced growth rates and weakened skeletal structures. Consequently, the intricate web of interactions within the reef community becomes compromised, leading to declines in fish populations and ultimately affecting commercial fisheries dependent on these resources. - Devastation of coral reefs worldwide - Decline in commercially valuable fish stocks - Loss of livelihoods for coastal communities reliant on fishing industries - Disruption of delicate ecosystems supporting diverse marine life Additionally, let us present a table highlighting some vulnerable marine organisms and their potential impacts due to ocean acidification: \|Planktonic Calcifiers\|\|Reduced shell formation\| \|Corals\|\|Bleaching events; decreased structural integrity\| \|Mollusks\|\|Weakened shells; hindered survival\| \|Crustaceans\|\|Impaired exoskeleton development\| This table serves as a visual representation of the vulnerability and potential consequences faced by various marine organisms in an increasingly acidic environment. In light of these findings, it is evident that ocean acidification poses significant threats to marine ecosystems, with implications for both environmental conservation and human well-being. The subsequent section will explore another crucial aspect affected by this phenomenon: the loss of biodiversity within our oceans. Such an exploration provides valuable insight into the multifaceted challenges posed by climate change on Earth’s delicate balance of life. Loss of biodiversity Disruption of the marine food chain has significant consequences for the overall health and functioning of ocean ecosystems. However, it is not just the disruption to this delicate balance that poses a threat; the loss of biodiversity further compounds the effects of ocean acidification in the context of climate change. To illustrate this point, let’s consider a hypothetical case study involving coral reefs. Coral reefs are known as one of the most diverse ecosystems on Earth, providing habitat for countless species. As ocean acidification intensifies due to increased carbon dioxide absorption, corals struggle to build their calcium carbonate structures essential for their survival. This leads to coral bleaching and eventual death, resulting in a cascade effect throughout the entire ecosystem. The loss of biodiversity caused by ocean acidification has far-reaching implications. To fully grasp its impact, we can examine four key aspects: - Ecosystem stability: Biodiversity ensures ecosystem resilience by increasing its ability to withstand disturbances such as disease outbreaks or extreme weather events. - Functional diversity: Different species play distinct roles within an ecosystem, contributing to important functions like nutrient cycling and predator-prey interactions. - Genetic diversity: A wider range of genetic variation allows populations to adapt more effectively to changing environmental conditions. - Intrinsic value: Biodiversity holds intrinsic worth beyond human benefits and contributes to our cultural heritage and sense of awe towards nature. A table summarizing these points could be presented as follows: \|Ecosystem Stability\|\|Increased vulnerability\| \|Functional Diversity\|\|Impaired ecological processes\| \|Genetic Diversity\|\|Reduced adaptive capacity\| \|Intrinsic Value\|\|Loss of natural wonder and inspiration\| This loss of biodiversity not only undermines the integrity and complexity of marine ecosystems but also threatens various services they provide us with – from fisheries resources to coastal protection against storms. As we delve into exploring further impacts of ocean acidification, it becomes evident that harm to marine plants and animals is another pressing concern. By examining the effects on these vital organisms, we can better understand the scope of damage caused by this environmental challenge. Harm to marine plants and animals Loss of Biodiversity The loss of biodiversity is just one of the many consequences brought about by ocean acidification. As we delve deeper into understanding the impacts of this phenomenon, it becomes evident that marine plants and animals are also greatly affected. To comprehend the gravity of harm caused to these vital components of our oceans, let us consider a hypothetical case study. Imagine a vibrant coral reef teeming with life; an intricate ecosystem where various species coexist in perfect harmony. However, due to rising levels of carbon dioxide emissions, the surrounding waters become increasingly acidic. This abrupt change disrupts the delicate balance within the reef, leading to significant implications for its inhabitants. Firstly, as acidity levels rise, certain marine organisms struggle to build and maintain their protective structures such as shells or skeletons made from calcium carbonate. For instance, oysters find it arduous to form strong enough shells under more acidic conditions. Consequently, they become vulnerable to predation and other environmental stressors which ultimately affects their population size and overall diversity within the ecosystem. Secondly, ocean acidification has been observed to alter reproductive processes in several marine species. In some cases, increased acidity interferes with fertilization rates or impairs larval development and survival. This disruption can have cascading effects on entire food webs since these early stages play a crucial role in replenishing populations and maintaining healthy ecosystems. Lastly, changes in pH levels impact the behavior and physiology of many marine organisms. Acidic waters can induce stress responses, impair sensory abilities essential for finding food or avoiding predators, and even affect growth rates in certain species. These physiological alterations further exacerbate the vulnerabilities already faced by marine plants and animals due to climate change-related stressors. - Reduced shell strength in mollusks - Impaired reproductive success in corals - Increased vulnerability to disease outbreaks - Altered behavior and growth patterns in fish Additionally, let us examine a table that highlights some of the observed impacts on marine plants and animals: \|Reduced calcification\|\|Weakened coral skeletons\| \|Decreased reproductive success\|\|Lower fertilization rates in oysters\| \|Disrupted behavior\|\|Loss of schooling behavior in certain fish\| In conclusion, ocean acidification poses significant harm to marine plants and animals. The loss of biodiversity within these ecosystems is not only detrimental for individual species but also has far-reaching implications for the overall health and functioning of our oceans. With this understanding, we can now explore how altered ecosystems are yet another consequence of this pressing issue. Harm to marine plants and animals due to ocean acidification is just one aspect of the broader impact this phenomenon has on our oceans. As we delve further into the consequences, it becomes evident that altered ecosystems are another grave concern. Imagine a coral reef teeming with vibrant colors and diverse species. Now envision the same ecosystem stripped of its vitality as ocean acidification takes hold. The increased acidity inhibits the ability of corals to build their calcium carbonate skeletons, leaving them vulnerable to erosion. This leads to bleaching events and ultimately results in the loss of entire reefs worldwide. For instance, in a study conducted in Australia’s Great Barrier Reef, researchers observed a significant decline in coral cover over a span of 27 years due to rising levels of carbon dioxide absorption by seawater. The repercussions extend far beyond coral reefs alone. Altered ecosystems emerge as various interconnected organisms struggle to adapt or survive amidst changing conditions caused by ocean acidification. Here are some notable effects: - Reduced biodiversity: As certain species prove more resilient than others, shifts occur within communities, leading to an imbalance in populations. - Disrupted food webs: Changes in key species’ abundance can disrupt the delicate balance within food chains, affecting predator-prey relationships and cascading effects throughout the ecosystem. - Decline in shell formation: Organisms such as mollusks and crustaceans face challenges when constructing shells or exoskeletons due to impaired calcification processes caused by ocean acidification. - Impaired reproductive success: Many marine organisms rely on specific environmental cues for successful reproduction. Alterations caused by ocean acidification can disturb these cues, resulting in reduced reproductive output. To highlight the gravity of these consequences visually: \|Reduced biodiversity\|\|Loss of critical habitats\|\|Extinction risk for specialized species\| \|Disrupted food webs\|\|Overpopulation of certain species\|\|Decline in prey availability for predators\| \|Decline in shell formation\|\|Vulnerability to predation\|\|Reduced survival rates for shelled organisms\| \|Impaired reproductive success\|\|Lower population growth\|\|Decreased recruitment rates and genetic diversity\| These impacts are not isolated incidents but rather a looming reality that our oceans face. As we grapple with addressing the issue of ocean acidification, it becomes increasingly crucial to acknowledge its role in altering ecosystems. The subsequent section will explore yet another alarming consequence: decreased fish populations. As we transition into discussing “Decreased fish populations,” let us recognize the intricate interconnectedness between various marine organisms and how their decline can significantly impact entire ecosystems. Decreased fish populations As we delve deeper into the impact of ocean acidification, it becomes evident that this phenomenon is not limited to altering marine chemistry but also has profound effects on entire ecosystems. One case study highlighting these consequences involves the Great Barrier Reef, a world-renowned coral reef system located off the coast of Australia. Researchers have observed a decline in coral cover and diversity due to increased acidity levels. As corals struggle to build their calcium carbonate structures, they become more vulnerable to predation and disease, leading to significant changes in the overall structure and function of the reef ecosystem. - Reduced calcification rates: Organisms such as corals, mollusks, and some phytoplankton species are unable to form their protective shells or skeletons effectively. - Changes in species distribution: Certain organisms may thrive under acidic conditions while others struggle to adapt, leading to shifts in community composition. - Disrupted nutrient cycling: Acidified waters can impair microbial processes responsible for recycling essential nutrients, influencing productivity at all trophic levels. - Loss of habitat complexity: The structural integrity of habitats like coral reefs diminishes as key framework-building organisms face challenges in maintaining their skeletal structures. To further comprehend the cascading impacts of altered ecosystems due to ocean acidification, let us examine a table showcasing some notable examples: \|Coral Reefs\|\|Bleaching events increase; reduced biodiversity\| \|Shellfish Industries\|\|Decreased shell growth; economic losses\| \|Planktonic Communities\|\|Altered composition; disrupted food webs\| \|Fish Populations\|\|Declining populations; reduced reproductive success\| These examples serve as a reminder of the profound ecological changes that can occur when ocean acidification disrupts the delicate balance within marine ecosystems. As we explore further, it becomes apparent that these alterations not only affect individual species but also have wider implications for their interactions and overall ecosystem functioning. Transitioning into the subsequent section on “Imbalance in Marine Ecosystems,” we continue to unravel how these disruptions extend beyond altered ecosystems, leading to broader consequences throughout our oceans. Imbalance in marine ecosystems Ocean Acidification: Imbalance in Marine Ecosystems The consequences of ocean acidification extend beyond the decline in fish populations. This phenomenon also has a profound impact on marine ecosystems, creating an imbalance that disrupts the delicate interplay among species and threatens the overall health of our oceans. Consider, for example, a hypothetical scenario where increased acidity leads to a reduction in coral reef growth. Coral reefs are not only breathtakingly beautiful but also serve as vital habitats for countless marine organisms. These vibrant underwater cities provide shelter, food, and breeding grounds for a myriad of species such as fish, crustaceans, and mollusks. In this case study, imagine how decreasing coral reef growth would have far-reaching effects throughout the entire ecosystem. To fully grasp the implications of ocean acidification on marine ecosystems, it is important to understand its mechanisms and impacts: - Altered Physiology: Many calcifying organisms like shellfish and corals struggle to build their protective shells or skeletons due to decreased availability of carbonate ions resulting from more acidic seawater. - Disrupted Food Chains: Changes in the abundance and distribution of certain species can lead to imbalances within food webs. As some primary producers like phytoplankton may be negatively affected by acidification, this could subsequently impact higher trophic levels. - Decline in Biodiversity: The loss of specific species due to changing conditions may result in reduced biodiversity within marine ecosystems. - Ecosystem Resilience: Ocean acidification affects not only individual species but also their ability to withstand other stressors such as pollution or rising sea temperatures. This table provides a snapshot of some key examples illustrating the potential repercussions of ocean acidification on different components of marine ecosystems: \|Coral Reefs\|\|Decreased growth; bleaching events\| \|Shellfish\|\|Weaker shells; declining populations\| \|Phytoplankton\|\|Reduced productivity; altered dynamics\| \|Fish\|\|Disrupted reproductive patterns\| The imbalance caused by ocean acidification poses a significant threat to marine species and ecosystems. As the delicate web of interactions is disrupted, the consequences ripple throughout the entire ecosystem, compromising its stability and resilience. Transitioning into the subsequent section on “Threat to Marine Species,” it becomes evident that addressing this issue requires urgent action to prevent further damage and preserve our oceans for generations to come. Threat to marine species Imbalance in marine ecosystems can have far-reaching consequences for the delicate web of life that exists beneath the ocean’s surface. As we delve deeper into the impact of ocean acidification, it becomes evident that this phenomenon is not only an isolated problem but also a significant threat to marine species and their habitats. To illustrate the gravity of this issue, let us consider a hypothetical case study involving coral reefs. Coral reefs are known as the rainforests of the sea due to their rich biodiversity and importance in providing habitat for numerous marine organisms. However, with increasing levels of carbon dioxide being absorbed by oceans, resulting in higher acidity levels, these vibrant ecosystems face imminent danger. The effects of ocean acidification on coral reefs are multifaceted and alarming. Here are some key points to highlight the threats faced by marine species: - Increased CO2 absorption leads to decreased pH levels in seawater, making it more difficult for corals to build their calcium carbonate structures. - Acidic conditions hinder the growth and development of juvenile corals, limiting their ability to form new colonies. - Weakened coral skeletons make them more vulnerable to physical damage from storms or wave action. - Reduced calcification rates affect various other organisms relying on reef structures for shelter or food sources. To further emphasize these concerns, let us examine a table showcasing different examples of marine species impacted by ocean acidification: \|Corals\|\|Impaired skeletal growth and increased vulnerability\| \|Shellfish\|\|Decreased shell formation and weakened immune systems\| \|Phytoplankton\|\|Disrupted reproductive cycles and reduced population sizes\| \|Fish\|\|Altered behavior patterns affecting feeding and reproduction\| These examples serve as evidence that ocean acidification poses a serious threat not just to individual species but also entire ecosystems within our oceans. The repercussions extend beyond immediate loss; they create ripple effects that can disrupt the delicate balance of marine life as a whole. Looking ahead, it is crucial to recognize the long-term consequences for the ocean. Understanding the gravity of this issue allows us to take proactive measures in mitigating further damage and promoting sustainable practices. In our subsequent section, we will explore these long-term consequences and potential strategies to address them effectively. Long-term consequences for the ocean Ocean Acidification: Its Impact in the Context of Climate Change Threat to Marine Species and Ecosystems The threat posed by Ocean acidification to marine species is a pressing concern within the context of climate change. This phenomenon, driven primarily by increased carbon dioxide (CO2) emissions into the atmosphere, has far-reaching consequences for various organisms that inhabit our oceans. For instance, coral reefs, often referred to as “the rainforests of the sea,” are particularly vulnerable to changes in ocean pH levels. A hypothetical scenario can help illustrate this point: imagine a coral reef ecosystem off the coast of Australia gradually succumbing to rising acidity levels due to excessive CO2 absorption. Amidst such scenarios, it becomes crucial to understand how different marine species respond to these changing conditions. Research suggests that some calcifying organisms like oysters and mussels may find it increasingly difficult to build their protective shells or exoskeletons under more acidic waters. As a result, these species become susceptible not only to direct mortality but also indirectly through disruptions in food chains and ecological interactions. The impacts extend beyond individual species; entire ecosystems reliant on healthy populations of shell-building organisms experience ripple effects throughout trophic levels. To grasp the magnitude of these threats and evoke an emotional response from audiences, consider the following bullet points: - Decreased biodiversity and potential extinction risks for numerous marine species. - Loss of critical habitats such as coral reefs and seagrass beds. - Reduced availability of seafood resources affecting both subsistence fishermen and commercial industries. - Disruptions in ecosystem services provided by healthy oceans, including carbon storage capacity and coastal protection against storms. Additionally, let us examine a table showcasing three key aspects affected by ocean acidification: \|Biodiversity\|\|Coral reefs, kelp forests\|\|Loss of habitat, decreased species richness\| \|Fisheries\|\|Commercially targeted fish stocks\|\|Reduced catches and economic losses\| \|Carbon sequestration\|\|Coastal vegetation (e.g., mangroves), phytoplankton blooms\|\|Impaired carbon storage capacity, exacerbating climate change effects\| These examples and the table shed light on the potential ecological and socioeconomic consequences of ocean acidification. They demonstrate that addressing this issue is not only essential for preserving marine biodiversity but also crucial for ensuring sustainable fisheries and mitigating climate change impacts. In summary, as we delve deeper into understanding ocean acidification’s impact in the context of climate change, it becomes evident that its threats extend beyond individual marine species. The loss of critical habitats, diminished biodiversity, reduced seafood resources, and impaired ecosystem services emphasize the urgent need to tackle this issue collaboratively. By doing so, we can work towards safeguarding our oceans’ health while striving for a more sustainable future.
Physics 121 • Topics: • Course announcements • Friction: • Drag forces • Gravitation: • The force of gravity • Motion of satellites • Kepler’s Laws Physics 121Course Announcements • Midterm 1 Feb 17 • Cheat Sheet (1 page) – no cheating (automatic zero for exam) • Calculator, but no laptops • Material from chapters 2 through 6 • Change date of third midterm? (to April 14, 19 or 21) Physics 121Course Announcements • Any complaints about the course? FrictionSlowing us down! Key problem: evaluating the normal force. Air “Friction” or Drag • Objects that move through the air also experience a “friction” type force. • The drag force has the following properties: • It is proportional to the cross sectional area of the object. • It is proportional to the velocity of the object. • It is directed in a direction opposite to the direction of motion. • The drag force is responsible for the object reaching a terminal velocity (when the drag force balances the gravitational force). Friction: Block on Slope Normal force Force of Friction Y-axis q mg y X-axis x Friction • Let’s test our understanding of the friction force by looking at the following concept questions: • Forces 6, 8, 9, 11,12 The Gravitational ForceIt keeps us together • The motion of the planets of our solar system is completely governed by the gravitational force between the components of the solar system. • The Law of Universal Gravitation was developed by Newton based on simple observations of the motion of the moon around the earth. The Gravitational Force • The force of gravity is the weakest force we know …… but it is the main force responsible for the motion of the components of our solar system and beyond. • This is a consequence of the fact that the gravitational force is always attractive. The other forces can be attractive, repulsive, or zero. The Gravitational Force • The gravitational force has the following properties: • It is always attractive. • It is proportional to the product of the masses between which it acts (proportional to m1m2). • It is inversely proportional to the square of the distance between the masses (proportional to 1/r122). • It is directed along the line connecting the two masses. The Gravitational Force • The magnitude of the gravitational force is given by the following relation: • The constant G is the gravitational constant which is equal to 6.67 x 10-11 N m2/kg2. The Gravitational ForceThe Shell Theorem (Appendix C) • The gravitational force law is only valid if the masses involved are point masses (mass located at a single point). • In reality we always are dealing with objects that are not point-like object, but have their mass distributed over a non-zero volume. • Using the principle of superposition you can show that the gravitational force exerted by or on a uniform sphere acts as if all the mass of the sphere is concentrated at its center. The Gravitational ForceMeasuring G • The gravitational constant G can be measured using the Cavendish apparatus. • The Cavendish apparatus relies on the attraction between small mass mounted on a rod and larger masses located nearby. • Let’s have a look at this experiment …….. The Gravitational ForceThe Mass of the Earth • Using Newton’s gravitational law and the measured gravitational acceleration on the surface of the earth, we can determine the mass of the earth: • Fgrav = GmMearth/Rearth2 • Fgrav = mg • By combining these two expressions for the gravitational force we find that Mearth = gRearth2/G or Mearth = 5.98 x 1024 kg The Gravitational ForceVariations in the gravitational force • The gravitational force on the surface of the earth is not uniform for a number of different reasons: • The effect of the rotation of the earth. • The earth is not a perfect sphere. • The mass is not distributed uniformly, and significant variations in density can be found (in fact using variations in the gravitational force is one way to discover oil fields). Orbital Motion • Consider an object of mass m moving in a circular orbit of radius r around the earth. • In order for this motion to be possible, a net force must be acting on this object with a magnitude of mv2/r, directed towards the center of the earth. • The only force that acts in this direction is the gravitational force and we must thus require that GmMearth/r2 = mv2/r or v2 = GMearth/r Orbital Motion • The orbital velocity is related to the period of motion: v = 2πr/T and the relation between v and r can be rewritten as a relation between T and r: r3 = GMearthT2/4π2 • This relation shows that based on the orbital properties of the moon we can determine the mass of the earth. Orbital Motion • The relation between orbit size and period can also be applied to our solar system and be used to determine the mass of the sun: r3 = GMsunT2/4π2 • Using the orbital information of the planets in our solar system we find that GMsun/4π2 = (3.360±0.005)x1018m3/s2 or Msun = (1.989±0.003)x1030 kg Orbital Motion • Let’s test our understanding of orbital motion by looking at the following concept questions: • Gravitation 2, 3, and 4 Orbital Motion and Weightlessness • One of the most confusing aspects of orbital motion is the concept of weightlessness. • Frequently people interpret this as implying the absence of the gravitational force. • Certainly this can not be the case since the gravitational force scales as 1/r2 and is thus not that different from the force we feel on the surface on the earth. Orbital Motion and Weightlessness • We experience apparent weightlessness anytime we fall with the same acceleration as our surroundings. • Consider a falling elevator. Every object in the elevator will fall with the same acceleration, and the elevator will not need to exert any additional forces, such as the normal force, on those inside it. • It appears as if the objects in the elevator are weightless (in reality they of course are not). Orbital Motion and Weightlessness • Weightlessness in space is based on the same principle: • Both astronaut and spaceship “fall” with the same acceleration towards the earth. • Since both of them fall in the same way (gravitational acceleration only depends on the mass of the earth, not on the mass of the spaceship or the astronaut) the astronaut appears to be weightless. That’s all! Next week:Work, Energy, and Conservation Laws:Chapter 7 Opportunity's Horizon Credit: Mars Exploration Rover Mission, JPL, NASA
A curve is a specific form of the is function which is used to describe the relationship between two or more variables. If one variable is increased by one unit, then the curve is increased by one unit. The curve is a particularly handy tool for describing the relationship between two variables. However, this tool is also kind of stupid in that it takes a rather non-linear approach. For instance, say we have the variable “snow depth” and the variable “temperature. A cold, wet cold, and cold, wet, wet winter has two important effects on the function we’re looking for in this function. First, the cold affects the function by increasing snow depth. Secondly, the warm, wet, cold, and cold, wet winter affects the function by increasing temperature. Thus, the warmer, wet winter increases the temperature by increasing snow depth. The curve is a kind of “slope” that you can plot on a graph. It represents the amount of slope that is being affected by a given variable by varying the other variable. This is a very useful tool for analyzing functions and looking for patterns. This is a little bit of a trick I picked up from the game. The is curve is really quite useful because it allows you to see how the slope of a function changes as the two variables change in value. When I first learned about the is curve, I thought that it was just a fancy way of plotting the slope of a function. In practice though, it has a lot to do with the way functions are plotted on a graph. The graph at the bottom of this post is a bit of a shame. I’ve always been intrigued by what is a curve, but as a writer I knew that there are two ways to think of it. On the one hand, it is very appealing to be able to look at a function’s data and then, if you really do have good data, you can start to see how it behaves when you start with a function. In many cases, the formula is not even a function, but it is a function that you can plot. When you use a function, it tells you exactly what the functions are doing, so you can see it behaves in a way you don’t expect it to behave. I often see very similar results when I try to visualize the graphs. For example, the graph at the bottom of this post is a little more interesting than the graph at the bottom of this post itself. The plot is a bit more abstract, but the two main axes are plotted separately. The first is the most interesting, the second is the least. The is curve is a plot of the function at a particular value. For example, the graph at the top of this post is a very intuitive plot, because it shows how the product of the height and width of a box should be on the hypotenuse of a triangle.
In this lesson students will investigate how to solve 2 digit and 3 digit (even 4 digit) multiplication using a ‘lattice diagram.’ Performing lattice multiplications in this manner offers students another way of solving these problems without the confusion of carrying as with the traditional method. There is also a handy poster found in the resources which can be printed off and hung about in the classroom to remind students of this process. Australian Curriculum Links: Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123) Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100) Lesson Plan Sequence: - Show student the traditional method of solving 2 digit multiplication. Ask two students for any 2 digit numbers. In this example we’ll use 38 and 25. - Draw up 38 x 25 the traditional way (as below) and talk about the process behind it. - Next ask students if there is any other way of completing such multiplication. Answer: Using a lattice! - Start off by getting students to draw this diagram in their books. 3. Ask students where they think 38 and 25 should be placed. Then show as follows. 4. Tell students to focus on the individual box, “in the top right hand box, we can see that 8 multiplied by 2 equals 16” So we place 16 in the box like so. NB* It is IMPORTANT to tell students that the tens column is the top triangle and the ones is the bottom triangle. 5. Fill out the rest of the grid. Use a zero in the tens column if the number is less than 10, for example 3 x 2. 6. Now think diagonally by adding the rows for example 5 + 4 + 6= 15. NB If the number is greater than 9, you will need to “carry” the tens to the next column like so. 7. Putting all the numbers together the students will see that you still arrive at the same number as per the traditional way. 8. Using either the template sheet provided and a deck of cards, (Remove the 10, J, Q, K) students can come up with their own sums and practice wither on the sheet or in their books. Ask students to nominate their preferred way of solving the problems as some students will prefer the alternative method of solving the 2 digit multiplications! Extension: Show your high flyers how to do 2,3,4 even 5 digit multiplication using the lattice! - Work Samples - Common Assessment Task- A little test at the end. If you like this lesson plan, or have an idea to improve it, please consider sharing it on Twitter, Pinterest and Facebook or leave a comment below.
All High School Math Resources Example Question #1 : Finding Sides There is not enough information The side-angle-side (SAS) postulate can be used to determine that the triangles are similar. Both triangles share the angle farthest to the right. In the smaller triangle, the upper edge has a length of , and in the larger triangle is has a length of . In the smaller triangle, the bottom edge has a length of , and in the larger triangle is has a length of . We can test for comparison. The statement is true, so the triangles must be similar. We can use this ratio to solve for the missing side length. To simplify, we will only use the lower edge and left edge comparison. Example Question #2 : Finding Sides We can solve using the trigonometric definition of tangent. We are given the angle and the adjacent side. We can find with a calculator. Example Question #3 : Finding Sides If equals and is , how long is ? Not enough information to solve This problem can be easily solved using trig identities. We are given the hypotenuse and . We can then calculate side using the . Rearrange to solve for . If you calculated the side to equal then you utilized the function rather than the . Example Question #4 : Graphs And Inverses Of Trigonometric Functions What is the length of CB?
A parametric curve in the plane is a pair of functions x = f(t) y = f(t) where the two continuous functions define the ordered pairs (x,y). The two functions are normally called parametric equations of a curve, and the curve is dependent upon the range of t. We will be investigating parametric curves using trigonometric functions. For a basic understanding of parametric equations, consider the following: Since t varies from 0 to, the full domain of the functions, then the equations completely describe a circle. Note that the radius of the circle is one, which is the coefficient of the two equations. If t only varies 75% of the domain, then the described curve will only be 75% of a circle. If we add constants to the parametric equations, such as then the constants will translate the circle +1 unit in the x-direction and -2 units in the y-direction as follows: If we chose different coefficients for the two functions, such as then the shape is altered, and it becomes an ellipse. The x-axis now becomes the minor axis with a distance of 2 units from the center (0,0), and the y-axis is now the major axis with a distance of 3 units from the center. Hence, we can conclude the general parametric equations for our exploratory study are where (m, n) is the center of the ellipse, 2A describes the length of the axis in the x-direction and 2B describes the length in the y-direction. These relationships can be graphically illustrated as (with the wonders of MacPaint) As an example of the above general equations, we have the following: with the associated graph, below. Note that the center is (1,-2), the x-distance from the center to the right edge is 2 units (along the minor axis), and the y-distance from the center to the top edge is 3 units (along the major axis). Now that we have covered the basics, we will investigate the following parametric equations where the basic function has a coefficient of two, and the function is raised to exponent n, Then we obtain an unusual set of curves: When n=1, the graph is a circle (purple) with radius 2, as expected. When n=2, the graph is a (line) segment (red) in Quadrant I, inside the circle. When n=3, the graph is a diamond (blue), inside the above line. When n=4, the graph is an arc (green) in Quadrant I, inside the diamond. When n=5, the graph is a smaller diamond (light blue), inside the larger diamond. When n=6, the graph is an arc (yellow) in Quadrant I, inside the smaller diamond. We can conclude that the even exponents produce a figure only in Quadrant I, whereas the odd exponents produce a symmetric figure that covers all four quadrants. As another interesting variation, we can observe the graphs of x = 2 cos (at) y = sin (bt) where a and b are integers. If a = 1 and b = 2, or greater, we note that b determines the number of loops. The boundaries of the loops lie between -2 and +2 along the x-axis, and -1 and +1 along the y-axis since the coefficients of cosine and sine are 2 and one, respectively. If b is even, the middle node is located at the origin. Observe the two graphs when a is fixed at one, and b is 4 and 5, respectively. RETURN to my Home Page..
Before going to learn about Solving Quadratic Equations, first recall a few facts about the quadratic equations. The word quadratic originated from the word quad and its meaning is “square”. It means that the quadratic equation has a variable raised to 2 as the greatest power term. The standard form of a quadratic equation is given by the equation ax2 + bx + c = 0, where a ≠ 0. We saw that quadratic equations can represent many real-life situations. Now that we know what quadratic equations are, let us learn about the definition of solving quadratic equations, and the different methods to solve them. Here we will try to develop the Quadratic Equation Formula and other methods of solving the quadratic equations. But the solving quadratic equations by factoring is the most popular method. You learn all the methods in detail here along with all 10th Grade Math Concepts all here. What is meant by Solving of Quadratic Equations \| Solving of Quadratic Equations-Definition It is defined as, that any value(s) of x that satisfies the equation is known as a solution (or) root of the equation, and the process of finding the values of x which satisfy the equation ax2 + bx + c = 0 is known as solving quadratic equations. Methods of Solving a Quadratic Equation \| How to Solve Quadratic Equations? Solving quadratic equations means finding a value (or) values of the variable which satisfies the equation. The value that satisfies the quadratic equation is called its roots (or) solutions (or) zeros. Hence the degree of the quadratic equation is 2, it can have a maximum of 2 roots. But how do find them if they are not given? The different methods of solving quadratic equations are: 1. Solving quadratic equations by factoring 2. Solving quadratic equations by using completing the square 3. Solving quadratic equations by graphing 4. Solving quadratic equations by quadratic formula Solving Quadratic Equations by Factoring This method is one of the most famous and simplest methods used to solve a quadratic equation and certain quadratic equations can be factorized. If we have done correctly will give get two linear equations in x. Hence, from that equations, we will get the value of x. The step-by-step process of solving quadratic equations by factoring is explained below along with an example we will solve the equation is x2-3x + 2 = 0. - Step 1: First, we get the equation into a standard form. - Step 2: Then factorize the quadratic equation. - Step 3: By zero product property, set each of the factors to zero. - Step 4: Now, solve each of the above equations. Example: Solve the equation step by step using the factoring method. The equation is x2-3x + 2 = 0. Solution: Given that, - Step1: Get the equation into standard form. i.e., Get all the terms to one side (usually to the left side) of the equation such that the other side will be 0. The equation x2 – 3x + 2 = 0 is already in standard form. - Step 2: Factor the quadratic expression. Then we will get as (x – 1) (x – 2) = 0. - Step 3: In zero product property, set each of the factors will be zero that is x – 1 = 0 (or) x – 2 = 0 - Step 4: Solve each of the above equations. x = 1 (or) x = 2 Thus, the solutions of the quadratic equation x2 – 3x + 2 = 0 are 1 and 2. This method is only applicable when the quadratic expression is factorable. If it is not factorable, then we can use one of the other methods. Similar to the quadratic equations we have a solution for linear equations, which are used to solve linear programming problems. Solving Quadratic Equations by using Completing the Square In this method, Completing the square means to write the quadratic expression as ax2+bx+c into the form a(x – h)2 + k (it is also known as vertex form), where h = -b/2a and ‘k’ can be obtained by substituting x = h in ax2 + bx + c. The step-by-step process of solving the quadratic equations by completing the square is given below, along with an example where we are going to find the solutions of the equation 2x2 + 8x = -3. - Step 1: First, we get the equation into a standard form. - Step 2: Now, complete the square on the left side. - Step 3: Solve it now, we get the value of x. Solve the equation using the complete square method. The equation is 2x2+8x = -3. Given that the equation is 2x2+8x = -3 Step 1: Initially, we get the equation into standard form. Now adding 3 on both sides, we get 2x2 + 8x + 3 = 0. Step 2: Complete the square on the left side, then we get 2(x + 2)2-5 = 0. Step 3: Now, Solve it for x. (We will take the square root on both sides along the way). Next, Adding 5 on both sides, that is 2 (x + 2)2 = 5. Dividing both sides by 2, (x + 2)2 = 5/2 Taking square root on both sides, x + 2 = √(5/2) = √5/√2 · √2/√2 = √10/2 Let Subtracte 2 from both sides, x = -2 ± (√10/2) = (-4 ± √10) / 2 Thus, the roots of the quadratic equation 2x2+8x = -3 are (-4 + √10)/2 and (-4 – √10)/2. Solving Quadratic Equations by Graphing To solve the quadratic equations by using graphing, first, we have to graph the quadratic expression (when the equation is in the standard form) either manually or by using a graphing calculator. Then the x-intercepts of the graph (the point(s) where the graph cuts the x-axis) are nothing but the roots of the quadratic equation. The process of solving quadratic equations by graphing is explained in steps along with an example, and we are going to solve the equation 3x2 + 5 = 11x. - Step 1: Initially, we get the equation into the standard form. - Step 2: Graph the quadratic expression which is on the right side. - Step 3: Identify the X-intercepts. - Step 4: Next, the x-coordinates of the x-intercepts are nothing but the roots of the quadratic equation. Solve the equation is 3x2 + 5 = 11x. Step 1: Initially, we get the equation into the standard form. First, subtracting 11x from both sides, 3x2 – 11x + 5 = 0. Step 2: Graph the quadratic expression which is on the left side. Graph the quadratic function y = 3x2 – 11x + 5 either manually or using a graphing calculator (GDC). Step 3: Identify the x-intercepts. For solving quadratic equations by graphing, the quadratic expression has to be graphed and identify the x-intercepts. Step 4: Now, the x-coordinates of the x-intercepts are nothing but the roots of the quadratic equation. Thus, the solutions of the quadratic equation 3x2 + 5 = 11x are 0.532 and 3.135. By observing the above example, we can see that the graphing method of solving quadratic equations may not give the exact solutions (i.e., it gives only the decimal approximations of the roots if they are irrational}. i.e., if we solve the same equation using completing the square, we get x = (11 + √61) / 6 and x = (11 – √61) / 6. But we will not get the exact roots by the graphing method. If the graph does not intersect the x-axis at all, it means that the quadratic equation has two complex roots that is the graphing method is not useful to find the roots if they are complex numbers. We can use the quadratic formula to find any type of the root’s value (it will be explained in the next section) Solving Quadratic Equations by Quadratic Formula As we have already seen, the previous methods for solving the quadratic equations have some limitations such as the factoring method is useful only when the quadratic expression is factorable, the graphing method is useful only when the quadratic equation has real roots, etc. But solving quadratic equations by quadratic formula overcomes all these limitations and is useful to solve any type of quadratic equation. Here is the step-by-step explanation of solving quadratic equations by quadratic formula along with an example where we will be finding the solutions of the quadratic 2x2 = 3x – 5. - Step 1: First, we get the equation into a standard form. - Step 2: Now, compare the equation with ax2+bx+c=0 and then find the values of a,b and c. - Step 3: Substitute the values into the quadratic formula which says x = [-b ± √(b² – 4ac)] / (2a). - Step 4: Now, simplify it, we get the x value. Solve the equation using the quadratic formula. The equation is 2x2 – 3x + 5 = 0. As given in the question. the equation is 2x2 – 3x + 5 = 0. - Step 1: Get into the standard form. Then the above equation becomes 2x2 – 3x + 5 = 0. - Step 2: Compare the equation with ax2 + bx + c = 0 and find the values of a, b, and c. Then we get the value of a is 2, b is -3. and c is 5. - Step 3: Substitute the values into the quadratic formula which says x = [-b ± √(b² – 4ac)] / (2a). Then we get x = [-(-3) ± √((-3)² – 4(2)(5))] / (2(2) - Step – 4: Simplify it, then the value of x is x = [ 3 ± √(9 – 40) ] / 4 = [ 3 ± √(-31) ] / 4 = [ 3 ± i√(31) ] / 4 Thus, the roots of the quadratic equation 2x2 = 3x – 5 are [ 3 + i√(31) ] / 4 and [ 3 – i√(31) ] / 4. In a quardratic formula, the expression of b² – 4ac is called as discriminant (which is denoted by D). i.e., D = b² – 4ac. This will used to determine the nature of roots of the quadratic equation. Nature of Roots Using Discriminant - If D > 0, then the equation ax2 + bx + c = 0 has two real and distinct roots. - If D = 0, then the equation ax2 + bx + c = 0 has only one real root. - If D < 0, then the equation ax2 + bx + c = 0 has two distinct complex roots. Thus, using the discriminant, we can find the number of solutions to quadratic equations without actually solving them. Apart from these methods, there are a few other methods that are used only in specific cases i.e., when the quadratic equation has missing terms like that, the below explained: Solving Quadratic Equations Missing b In a quadratic equation ax^2 + bx + c = 0, if the term with b is missing then the equation becomes ax^2 + c = 0. Now, we can solve this by taking square root on both sides. The below explained the process with examples. The equation is x^2 – 4 = 0 ⇒ x^2 = 4 ⇒ x = ±√4 ⇒ x = ± 2 So, the equation roots are 2 and -2. The another example is, x^2 + 36 = 0 ⇒ x^2 = -36 ⇒ x = ±√(-36) ⇒ x = ± 6i Thus, the roots of the equation are 6i and -6i (note that these are imaginary numbers (or) complex numbers). Solving Quadratic Equations Missing c In a quadratic equation ax^2 + bx + c = 0, if the term with c is missing then the equation becomes ax^2 + bx = 0. To solve this type of equation, we simply factor x out from the left side, set each of the factors to zero, and solve them. The process will explained in below with examples: The equation is x^2 – 5x = 0 ⇒ x (x – 5) = 0 ⇒ x = 0; x – 5 = 0 ⇒ x = 0; x = 5 So, the equation roots are 0 and 5. Next, the equation is x^2 + 11x = 0 ⇒ x (x + 11) = 0 ⇒ x = 0; x + 11 = 0 ⇒ x = 0; x = -11 Hence, the roots of the equations are 0 and -11. Solving Quadratic Equations Examples with Answers Problem 1: The length of a park is 5 ft less than twice its width. If its area is 250 square feet, find the dimensions of the park? The data is as given in the question, Assume that, the width of the park is x ft. Then the length of the park is (2x – 5) ft. The area of a park is 250 sq. ft So, the length × width is 250. Substitute the values, it will be (2x – 5)x = 250. 2x^2 – 5x – 250 = 0. So, this is a word problem that is related to solving quadratic equations. Now, let us solve this quadratic equation by using the factoring method. In this, the value of a is 2, b is -5, and c is -250. So, a x c is 2(-250) = -500. Next, the two numbers whose sum is -5 and whose product is -500 are -25 and 20. So we can split the middle term using these two numbers. 2x^2 – 25x + 20x – 250 = 0 x(2x – 25) + 10 (2x – 25) = 0 (2x – 25) (x + 10) = 0 2x – 25 = 0 i.e., x + 10 = 0 The value of x is x = 25/2 = 12.5 (or) x = -10. x = 12.5, x value cannot be in negative. So the width is 12.5 ft and the length is (2x – 5) ft = 2(12.5)-5 = 20 ft. Thus, the dimensions of the park are 20 ft × 12.5. Problem 2: Let the two positive consecutive numbers is 156. Find the value of two numbers? The two positive consecutive numbers product is 156. Now, we will find the values of two numbers. Assume that the two consecutive numbers be x and x + 1. Then the equation is, x (x + 1) = 156 x^2 + x – 156 = 0 Now, solve this quadratic equation by the factoring method. In this a = 1, b = 1 and c = -156. So, the ac is 1(-156) = -156. The two numbers whose sum is 1 and whose product is -156 are 13 and -12. So we can split the middle term using these two numbers. i.e., x^2 + 13x – 12x – 156 = 0 x (x + 13) – 12 (x + 13) = 0 (x + 13) (x – 12) = 0 The value of x + 13 = 0, and x – 12 = 0 Therefore, x = -13 (or) x = 12 we know, x is positive, x cannot be in negative i.e.,-13. So the value of x is 12. Thus, the required consecutive numbers are 12 and 13 (12 + 1). FAQs on Solving Quadratic Equations 1. What is a quadratic equation? We Simply say that a quadratic equation is an equation of degree 2, which means that the highest exponent of this function is 2. Moreover, the standard quadratic equation is ax^2 + bx + c, where a, b, and c are just numbered and ‘a’ cannot be 0. An example of quadratic equation is 3x^2 + 2x + 1. 2. What are the different methods by which you can solve quadratic equations? There are various methods by which you can solve a quadratic equation such as factorization, completing the square, quadratic formula, and graphing. All these are the four general methods that we can use to solve a quadratic equation. 3. What are the three forms of a quadratic function? The three functions are listed below which can be written as: 1. Standard Form: y = ax2 + bx + c, where a, b, and c are just numbers. 2. Factored Form: y = (ax + c) (bx + d) where a, b, and c are just numbers. 3. Vertex Form: y = a (x + b)2 + c, and here also a, b, and c are numbers. 4. What is the formula for solving quadratic equations? The general quadratic equation formula is “ax2 + bx + c”. In this formula, a, b, and c numbers, are the numerical coefficient of the quadratic equation, and ‘a’ is not zero a 0. 5. How is the Factored Form Helpful in Solving Quadratic Equations? If the quadratic expression that is in the standard form of quadratic expression in it is factorable, then we can just set each factor to zero, and solve them. Thus, the solutions are nothing but the roots of a quadratic equation.
The scientific method is a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry is commonly based on empirical or measurable evidence subject to specific principles of reasoning. The Oxford English Dictionary defines the scientific method as "a method or procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses." The scientific method is an ongoing process, which usually begins with observations about the natural world. Human beings are naturally inquisitive, so they often come up with questions about things they see or hear and often develop ideas (hypotheses) about why things are the way they are. The best hypotheses lead to predictions that can be tested in various ways, including making further observations about nature. In general, the strongest tests of hypotheses come from carefully controlled and replicated experiments that gather empirical data. Depending on how well the tests match the predictions, the original hypothesis may require refinement, alteration, expansion or even rejection. If a particular hypothesis becomes very well supported a general theory may be developed. Although procedures vary from one field of inquiry to another, identifiable features are frequently shared in common between them. The overall process of the scientific method involves making conjectures (hypotheses), deriving predictions from them as logical consequences, and then carrying out experiments based on those predictions. A hypothesis is a conjecture, based on knowledge obtained while formulating the question. The hypothesis might be very specific or it might be broad. Scientists then test hypotheses by conducting experiments. Under modern interpretations, a scientific hypothesis must be falsifiable, implying that it is possible to identify a possible outcome of an experiment that conflicts with predictions deduced from the hypothesis; otherwise, the hypothesis cannot be meaningfully tested. The purpose of an experiment is to determine whether observations agree with or conflict with the predictions derived from a hypothesis. Experiments can take place in a college lab, on a kitchen table, at CERN's Large Hadron Collider, at the bottom of an ocean, on Mars, and so on. There are difficulties in a formulaic statement of method, however. Though the scientific method is often presented as a fixed sequence of steps, it represents rather a set of general principles. Not all steps take place in every scientific inquiry (or to the same degree), and are not always in the same order. - 1 Overview - 2 Scientific inquiry - 3 Elements of the scientific method - 3.1 Characterizations - 3.2 Hypothesis development - 3.3 Predictions from the hypothesis - 3.4 Experiments - 3.5 Evaluation and improvement - 3.6 Confirmation - 4 Models of scientific inquiry - 5 Communication and community - 6 Philosophy and sociology of science - 7 History - 8 Relationship with mathematics - 9 See also - 10 Notes - 11 References - 12 Further reading - 13 External links - The DNA example below is a synopsis of this method The scientific method is the process by which science is carried out. As in other areas of inquiry, science (through the scientific method) can build on previous knowledge and develop a more sophisticated understanding of its topics of study over time. This model can be seen to underlay the scientific revolution. One thousand years ago, Alhazen argued the importance of forming questions and subsequently testing them, an approach which was advocated by Galileo in 1638 with the publication of Two New Sciences. The current method is based on a hypothetico-deductive model formulated in the 20th century, although it has undergone significant revision since first proposed (for a more formal discussion, see below). The overall process involves making conjectures (hypotheses), deriving predictions from them as logical consequences, and then carrying out experiments based on those predictions to determine whether the original conjecture was correct. There are difficulties in a formulaic statement of method, however. Though the scientific method is often presented as a fixed sequence of steps, they are better considered as general principles. Not all steps take place in every scientific inquiry (or to the same degree), and are not always in the same order. As noted by William Whewell (1794–1866), "invention, sagacity, [and] genius" are required at every step. Formulation of a question The question can refer to the explanation of a specific observation, as in "Why is the sky blue?", but can also be open-ended, as in "How can I design a drug to cure this particular disease?" This stage frequently involves looking up and evaluating evidence from previous experiments, personal scientific observations or assertions, and/or the work of other scientists. If the answer is already known, a different question that builds on the previous evidence can be posed. When applying the scientific method to scientific research, determining a good question can be very difficult and affects the final outcome of the investigation. An hypothesis is a conjecture, based on knowledge obtained while formulating the question, that may explain the observed behavior of a part of our universe. The hypothesis might be very specific, e.g., Einstein's equivalence principle or Francis Crick's "DNA makes RNA makes protein", or it might be broad, e.g., unknown species of life dwell in the unexplored depths of the oceans. A statistical hypothesis is a conjecture about some population. For example, the population might be people with a particular disease. The conjecture might be that a new drug will cure the disease in some of those people. Terms commonly associated with statistical hypotheses are null hypothesis and alternative hypothesis. A null hypothesis is the conjecture that the statistical hypothesis is false, e.g., that the new drug does nothing and that any cures are due to chance effects. Researchers normally want to show that the null hypothesis is false. The alternative hypothesis is the desired outcome, e.g., that the drug does better than chance. A final point: a scientific hypothesis must be falsifiable, meaning that one can identify a possible outcome of an experiment that conflicts with predictions deduced from the hypothesis; otherwise, it cannot be meaningfully tested. This step involves determining the logical consequences of the hypothesis. One or more predictions are then selected for further testing. The more unlikely that a prediction would be correct simply by coincidence, then the more convincing it would be if the prediction were fulfilled; evidence is also stronger if the answer to the prediction is not already known, due to the effects of hindsight bias (see also postdiction). Ideally, the prediction must also distinguish the hypothesis from likely alternatives; if two hypotheses make the same prediction, observing the prediction to be correct is not evidence for either one over the other. (These statements about the relative strength of evidence can be mathematically derived using Bayes' Theorem). This is an investigation of whether the real world behaves as predicted by the hypothesis. Scientists (and other people) test hypotheses by conducting experiments. The purpose of an experiment is to determine whether observations of the real world agree with or conflict with the predictions derived from an hypothesis. If they agree, confidence in the hypothesis increases; otherwise, it decreases. Agreement does not assure that the hypothesis is true; future experiments may reveal problems. Karl Popper advised scientists to try to falsify hypotheses, i.e., to search for and test those experiments that seem most doubtful. Large numbers of successful confirmations are not convincing if they arise from experiments that avoid risk. Experiments should be designed to minimize possible errors, especially through the use of appropriate scientific controls. For example, tests of medical treatments are commonly run as double-blind tests. Test personnel, who might unwittingly reveal to test subjects which samples are the desired test drugs and which are placebos, are kept ignorant of which are which. Such hints can bias the responses of the test subjects. Furthermore, failure of an experiment does not necessarily mean the hypothesis is false. Experiments always depend on several hypotheses, e.g., that the test equipment is working properly, and a failure may be a failure of one of the auxiliary hypotheses. (See the Duhem-Quine thesis.) Experiments can be conducted in a college lab, on a kitchen table, at CERN's Large Hadron Collider, at the bottom of an ocean, on Mars (using one of the working rovers), and so on. Astronomers do experiments, searching for planets around distant stars. Finally, most individual experiments address highly specific topics for reasons of practicality. As a result, evidence about broader topics is usually accumulated gradually. This involves determining what the results of the experiment show and deciding on the next actions to take. The predictions of the hypothesis are compared to those of the null hypothesis, to determine which is better able to explain the data. In cases where an experiment is repeated many times, a statistical analysis such as a chi-squared test may be required. If the evidence has falsified the hypothesis, a new hypothesis is required; if the experiment supports the hypothesis but the evidence is not strong enough for high confidence, other predictions from the hypothesis must be tested. Once a hypothesis is strongly supported by evidence, a new question can be asked to provide further insight on the same topic. Evidence from other scientists and experience are frequently incorporated at any stage in the process. Depending on the complexity of the experiment, many iterations may be required to gather sufficient evidence to answer a question with confidence, or to build up many answers to highly specific questions in order to answer a single broader question. \|The basic elements of the scientific method are illustrated by the following example from the discovery of the structure of DNA: The discovery became the starting point for many further studies involving the genetic material, such as the field of molecular genetics, and it was awarded the Nobel Prize in 1962. Each step of the example is examined in more detail later in the article. The scientific method also includes other components required even when all the iterations of the steps above have been completed: If an experiment cannot be repeated to produce the same results, this implies that the original results might have been in error. As a result, it is common for a single experiment to be performed multiple times, especially when there are uncontrolled variables or other indications of experimental error. For significant or surprising results, other scientists may also attempt to replicate the results for themselves, especially if those results would be important to their own work. The process of peer review involves evaluation of the experiment by experts, who typically give their opinions anonymously. Some journals request that the experimenter provide lists of possible peer reviewers, especially if the field is highly specialized. Peer review does not certify correctness of the results, only that, in the opinion of the reviewer, the experiments themselves were sound (based on the description supplied by the experimenter). If the work passes peer review, which occasionally may require new experiments requested by the reviewers, it will be published in a peer-reviewed scientific journal. The specific journal that publishes the results indicates the perceived quality of the work. Data recording and sharing Scientists typically are careful in recording their data, a requirement promoted by Ludwik Fleck (1896–1961) and others. Though not typically required, they might be requested to supply this data to other scientists who wish to replicate their original results (or parts of their original results), extending to the sharing of any experimental samples that may be difficult to obtain. Scientific inquiry generally aims to obtain knowledge in the form of testable explanations that can be used to predict the results of future experiments. This allows scientists to gain a better understanding of the topic being studied, and later be able to use that understanding to intervene in its causal mechanisms (such as to cure disease). The better an explanation is at making predictions, the more useful it frequently can be, and the more likely it is to continue explaining a body of evidence better than its alternatives. The most successful explanations, which explain and make accurate predictions in a wide range of circumstances, are often called scientific theories. Most experimental results do not produce large changes in human understanding; improvements in theoretical scientific understanding is typically the result of a gradual process of development over time, sometimes across different domains of science. Scientific models vary in the extent to which they have been experimentally tested and for how long, and in their acceptance in the scientific community. In general, explanations become accepted over time as evidence accumulates on a given topic, and the explanation in question is more powerful than its alternatives at explaining the evidence. Often the explanations are altered over time, or explanations are combined to produce new explanations. Properties of scientific inquiry Scientific knowledge is closely tied to empirical findings, and can remain subject to falsification if new experimental observation incompatible with it is found. That is, no theory can ever be considered final, since new problematic evidence might be discovered. If such evidence is found, a new theory may be proposed, or (more commonly) it is found that modifications to the previous theory are sufficient to explain the new evidence. The strength of a theory can be argued to be related to how long it has persisted without major alteration to its core principles. Theories can also subject to subsumption by other theories. For example, thousands of years of scientific observations of the planets were explained almost perfectly by Newton's laws. However, these laws were then determined to be special cases of a more general theory (relativity), which explained both the (previously unexplained) exceptions to Newton's laws and predicting and explaining other observations such as the deflection of light by gravity. Thus, in certain cases independent, unconnected, scientific observations can be connected to each other, unified by principles of increasing explanatory power. Since new theories might be more comprehensive than what preceded them, and thus be able to explain more than previous ones, successor theories might be able to meet a higher standard by explaining a larger body of observations than their predecessors. For example, the theory of evolution explains the diversity of life on Earth, how species adapt to their environments, and many other patterns observed in the natural world; its most recent major modification was unification with genetics to form the modern evolutionary synthesis. In subsequent modifications, it has also subsumed aspects of many other fields such as biochemistry and molecular biology. Beliefs and biases Scientific methodology often directs that hypotheses be tested in controlled conditions wherever possible. This is frequently possible in certain areas, such as in the biological sciences, and more difficult in other areas, such as in astronomy. The practice of experimental control and reproducibility can have the effect of diminishing the potentially harmful effects of circumstance, and to a degree, personal bias. For example, pre-existing beliefs can alter the interpretation of results, as in confirmation bias; this is a heuristic that leads a person with a particular belief to see things as reinforcing their belief, even if another observer might disagree (in other words, people tend to observe what they expect to observe). A historical example is the belief that the legs of a galloping horse are splayed at the point when none of the horse's legs touches the ground, to the point of this image being included in paintings by its supporters. However, the first stop-action pictures of a horse's gallop by Eadweard Muybridge showed this to be false, and that the legs are instead gathered together. Another important human bias that plays a role is a preference for new, surprising statements (see appeal to novelty), which can result in a search for evidence that the new is true. In contrast to this standard in the scientific method, poorly attested beliefs can be believed and acted upon via a less rigorous heuristic, sometimes taking advantage of the narrative fallacy that when narrative is constructed its elements become easier to believe. Sometimes, these have their elements assumed a priori, or contain some other logical or methodological flaw in the process that ultimately produced them. Elements of the scientific method There are different ways of outlining the basic method used for scientific inquiry. The scientific community and philosophers of science generally agree on the following classification of method components. These methodological elements and organization of procedures tend to be more characteristic of natural sciences than social sciences. Nonetheless, the cycle of formulating hypotheses, testing and analyzing the results, and formulating new hypotheses, will resemble the cycle described below. - Four essential elements of the scientific method are iterations, recursions, interleavings, or orderings of the following: - Characterizations (observations, definitions, and measurements of the subject of inquiry) - Hypotheses (theoretical, hypothetical explanations of observations and measurements of the subject) - Predictions (reasoning including logical deduction from the hypothesis or theory) - Experiments (tests of all of the above) Each element of the scientific method is subject to peer review for possible mistakes. These activities do not describe all that scientists do (see below) but apply mostly to experimental sciences (e.g., physics, chemistry, and biology). The elements above are often taught in the educational system as "the scientific method". The scientific method is not a single recipe: it requires intelligence, imagination, and creativity. In this sense, it is not a mindless set of standards and procedures to follow, but is rather an ongoing cycle, constantly developing more useful, accurate and comprehensive models and methods. For example, when Einstein developed the Special and General Theories of Relativity, he did not in any way refute or discount Newton's Principia. On the contrary, if the astronomically large, the vanishingly small, and the extremely fast are removed from Einstein's theories – all phenomena Newton could not have observed – Newton's equations are what remain. Einstein's theories are expansions and refinements of Newton's theories and, thus, increase our confidence in Newton's work. A linearized, pragmatic scheme of the four points above is sometimes offered as a guideline for proceeding: - Define a question - Gather information and resources (observe) - Form an explanatory hypothesis - Test the hypothesis by performing an experiment and collecting data in a reproducible manner - Analyze the data - Interpret the data and draw conclusions that serve as a starting point for new hypothesis - Publish results - Retest (frequently done by other scientists) The iterative cycle inherent in this step-by-step method goes from point 3 to 6 back to 3 again. While this schema outlines a typical hypothesis/testing method, it should also be noted that a number of philosophers, historians and sociologists of science (perhaps most notably Paul Feyerabend) claim that such descriptions of scientific method have little relation to the ways that science is actually practiced. - Operation – Some action done to the system being investigated - Observation – What happens when the operation is done to the system - Model – A fact, hypothesis, theory, or the phenomenon itself at a certain moment - Utility Function – A measure of the usefulness of the model to explain, predict, and control, and of the cost of use of it. One of the elements of any scientific utility function is the refutability of the model. Another is its simplicity, on the Principle of Parsimony more commonly known as Occam's Razor. The scientific method depends upon increasingly sophisticated characterizations of the subjects of investigation. (The subjects can also be called unsolved problems or the unknowns.) For example, Benjamin Franklin conjectured, correctly, that St. Elmo's fire was electrical in nature, but it has taken a long series of experiments and theoretical changes to establish this. While seeking the pertinent properties of the subjects, careful thought may also entail some definitions and observations; the observations often demand careful measurements and/or counting. The systematic, careful collection of measurements or counts of relevant quantities is often the critical difference between pseudo-sciences, such as alchemy, and science, such as chemistry or biology. Scientific measurements are usually tabulated, graphed, or mapped, and statistical manipulations, such as correlation and regression, performed on them. The measurements might be made in a controlled setting, such as a laboratory, or made on more or less inaccessible or unmanipulatable objects such as stars or human populations. The measurements often require specialized scientific instruments such as thermometers, spectroscopes, particle accelerators, or voltmeters, and the progress of a scientific field is usually intimately tied to their invention and improvement. Measurements in scientific work are also usually accompanied by estimates of their uncertainty. The uncertainty is often estimated by making repeated measurements of the desired quantity. Uncertainties may also be calculated by consideration of the uncertainties of the individual underlying quantities used. Counts of things, such as the number of people in a nation at a particular time, may also have an uncertainty due to data collection limitations. Or counts may represent a sample of desired quantities, with an uncertainty that depends upon the sampling method used and the number of samples taken. Measurements demand the use of operational definitions of relevant quantities. That is, a scientific quantity is described or defined by how it is measured, as opposed to some more vague, inexact or "idealized" definition. For example, electric current, measured in amperes, may be operationally defined in terms of the mass of silver deposited in a certain time on an electrode in an electrochemical device that is described in some detail. The operational definition of a thing often relies on comparisons with standards: the operational definition of "mass" ultimately relies on the use of an artifact, such as a particular kilogram of platinum-iridium kept in a laboratory in France. The scientific definition of a term sometimes differs substantially from its natural language usage. For example, mass and weight overlap in meaning in common discourse, but have distinct meanings in mechanics. Scientific quantities are often characterized by their units of measure which can later be described in terms of conventional physical units when communicating the work. New theories are sometimes developed after realizing certain terms have not previously been sufficiently clearly defined. For example, Albert Einstein's first paper on relativity begins by defining simultaneity and the means for determining length. These ideas were skipped over by Isaac Newton with, "I do not define time, space, place and motion, as being well known to all." Einstein's paper then demonstrates that they (viz., absolute time and length independent of motion) were approximations. Francis Crick cautions us that when characterizing a subject, however, it can be premature to define something when it remains ill-understood. In Crick's study of consciousness, he actually found it easier to study awareness in the visual system, rather than to study free will, for example. His cautionary example was the gene; the gene was much more poorly understood before Watson and Crick's pioneering discovery of the structure of DNA; it would have been counterproductive to spend much time on the definition of the gene, before them. The history of the discovery of the structure of DNA is a classic example of the elements of the scientific method: in 1950 it was known that genetic inheritance had a mathematical description, starting with the studies of Gregor Mendel, and that DNA contained genetic information (Oswald Avery's transforming principle). But the mechanism of storing genetic information (i.e., genes) in DNA was unclear. Researchers in Bragg's laboratory at Cambridge University made X-ray diffraction pictures of various molecules, starting with crystals of salt, and proceeding to more complicated substances. Using clues painstakingly assembled over decades, beginning with its chemical composition, it was determined that it should be possible to characterize the physical structure of DNA, and the X-ray images would be the vehicle. ..2. DNA-hypotheses Another example: precession of Mercury The characterization element can require extended and extensive study, even centuries. It took thousands of years of measurements, from the Chaldean, Indian, Persian, Greek, Arabic and European astronomers, to fully record the motion of planet Earth. Newton was able to include those measurements into consequences of his laws of motion. But the perihelion of the planet Mercury's orbit exhibits a precession that cannot be fully explained by Newton's laws of motion (see diagram to the right), as Leverrier pointed out in 1859. The observed difference for Mercury's precession between Newtonian theory and observation was one of the things that occurred to Einstein as a possible early test of his theory of General Relativity. His relativistic calculations matched observation much more closely than did Newtonian theory. The difference is approximately 43 arc-seconds per century. An hypothesis is a suggested explanation of a phenomenon, or alternately a reasoned proposal suggesting a possible correlation between or among a set of phenomena. Normally hypotheses have the form of a mathematical model. Sometimes, but not always, they can also be formulated as existential statements, stating that some particular instance of the phenomenon being studied has some characteristic and causal explanations, which have the general form of universal statements, stating that every instance of the phenomenon has a particular characteristic. Scientists are free to use whatever resources they have – their own creativity, ideas from other fields, induction, Bayesian inference, and so on – to imagine possible explanations for a phenomenon under study. Charles Sanders Peirce, borrowing a page from Aristotle (Prior Analytics, 2.25) described the incipient stages of inquiry, instigated by the "irritation of doubt" to venture a plausible guess, as abductive reasoning. The history of science is filled with stories of scientists claiming a "flash of inspiration", or a hunch, which then motivated them to look for evidence to support or refute their idea. Michael Polanyi made such creativity the centerpiece of his discussion of methodology. William Glen observes that - the success of a hypothesis, or its service to science, lies not simply in its perceived "truth", or power to displace, subsume or reduce a predecessor idea, but perhaps more in its ability to stimulate the research that will illuminate ... bald suppositions and areas of vagueness. In general scientists tend to look for theories that are "elegant" or "beautiful". In contrast to the usual English use of these terms, they here refer to a theory in accordance with the known facts, which is nevertheless relatively simple and easy to handle. Occam's Razor serves as a rule of thumb for choosing the most desirable amongst a group of equally explanatory hypotheses. Linus Pauling proposed that DNA might be a triple helix. This hypothesis was also considered by Francis Crick and James D. Watson but discarded. When Watson and Crick learned of Pauling's hypothesis, they understood from existing data that Pauling was wrong and that Pauling would soon admit his difficulties with that structure. So, the race was on to figure out the correct structure (except that Pauling did not realize at the time that he was in a race) ..3. DNA-predictions Predictions from the hypothesis Any useful hypothesis will enable predictions, by reasoning including deductive reasoning. It might predict the outcome of an experiment in a laboratory setting or the observation of a phenomenon in nature. The prediction can also be statistical and deal only with probabilities. It is essential that the outcome of testing such a prediction be currently unknown. Only in this case does a successful outcome increase the probability that the hypothesis is true. If the outcome is already known, it is called a consequence and should have already been considered while formulating the hypothesis. If the predictions are not accessible by observation or experience, the hypothesis is not yet testable and so will remain to that extent unscientific in a strict sense. A new technology or theory might make the necessary experiments feasible. Thus, much scientifically based speculation might convince one (or many) that the hypothesis that other intelligent species exist is true. But since there no experiment now known which can test this hypothesis, science itself can have little to say about the possibility. In future, some new technique might lead to an experimental test and the speculation would then become part of accepted science. James D. Watson, Francis Crick, and others hypothesized that DNA had a helical structure. This implied that DNA's X-ray diffraction pattern would be 'x shaped'. This prediction followed from the work of Cochran, Crick and Vand (and independently by Stokes). The Cochran-Crick-Vand-Stokes theorem provided a mathematical explanation for the empirical observation that diffraction from helical structures produces x shaped patterns. In their first paper, Watson and Crick also noted that the double helix structure they proposed provided a simple mechanism for DNA replication, writing, "It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material". ..4. DNA-experiments Another example: general relativity Einstein's theory of General Relativity makes several specific predictions about the observable structure of space-time, such as that light bends in a gravitational field, and that the amount of bending depends in a precise way on the strength of that gravitational field. Arthur Eddington's observations made during a 1919 solar eclipse supported General Relativity rather than Newtonian gravitation. Once predictions are made, they can be sought by experiments. If the test results contradict the predictions, the hypotheses which entailed them are called into question and become less tenable. Sometimes the experiments are conducted incorrectly or are not very well designed, when compared to a crucial experiment. If the experimental results confirm the predictions, then the hypotheses are considered more likely to be correct, but might still be wrong and continue to be subject to further testing. The experimental control is a technique for dealing with observational error. This technique uses the contrast between multiple samples (or observations) under differing conditions to see what varies or what remains the same. We vary the conditions for each measurement, to help isolate what has changed. Mill's canons can then help us figure out what the important factor is. Factor analysis is one technique for discovering the important factor in an effect. Depending on the predictions, the experiments can have different shapes. It could be a classical experiment in a laboratory setting, a double-blind study or an archaeological excavation. Even taking a plane from New York to Paris is an experiment which tests the aerodynamical hypotheses used for constructing the plane. Scientists assume an attitude of openness and accountability on the part of those conducting an experiment. Detailed record keeping is essential, to aid in recording and reporting on the experimental results, and supports the effectiveness and integrity of the procedure. They will also assist in reproducing the experimental results, likely by others. Traces of this approach can be seen in the work of Hipparchus (190–120 BCE), when determining a value for the precession of the Earth, while controlled experiments can be seen in the works of Jābir ibn Hayyān (721–815 CE), al-Battani (853–929) and Alhazen (965–1039). Watson and Crick showed an initial (and incorrect) proposal for the structure of DNA to a team from Kings College – Rosalind Franklin, Maurice Wilkins, and Raymond Gosling. Franklin immediately spotted the flaws which concerned the water content. Later Watson saw Franklin's detailed X-ray diffraction images which showed an X-shape and was able to confirm the structure was helical. This rekindled Watson and Crick's model building and led to the correct structure. ..1. DNA-characterizations Evaluation and improvement The scientific method is iterative. At any stage it is possible to refine its accuracy and precision, so that some consideration will lead the scientist to repeat an earlier part of the process. Failure to develop an interesting hypothesis may lead a scientist to re-define the subject under consideration. Failure of a hypothesis to produce interesting and testable predictions may lead to reconsideration of the hypothesis or of the definition of the subject. Failure of an experiment to produce interesting results may lead a scientist to reconsider the experimental method, the hypothesis, or the definition of the subject. Other scientists may start their own research and enter the process at any stage. They might adopt the characterization and formulate their own hypothesis, or they might adopt the hypothesis and deduce their own predictions. Often the experiment is not done by the person who made the prediction, and the characterization is based on experiments done by someone else. Published results of experiments can also serve as a hypothesis predicting their own reproducibility. After considerable fruitless experimentation, being discouraged by their superior from continuing, and numerous false starts, Watson and Crick were able to infer the essential structure of DNA by concrete modeling of the physical shapes of the nucleotides which comprise it. They were guided by the bond lengths which had been deduced by Linus Pauling and by Rosalind Franklin's X-ray diffraction images. ..DNA Example Science is a social enterprise, and scientific work tends to be accepted by the scientific community when it has been confirmed. Crucially, experimental and theoretical results must be reproduced by others within the scientific community. Researchers have given their lives for this vision; Georg Wilhelm Richmann was killed by ball lightning (1753) when attempting to replicate the 1752 kite-flying experiment of Benjamin Franklin. To protect against bad science and fraudulent data, government research-granting agencies such as the National Science Foundation, and science journals, including Nature and Science, have a policy that researchers must archive their data and methods so that other researchers can test the data and methods and build on the research that has gone before. Scientific data archiving can be done at a number of national archives in the U.S. or in the World Data Center. Models of scientific inquiry The classical model of scientific inquiry derives from Aristotle, who distinguished the forms of approximate and exact reasoning, set out the threefold scheme of abductive, deductive, and inductive inference, and also treated the compound forms such as reasoning by analogy. In 1877, Charles Sanders Peirce (// like "purse"; 1839–1914) characterized inquiry in general not as the pursuit of truth per se but as the struggle to move from irritating, inhibitory doubts born of surprises, disagreements, and the like, and to reach a secure belief, belief being that on which one is prepared to act. He framed scientific inquiry as part of a broader spectrum and as spurred, like inquiry generally, by actual doubt, not mere verbal or hyperbolic doubt, which he held to be fruitless. He outlined four methods of settling opinion, ordered from least to most successful: - The method of tenacity (policy of sticking to initial belief) – which brings comforts and decisiveness but leads to trying to ignore contrary information and others' views as if truth were intrinsically private, not public. It goes against the social impulse and easily falters since one may well notice when another's opinion is as good as one's own initial opinion. Its successes can shine but tend to be transitory. - The method of authority – which overcomes disagreements but sometimes brutally. Its successes can be majestic and long-lived, but it cannot operate thoroughly enough to suppress doubts indefinitely, especially when people learn of other societies present and past. - The method of the a priori – which promotes conformity less brutally but fosters opinions as something like tastes, arising in conversation and comparisons of perspectives in terms of "what is agreeable to reason." Thereby it depends on fashion in paradigms and goes in circles over time. It is more intellectual and respectable but, like the first two methods, sustains accidental and capricious beliefs, destining some minds to doubt it. - The scientific method – the method wherein inquiry regards itself as fallible and purposely tests itself and criticizes, corrects, and improves itself. Peirce held that slow, stumbling ratiocination can be dangerously inferior to instinct and traditional sentiment in practical matters, and that the scientific method is best suited to theoretical research, which in turn should not be trammeled by the other methods and practical ends; reason's "first rule" is that, in order to learn, one must desire to learn and, as a corollary, must not block the way of inquiry. The scientific method excels the others by being deliberately designed to arrive – eventually – at the most secure beliefs, upon which the most successful practices can be based. Starting from the idea that people seek not truth per se but instead to subdue irritating, inhibitory doubt, Peirce showed how, through the struggle, some can come to submit to truth for the sake of belief's integrity, seek as truth the guidance of potential practice correctly to its given goal, and wed themselves to the scientific method. For Peirce, rational inquiry implies presuppositions about truth and the real; to reason is to presuppose (and at least to hope), as a principle of the reasoner's self-regulation, that the real is discoverable and independent of our vagaries of opinion. In that vein he defined truth as the correspondence of a sign (in particular, a proposition) to its object and, pragmatically, not as actual consensus of some definite, finite community (such that to inquire would be to poll the experts), but instead as that final opinion which all investigators would reach sooner or later but still inevitably, if they were to push investigation far enough, even when they start from different points. In tandem he defined the real as a true sign's object (be that object a possibility or quality, or an actuality or brute fact, or a necessity or norm or law), which is what it is independently of any finite community's opinion and, pragmatically, depends only on the final opinion destined in a sufficient investigation. That is a destination as far, or near, as the truth itself to you or me or the given finite community. Thus, his theory of inquiry boils down to "Do the science." Those conceptions of truth and the real involve the idea of a community both without definite limits (and thus potentially self-correcting as far as needed) and capable of definite increase of knowledge. As inference, "logic is rooted in the social principle" since it depends on a standpoint that is, in a sense, unlimited. Paying special attention to the generation of explanations, Peirce outlined the scientific method as a coordination of three kinds of inference in a purposeful cycle aimed at settling doubts, as follows (in §III–IV in "A Neglected Argument" except as otherwise noted): - Abduction (or retroduction). Guessing, inference to explanatory hypotheses for selection of those best worth trying. From abduction, Peirce distinguishes induction as inferring, on the basis of tests, the proportion of truth in the hypothesis. Every inquiry, whether into ideas, brute facts, or norms and laws, arises from surprising observations in one or more of those realms (and for example at any stage of an inquiry already underway). All explanatory content of theories comes from abduction, which guesses a new or outside idea so as to account in a simple, economical way for a surprising or complicative phenomenon. Oftenest, even a well-prepared mind guesses wrong. But the modicum of success of our guesses far exceeds that of sheer luck and seems born of attunement to nature by instincts developed or inherent, especially insofar as best guesses are optimally plausible and simple in the sense, said Peirce, of the "facile and natural", as by Galileo's natural light of reason and as distinct from "logical simplicity". Abduction is the most fertile but least secure mode of inference. Its general rationale is inductive: it succeeds often enough and, without it, there is no hope of sufficiently expediting inquiry (often multi-generational) toward new truths. Coordinative method leads from abducing a plausible hypothesis to judging it for its testability and for how its trial would economize inquiry itself. Peirce calls his pragmatism "the logic of abduction". His pragmatic maxim is: "Consider what effects that might conceivably have practical bearings you conceive the objects of your conception to have. Then, your conception of those effects is the whole of your conception of the object". His pragmatism is a method of reducing conceptual confusions fruitfully by equating the meaning of any conception with the conceivable practical implications of its object's conceived effects—a method of experimentational mental reflection hospitable to forming hypotheses and conducive to testing them. It favors efficiency. The hypothesis, being insecure, needs to have practical implications leading at least to mental tests and, in science, lending themselves to scientific tests. A simple but unlikely guess, if uncostly to test for falsity, may belong first in line for testing. A guess is intrinsically worth testing if it has instinctive plausibility or reasoned objective probability, while subjective likelihood, though reasoned, can be misleadingly seductive. Guesses can be chosen for trial strategically, for their caution (for which Peirce gave as example the game of Twenty Questions), breadth, and incomplexity. One can hope to discover only that which time would reveal through a learner's sufficient experience anyway, so the point is to expedite it; the economy of research is what demands the leap, so to speak, of abduction and governs its art. - Deduction. Two stages: - Explication. Unclearly premissed, but deductive, analysis of the hypothesis in order to render its parts as clear as possible. - Demonstration: Deductive Argumentation, Euclidean in procedure. Explicit deduction of hypothesis's consequences as predictions, for induction to test, about evidence to be found. Corollarial or, if needed, Theorematic. - Induction. The long-run validity of the rule of induction is deducible from the principle (presuppositional to reasoning in general) that the real is only the object of the final opinion to which adequate investigation would lead; anything to which no such process would ever lead would not be real. Induction involving ongoing tests or observations follows a method which, sufficiently persisted in, will diminish its error below any predesignate degree. Three stages: - Classification. Unclearly premissed, but inductive, classing of objects of experience under general ideas. - Probation: direct inductive argumentation. Crude (the enumeration of instances) or gradual (new estimate of proportion of truth in the hypothesis after each test). Gradual induction is qualitative or quantitative; if qualitative, then dependent on weightings of qualities or characters; if quantitative, then dependent on measurements, or on statistics, or on countings. - Sentential Induction. "...which, by inductive reasonings, appraises the different probations singly, then their combinations, then makes self-appraisal of these very appraisals themselves, and passes final judgment on the whole result". Communication and community Frequently the scientific method is employed not only by a single person, but also by several people cooperating directly or indirectly. Such cooperation can be regarded as an important element of a scientific community. Various standards of scientific methodology are used within such an environment. Peer review evaluation Scientific journals use a process of peer review, in which scientists' manuscripts are submitted by editors of scientific journals to (usually one to three) fellow (usually anonymous) scientists familiar with the field for evaluation. In certain journals, the journal itself selects the referees; while in others (especially journals that are extremely specialized), the manuscript author might recommend referees. The referees may or may not recommend publication, or they might recommend publication with suggested modifications, or sometimes, publication in another journal. This standard is practiced to various degrees by different journals, and can have the effect of keeping the literature free of obvious errors and to generally improve the quality of the material, especially in the journals who use the standard most rigorously. The peer review process can have limitations when considering research outside the conventional scientific paradigm: problems of "groupthink" can interfere with open and fair deliberation of some new research. Documentation and replication Sometimes experimenters may make systematic errors during their experiments, veer from standard methods and practices (Pathological science) for various reasons, or, in rare cases, deliberately report false results. Occasionally because of this then, other scientists might attempt to repeat the experiments in order to duplicate the results. Researchers sometimes practice scientific data archiving, such as in compliance with the policies of government funding agencies and scientific journals. In these cases, detailed records of their experimental procedures, raw data, statistical analyses and source code can be preserved in order to provide evidence of the methodology and practice of the procedure and assist in any potential future attempts to reproduce the result. These procedural records may also assist in the conception of new experiments to test the hypothesis, and may prove useful to engineers who might examine the potential practical applications of a discovery. When additional information is needed before a study can be reproduced, the author of the study might be asked to provide it. They might provide it, or if the author refuses to share data, appeals can be made to the journal editors who published the study or to the institution which funded the research. Since it is impossible for a scientist to record everything that took place in an experiment, facts selected for their apparent relevance are reported. This may lead, unavoidably, to problems later if some supposedly irrelevant feature is questioned. For example, Heinrich Hertz did not report the size of the room used to test Maxwell's equations, which later turned out to account for a small deviation in the results. The problem is that parts of the theory itself need to be assumed in order to select and report the experimental conditions. The observations are hence sometimes described as being 'theory-laden'. Dimensions of practice The primary constraints on contemporary science are: - Publication, i.e. Peer review - Resources (mostly funding) It has not always been like this: in the old days of the "gentleman scientist" funding (and to a lesser extent publication) were far weaker constraints. Both of these constraints indirectly require scientific method – work that violates the constraints will be difficult to publish and difficult to get funded. Journals require submitted papers to conform to "good scientific practice" and to a degree this can be enforced by peer review. Originality, importance and interest are more important – see for example the author guidelines for Nature. Philosophy and sociology of science Philosophy of science looks at the underpinning logic of the scientific method, at what separates science from non-science, and the ethic that is implicit in science. There are basic assumptions, derived from philosophy by at least one prominent scientist, that form the base of the scientific method – namely, that reality is objective and consistent, that humans have the capacity to perceive reality accurately, and that rational explanations exist for elements of the real world. These assumptions from methodological naturalism form a basis on which science may be grounded. Logical Positivist, empiricist, falsificationist, and other theories have criticized these assumptions and given alternative accounts of the logic of science, but each has also itself been criticized. Thomas Kuhn examined the history of science in his The Structure of Scientific Revolutions, and found that the actual method used by scientists differed dramatically from the then-espoused method. His observations of science practice are essentially sociological and do not speak to how science is or can be practiced in other times and other cultures. Norwood Russell Hanson, Imre Lakatos and Thomas Kuhn have done extensive work on the "theory laden" character of observation. Hanson (1958) first coined the term for the idea that all observation is dependent on the conceptual framework of the observer, using the concept of gestalt to show how preconceptions can affect both observation and description. He opens Chapter 1 with a discussion of the Golgi bodies and their initial rejection as an artefact of staining technique, and a discussion of Brahe and Kepler observing the dawn and seeing a "different" sun rise despite the same physiological phenomenon. Kuhn and Feyerabend acknowledge the pioneering significance of his work. Kuhn (1961) said the scientist generally has a theory in mind before designing and undertaking experiments so as to make empirical observations, and that the "route from theory to measurement can almost never be traveled backward". This implies that the way in which theory is tested is dictated by the nature of the theory itself, which led Kuhn (1961, p. 166) to argue that "once it has been adopted by a profession ... no theory is recognized to be testable by any quantitative tests that it has not already passed". Paul Feyerabend similarly examined the history of science, and was led to deny that science is genuinely a methodological process. In his book Against Method he argues that scientific progress is not the result of applying any particular method. In essence, he says that for any specific method or norm of science, one can find a historic episode where violating it has contributed to the progress of science. Thus, if believers in scientific method wish to express a single universally valid rule, Feyerabend jokingly suggests, it should be 'anything goes'. Criticisms such as his led to the strong programme, a radical approach to the sociology of science. The postmodernist critiques of science have themselves been the subject of intense controversy. This ongoing debate, known as the science wars, is the result of conflicting values and assumptions between the postmodernist and realist camps. Whereas postmodernists assert that scientific knowledge is simply another discourse (note that this term has special meaning in this context) and not representative of any form of fundamental truth, realists in the scientific community maintain that scientific knowledge does reveal real and fundamental truths about reality. Many books have been written by scientists which take on this problem and challenge the assertions of the postmodernists while defending science as a legitimate method of deriving truth. Role of chance in discovery Somewhere between 33% and 50% of all scientific discoveries are estimated to have been stumbled upon, rather than sought out. This may explain why scientists so often express that they were lucky. Louis Pasteur is credited with the famous saying that "Luck favours the prepared mind", but some psychologists have begun to study what it means to be 'prepared for luck' in the scientific context. Research is showing that scientists are taught various heuristics that tend to harness chance and the unexpected. This is what Nassim Nicholas Taleb calls "Anti-fragility"; while some systems of investigation are fragile in the face of human error, human bias, and randomness, the scientific method is more than resistant or tough – it actually benefits from such randomness in many ways (it is anti-fragile). Taleb believes that the more anti-fragile the system, the more it will flourish in the real world. Psychologist Kevin Dunbar says the process of discovery often starts with researchers finding bugs in their experiments. These unexpected results lead researchers to try to fix what they think is an error in their method. Eventually, the researcher decides the error is too persistent and systematic to be a coincidence. The highly controlled, cautious and curious aspects of the scientific method are thus what make it well suited for identifying such persistent systematic errors. At this point, the researcher will begin to think of theoretical explanations for the error, often seeking the help of colleagues across different domains of expertise. \|\|The following text needs to be harmonized with text in History of scientific method. \|\|This section may contain an excessive amount of intricate detail that may only interest a specific audience. (June 2015)\| The development of the scientific method emerges in the history of science itself. Ancient Egyptian documents describe empirical methods in astronomy, mathematics, and medicine. The Greeks made contributions to the scientific method, most notably through Aristotle in his six works of logic collected as the Organon. Aristotle's inductive-deductive method used inductions from observations to infer general principles, deductions from those principles to check against further observations, and more cycles of induction and deduction to continue the advance of knowledge According to Karl Popper, Parmenides (fl. 5th century BCE) had conceived an axiomatic-deductive methodAccording to David Lindberg, Aristotle (4th century BCE) wrote about the scientific method even if he and his followers did not actually follow what he said. Lindberg also notes that Ptolemy (2nd century CE) and Ibn al-Haytham (11th century CE) are among the early examples of people who carried out scientific experiments. Also, John Losee writes that "the Physics and the Metaphysics contain discussions of certain aspects of scientific method", of which, he says "Aristotle viewed scientific inquiry as a progression from observations to general principles and back to observations." Early Christian leaders such as Clement of Alexandria (150–215) and Basil of Caesarea (330–379) encouraged future generations to view the Greek wisdom as "handmaidens to theology" and science was considered a means to more accurate understanding of the Bible and of God. Augustine of Hippo (354–430) who contributed great philosophical wealth to the Latin Middle Ages, advocated the study of science and was wary of philosophies that disagreed with the Bible, such as astrology and the Greek belief that the world had no beginning. This Christian accommodation with Greek science "laid a foundation for the later widespread, intensive study of natural philosophy during the Late Middle Ages." However, the division of Latin-speaking Western Europe from the Greek-speaking East, followed by barbarian invasions, the Plague of Justinian, and the Islamic conquests, resulted in the West largely losing access to Greek wisdom. By the 8th century Islam had conquered the Christian lands of Syria, Iraq, Iran and Egypt This swift conquest further severed Western Europe from many of the great works of Aristotle, Plato, Euclid and others, many of which were housed in the great library of Alexandria. Having come upon such a wealth of knowledge, the Arabs, who viewed non-Arab languages as inferior, even as a source of pollution, employed conquered Christians and Jews to translate these works from the native Greek and Syriac into Arabic Thus equipped, Arab philosopher Alhazen (Ibn al-Haytham) performed optical and physiological experiments, reported in his manifold works, the most famous being Book of Optics (1021). He was thus a forerunner of scientific method, having understood that a controlled environment involving experimentation and measurement is required in order to draw educated conclusions. Other Arab polymaths of the same era produced copious works on mathematics, philosophy, astronomy and alchemy. Most stuck closely to Aristotle, being hesitant to admit that some of Aristotle's thinking was errant, while others strongly criticized him. During these years, occasionally a paraphrased translation from the Arabic, which itself had been translated from Greek and Syriac, might make its way to the West for scholarly study. It was not until 1204, during which the Latins conquered and took Constantinople from the Byzantines in the name of the fourth Crusade, that a renewed scholarly interest in the original Greek manuscripts began to grow. Due to the new easier access to the libraries of Constantinople by Western scholars, a certain revival in the study and analysis of the original Greek texts by Western scholars began. From that point a functional scientific method that would launch modern science was on the horizon. Grosseteste (1175–1253), an English statesman, scientist and Christian theologian, was "the principal figure" in bringing about "a more adequate method of scientific inquiry" by which "medieval scientists were able eventually to outstrip their ancient European and Muslim teachers" (Dales 1973:62). ... His thinking influenced Roger Bacon, who spread Grosseteste's ideas from Oxford to the University of Paris during a visit there in the 1240s. From the prestigious universities in Oxford and Paris, the new experimental science spread rapidly throughout the medieval universities: "And so it went to Galileo, William Gilbert, Francis Bacon, William Harvey, Descartes, Robert Hooke, Newton, Leibniz, and the world of the seventeenth century" (Crombie 1962:15). So it went to us as well.\| Hugh G. Gauch, 2003. Roger Bacon (1214–1294), an English thinker and experimenter, is recognized by many to be the father of modern scientific method. His view that mathematics was essential to a correct understanding of natural philosophy was considered to be 400 years ahead of its time. He was viewed as "a lone genius proclaiming the truth about time," having correctly calculated the calendar His work in optics provided the platform on which Newton, Descartes, Huygens and others later transformed the science of light. Bacon's groundbreaking advances were due largely to his discovery that experimental science must be based on mathematics. (186–187) His works Opus Majus and De Speculis Comburentibus contain many "carefully drawn diagrams showing Bacon's meticulous investigations into the behavior of light." He gives detailed descriptions of systematic studies using prisms and measurements by which he shows how a rainbow functions. Others who advanced scientific method during this era included Albertus Magnus (c. 1193 – 1280), Theodoric of Freiberg, (c. 1250 – c. 1310), William of Ockham (c. 1285 – c. 1350), and Jean Buridan (c. 1300 – c. 1358). These were not only scientists but leaders of the church – Christian archbishops, friars and priests. By the late 15th century, the physician-scholar Niccolò Leoniceno was finding errors in Pliny's Natural History. As a physician, Leoniceno was concerned about these botanical errors propagating to the materia medica on which medicines were based. To counter this, a botanical garden was established at Orto botanico di Padova, University of Padua (in use for teaching by 1546), in order that medical students might have empirical access to the plants of a pharmacopia. The philosopher and physician Francisco Sanches was led by his medical training at Rome, 1571–73, and by the philosophical skepticism recently placed in the European mainstream by the publication of Sextus Empiricus' "Outlines of Pyrrhonism", to search for a true method of knowing (modus sciendi), as nothing clear can be known by the methods of Aristotle and his followers – for example, syllogism fails upon circular reasoning. Following the physician Galen's method of medicine, Sanches lists the methods of judgement and experience, which are faulty in the wrong hands, and we are left with the bleak statement That Nothing is Known (1581). This challenge was taken up by René Descartes in the next generation (1637), but at the least, Sanches warns us that we ought to refrain from the methods, summaries, and commentaries on Aristotle, if we seek scientific knowledge. In this, he is echoed by Francis Bacon, also influenced by skepticism; Sanches cites the humanist Juan Luis Vives who sought a better educational system, as well as a statement of human rights as a pathway for improvement of the lot of the poor. The modern scientific method crystallized no later than in the 17th and 18th centuries. In his work Novum Organum (1620) – a reference to Aristotle's Organon – Francis Bacon outlined a new system of logic to improve upon the old philosophical process of syllogism. Then, in 1637, René Descartes established the framework for scientific method's guiding principles in his treatise, Discourse on Method. The writings of Alhazen, Bacon and Descartes are considered critical in the historical development of the modern scientific method, as are those of John Stuart Mill. In the late 19th century, Charles Sanders Peirce proposed a schema that would turn out to have considerable influence in the development of current scientific methodology generally. Peirce accelerated the progress on several fronts. Firstly, speaking in broader context in "How to Make Our Ideas Clear" (1878), Peirce outlined an objectively verifiable method to test the truth of putative knowledge on a way that goes beyond mere foundational alternatives, focusing upon both deduction and induction. He thus placed induction and deduction in a complementary rather than competitive context (the latter of which had been the primary trend at least since David Hume, who wrote in the mid-to-late 18th century). Secondly, and of more direct importance to modern method, Peirce put forth the basic schema for hypothesis/testing that continues to prevail today. Extracting the theory of inquiry from its raw materials in classical logic, he refined it in parallel with the early development of symbolic logic to address the then-current problems in scientific reasoning. Peirce examined and articulated the three fundamental modes of reasoning that, as discussed above in this article, play a role in inquiry today, the processes that are currently known as abductive, deductive, and inductive inference. Thirdly, he played a major role in the progress of symbolic logic itself – indeed this was his primary specialty. Beginning in the 1930s, Karl Popper argued that there is no such thing as inductive reasoning. All inferences ever made, including in science, are purely deductive according to this view. Accordingly, he claimed that the empirical character of science has nothing to do with induction – but with the deductive property of falsifiability that scientific hypotheses have. Contrasting his views with inductivism and positivism, he even denied the existence of the scientific method: "(1) There is no method of discovering a scientific theory (2) There is no method for ascertaining the truth of a scientific hypothesis, i.e., no method of verification; (3) There is no method for ascertaining whether a hypothesis is 'probable', or probably true". Instead, he held that there is only one universal method, a method not particular to science: The negative method of criticism, or colloquially termed trial and error. It covers not only all products of the human mind, including science, mathematics, philosophy, art and so on, but also the evolution of life. Following Peirce and others, Popper argued that science is fallible and has no authority. In contrast to empiricist-inductivist views, he welcomed metaphysics and philosophical discussion and even gave qualified support to myths and pseudosciences. Popper's view has become known as critical rationalism. Although science in a broad sense existed before the modern era, and in many historical civilizations (as described above), modern science is so distinct in its approach and successful in its results that it now defines what science is in the strictest sense of the term. Relationship with mathematics Science is the process of gathering, comparing, and evaluating proposed models against observables. A model can be a simulation, mathematical or chemical formula, or set of proposed steps. Science is like mathematics in that researchers in both disciplines can clearly distinguish what is known from what is unknown at each stage of discovery. Models, in both science and mathematics, need to be internally consistent and also ought to be falsifiable (capable of disproof). In mathematics, a statement need not yet be proven; at such a stage, that statement would be called a conjecture. But when a statement has attained mathematical proof, that statement gains a kind of immortality which is highly prized by mathematicians, and for which some mathematicians devote their lives. Mathematical work and scientific work can inspire each other. For example, the technical concept of time arose in science, and timelessness was a hallmark of a mathematical topic. But today, the Poincaré conjecture has been proven using time as a mathematical concept in which objects can flow (see Ricci flow). Nevertheless, the connection between mathematics and reality (and so science to the extent it describes reality) remains obscure. Eugene Wigner's paper, The Unreasonable Effectiveness of Mathematics in the Natural Sciences, is a very well known account of the issue from a Nobel Prize-winning physicist. In fact, some observers (including some well known mathematicians such as Gregory Chaitin, and others such as Lakoff and Núñez) have suggested that mathematics is the result of practitioner bias and human limitation (including cultural ones), somewhat like the post-modernist view of science. George Pólya's work on problem solving, the construction of mathematical proofs, and heuristic show that the mathematical method and the scientific method differ in detail, while nevertheless resembling each other in using iterative or recursive steps. \|Mathematical method\|\|Scientific method\| \|1\|\|Understanding\|\|Characterization from experience and observation\| \|2\|\|Analysis\|\|Hypothesis: a proposed explanation\| \|3\|\|Synthesis\|\|Deduction: prediction from the hypothesis\| \|4\|\|Review/Extend\|\|Test and experiment\| In Pólya's view, understanding involves restating unfamiliar definitions in your own words, resorting to geometrical figures, and questioning what we know and do not know already; analysis, which Pólya takes from Pappus, involves free and heuristic construction of plausible arguments, working backward from the goal, and devising a plan for constructing the proof; synthesis is the strict Euclidean exposition of step-by-step details of the proof; review involves reconsidering and re-examining the result and the path taken to it. Imre Lakatos argued that mathematicians actually use contradiction, criticism and revision as principles for improving their work. In like manner to science, where truth is sought, but certainty is not found, in Proofs and refutations (1976), what Lakatos tried to establish was that no theorem of informal mathematics is final or perfect. This means that we should not think that a theorem is ultimately true, only that no counterexample has yet been found. Once a counterexample, i.e. an entity contradicting/not explained by the theorem is found, we adjust the theorem, possibly extending the domain of its validity. This is a continuous way our knowledge accumulates, through the logic and process of proofs and refutations. (If axioms are given for a branch of mathematics, however, Lakatos claimed that proofs from those axioms were tautological, i.e. logically true, by rewriting them, as did Poincaré (Proofs and Refutations, 1976).) Lakatos proposed an account of mathematical knowledge based on Polya's idea of heuristics. In Proofs and Refutations, Lakatos gave several basic rules for finding proofs and counterexamples to conjectures. He thought that mathematical 'thought experiments' are a valid way to discover mathematical conjectures and proofs. Problems and issues History, philosophy, sociology - Goldhaber & Nieto 2010, p. 940 - " Rules for the study of natural philosophy", Newton transl 1999, pp. 794–6, after Book 3, The System of the World. - From the Oxford English Dictionary definition for "scientific". - Peirce (1908), "A Neglected Argument for the Reality of God", Hibbert Journal v. 7, pp. 90–112. s:A Neglected Argument for the Reality of God with added notes. Reprinted with previously unpublished part, Collected Papers v. 6, paragraphs 452-85, The Essential Peirce v. 2, pp. 434–50, and elsewhere. - See, for example, Galileo 1638. His thought experiments disprove Aristotle's physics of falling bodies, in Two New Sciences. - Popper 1959:p273 - Karl R. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge, Routledge, 2003 ISBN 0-415-28594-1 - Gauch, Hugh G. (2003). Scientific Method in Practice (Reprint ed.). Cambridge University Press. p. 3. ISBN 9780521017084. Retrieved 2015-01-26. The scientific method 'is often misrepresented as a fixed sequence of steps,' rather than being seen for what it truly is, 'a highly variable and creative process' (AAAS 2000:18). The claim here is that science has general principles that must be mastered to increase productivity and enhance perspective, not that these principles provide a simple and automated sequence of steps to follow. - History of Inductive Science (1837), and in Philosophy of Inductive Science (1840) - Jim Al-Khalili (4 January 2009). "The 'first true scientist'". BBC News. - Tracey Tokuhama-Espinosa (2010). Mind, Brain, and Education Science: A Comprehensive Guide to the New Brain-Based Teaching. W. W. Norton & Company. p. 39. ISBN 9780393706079. Alhazen (or Al-Haytham; 965–1039 C.E.) was perhaps one of the greatest physicists of all times and a product of the Islamic Golden Age or Islamic Renaissance (7th–13th centuries). He made significant contributions to anatomy, astronomy, engineering, mathematics, medicine, ophthalmology, philosophy, physics, psychology, and visual perception and is primarily attributed as the inventor of the scientific method, for which author Bradley Steffens (2006) describes him as the "first scientist". - Peirce, C. S., Collected Papers v. 1, paragraph 74. - Morris Kline (1985) Mathematics for the nonmathematician. Courier Dover Publications. p. 284. ISBN 0-486-24823-2 - Shapere, Dudley (1974). Galileo: A Philosophical Study. University of Chicago Press. ISBN 0-226-75007-8. - " The thesis of this book, as set forth in Chapter One, is that there are general principles applicable to all the sciences." __ Gauch 2003, p. xv - Peirce (1877), "The Fixation of Belief", Popular Science Monthly, v. 12, pp. 1–15. Reprinted often, including (Collected Papers of Charles Sanders Peirce v. 5, paragraphs 358–87), (The Essential Peirce, v. 1, pp. 109–23). Peirce.org Eprint. Wikisource Eprint. - Gauch 2003, p. 1 The scientific method can function in the same way; This is the principle of noncontradiction. - Francis Bacon(1629) New Organon, lists 4 types of error: Idols of the tribe (error due to the entire human race), the cave (errors due to an individual's own intellect), the marketplace (errors due to false words), and the theater (errors due to incredulous acceptance). - Peirce, C. S., Collected Papers v. 5, in paragraph 582, from 1898: ... [rational] inquiry of every type, fully carried out, has the vital power of self-correction and of growth. This is a property so deeply saturating its inmost nature that it may truly be said that there is but one thing needful for learning the truth, and that is a hearty and active desire to learn what is true. - Taleb contributes a brief description of anti-fragility, http://www.edge.org/q2011/q11_3.html - For example, the concept of falsification (first proposed in 1934) formalizes the attempt to disprove hypotheses rather than prove them. Karl R. Popper (1963), 'The Logic of Scientific Discovery'. The Logic of Scientific Discovery pp. 17–20, 249–252, 437–438, and elsewhere. - Leon Lederman, for teaching physics first, illustrates how to avoid confirmation bias: Ian Shelton, in Chile, was initially skeptical that supernova 1987a was real, but possibly an artifact of instrumentation (null hypothesis), so he went outside and disproved his null hypothesis by observing SN 1987a with the naked eye. The Kamiokande experiment, in Japan, independently observed neutrinos from SN 1987a at the same time. - Lindberg 2007, pp. 2–3: "There is a danger that must be avoided. ... If we wish to do justice to the historical enterprise, we must take the past for what it was. And that means we must resist the temptation to scour the past for examples or precursors of modern science. ...My concern will be with the beginnings of scientific theories, the methods by which they were formulated, and the uses to which they were put; ... " - "How does light travel through transparent bodies? Light travels through transparent bodies in straight lines only.... We have explained this exhaustively in our Book of Optics. But let us now mention something to prove this convincingly: the fact that light travels in straight lines is clearly observed in the lights which enter into dark rooms through holes.... [T]he entering light will be clearly observable in the dust which fills the air. – Alhazen, translated into English from German by M. Schwarz, from "Abhandlung über das Licht", J. Baarmann (ed. 1882) Zeitschrift der Deutschen Morgenländischen Gesellschaft Vol 36 as quoted in Sambursky 1974, p. 136. - He demonstrated his conjecture that "light travels through transparent bodies in straight lines only" by placing a straight stick or a taut thread next to the light beam, as quoted in Sambursky 1974, p. 136 to prove that light travels in a straight line. - David Hockney, (2001, 2006) in Secret Knowledge: rediscovering the lost techniques of the old masters ISBN 0-14-200512-6 (expanded edition) cites Alhazen several times as the likely source for the portraiture technique using the camera obscura, which Hockney rediscovered with the aid of an optical suggestion from Charles M. Falco. Kitab al-Manazir, which is Alhazen's Book of Optics, at that time denoted Opticae Thesaurus, Alhazen Arabis, was translated from Arabic into Latin for European use as early as 1270. Hockney cites Friedrich Risner's 1572 Basle edition of Opticae Thesaurus. Hockney quotes Alhazen as the first clear description of the camera obscura in Hockney, p. 240. - Galilei, Galileo (1638), Discorsi e Dimonstrazioni Matematiche, intorno a due nuoue scienze, Leida: Apresso gli Elsevirri, ISBN 0-486-60099-8, Dover reprint of the 1914 Macmillan translation by Henry Crew and Alfonso de Salvio of Two New Sciences, Galileo Galilei Linceo (1638). Additional publication information is from the collection of first editions of the Library of Congress surveyed by Bruno 1989, pp. 261–264. - Godfrey-Smith 2003 p. 236. - Gauch 2003, p. 3 - Schuster and Powers (2005), Translational and Experimental Clinical Research, Ch. 1. Link. This chapter also discusses the different types of research questions and how they are produced. - This phrasing is attributed to Marshall Nirenberg. - Note: for a discussion of multiple hypotheses, see Bayesian inference#Informal - October 1951, as noted in McElheny 2004, p. 40:"That's what a helix should look like!" Crick exclaimed in delight (This is the Cochran-Crick-Vand-Stokes theory of the transform of a helix). - June 1952, as noted in McElheny 2004, p. 43: Watson had succeeded in getting X-ray pictures of TMV showing a diffraction pattern consistent with the transform of a helix. - Watson did enough work on Tobacco mosaic virus to produce the diffraction pattern for a helix, per Crick's work on the transform of a helix. pp. 137–138, Horace Freeland Judson (1979) The Eighth Day of Creation ISBN 0-671-22540-5 - – Cochran W, Crick FHC and Vand V. (1952) "The Structure of Synthetic Polypeptides. I. The Transform of Atoms on a Helix", Acta Cryst., 5, 581–586. - Friday, January 30, 1953. Tea time, as noted in McElheny 2004, p. 52: Franklin confronts Watson and his paper – "Of course it [Pauling's pre-print] is wrong. DNA is not a helix." However, Watson then visits Wilkins' office, sees photo 51, and immediately recognizes the diffraction pattern of a helical structure. But additional questions remained, requiring additional iterations of their research. For example, the number of strands in the backbone of the helix (Crick suspected 2 strands, but cautioned Watson to examine that more critically), the location of the base pairs (inside the backbone or outside the backbone), etc. One key point was that they realized that the quickest way to reach a result was not to continue a mathematical analysis, but to build a physical model. - "The instant I saw the picture my mouth fell open and my pulse began to race." – Watson 1968, p. 167 Page 168 shows the X-shaped pattern of the B-form of DNA, clearly indicating crucial details of its helical structure to Watson and Crick. - McElheny 2004 p.52 dates the Franklin-Watson confrontation as Friday, January 30, 1953. Later that evening, Watson urges Wilkins to begin model-building immediately. But Wilkins agrees to do so only after Franklin's departure. - Saturday, February 28, 1953, as noted in McElheny 2004, pp. 57–59: Watson found the base pairing mechanism which explained Chargaff's rules using his cardboard models. - Galileo Galilei (1638) Two new sciences - Reconstruction of Galileo Galilei's experiment - the inclined plane - In Two new sciences, there are three 'reviewers': Simplicio, Sagredo, and Salviati, who serve as foil, antagonist, and protagonist. Galileo speaks for himself only briefly. But note that Einstein's 1905 papers were not peer reviewed before their publication. - Fleck 1979, pp. xxvii–xxviii - "NIH Data Sharing Policy." - Stanovich, Keith E. (2007). How to Think Straight About Psychology. Boston: Pearson Education. pg 123 - Brody 1993, pp. 44–45 - Hall, B. K.; Hallgrímsson, B., eds. (2008). Strickberger's Evolution (4th ed.). Jones & Bartlett. p. 762. ISBN 0-7637-0066-5. - Cracraft, J.; Donoghue, M. J., eds. (2005). Assembling the tree of life. Oxford University Press. p. 592. ISBN 0-19-517234-5. - Needham & Wang 1954 p.166 shows how the 'flying gallop' image propagated from China to the West. - "A myth is a belief given uncritical acceptance by members of a group ..." – Weiss, Business Ethics p. 15, as cited by Ronald R. Sims (2003) Ethics and corporate social responsibility: why giants fall p.21 - Imre Lakatos (1976), Proofs and Refutations. Taleb 2007, p. 72 lists ways to avoid narrative fallacy and confirmation bias. - For more on the narrative fallacy, see also Fleck 1979, p. 27: "Words and ideas are originally phonetic and mental equivalences of the experiences coinciding with them. ... Such proto-ideas are at first always too broad and insufficiently specialized. ... Once a structurally complete and closed system of opinions consisting of many details and relations has been formed, it offers enduring resistance to anything that contradicts it." - The scientific method requires testing and validation a posteriori before ideas are accepted. "Invariably one came up against fundamental physical limits to the accuracy of measurement. ... The art of physical measurement seemed to be a matter of compromise, of choosing between reciprocally related uncertainties. ... Multiplying together the conjugate pairs of uncertainty limits mentioned, however, I found that they formed invariant products of not one but two distinct kinds. ... The first group of limits were calculable a priori from a specification of the instrument. The second group could be calculated only a posteriori from a specification of what was done with the instrument. ... In the first case each unit [of information] would add one additional dimension (conceptual category), whereas in the second each unit would add one additional atomic fact.", – pp. 1–4: MacKay, Donald M. (1969), Information, Mechanism, and Meaning, Cambridge, MA: MIT Press, ISBN 0-262-63-032-X - See the hypothethico-deductive method, for example, Godfrey-Smith 2003, p. 236. - Jevons 1874, pp. 265–6. - pp. 65,73, 92, 398 – Andrew J. Galambos, Sic Itur ad Astra ISBN 0-88078-004-5(AJG learned scientific method from Felix Ehrenhaft - Galileo 1638, pp. v–xii,1–300 - Brody 1993, pp. 10–24 calls this the "epistemic cycle": "The epistemic cycle starts from an initial model; iterations of the cycle then improve the model until an adequate fit is achieved." - Iteration example: Chaldean astronomers such as Kidinnu compiled astronomical data. Hipparchus was to use this data to calculate the precession of the Earth's axis. Fifteen hundred years after Kidinnu, Al-Batani, born in what is now Turkey, would use the collected data and improve Hipparchus' value for the precession of the Earth's axis. Al-Batani's value, 54.5 arc-seconds per year, compares well to the current value of 49.8 arc-seconds per year (26,000 years for Earth's axis to round the circle of nutation). - Recursion example: the Earth is itself a magnet, with its own North and South Poles William Gilbert (in Latin 1600) De Magnete, or On Magnetism and Magnetic Bodies. Translated from Latin to English, selection by Moulton & Schifferes 1960, pp. 113–117. Gilbert created a terrella, a lodestone ground into a spherical shape, which served as Gilbert's model for the Earth itself, as noted in Bruno 1989, p. 277. - "The foundation of general physics ... is experience. These ... everyday experiences we do not discover without deliberately directing our attention to them. Collecting information about these is observation." – Hans Christian Ørsted("First Introduction to General Physics" ¶13, part of a series of public lectures at the University of Copenhagen. Copenhagen 1811, in Danish, printed by Johan Frederik Schulz. In Kirstine Meyer's 1920 edition of Ørsted's works, vol.III pp. 151–190. ) "First Introduction to Physics: the Spirit, Meaning, and Goal of Natural Science". Reprinted in German in 1822, Schweigger's Journal für Chemie und Physik 36, pp. 458–488, as translated in Ørsted 1997, p. 292 - "When it is not clear under which law of nature an effect or class of effect belongs, we try to fill this gap by means of a guess. Such guesses have been given the name conjectures or hypotheses." – Hans Christian Ørsted(1811) "First Introduction to General Physics" as translated in Ørsted 1997, p. 297. - "In general we look for a new law by the following process. First we guess it. ...", – Feynman 1965, p. 156 - "... the statement of a law – A depends on B – always transcends experience." – Born 1949, p. 6 - "The student of nature ... regards as his property the experiences which the mathematician can only borrow. This is why he deduces theorems directly from the nature of an effect while the mathematician only arrives at them circuitously." – Hans Christian Ørsted(1811) "First Introduction to General Physics" ¶17. as translated in Ørsted 1997, p. 297. - Salviati speaks: "I greatly doubt that Aristotle ever tested by experiment whether it be true that two stones, one weighing ten times as much as the other, if allowed to fall, at the same instant, from a height of, say, 100 cubits, would so differ in speed that when the heavier had reached the ground, the other would not have fallen more than 10 cubits." Two New Sciences (1638) – Galileo 1638, pp. 61–62. A more extended quotation is referenced by Moulton & Schifferes 1960, pp. 80–81. - In the inquiry-based education paradigm, the stage of "characterization, observation, definition, ..." is more briefly summed up under the rubric of a Question - "To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advance in science." – Einstein & Infeld 1938, p. 92. - Crawford S, Stucki L (1990), "Peer review and the changing research record", "J Am Soc Info Science", vol. 41, pp. 223–228 - See, e.g., Gauch 2003, esp. chapters 5–8 - Cartwright, Nancy (1983), How the Laws of Physics Lie. Oxford: Oxford University Press. ISBN 0-19-824704-4 - Andreas Vesalius, Epistola, Rationem, Modumque Propinandi Radicis Chynae Decocti (1546), 141. Quoted and translated in C.D. O'Malley, Andreas Vesalius of Brussels, (1964), 116. As quoted by Bynum & Porter 2005, p. 597: Andreas Vesalius,597#1. - Crick, Francis (1994), The Astonishing Hypothesis ISBN 0-684-19431-7 p.20 - McElheny 2004 p.34 - Glen 1994, pp. 37–38. - "The structure that we propose is a three-chain structure, each chain being a helix" – Linus Pauling, as quoted on p. 157 by Horace Freeland Judson (1979), The Eighth Day of Creation ISBN 0-671-22540-5 - McElheny 2004, pp. 49–50: January 28, 1953 – Watson read Pauling's pre-print, and realized that in Pauling's model, DNA's phosphate groups had to be un-ionized. But DNA is an acid, which contradicts Pauling's model. - June 1952. as noted in McElheny 2004, p. 43: Watson had succeeded in getting X-ray pictures of TMV showing a diffraction pattern consistent with the transform of a helix. - McElheny 2004 p.68: Nature April 25, 1953. - In March 1917, the Royal Astronomical Society announced that on May 29, 1919, the occasion of a total eclipse of the sun would afford favorable conditions for testing Einstein's General theory of relativity. One expedition, to Sobral, Ceará, Brazil, and Eddington's expedition to the island of Principe yielded a set of photographs, which, when compared to photographs taken at Sobral and at Greenwich Observatory showed that the deviation of light was measured to be 1.69 arc-seconds, as compared to Einstein's desk prediction of 1.75 arc-seconds. – Antonina Vallentin (1954), Einstein, as quoted by Samuel Rapport and Helen Wright (1965), Physics, New York: Washington Square Press, pp 294–295. - Mill, John Stuart, "A System of Logic", University Press of the Pacific, Honolulu, 2002, ISBN 1-4102-0252-6. - al-Battani, De Motu Stellarum translation from Arabic to Latin in 1116, as cited by "Battani, al-" (c. 858 – 929) Encyclopædia Britannica, 15th. ed. Al-Battani is known for his accurate observations at al-Raqqah in Syria, beginning in 877. His work includes measurement of the annual precession of the equinoxes. - McElheny 2004 p.53: The weekend (January 31 – February 1) after seeing photo 51, Watson informed Bragg of the X-ray diffraction image of DNA in B form. Bragg gave them permission to restart their research on DNA (that is, model building). - McElheny 2004 p.54: On Sunday February 8, 1953, Maurice Wilkes gave Watson and Crick permission to work on models, as Wilkes would not be building models until Franklin left DNA research. - McElheny 2004 p.56: Jerry Donohue, on sabbatical from Pauling's lab and visiting Cambridge, advises Watson that textbook form of the base pairs was incorrect for DNA base pairs; rather, the keto form of the base pairs should be used instead. This form allowed the bases' hydrogen bonds to pair 'unlike' with 'unlike', rather than to pair 'like' with 'like', as Watson was inclined to model, on the basis of the textbook statements. On February 27, 1953, Watson was convinced enough to make cardboard models of the nucleotides in their keto form. - "Suddenly I became aware that an adenine-thymine pair held together by two hydrogen bonds was identical in shape to a guanine-cytosine pair held together by at least two hydrogen bonds. ..." – Watson 1968, pp. 194–197. - McElheny 2004 p.57 Saturday, February 28, 1953, Watson tried 'like with like' and admitted these base pairs didn't have hydrogen bonds that line up. But after trying 'unlike with unlike', and getting Jerry Donohue's approval, the base pairs turned out to be identical in shape (as Watson stated above in his 1968 Double Helix memoir quoted above). Watson now felt confident enough to inform Crick. (Of course, 'unlike with unlike' increases the number of possible codons, if this scheme were a genetic code.) - See, e.g., Physics Today, 59(1), p42. Richmann electrocuted in St. Petersburg (1753) - Aristotle, "Prior Analytics", Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938. - "What one does not in the least doubt one should not pretend to doubt; but a man should train himself to doubt," said Peirce in a brief intellectual autobiography; see Ketner, Kenneth Laine (2009) "Charles Sanders Peirce: Interdisciplinary Scientist" in The Logic of Interdisciplinarity). Peirce held that actual, genuine doubt originates externally, usually in surprise, but also that it is to be sought and cultivated, "provided only that it be the weighty and noble metal itself, and no counterfeit nor paper substitute"; in "Issues of Pragmaticism", The Monist, v. XV, n. 4, pp. 481–99, see p. 484, and p. 491. (Reprinted in Collected Papers v. 5, paragraphs 438-63, see 443 and 451). - But see Scientific method and religion. - Peirce (1898), "Philosophy and the Conduct of Life", Lecture 1 of the Cambridge (MA) Conferences Lectures, published in Collected Papers v. 1, paragraphs 616-48 in part and in Reasoning and the Logic of Things, Ketner (ed., intro.) and Putnam (intro., comm.), pp. 105–22, reprinted in Essential Peirce v. 2, pp. 27–41. - " ... in order to learn, one must desire to learn ..." – Peirce (1899), "F.R.L." [First Rule of Logic], Collected Papers v. 1, paragraphs 135-40, Eprint at the Wayback Machine (archived January 6, 2012) - Peirce (1877), "How to Make Our Ideas Clear", Popular Science Monthly, v. 12, pp. 286–302. Reprinted often, including Collected Papers v. 5, paragraphs 388–410, Essential Peirce v. 1, pp. 124–41. ArisbeEprint. Wikisource Eprint. - Peirce (1868), "Some Consequences of Four Incapacities", Journal of Speculative Philosophy v. 2, n. 3, pp. 140–57. Reprinted Collected Papers v. 5, paragraphs 264–317, The Essential Peirce v. 1, pp. 28–55, and elsewhere. Arisbe Eprint - Peirce (1878), "The Doctrine of Chances", Popular Science Monthly v. 12, pp. 604–15, see pp. 610-11 via Internet Archive. Reprinted Collected Papers v. 2, paragraphs 645-68, Essential Peirce v. 1, pp. 142–54. "...death makes the number of our risks, the number of our inferences, finite, and so makes their mean result uncertain. The very idea of probability and of reasoning rests on the assumption that this number is indefinitely great. .... ...logicality inexorably requires that our interests shall not be limited. .... Logic is rooted in the social principle." - Peirce (c. 1906), "PAP (Prolegomena for an Apology to Pragmatism)" (Manuscript 293, not the like-named article), The New Elements of Mathematics (NEM) 4:319–320, see first quote under "Abduction" at Commens Dictionary of Peirce's Terms. - Peirce, Carnegie application (L75, 1902), New Elements of Mathematics v. 4, pp. 37–38: For it is not sufficient that a hypothesis should be a justifiable one. Any hypothesis which explains the facts is justified critically. But among justifiable hypotheses we have to select that one which is suitable for being tested by experiment. - Peirce (1902), Carnegie application, see MS L75.329–330, from Draft D of Memoir 27: Consequently, to discover is simply to expedite an event that would occur sooner or later, if we had not troubled ourselves to make the discovery. Consequently, the art of discovery is purely a question of economics. The economics of research is, so far as logic is concerned, the leading doctrine with reference to the art of discovery. Consequently, the conduct of abduction, which is chiefly a question of heuretic and is the first question of heuretic, is to be governed by economical considerations. - Peirce (1903), "Pragmatism – The Logic of Abduction", Collected Papers v. 5, paragraphs 195–205, especially 196. Eprint. - Peirce, "On the Logic of Drawing Ancient History from Documents", Essential Peirce v. 2, see pp. 107–9. On Twenty Questions, p. 109: Thus, twenty skillful hypotheses will ascertain what 200,000 stupid ones might fail to do. - Peirce (1878), "The Probability of Induction", Popular Science Monthly, v. 12, pp. 705–18, see 718 Google Books; 718 via Internet Archive. Reprinted often, including (Collected Papers v. 2, paragraphs 669-93), (The Essential Peirce v. 1, pp. 155–69). - Peirce (1905 draft "G" of "A Neglected Argument"), "Crude, Quantitative, and Qualitative Induction", Collected Papers v. 2, paragraphs 755–760, see 759. Find under "Induction" at Commens Dictionary of Peirce's Terms. - . Brown, C. (2005) Overcoming Barriers to Use of Promising Research Among Elite Middle East Policy Groups, Journal of Social Behaviour and Personality, Select Press. - Einstein, Albert (1936, 1956) One may say "the eternal mystery of the world is its comprehensibility." From the article "Physics and Reality" (1936), reprinted in Out of My Later Years (1956). 'It is one of the great realizations of Immanuel Kant that the setting up of a real external world would be senseless without this comprehensibility.' - Hanson, Norwood (1958), Patterns of Discovery, Cambridge University Press, ISBN 0-521-05197-5 - Kuhn 1962, p. 113 ISBN 978-1-4432-5544-8 - Feyerabend, Paul K (1960) "Patterns of Discovery" The Philosophical Review (1960) vol. 69 (2) pp. 247–252 - Kuhn, Thomas S., "The Function of Measurement in Modern Physical Science", ISIS 52(2), 161–193, 1961. - Feyerabend, Paul K., Against Method, Outline of an Anarchistic Theory of Knowledge, 1st published, 1975. Reprinted, Verso, London, UK, 1978. - Higher Superstition: The Academic Left and Its Quarrels with Science, The Johns Hopkins University Press, 1997 - Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science, Picador; 1st Picador USA Pbk. Ed edition, 1999 - The Sokal Hoax: The Sham That Shook the Academy, University of Nebraska Press, 2000 ISBN 0-8032-7995-7 - A House Built on Sand: Exposing Postmodernist Myths About Science, Oxford University Press, 2000 - Intellectual Impostures, Economist Books, 2003 - Dunbar, K., & Fugelsang, J. (2005). Causal thinking in science: How scientists and students interpret the unexpected. In M. E. Gorman, R. D. Tweney, D. Gooding & A. Kincannon (Eds.), Scientific and Technical Thinking (pp. 57–79). Mahwah, NJ: Lawrence Erlbaum Associates. - Oliver, J.E. (1991) Ch2. of The incomplete guide to the art of discovery. New York:NY, Columbia University Press. - Riccardo Pozzo (2004) The impact of Aristotelianism on modern philosophy. CUA Press. p.41. ISBN 0-8132-1347-9 - The ancient Egyptians observed that heliacal rising of a certain star, Sothis (Greek for Sopdet (Egyptian), known to the West as Sirius), marked the annual flooding of the Nile river. See Neugebauer, Otto (1969) , The Exact Sciences in Antiquity (2 ed.), Dover Publications, ISBN 978-0-486-22332-2, p.82, and also the 1911 Britannica, "Egypt". - The Rhind papyrus lists practical examples in arithmetic and geometry – 1911 Britannica, "Egypt". - The Ebers papyrus lists some of the 'mysteries of the physician', as cited in the 1911 Britannica, "Egypt" - Gauch, Hugh G. (2003). Scientific Method in Practice. Cambridge University Press. p. 45. ISBN 9780521017084. Retrieved 10 February 2015. - Popper, Karl (1998). The world of Parmenides: essays on the Presocratic enlightenment. Routledge. p. 91. ISBN 0415173019. So what was really new in Parmenides was his axiomatic-deductive method, which Leucippus and Democritus turned into a hypothetical-deductive method, and thus made part of scientific methodology. - Lindberg, David (2007). The beginnings of western science: the European scientific tradition in philosophical, religious, and institutional context, Prehistory to A.D. 1450. The University of Chicago Press. p. 362. ISBN 0226482057. - Losee, John (2001). A Historical Introduction to the Philosophy of Science. Oxford University Press. pp. 4–5. ISBN 0198700555. - Grant, Edward. “The Foundations of Modern Science in the Middle Ages”. Cambridge University Press, UK, pp. 4–5. - Hodges, Richard and David Whitehouse. Mohammed, Charlemagne and the Origins of Europe. Cornell University Press, Ithaca, NY, 1983, p. 76. - Lewis, Bernard. Muslim Discovery of Europe. W. W. Norton and Company Ltd., New York, NY, 2001, p. 74. - Dowley, Tim, Ed. "The Baker Atlas of Christian History." 2001, p. 89 - Lewis, Muslim Discovery, p. 72. - Meri, Josef W. and Jere L. Bacharach. “Medieval Islamic Civilization”. Vol. 1 Index A – K. 2006, p. 304. - R. L. Verma (1969). Al-Hazen: father of modern optics. - Jaki, Stanley. Science and Creation: From Eternal Cycles to an Oscillating Universe. Science History Publications, NY, 1974, p. 206. - Mathpages. “Translating Aristotle”. Accessed July 2013. - Gauch 2003, pp. 52–53 - George Sampson (1970). The concise Cambridge history of English literature. Cambridge University Press. p.174. ISBN 0-521-09581-6 - Clegg, Brian. “The First Scientist: A Life of Roger Bacon”. Carroll and Graf Publishers, NY, 2003, p. 2. - Niccolò Leoniceno (1509), De Plinii et aliorum erroribus liber apud Ferrara, as cited by Sanches, Limbrick & Thomson 1988, p. 13 - 'I have sometimes seen a verbose quibbler attempting to persuade some ignorant person that white was black; to which the latter replied, "I do not understand your reasoning, since I have not studied as much as you have; yet I honestly believe that white differs from black. But pray go on refuting me for just as long as you like." ' – Sanches, Limbrick & Thomson 1988, p. 276 - Sanches, Limbrick & Thomson 1988, p. 278. - Bacon, Francis Novum Organum (The New Organon), 1620. Bacon's work described many of the accepted principles, underscoring the importance of empirical results, data gathering and experiment. Encyclopædia Britannica (1911), "Bacon, Francis" states: [In Novum Organum, we ] "proceed to apply what is perhaps the most valuable part of the Baconian method, the process of exclusion or rejection. This elimination of the non-essential, ..., is the most important of Bacon's contributions to the logic of induction, and that in which, as he repeatedly says, his method differs from all previous philosophies." - "John Stuart Mill (Stanford Encyclopedia of Philosophy)". plato.stanford.edu. Retrieved 2009-07-31. - Logik der Forschung, new appendices XVII–XIX (not yet available in the English edition Logic of scientific discovery) - Logic of Scientific discovery, p. 20 - Karl Popper: On the non-existence of scientific method. Realism and the Aim of Science (1983) - Karl Popper: Science: Conjectures and Refutations. Conjectures and Refuations, section VII - Karl Popper: On knowledge. In search of a better world, section II - "The historian ... requires a very broad definition of "science" – one that ... will help us to understand the modern scientific enterprise. We need to be broad and inclusive, rather than narrow and exclusive ... and we should expect that the farther back we go [in time] the broader we will need to be." – David Pingree (1992), "Hellenophilia versus the History of Science" Isis 83 554–63, as cited on p.3, David C. Lindberg (2007), The beginnings of Western science: the European Scientific tradition in philosophical, religious, and institutional context, Second ed. Chicago: Univ. of Chicago Press ISBN 978-0-226-48205-7 - "When we are working intensively, we feel keenly the progress of our work; we are elated when our progress is rapid, we are depressed when it is slow." – the mathematician Pólya 1957, p. 131 in the section on 'Modern heuristic'. - "Philosophy [i.e., physics] is written in this grand book – I mean the universe – which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth." – Galileo Galilei, Il Saggiatore (The Assayer, 1623), as translated by Stillman Drake (1957), Discoveries and Opinions of Galileo pp. 237–8, as quoted by di Francia 1981, p. 10. - Pólya 1957 2nd ed. - George Pólya (1954), Mathematics and Plausible Reasoning Volume I: Induction and Analogy in Mathematics, - George Pólya (1954), Mathematics and Plausible Reasoning Volume II: Patterns of Plausible Reasoning. - Pólya 1957, p. 142 - Pólya 1957, p. 144 - Mackay 1991 p.100 - See the development, by generations of mathematicians, of Euler's formula for polyhedra as documented by Lakatos, Imre (1976), Proofs and refutations, Cambridge: Cambridge University Press, ISBN 0-521-29038-4 - Lakatos, Imre (Worrall & Zahar, eds. 1976) Proofs and Refutations, p.55 Cite error: Invalid <ref> tag; name "Grant.2C_Foundations" defined multiple times with different content Cite error: Invalid <ref> tag; name "Grant.2C_Foundations" defined multiple times with different content Cite error: Invalid <ref> tag; name "Grant.2C_Foundations" defined multiple times with different content Cite error: Invalid <ref> tag; name "First_Scientist.2C_Clegg" defined multiple times with different content Cite error: Invalid <ref> tag; name "First_Scientist.2C_Clegg" defined multiple times with different content Cite error: Invalid <ref> tag; name "First_Scientist.2C_Clegg" defined multiple times with different content - Born, Max (1949), Natural Philosophy of Cause and Chance, Peter Smith, also published by Dover, 1964. From the Waynflete Lectures, 1948. On the web. N.B.: the web version does not have the 3 addenda by Born, 1950, 1964, in which he notes that all knowledge is subjective. Born then proposes a solution in Appendix 3 (1964) - Brody, Thomas A. (1993), The Philosophy Behind Physics, Springer Verlag, ISBN 0-387-55914-0. (Luis De La Peña and Peter E. Hodgson, eds.) - Bruno, Leonard C. (1989), The Landmarks of Science, ISBN 0-8160-2137-6 - Bynum, W.F.; Porter, Roy (2005), Oxford Dictionary of Scientific Quotations, Oxford, ISBN 0-19-858409-1. - di Francia, G. Toraldo (1981), The Investigation of the Physical World, Cambridge University Press, ISBN 0-521-29925-X. - Einstein, Albert; Infeld, Leopold (1938), The Evolution of Physics: from early concepts to relativity and quanta, New York: Simon and Schuster, ISBN 0-671-20156-5 - Feynman, Richard (1965), The Character of Physical Law, Cambridge: M.I.T. Press, ISBN 0-262-56003-8. - Fleck, Ludwik (1979), Genesis and Development of a Scientific Fact, Univ. of Chicago, ISBN 0-226-25325-2. (written in German, 1935, Entstehung und Entwickelung einer wissenschaftlichen Tatsache: Einführung in die Lehre vom Denkstil und Denkkollectiv) English translation, 1979 - Galileo (1638), Two New Sciences, Leiden: Lodewijk Elzevir, ISBN 0-486-60099-8 Translated from Italian to English in 1914 by Henry Crew and Alfonso de Salvio. Introduction by Antonio Favaro. xxv+300 pages, index. New York: Macmillan, with later reprintings by Dover. - Gauch, Hugh G., Jr. (2003), Scientific Method in Practice, Cambridge University Press, ISBN 0-521-01708-4 435 pages - Glen, William (ed.) (1994), The Mass-Extinction Debates: How Science Works in a Crisis, Stanford, CA: Stanford University Press, ISBN 0-8047-2285-4. - Godfrey-Smith, Peter (2003), Theory and Reality: An introduction to the philosophy of science, University of Chicago Press, ISBN 0-226-30063-3. - Goldhaber, Alfred Scharff; Nieto, Michael Martin (January–March 2010), "Photon and graviton mass limits", Rev. Mod. Phys. (American Physical Society) 82: 939, doi:10.1103/RevModPhys.82.939. pages 939–979. - Jevons, William Stanley (1874), The Principles of Science: A Treatise on Logic and Scientific Method, Dover Publications, ISBN 1-4304-8775-5. 1877, 1879. Reprinted with a foreword by Ernst Nagel, New York, NY, 1958. - Kuhn, Thomas S. (1962), The Structure of Scientific Revolutions, Chicago, IL: University of Chicago Press. 2nd edition 1970. 3rd edition 1996. - Lindberg, David C. (2007), The Beginnings of Western Science, University of Chicago Press 2nd edition 2007. - Mackay, Alan L. (ed.) (1991), Dictionary of Scientific Quotations, London: IOP Publishing Ltd, ISBN 0-7503-0106-6 - McElheny, Victor K. (2004), Watson & DNA: Making a scientific revolution, Basic Books, ISBN 0-7382-0866-3. - Moulton, Forest Ray; Schifferes, Justus J. (eds., Second Edition) (1960), The Autobiography of Science, Doubleday. - Needham, Joseph; Wang, Ling (王玲) (1954), Science and Civilisation in China, 1 Introductory Orientations, Cambridge University Press - Newton, Isaac (1999) [1687, 1713, 1726], Philosophiae Naturalis Principia Mathematica, University of California Press, ISBN 0-520-08817-4, Third edition. From I. Bernard Cohen and Anne Whitman's 1999 translation, 974 pages. - Ørsted, Hans Christian (1997), Selected Scientific Works of Hans Christian Ørsted, Princeton, ISBN 0-691-04334-5. Translated to English by Karen Jelved, Andrew D. Jackson, and Ole Knudsen, (translators 1997). - Peirce, C. S. – see Charles Sanders Peirce bibliography. - Poincaré, Henri (1905), Science and Hypothesis Eprint - Pólya, George (1957), How to Solve It, Princeton University Press, ISBN 978-4871878302, OCLC 706968824 (reprinted 2009) - Popper, Karl R. (1959), The Logic of Scientific Discovery 1934, 1959. - Sambursky, Shmuel (ed.) (1974), Physical Thought from the Presocratics to the Quantum Physicists, Pica Press, ISBN 0-87663-712-8. - Sanches, Francisco; Limbrick, Elaine. Introduction, Notes, and Bibliography; Thomson, Douglas F.S. Latin text established, annotated, and translated. (1988), That Nothing is Known, Cambridge: Cambridge University Press, ISBN 0-521-35077-8 Critical edition. - Taleb, Nassim Nicholas (2007), The Black Swan, Random House, ISBN 978-1-4000-6351-2 - Bauer, Henry H., Scientific Literacy and the Myth of the Scientific Method, University of Illinois Press, Champaign, IL, 1992 - Beveridge, William I. B., The Art of Scientific Investigation, Heinemann, Melbourne, Australia, 1950. - Bernstein, Richard J., Beyond Objectivism and Relativism: Science, Hermeneutics, and Praxis, University of Pennsylvania Press, Philadelphia, PA, 1983. - Brody, Baruch A. and Capaldi, Nicholas, Science: Men, Methods, Goals: A Reader: Methods of Physical Science, W. A. Benjamin, 1968 - Brody, Baruch A., and Grandy, Richard E., Readings in the Philosophy of Science, 2nd edition, Prentice Hall, Englewood Cliffs, NJ, 1989. - Burks, Arthur W., Chance, Cause, Reason – An Inquiry into the Nature of Scientific Evidence, University of Chicago Press, Chicago, IL, 1977. - Alan Chalmers. What is this thing called science?. Queensland University Press and Open University Press, 1976. - Crick, Francis (1988), What Mad Pursuit: A Personal View of Scientific Discovery, New York: Basic Books, ISBN 0-465-09137-7. - Dewey, John, How We Think, D.C. Heath, Lexington, MA, 1910. Reprinted, Prometheus Books, Buffalo, NY, 1991. - Earman, John (ed.), Inference, Explanation, and Other Frustrations: Essays in the Philosophy of Science, University of California Press, Berkeley & Los Angeles, CA, 1992. - Fraassen, Bas C. van, The Scientific Image, Oxford University Press, Oxford, UK, 1980. - Franklin, James (2009), What Science Knows: And How It Knows It, New York: Encounter Books, ISBN 1-59403-207-6. - Gadamer, Hans-Georg, Reason in the Age of Science, Frederick G. Lawrence (trans.), MIT Press, Cambridge, MA, 1981. - Giere, Ronald N. (ed.), Cognitive Models of Science, vol. 15 in 'Minnesota Studies in the Philosophy of Science', University of Minnesota Press, Minneapolis, MN, 1992. - Hacking, Ian, Representing and Intervening, Introductory Topics in the Philosophy of Natural Science, Cambridge University Press, Cambridge, UK, 1983. - Heisenberg, Werner, Physics and Beyond, Encounters and Conversations, A.J. Pomerans (trans.), Harper and Row, New York, NY 1971, pp. 63–64. - Holton, Gerald, Thematic Origins of Scientific Thought, Kepler to Einstein, 1st edition 1973, revised edition, Harvard University Press, Cambridge, MA, 1988. - Kuhn, Thomas S., The Essential Tension, Selected Studies in Scientific Tradition and Change, University of Chicago Press, Chicago, IL, 1977. - Latour, Bruno, Science in Action, How to Follow Scientists and Engineers through Society, Harvard University Press, Cambridge, MA, 1987. - Losee, John, A Historical Introduction to the Philosophy of Science, Oxford University Press, Oxford, UK, 1972. 2nd edition, 1980. - Maxwell, Nicholas, The Comprehensibility of the Universe: A New Conception of Science, Oxford University Press, Oxford, 1998. Paperback 2003. - McCarty, Maclyn (1985), The Transforming Principle: Discovering that genes are made of DNA, New York: W. W. Norton, pp. 252 , ISBN 0-393-30450-7. Memoir of a researcher in the Avery–MacLeod–McCarty experiment. - McComas, William F., ed. PDF (189 KB), from The Nature of Science in Science Education, pp53–70, Kluwer Academic Publishers, Netherlands 1998. - Misak, Cheryl J., Truth and the End of Inquiry, A Peircean Account of Truth, Oxford University Press, Oxford, UK, 1991. - Piattelli-Palmarini, Massimo (ed.), Language and Learning, The Debate between Jean Piaget and Noam Chomsky, Harvard University Press, Cambridge, MA, 1980. - Popper, Karl R., Unended Quest, An Intellectual Autobiography, Open Court, La Salle, IL, 1982. - Putnam, Hilary, Renewing Philosophy, Harvard University Press, Cambridge, MA, 1992. - Rorty, Richard, Philosophy and the Mirror of Nature, Princeton University Press, Princeton, NJ, 1979. - Salmon, Wesley C., Four Decades of Scientific Explanation, University of Minnesota Press, Minneapolis, MN, 1990. - Shimony, Abner, Search for a Naturalistic World View: Vol. 1, Scientific Method and Epistemology, Vol. 2, Natural Science and Metaphysics, Cambridge University Press, Cambridge, UK, 1993. - Thagard, Paul, Conceptual Revolutions, Princeton University Press, Princeton, NJ, 1992. - Ziman, John (2000). Real Science: what it is, and what it means. Cambridge, UK: Cambridge University Press. \|Wikibooks has a book on the topic of: The Scientific Method\| - Confirmation and Induction entry in the Internet Encyclopedia of Philosophy - Scientific method at PhilPapers - Scientific method at the Indiana Philosophy Ontology Project - An Introduction to Science: Scientific Thinking and a scientific method by Steven D. Schafersman. - Introduction to the scientific method at the University of Rochester - Theory-ladenness by Paul Newall at The Galilean Library - Lecture on Scientific Method by Greg Anderson - Using the scientific method for designing science fair projects - SCIENTIFIC METHODS an online book by Richard D. Jarrard - Richard Feynman on the Key to Science (one minute, three seconds), from the Cornell Lectures. - Lectures on the Scientific Method by Nick Josh Karean, Kevin Padian, Michael Shermer and Richard Dawkins \|Library resources about
These pages will teach you about the architecture of the CPU and differences between CPU architecture. A central processing unit (CPU) is the electronic circuitry within a computer that carries out the instructions of a computer program by performing the basic arithmetic, logical, control and input/output (I/O) operations specified by the instructions.1 Below we see a simplified diagram describing the overall architecture of a CPU. You must be able to outline the architecture of the central processing unit (CPU) and the functions of the arithmetic logic unit (ALU) and the control unit (CU) and the registers within the CPU. The image in the above paragraph notes the following: - Memory holds both data and instructions. - The arithmetic/logic gate unit is capable of performing arithmetic and logic operations on data. - A processor register is a quickly accessible location available to a digital processor’s central processing unit (CPU). Registers usually consist of a small amount of fast storage, although some registers have specific hardware functions, and may be read-only or write-only. - The control unit controls the flow of data within the CPU – (which is the Fetch-Execute cycle). - Input arrives into a CPU via a bus. - Output exits the CPU via a bus. Comparing CPU’sWhen we compare CPU’s, we weigh a number of important factors, such as clock speed, number of cores, tdp, socket type and class (desktop, laptop, mobile device). But really, in a nutshell, it comes down to how much computing can be done when all parts of a CPU come together in a single clock cycle. If performing Task X takes two clock cycles on CPU A and one clock cycle on CPU B, then CPU B might be the better processor even if CPU A has a higher clock speed. Outline the architecture of the central processing unit (CPU) and the functions of the arithmetic logic unit (ALU) and the control unit (CU) and the registers within the CPU. Parts of a CPU: - ALU – The arithmetic logic unit executes all calculations within the CPU - CU – control unit, coordinates how data moves around Registers, a memory location within the actual processor that work at very fast speeds. It stores instructions which await to be decoded or executed. - PC – program counter – stores address of the -> next <- instruction in RAM - MAR – memory address register – stores the address of the current instruction being executed - MDR – memory data register – stores the data that is to be sent to or fetched from memory - CIR – current instruction register – stores actual instruction that is being decoded and executed - ACC – accumulator – stores result of calculations - address bus – carries the ADDRESS of the instruction or data - data bus – carries data between processor and the memory - control bus – sends control signals such as: memory read, memory write Together, these buses may be referred to as the “system bus” or the “front-side bus”2.
Transpose operator homework help If you have opted for or are planning to take up a mathematics course on campus. You will definitely come across matrices. A matrix is a two-dimension array from which mathematical computations such as addition, subtraction, multiplications, and division can be done. An example of a matrix is the one shown below. The numbers or symbols of the matrix are known as elements, the vertical elements are the column, and the horizontal are the rows. We define the size of a matrix as the number of columns and rows it contains. For example, an M X N matrix contains M and N dimensions. The number of rows and columns that a matrix can contain can be infinite, while it is possible to contain a matrix with one column or row. Such a matrix is called a column vector and a row vector, respectively. If the matrix has the same number of rows and columns, it is known as a square matrix. An example shown above is a matrix with three rows. An empty matrix does not have any element. Howsoever, simple the idea of matrices may sound, they have applications in real life. Examples are in robotics and are the common way of storing data for most organizations. A transpose operator of a matrix is defined as the operator that flips a matrix over its diagonal. It changes the row of a matrix to be it’s diagonal. In mathematics, the transpose of a matrix denoted with a superscript t on the matrix name. For a matrix A above, its transpose is denoted by ATor At. How to find the transpose of a matrix. We shall use Matrix A to demonstrate this example. The first step is reflecting the matrix over its diagonal. - Write the columns of A as rows of AT - Write rows of A as columns of AT - The final result of AT is given below. Transpose operator for a vector. A vector is a one-dimensional array. In some cases, we can say a vector is simply a single row or column matrix. Having found the transpose of the matrix, we can do all the mathematical manipulations, including multiplication, division, addition, subtraction, and even finding the determinant. Properties of the transpose operator. Let us take two arbitrary matrices A and B, and we assume that they have a transpose. Below are the common properties of a transpose matrix. - (AT)T= A - AT+BT= (A+B)T The addition transpose of matrices A and B is the same as adding matrix A and B then transposing the answer. The same can be said in the multiplication of transpose matrices. 3.The determinant of the transpose of matrix A is the same as the determinant of matrix A. Transpose Operator in Matlab. Matlab is one of the trusted statistical computing software capable of solving any mathematical problem. A large number of universities and colleges have incorporated a course on Matlab and they offer assignments related to Matlab. The assignments improve their knowledge of the software. With Matlab, you can easily create a matrix and find the transpose using different functions. The simplest function in Matlab is the transpose. For one or more reasons, a student might find completing his/her assignments challenging. As a result, s(he) might need help from people with detailed knowledge of transposing a matrix. We at Matlab assignment experts offer online tutoring for transpose operator and transpose operator homework help to students from different corners of the world. We are a reputable online assistance company having a group of highly skilled experts as our arsenal. With us, you enjoy the best services at an affordable price, get a plagiarism-free assignment solution. We always adhere to the deadlines. In addition, you can always track the progress of your assignment at any time. Contact us at email@example.com to get transpose operator using Matlab homework help.
Validity tells you how accurately a method measures something. If a method measures what it claims to measure, and the results closely correspond to real-world values, then it can be considered valid. There are four main types of validity: Reliability tells you how consistently a method measures something. When you apply the same method to the same sample under the same conditions, you should get the same results. If not, the method of measurement may be unreliable. There are four main types of reliability. Each can be estimated by comparing different sets of results produced by the same method. Reliability and validity are concepts used to evaluate the quality of research. They indicate how well a method, technique or test measures something. Reliability is about the consistency of a measure, and validity is about the accuracy of a measure. It’s important to consider reliability and validity when you are creating your research design, planning your methods, and writing up your results, especially in quantitative research. Reliability vs validity What does it tell you? The extent to which the results can be reproduced when the research is repeated under the same conditions. The extent to which the results really measure what they are supposed to measure. How is it assessed? By checking the consistency of results across time, across different observers, and across parts of the test itself. By checking how well the results correspond to established theories and other measures of the same concept. How do they relate? A reliable measurement is not always valid: the results might be reproducible, but they’re not necessarily correct. A valid measurement is generally reliable: if a test produces accurate results, they should be reproducible. Uncountable nouns, also known as mass nouns or noncount nouns, refer to a mass of something or an abstract concept that can’t be counted (except with a unit of measurement). In contrast, countable nouns can be counted as individual items. The main rules to remember for uncountable nouns are that they cannot be pluralized, and that they never take indefinite articles (“a” or “an”). Indicating a contraction (e.g., She’s writing a paper) Contractions should be avoided in academic writing, but possessive apostrophes are used in all types of writing. Make sure to use them correctly, especially when dealing with plurals and abbreviations. Subject-verb agreement means that the subject of the sentence matches the verb describing its action. This helps your reader understand who or what is doing something and makes your writing easier to read. First, identify the subject (the person or thing doing the action) and the verb (the action word) in a sentence. If the subject is singular, the verb describing its action should be singular. If the subject is plural, the verb should be plural. Singular subject + verb Plural subject + verb The resultis significant. The resultsare significant. The studentdoes her best. The studentsdo their best. The childbecomes happier. The childrenbecome happier. That treecauses hay fever. Those treescause hay fever. The authoranalyzes the text. The authorsanalyze the text. While subject-verb agreement is easy in simple sentences like these, it can become tricky in more complex sentences. This article teaches you the most important rules and common mistakes.
Rounding a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing £23.4476 with £23.45, or the fraction 312/937 with 1/3, or the expression √2 with 1.414. Rounding is often done to obtain a value that is easier to report and communicate than the original. Rounding can also be important to avoid misleadingly precise reporting of a computed number, measurement or estimate; for example, a quantity that was computed as 123,456 but is known to be accurate only to within a few hundred units is better stated as "about 123,500." On the other hand, rounding of exact numbers will introduce some round-off error in the reported result. Rounding is almost unavoidable when reporting many computations — especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines; or when using a floating point representation with a fixed number of significant digits. In a sequence of calculations, these rounding errors generally accumulate, and in certain ill-conditioned cases they may make the result meaningless. Accurate rounding of transcendental mathematical functions is difficult because the number of extra digits that need to be calculated to resolve whether to round up or down cannot be known in advance. This problem is known as "the table-maker's dilemma". - 1 Types of rounding - 2 Rounding to a specified increment - 3 Rounding to integer - 4 Dithering and error diffusion - 5 Rounding to simple fractions - 6 Scaled rounding - 7 Round to available value - 8 Floating-point rounding - 9 Double rounding - 10 Exact computation with rounded arithmetic - 11 Table-maker's dilemma - 12 History - 13 Rounding functions in programming languages - 14 Other rounding standards - 15 See also - 16 References - 17 External links Types of rounding Typical rounding problems are: - approximating an irrational number by a fraction, e.g., π by 22/7; - approximating a fraction with periodic decimal expansion by a finite decimal fraction, e.g., 5/3 by 1.6667; - replacing a rational number by a fraction with smaller numerator and denominator, e.g., 3122/9417 by 1/3; - replacing a fractional decimal number by one with fewer digits, e.g., 2.1784 dollars by 2.18 dollars; - replacing a decimal integer by an integer with more trailing zeros, e.g., 23,217 people by 23,200 people; or, in general, - replacing a value by a multiple of a specified amount, e.g., 48.2 seconds by 45 seconds (a multiple of 15 s). Rounding to a specified increment The most common type of rounding is to round to an integer; or, more generally, to an integer multiple of some increment — such as rounding to whole tenths of seconds, hundredths of a dollar, to whole multiples of 1/2 or 1/8 inch, to whole dozens or thousands, etc. In general, rounding a number x to a multiple of some specified increment m entails the following steps: - Divide x by m, let the result be y; - Round y to an integer value, call it q; - Multiply q by m to obtain the rounded value z. For example, rounding x = 2.1784 dollars to whole cents (i.e., to a multiple of 0.01) entails computing y = x/m = 2.1784/0.01 = 217.84, then rounding y to the integer q = 218, and finally computing z = q×m = 218×0.01 = 2.18. When rounding to a predetermined number of significant digits, the increment m depends on the magnitude of the number to be rounded (or of the rounded result). The increment m is normally a finite fraction in whatever number system is used to represent the numbers. For display to humans, that usually means the decimal number system (that is, m is an integer times a power of 10, like 1/1000 or 25/100). For intermediate values stored in digital computers, it often means the binary number system (m is an integer times a power of 2). The abstract single-argument "round()" function that returns an integer from an arbitrary real value has at least a dozen distinct concrete definitions presented in the rounding to integer section. The abstract two-argument "round()" function is formally defined here, but in many cases it is used with the implicit value m = 1 for the increment and then reduces to the equivalent abstract single-argument function, with also the same dozen distinct concrete definitions. Rounding to integer The most basic form of rounding is to replace an arbitrary number by an integer. All the following rounding modes are concrete implementations of the abstract single-argument "round()" function presented and used in the previous sections. There are many ways of rounding a number y to an integer q. The most common ones are - round down (or take the floor, or round towards minus infinity): q is the largest integer that does not exceed y. - round up (or take the ceiling, or round towards plus infinity): q is the smallest integer that is not less than y. - round towards zero (or truncate, or round away from infinity): q is the integer part of y, without its fraction digits. - round away from zero (or round towards infinity): if y is an integer, q is y; else q is the integer that is closest to 0 and is such that y is between 0 and q. - round to nearest: q is the integer that is closest to y (see below for tie-breaking rules). The first four methods are called directed rounding, as the displacements from the original number y to the rounded value q are all directed towards or away from the same limiting value (0, +∞, or −∞). If y is positive, round-down is the same as round-towards-zero, and round-up is the same as round-away-from-zero. If y is negative, round-down is the same as round-away-from-zero, and round-up is the same as round-towards-zero. In any case, if y is integer, q is just y. Where many calculations are done in sequence, the choice of rounding method can have a very significant effect on the result. A famous instance involved a new index set up by the Vancouver Stock Exchange in 1982. It was initially set at 1000.000 (three decimal places of accuracy), and after 22 months had fallen to about 520 — whereas stock prices had generally increased in the period. The problem was caused by the index being recalculated thousands of times daily, and always being rounded down to 3 decimal places, in such a way that the rounding errors accumulated. Recalculating with better rounding gave an index value of 1098.892 at the end of the same period. Rounding a number y to the nearest integer requires some tie-breaking rule for those cases when y is exactly half-way between two integers — that is, when the fraction part of y is exactly 0.5. Round half up The following tie-breaking rule, called round half up (or round half towards positive infinity), is widely used in many disciplines. That is, half-way values y are always rounded up. - If the fraction of y is exactly 0.5, then q = y + 0.5. For example, by this rule the value 23.5 gets rounded to 24, but −23.5 gets rounded to −23. However, some programming languages (such as Java) define HALF_UP as round half away from zero. If it were not for the 0.5 fractions, the round-off errors introduced by the round to nearest method would be symmetric: for every fraction that gets rounded up (such as 0.268), there is a complementary fraction (namely, 0.732) that gets rounded down by the same amount. When rounding a large set of numbers with random fractional parts, these rounding errors would statistically compensate each other, and the expected (average) value of the rounded numbers would be equal to the expected value of the original numbers. However, the round half up tie-breaking rule is not symmetric, as the fractions that are exactly 0.5 always get rounded up. This asymmetry introduces a positive bias in the round-off errors. For example, if the fraction of y consists of three random decimal digits, then the expected value of q will be 0.0005 higher than the expected value of y. For this reason, round-to-nearest with the round half up rule is also (ambiguously) known as asymmetric rounding. One reason for rounding up at 0.5 is that for positive decimals, only the first figure after the decimal point needs be examined. For example, when looking at 17.5000…, the "5" alone determines that the number should be rounded up, to 18 in this case. This is not true for negative decimals, such as −17.5000…, where all the fractional figures of the value need to be examined to determine if it should round to −17, if it were −17.5000000, or to −18, if it were −17.5000001 or smaller. Round half down One may also use round half down (or round half towards negative infinity) as opposed to the more common round half up. - If the fraction of y is exactly 0.5, then q = y − 0.5. For example, 23.5 gets rounded to 23, and −23.5 gets rounded to −24. The round half down tie-breaking rule is not symmetric, as the fractions that are exactly 0.5 always get rounded down. This asymmetry introduces a negative bias in the roundoff errors. For example, if the fraction of y consists of three random decimal digits, then the expected value of q will be 0.0005 lower than the expected value of y. For this reason, round-to-nearest with the round half down rule is also (ambiguously) known as asymmetric rounding. Round half towards zero One may also round half towards zero (or round half away from infinity) as opposed to the conventional round half away from zero. - If the fraction of y is exactly 0.5, then q = y − 0.5 if y is positive, and q = y + 0.5 if y is negative. For example, 23.5 gets rounded to 23, and −23.5 gets rounded to −23. This method also treats positive and negative values symmetrically, and therefore is free of overall bias if the original numbers are positive or negative with equal probability. Round half away from zero The other tie-breaking method commonly taught and used is the round half away from zero (or round half towards infinity), namely: - If the fraction of y is exactly 0.5, then q = y + 0.5 if y is positive, and q = y − 0.5 if y is negative. For example, 23.5 gets rounded to 24, and −23.5 gets rounded to −24. This method treats positive and negative values symmetrically, and therefore is free of overall bias if the original numbers are positive or negative with equal probability. It is often used for currency conversions and price roundings (when the amount is first converted into the smallest significant subdivision of the currency, such as cents of a euro) as it is easy to explain by just considering the first fractional digit, independently of supplementary precision digits or sign of the amount (for strict equivalence between the paying and recipient of the amount). Round half to even A tie-breaking rule that is less biased is round half to even, namely: - If the fraction of y is 0.5, then q is the even integer nearest to y. Thus, for example, +23.5 becomes +24, as does +24.5; while −23.5 becomes −24, as does −24.5. This method treats positive and negative values symmetrically, and is therefore free of sign bias. More importantly, for reasonable distributions of y values, the expected (average) value of the rounded numbers is the same as that of the original numbers. However, this rule will introduce a towards-zero bias when y − 0.5 is even, and a towards-infinity bias for when it is odd. This variant of the round-to-nearest method is also called unbiased rounding, convergent rounding, statistician's rounding, Dutch rounding, Gaussian rounding, odd–even rounding, or bankers' rounding. This is the default rounding mode used in IEEE 754 computing functions and operators. Round half to odd A similar tie-breaking rule is round half to odd: - If the fraction of y is 0.5, then q is the odd integer nearest to y. Thus, for example, +23.5 becomes +23, as does +22.5; while −23.5 becomes −23, as does −22.5. This method also treats positive and negative values symmetrically, and is therefore free of sign bias. More importantly, for reasonable distributions of y values, the expected (average) value of the rounded numbers is the same as that of the original numbers. However, this rule will introduce a towards-zero bias when y − 0.5 is odd, and a towards-infinity bias for when it is even. This variant is almost never used in computations, except in situations where one wants to avoid rounding 0.5 or −0.5 to zero; or to avoid increasing the scale of floating point numbers, which have a limited exponent range. With round half to even, a non infinite number would round to infinity, and a small denormal value would round to a normal non-zero value. Effectively, this mode prefers preserving the existing scale of tie numbers, avoiding out of range results when possible for even based number systems (such as binary and decimal). away from zero away from zero Another unbiased tie-breaking method is stochastic rounding: - If the fractional part of y is 0.5, choose q randomly among y + 0.5 and y − 0.5, with equal probability. Like round-half-to-even, this rule is essentially free of overall bias; but it is also fair among even and odd q values. On the other hand, it introduces a random component into the result; performing the same computation twice on the same data may yield two different results. Also, it is open to nonconscious bias if humans (rather than computers or devices of chance) are "randomly" deciding in which direction to round. One method, more obscure than most, is round half alternatingly. - If the fractional part is 0.5, alternate round up and round down: for the first occurrence of a 0.5 fractional part, round up; for the second occurrence, round down; so on so forth. This suppresses the random component of the result, if occurrences of 0.5 fractional parts can be effectively numbered. But it can still introduce a positive or negative bias according to the direction of rounding assigned to the first occurrence, if the total number of occurrences is odd. Dithering and error diffusion When digitising continuous signals, for example images or sound, the overall effect of a number of measurements is more important than the accuracy of each individual measurement. In these circumstances dithering, and a related technique, error diffusion, are normally used. A related technique called pulse-width modulation is used to achieve analogue type output from an inertial device by rapidly pulsing the power with a variable duty cycle. Error diffusion tries to ensure the error on average is minimized. When dealing with a gentle slope from one to zero the output would be zero for the first few terms until the sum of the error and the current value becomes greater than 0.5, in which case a 1 is output and the difference subtracted from the error so far. Floyd–Steinberg dithering is a popular error diffusion procedure when digitising images. Rounding to simple fractions In some contexts it is desirable to round a given number x to a "neat" fraction — that is, the nearest fraction z = m/n whose numerator m and denominator n do not exceed a given maximum. This problem is fairly distinct from that of rounding a value to a fixed number of decimal or binary digits, or to a multiple of a given unit m. This problem is related to Farey sequences, the Stern–Brocot tree, and continued fractions. This type of rounding, which is also named rounding to a logarithmic scale, is a variant of Rounding to a specified increment. Rounding on a logarithmic scale is accomplished by taking the log of the amount and doing normal rounding to the nearest value on the log scale. For example resistors are supplied with preferred numbers on a logarithmic scale. For example for resistors with 10% accuracy they are supplied with nominal values 100, 121, 147, 178, 215 etc. If a calculation indicates a resistor of 165 ohms is required then log(147)=2.167, log(165)=2.217 and log(178)=2.250. The logarithm of 165 is closer to the logarithm of 178 therefore a 178 ohm resistor would be the first choice if there are no other considerations. Round to available value Finished lumber, writing paper, capacitors, and many other products are usually sold in only a few standard sizes. Many design procedures describe how to calculate an approximate value, and then "round" to some standard size using phrases such as "round down to nearest standard value", "round up to nearest standard value", or "round to nearest standard value". When a set of preferred values is equally spaced on a logarithmic scale, choosing the closest preferred value to any given value can be seen as a kind of scaled rounding. Such "rounded" values can be directly calculated. In floating-point arithmetic, rounding aims to turn a given value x into a value z with a specified number of significant digits. In other words, z should be a multiple of a number m that depends on the magnitude of x. The number m is a power of the base (usually 2 or 10) of the floating-point representation. Apart from this detail, all the variants of rounding discussed above apply to the rounding of floating-point numbers as well. The algorithm for such rounding is presented in the Scaled rounding section above, but with a constant scaling factor s = 1, and an integer base b > 1. For results where the rounded result would overflow the result for a directed rounding is either the appropriate signed infinity, or the highest representable positive finite number (or the lowest representable negative finite number if x is negative), depending on the direction of rounding. The result of an overflow for the usual case of round to nearest is always the appropriate infinity. Rounding a number twice in succession to different precisions, with the latter precision being coarser, is not guaranteed to give the same result as rounding once to the final precision except in the case of directed rounding. For instance rounding 9.46 to one decimal gives 9.5, and then 10 when rounding to integer using rounding half to even, but would give 9 when rounded to integer directly. Borman and Chatfield discuss the implications of double rounding when comparing data rounded to one decimal place to specification limits expressed using integers. In Martinez v. Allstate and Sendejo v. Farmers, litigated between 1995 and 1997, the insurance companies argued that double rounding premiums was permissible and in fact required. The US courts ruled against the insurance companies and ordered them to adopt rules to ensure single rounding. Some computer languages and the IEEE 754-2008 standard dictate that in straightforward calculations the result should not be rounded twice. This has been a particular problem with Java as it is designed to be run identically on different machines, special programming tricks have had to be used to achieve this with x87 floating point. The Java language was changed to allow different results where the difference does not matter and require a strictfp qualifier to be used when the results have to conform accurately. Exact computation with rounded arithmetic It is possible to use rounded arithmetic to evaluate the exact value of a function with a discrete domain and range. For example, if we know that an integer n is a perfect square, we can compute its square root by converting n to a floating-point value x, computing the approximate square root y of x with floating point, and then rounding y to the nearest integer q. If n is not too big, the floating-point roundoff error in y will be less than 0.5, so the rounded value q will be the exact square root of n. In most modern computers, this method may be much faster than computing the square root of n by an all-integer algorithm. "Nobody knows how much it would cost to compute yw correctly rounded for every two floating-point arguments at which it does not over/underflow. Instead, reputable math libraries compute elementary transcendental functions mostly within slightly more than half an ulp and almost always well within one ulp. Why can't yw be rounded within half an ulp like SQRT? Because nobody knows how much computation it would cost... No general way exists to predict how many extra digits will have to be carried to compute a transcendental expression and round it correctly to some preassigned number of digits. Even the fact (if true) that a finite number of extra digits will ultimately suffice may be a deep theorem." The IEEE floating point standard guarantees that add, subtract, multiply, divide, fused multiply–add, square root, and floating point remainder will give the correctly rounded result of the infinite precision operation. No such guarantee was given in the 1985 standard for more complex functions and they are typically only accurate to within the last bit at best. However, the 2008 standard guarantees that conforming implementations will give correctly rounded results which respect the active rounding mode; implementation of the functions, however, is optional. Using the Gelfond–Schneider theorem and Lindemann–Weierstrass theorem many of the standard elementary functions can be proved to return transcendental results when given rational non-zero arguments; therefore it is always possible to correctly round such functions. However, determining a limit for a given precision on how accurate results need to be computed, before a correctly rounded result can be guaranteed, may demand a lot of computation time. Some packages offer correct rounding. The GNU MPFR package gives correctly rounded arbitrary precision results. Some other libraries implement elementary functions with correct rounding in double precision: - IBM's libultim, in rounding to nearest only. - Sun Microsystems's libmcr, in the 4 rounding modes. - CRlibm, written in the Arénaire team (LIP, ENS Lyon). It supports the 4 rounding modes and is proved. There exist computable numbers which a rounded value can never be determined no matter how many digits are calculated. Specific instances cannot be given but this follows from the undecidability of the halting problem. For instance, if Goldbach's conjecture is true but unprovable, then the result of rounding the following value up to the next integer cannot be determined: 10−n where n is the first even number greater than 4 which is not the sum of two primes, or 0 if there is no such number. The result is 1 if such a number exists and 0 if no such number exists. The value before rounding can however be approximated to any given precision even if the conjecture is unprovable. The concept of rounding is very old, perhaps older even than the concept of division. Some ancient clay tablets found in Mesopotamia contain tables with rounded values of reciprocals and square roots in base 60. Rounded approximations to π, the length of the year, and the length of the month are also ancient—see base 60#Examples. The Round-to-even method has served as the ASTM (E-29) standard since 1940. The origin of the terms unbiased rounding and statistician's rounding are fairly self-explanatory. In the 1906 4th edition of Probability and Theory of Errors Robert Simpson Woodward called this "the computer's rule" indicating that it was then in common use by human computers who calculated mathematical tables. Churchill Eisenhart indicated the practice was already "well established" in data analysis by the 1940s. The origin of the term bankers' rounding remains more obscure. If this rounding method was ever a standard in banking, the evidence has proved extremely difficult to find. To the contrary, section 2 of the European Commission report The Introduction of the Euro and the Rounding of Currency Amounts suggests that there had previously been no standard approach to rounding in banking; and it specifies that "half-way" amounts should be rounded up. Until the 1980s, the rounding method used in floating-point computer arithmetic was usually fixed by the hardware, poorly documented, inconsistent, and different for each brand and model of computer. This situation changed after the IEEE 754 floating point standard was adopted by most computer manufacturers. The standard allows the user to choose among several rounding modes, and in each case specifies precisely how the results should be rounded. These features made numerical computations more predictable and machine-independent, and made possible the efficient and consistent implementation of interval arithmetic. Rounding functions in programming languages Most programming languages provide functions or special syntax to round fractional numbers in various ways. The earliest numeric languages, such as FORTRAN and C, would provide only one method, usually truncation (towards zero). This default method could be implied in certain contexts, such as when assigning a fractional number to an integer variable, or using a fractional number as an index of an array. Other kinds of rounding had to be programmed explicitly; for example, rounding a positive number to the nearest integer could be implemented by adding 0.5 and truncating. In the last decades, however, the syntax and/or the standard libraries of most languages have commonly provided at least the four basic rounding functions (up, down, to nearest, and towards zero). The tie-breaking method may vary depending the language and version, and/or may be selectable by the programmer. Several languages follow the lead of the IEEE-754 floating-point standard, and define these functions as taking a double precision float argument and returning the result of the same type, which then may be converted to an integer if necessary. This approach may avoid spurious overflows since floating-point types have a larger range than integer types. Some languages, such as PHP, provide functions that round a value to a specified number of decimal digits, e.g. from 4321.5678 to 4321.57 or 4300. In addition, many languages provide a printf or similar string formatting function, which allows one to convert a fractional number to a string, rounded to a user-specified number of decimal places (the precision). On the other hand, truncation (round to zero) is still the default rounding method used by many languages, especially for the division of two integer values. Other rounding standards Some disciplines or institutions have issued standards or directives for rounding. U.S. Weather Observations In a guideline issued in mid-1966, the U.S. Office of the Federal Coordinator for Meteorology determined that weather data should be rounded to the nearest round number, with the "round half up" tie-breaking rule. For example, 1.5 rounded to integer should become 2, and −1.5 should become −1. Prior to that date, the tie-breaking rule was "round half away from zero". Negative zero in meteorology Some meteorologists may write "−0" to indicate a temperature between 0.0 and −0.5 degrees (exclusive) that was rounded to integer. This notation is used when the negative sign is considered important, no matter how small is the magnitude; for example, when rounding temperatures in the Celsius scale, where below zero indicates freezing. - Gal's accurate tables - Interval arithmetic - ISO 80000-1:2009 - Kahan summation algorithm - Nearest integer function - Signed-digit representation - Swedish rounding, to avoid the use of coins of extremely low value - Nicholas J. Higham (2002). Accuracy and stability of numerical algorithms. p. 54. ISBN 978-0-89871-521-7. - "java.math.RoundingMode". Oracle. - Engineering Drafting Standards Manual (NASA), X-673-64-1F, p90 - "Zener Diode Voltage Regulators" - "Build a Mirror Tester" - Bruce Trump, Christine Schneider. "Excel Formula Calculates Standard 1%-Resistor Values". Electronic Design, January 21, 2002. - Borman, Phil; Chatfield, Marion (10 November 2015). "Avoid the perils of using rounded data". Journal of Pharmaceutical and Biomedical Analysis 115: 506-507. doi:10.1016/j.jpba.2015.07.021. - Deborah R. Hensler (2000). Class Action Dilemmas: Pursuing Public Goals for Private Gain. RAND. pp. 255–293. ISBN 0-8330-2601-1. - Samuel A. Figueroa (July 1995). "When is double rounding innocuous?". ACM SIGNUM Newsletter (ACM) 30 (3): 21–25. doi:10.1145/221332.221334. - Roger Golliver (October 1998). "Efficiently producing default orthogonal IEEE double results using extended IEEE hardware" (PDF). Intel. - Kahan, William. "A Logarithm Too Clever by Half". Retrieved 2008-11-14. - Handbook of Floating-Point Arithmetic, J.-M. Muller et al., Chapter 12 Solving the Table Maker's Dilemma, 2011. - "libultim – ultimate correctly-rounded elementary-function library". - "libmcr – correctly-rounded elementary-function library". - "CRlibm – Correctly Rounded mathematical library". - Duncan J. Melville. "YBC 7289 clay tablet". 2006 - Churchill Eisenhart (1947). "Effects of Rounding or Grouping Data". In Eisenhart, Hastay, and Wallis. Selected Techniques of Statistical Analysis for Scientific and Industrial Research, and Production and Management Engineering. New York: McGraw-Hill. pp. 187–223. Retrieved 30 January 2014. - ECMA-262 ECMAScript Language Specification - OFCM, 2005: Federal Meteorological Handbook No. 1, Washington, DC., 104 pp.
Rosetta’s comet in August 2015, when it was closest to the sun and when most of the glycine was detected. Ingredients crucial for the origin of life on Earth, including the simple amino acid glycine and phosphorus, key components of DNA and cell membranes, have been discovered at Comet 67P/Churyumov-Gerasimenko. The possibility that water and organic molecules were brought to the early Earth through impacts of objects like asteroids and comets have long been the subject of important debate. While Rosetta’s ROSINA instrument already showed a significant difference in composition between Comet 67P/C-G’s water and that of Earth, the same instrument has now shown that even if comets did not play as big a role in delivering water as once thought, they certainly had the potential to deliver life’s ingredients. While more than 140 different molecules have already been identified in the interstellar medium, amino acids could not be traced. However, hints of the amino acid glycine, a biologically important organic compound commonly found in proteins, were found during NASA’s Stardust mission that flew by Comet Wild 2 in 2004, but terrestrial contamination of the collected dust samples during the analysis could not be ruled out. Now, for the first time, repeated detections at a comet have been confirmed by Rosetta in Comet 67P/C-G’s fuzzy atmosphere, or coma. The first detection was made in October 2014, while most measurements were taken during the perihelion in August 2015 — the closest point to the Sun along the comet’s orbit while the outgassing was strongest. “This is the first unambiguous detection of glycine in the thin atmosphere of a comet,” says Kathrin Altwegg, principal investigator of the ROSINA instrument at the Center of Space and Habitability of the University of Bern and lead author of the study. The results are now being published in Science. Primordial chemistry in the ice Glycine is very hard to detect due to its non-reactive nature: it sublimates at slightly below 150°C, meaning that little is released as gas from the comet’s surface or subsurface due to its cold temperatures. “We see a strong correlation of glycine to dust, suggesting that it is probably released from the grains’ icy mantles once they have warmed up in the coma, perhaps together with other volatiles,” says Altwegg. At the same time, the researchers also detected the organic molecules methylamine and ethylamine, which are precursors to forming glycine. Unlike other amino acids, glycine is the only one that has been shown to be able to form without liquid water. “The simultaneous presence of methylamine and ethylamine, and the correlation between dust and glycine, also hints at how the glycine was formed,” says Altwegg. Phosphorus, a key element for terrestrial life Another exciting detection by ROSINA made for the first time at a comet is of phosphorus. It is a key element in all living organisms and is found in the structural framework of DNA and RNA. “The multitude of organic molecules already identified by ROSINA, now joined by the exciting confirmation of fundamental ingredients like glycine and phosphorus, confirms our idea that comets have the potential to deliver key molecules for prebiotic chemistry,” says Matt Taylor, Rosetta project scientist of the European Space Agency ESA. “Demonstrating that comets are reservoirs of primitive material in the Solar System, and vessels that could have transported these vital ingredients to Earth, is one of the key goals of the Rosetta mission, and we are delighted with this result.” Source: University of Bern - K. Altwegg, H. Balsiger, A. Bar-Nun, J.-J. Berthelier, A. Bieler, P. Bochsler, C. Briois, U. Calmonte, M. Combi, H. Cottin, J. De Keyser, F. Dhooghe, B. Fiethe, S. A. Fuselier, S. Gasc, T. I. Gombosi, K. C. Hansen, M. Hässig, A. Jäckel, E. Kopp, A. Korth, L. Le Roy, U. Mall, B. Marty, O. Mousis, T. Owen, H. Rème, M. Rubin, T. Sémon, C.-Y. Tzou, J. H. Waite, P. Wurz.Prebiotic chemicals – amino acid and phosphorus – in the coma of comet 67P/Churyumov-Gerasimenko. Science Advances, 27 May 2016 DOI: 10.1126/sciadv.1600285
Published at Tuesday, September 29th 2020. by Laurette Vaillant in Addition Worksheets. Moreover, some math software programs are available also in different languages such as Spanish and French. There are also those with a Learning Management System (LMS) that automatically tracks students test scores and provides the teacher with a database to sort and print as needed. Kindergarten and 1st grade math students will be able to start at the beginning with the basic concepts of relative position followed by counting and number sequences. Second grade math students and third grade math students will benefit from practicing sequences before moving on to addition and subtraction. Fourth grade math students may first review addition before moving on to multiplication. While fifth grade math students will review the basics of multiplication before learning the detailed steps of long division. When reaching sixth grade, students will benefit from reviewing the material studied in previous years and supplement with challenging worksheets including the concept of time, geometry, figural analogies and much more. Learning about numbers includes recognizing written numbers as well as the quantity those numbers represent. Mathematics worksheets should provide a variety of fun activities that teach your child both numbers and quantity. Look for a variety of different ways to present the same concepts. This aids understanding and prevents boredom. Color-by-Numbers pictures are a fun way to learn about numbers and colors too. The next step is learning to write numbers, and this is where mathematics worksheets become almost a necessity. Unless you have great handwriting, lots of spare time and a fair amount of patience, writing worksheets will help you teach this valuable skill to your child. Dot-to-dot, tracing, following the lines and other writing exercises will help your child learn how to write numbers. A good set of worksheets will include practice sheets with various methods to help your child learn to write numbers. Math is a subject that many kids have trouble with as they progress through school. It is essential that math basic skills be mastered early on, as these skills build the foundation for understanding harder concepts introduced in higher grades. First grade math contains quite a few important skills, and using online games may be able to give students the help they need in order to become fluent in working with numbers. In kindergarten, kids learn simple math skills like number recognition and counting. They are able to begin to recognize that higher numbers are bigger numbers and can understand concepts like counting by twos and tens. Using online games with these children when they reach first grade can help them transition between beginning math skills and more complex numerical concepts. Providing a wide variety of different games in an entertaining online environment gets kids excited about tackling new ideas and puts math in a positive context. Once the foundation has been laid for basic comprehension and computational skills, children can use these games to progress even further. When you are teaching your student to write, there are a whole host of worksheets online that you can use. Many of these include clipart that will help the students learn the sounds of letters and letter combinations. There are other sheets that help the student learn to write his or her numbers. It is helpful having printable worksheets for something like this, because parents often go through quite a few of these before the child masters writing the numbers or letters correctly. Even the youngest students--kindergarteners--will benefit from printable worksheets. They will help your little one learn and master basic concepts in way that will capture and hold their attention. Remember that small kids enjoy doing things rather than simply reading or listening. For this reason, attractive, well-illustrated worksheets with something to do will make learning fun for them. What is more, completing your worksheet will give the child a tremendous sense of fulfillment. Most volumes begin with an explanation of basic arithmetic operations namely: addition, subtraction, multiplication, and division. Reference tables are supplied to provide clues for quick mental arithmetic and mastery of math facts. When ready to be tested, the student can select a drill, which has 10 questions and are selected from a database of number pairs for calculation. The Basic Level volumes use simple single digit numbers and the interactive math software at the Advanced Level uses mostly double digit numbers for math practice problems. Each drill is then scored and timed with the results saved. With the test records, students can follow their own progress and adults who may be supervising can monitor progress and assess if there are any learning issues that require intervention. The most important thing about these math worksheets is that they are used for tutoring and not for the main course studies. That is why they are used by tutors to offer remedial tuition and by parents at home so that they can offer their kids extra tuition to sharpen their skills. Math is known to be difficult and is often a headache for the young and so the math worksheets come in handy in helping resolve this problem. Thanks to the sites over the internet that offer free printable math worksheets, you do not need to worry about the cost of purchasing one, maybe only the ink cost. So do not go making excuses for not being able to access a math work sheet. Children can work with simple numbers worksheets from quite an early age and you will have greater success in getting them to work on the worksheets if you combine that learning work with something practical, or at least something they enjoy doing. For example, if you are using a simple addition and subtraction worksheet with your child, draw or type up another sheet of with squares and numbers printed onto them. Instead of writing the answers to the questions on the worksheet you can get your child to cut and paste the required numbers for the answers from from the second worksheet onto the first. 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Ceres may be a cold, dark, and dead world today, but scientists poring over a trove of data returned by the Dawn spacecraft have found that has not always been the case. Rather, new discoveries of ice on the surface of Ceres and other emerging clues have led planetary scientists to conclude the dwarf planet once had an inner ocean, and perhaps it even harbored life. They discussed their findings Thursday at the annual American Geophysical Union meeting during a news conference. Ceres is the largest object in the asteroid belt. Since Dawn reached it in early 2015, the spacecraft has returned 54,000 images, 16 million visible spectra, and 21 million infrared spectra. It mapped out the dwarf planet’s gravity field in great deal. Additionally, Dawn carries a detector to study the collision of neutrons with the surface of Ceres. Based upon the energy of gamma rays produced by such collisions, the spacecraft can detect various elements at the surface and to a depth of about one meter. In the last two years Dawn has found a lot of hydrogen. Scientists have good reason to believe that, in addition to hydrates such as OH, much of the hydrogen near the surface of Ceres exists in the form of water ice. This is partly because concentrations of hydrogen, by weight, are double at the poles of Ceres compared to the equator. This fits within a model that suggests that, over time, water molecules on the surface of Ceres would bounce around. During this time, they would eventually sublimate in warmer areas or get trapped in permanently shadowed craters at the poles of the world. When Dawn flew over the poles, it captured images and other data to find bright deposits consisting of water ice in 10 craters. Ice can persist in such craters on an airless world over billions of years because temperatures are very cold, about 110 Kelvin. Dawn also found ice at the edge of a shadowed crater in the bright, small Oxo crater near Ceres’ north pole. Carol Raymond, deputy principal investigator of the Dawn mission, said this unstable ice was likely recently exposed by a landslide in the crater wall. Some of Ceres’ surface ice probably comes from asteroid and comet impacts, but much of it has probably come from within the dwarf planet. Dawn scientists said all of the new evidence points convincingly toward the existence of an interior ocean in the dwarf planet’s distant past. “We can only investigate for the fingerprints on the surface, but we have ample evidence to say the presence of a subsurface ocean was likely,” Raymond said. “I think the data is pointing toward Ceres being an interesting object equivalent to Europa and Enceladus in terms of its potential habitability.” Making an ocean in the asteroid belt NASA sent Dawn to Ceres in order to better understand conditions in the primordial Solar System, as the planets formed along with the asteroid belt. At this early stage, as matter in the churning Solar System began to coalesce due to gravitational forces, scientists say that chunks of ice and rock-forming minerals called silicates would have been accreting to form Ceres. As Ceres added mass, radiation would have warmed the interior of the world and melted the ice. At some point within the first 1 to 2 billion years of the Solar System’s formation, scientists expect that Ceres therefore had an interior ocean, perhaps a rather large one. Whether this was some sort of very salty, briny layer of water or a more familiar ocean like those on Earth, and whether its pH level and chemistry would have been conducive to life, remains a subject for further study. Alas, as the dwarf world drifted far from the Sun and, without an atmosphere, cooled, this ocean would have slowly frozen out. Today, some liquid water likely remains inside, although it is very briny, Raymond said, with a much lower freezing point than less salty water. It's likely this briny water is a source of material for Ahuna Mons, the tallest mountain on Ceres at 4km high and a suspected cryovolcano. Dawn has two working reaction wheels and enough hydrazine fuel to power them, such that the spacecraft should be able to continue operations through 2017. Perhaps more answers about this intriguing world will be found in subsequent data. This post originated on Ars Technica Listing image by NASA/JPL-Caltech/UCLA/MPS/DLR/IDA
When you have completed this unit you should be able to: Explain why the body needs glucose. List the dangers of hypoglycaemia. Identify infants at risk of hypoglycaemia. Prevent and treat hypoglycaemia. Discuss the causes and management of hyperglycaemia. 8-1 What is glucose? Glucose is a simple sugar. It is obtained from the diet by the breakdown of more complex carbohydrates (such as starch) and from the conversion of other dietary sugars (such as lactose in milk). Fat and protein in the diet can also be converted by the liver into glucose. Glucose is an essential source of energy to many cells of the body, especially the brain. Glucose is absorbed from the gut and stored in the body as: Glycogen in the liver Protein in muscles Fat under the skin Glycogen, protein and fat form the body’s energy stores. They can all be converted back into glucose by the liver if needed. The amount of glucose available to the cells can be assessed by measuring the concentration of glucose in the blood. Glucose is the same as dextrose. The fetus gets most of its energy from the mother in the form of glucose which crosses the placenta. The higher the mother’s blood glucose concentration, the more glucose the fetus will receive. 8-2 How is glucose measured in the blood? The concentration of blood glucose can be measured by different methods: The quickest, cheapest and easiest method in the nursery to measure the blood glucose concentration is to use a reagent strip such as Haemo-Glukotest (Dextrostix is no longer available). The colour of the reagent strip is then compared to the colour range on the bottle to determine the blood glucose concentration. Unfortunately reading the result by eye is not reliable while reagent strips may give a false low reading if the method is not done correctly. A more accurate method to screen for hypoglycaemia is to use a glucose meter (a reflectance meter) such as reading Haemo-Glukotest strips with a Reflolux meter or AccuChek Active strips with a Glucotrend meter or AccuChek Active meter. This is much better than simply reading the reagent strip by eye. It is essential that the correct meter is used with the reagent strips designed for that meter. In a laboratory the serum glucose concentration can be measured using a more complicated method. The laboratory method is more accurate than reagent strips but takes longer, is more expensive and requires more blood. The blood glucose concentration in the nursery is usually measured with a reagent strip and a glucose meter. 8-3 What is the normal concentration of glucose in the blood? The normal concentration of glucose in the blood of newborn infants is 2.5 mmol/l (45 mg/dl) to 7.0 mmol/l (126 mg/dl). This is called normoglycaemia (normo = normal; glycaemia = blood glucose). Most newborn infants have a blood glucose concentration in the middle of the normal range, about 3.5 to 5 mmol/l. The normal range for older children and adults is higher than this. It is preferable to use the metric units of mmol/l rather than the old units of mg/dl. The normal range of blood glucose concentration in newborn infants is 2.5 mmol/l to 7.0 mmol/l. The range of normal glucose concentration and the definition of hypoglycaemia is confusing as the glucose concentration in whole bood is 0.5 mm/l lower than that of serum in newborn infants due to their high PCV. 8-4 What is hypoglycaemia? A blood glucose concentration below 2.5 mmol/l (45 mg/dl) is abnormal and, therefore, defined as hypoglycaemia (hypo = low; glycaemia = blood glucose). Mild hypoglycaemia is defined as a blood glucose concentration between 1.4 to 2.5 mmol/l while severe hypoglycaemia is defined as a blood glucose concentration of less than 1.4 mmol/l (25 mg/dl). Whenever a reagent strip gives a reading below 1.4 mmol/l, a sample of blood should be taken, if possible, to confirm the diagnosis of hypoglycaemia by a laboratory measurement. By convention the cut off of 2.5 mmol/l for serum is used for both whole blood and serum. Hypoglycaemia is defined as a blood glucose concentration below 2.0 mmol/l. 8-5 What are the dangers of hypoglycaemia? Hypoglycaemia is extremely dangerous especially when the blood glucose concentration is below 1.4 mmol/l. When the blood glucose concentration is low the cells of the body, particularly the brain, do not receive enough glucose and cannot produce energy for their metabolism. As a result the brain cells can be damaged or die, causing cerebral palsy, mental retardation or death. Hypoglycaemia may cause brain damage or death. 8-6 When are infants at risk of developing hypoglycaemia? Infants are at an increased risk of developing hypoglycaemia when: They have reduced energy stores. They have increased energy needs. 8-7 Which infants have reduced energy stores? The supply of glucose into the blood is reduced when the body’s energy stores are low, such as reduced glycogen in the liver, protein in muscles, and fat under the skin. The following newborn infants do not have adequate energy stores to convert into glucose: Preterm infants. They are born before adequate amounts of glycogen, protein and fat are stored in their tissues. The fetus gets most of its energy stores in the last 6 weeks of pregnancy. Therefore, most preterm infants have very small energy stores. Underweight for gestational age or wasted infants. They have either not built up energy stores or have used up most of their energy stores before delivery because they have not been getting enough glucose from their mother. Starved infants. Infants that are not fed, either orally or intravenously soon after delivery, rapidly use up their energy stores. Stressed infants, such as infants who are infected or who have suffered hypoxia, may be unable to convert their energy stores into glucose. This includes infants who need active resuscitation at birth. Infants with liver damage, such as hepatitis, often have low stores of liver glycogen and also are unable to convert other energy stores into glucose. 8-8 Which infants have increased energy needs? The following infants have increased energy needs and, therefore, rapidly use up their energy stores: Infants with respiratory distress. Their respiratory muscles are doing a lot of work and require large amounts of glucose to provide the energy needed for respiration. Hypothermic infants. These infants use large amounts of glucose and fat to produce heat in an attempt to correct their body temperature. Infants of diabetic mothers. Before delivery these infants receive excess glucose across the placenta, especially if the maternal diabetes is poorly controlled. The higher the maternal glucose concentration, the more glucose the infant receives. This large supply of glucose makes the fetus obese and stimulates the fetal pancreas to secrete extra insulin. At delivery the supply of glucose from the mother suddenly stops when the umbilical cord is clamped. However, the stimulated fetal pancreas continues to secrete excessive amounts of insulin after delivery, and the high insulin concentration in the blood of the newborn infant causes hypoglycaemia. Overweight for gestational age infants. Some of the mothers of these infants may be undiagnosed diabetics. Think of maternal diabetes in all obese infants. Polycythaemic infants. Their increased number of red cells use a lot of glucose. Hypothermia causes hypoglycaemia. With maternal diabetes, the mother is diabetic but the infant is not. In fact the problem in the infant is exactly the opposite to that in the mother. While the mother secretes too little insulin and, therefore, has a high blood glucose, the newborn infant secretes too much insulin and, therefore, becomes hypoglycaemic. Insulin acts as a fetal growth hormone. Excess fetal insulin, therefore, results in macrosomia. 8-9 Which infants have an increased risk of hypoglycaemia? Those infants with a decreased supply of glucose or an increased demand for glucose (i.e. infants with small energy stores or large energy needs): Low birth weight infants (either preterm or underweight for gestational age) Infants where there is a delay in the onset of feeding (infants who have not been fed) Hypoxic infants and infants who need active resuscitation at birth Infants with liver disease Infants with respiratory distress Infants of diabetic mothers Overweight for gestational age infants Low birth weight infants and starved infants are at high risk for hypoglycaemia. 8-10 What are the clinical signs of hypoglycaemia? Hypoglycaemia may produce no clinical signs or present with non-specific signs only. This makes the clinical diagnosis of hypoglycaemia very difficult. When present, the signs of hypoglycaemia are: Depression of brain function. The infant may be lethargic and hypotonic, feed poorly, have a weak cry, apnoea, cyanosis or an absent Moro reflex. Overstimulation of brain function. The infant may be jittery with a high-pitched cry, a fixed stare and fisting, have abnormal eye movements or convulsions. Excessive sweating. This sign may not be present, however, especially in preterm infants. Often an infant has some signs of brain stimulation (such as jitteriness )and other signs of brain depression (such as poor feeding) at the same time. Therefore, while some parts of the brain may be stimulated other parts may be depressed by hypoglycaemia. As a result, the clinical presentation of hypoglycaemia is very variable, making the clinical diagnosis of hypoglycaemia very unreliable. Hypoglycaemic infants may have no abnormal clinical signs. 8-11 How can you diagnose hypoglycaemia? The clinical diagnosis is difficult and often missed. Therefore, it is essential that all infants at risk of hypoglycaemia, and infants with clinical signs that may be caused by hypoglycaemia, be screened with reagent strips. Whenever possible, use a reflectance meter such as an Accu-chek or Glucotrend meter rather than reading the reagent strip by eye. Ideally a diagnosis of hypoglycaemia made with reagent strips should be confirmed with a laboratory serum glucose measurement. An infant’s blood glucose concentration will fall into one of the following groups: 2.5 mmol/l or more. Remember that the normal range of blood glucose in newborn infants is 2.5 mmol/l to 7.0 mmol/l. Between 1.4 mmol/l and 2.5 mmol/l. This is mild hypoglycaemia. These infants’ blood glucose concentration is abnormally low and they are at high risk of developing severe hypoglycaemia. Less than 1.4 mmol/l. This is the definition of severe hypoglycaemia, which is very dangerous. 8-12 How can you prevent hypoglycaemia? The following steps must be taken to prevent hypoglycaemia: Identify all infants at high risk of developing hypoglycaemia. Monitor the blood glucose concentration of these infants with reagent strips so that a falling blood glucose can be detected before hypoglycaemic levels are reached. Feed all infants as soon as possible after delivery, especially preterm, underweight for gestational age and wasted infants, as well as infants of diabetic women. Whenever possible, milk feeds should be given. Both clear feeds orally and oral dextrose feeds should not be used in newborn infants as they are low in energy and may result in hypoglycaemia. If milk feeds cannot be given, then an intravenous infusion of 10% glucose (e.g. Neonatalyte) should be started. Early feeding with milk helps to prevent hypoglycaemia. 8-13 How should you treat an infant with mild hypoglycaemia? These infants, with a blood glucose concentration between 1.4 mmol/l and 2.5 mmol/l, need milk feeds or 10% intravenous glucose (Neonatalyte) urgently to prevent severe hypoglycaemia: If they tolerate oral or nasogastric feeds, give 10 ml/kg breast milk or milk formula immediately. Do not give 5% or 10% dextrose orally as the energy content is less than that of breast milk or milk formula. Repeat the blood glucose measurement 30 minutes after the feed to determine whether the blood glucose concentration has returned to the normal range. If it is still in the mild hypoglycaemia range, repeat the feed with an added 5 ml sugar (one teaspoon) per 30 ml milk and repeat the blood glucose measurement after a further 30 minutes. If still low treat as for severe hypoglycaemia. When the blood glucose concentration has returned to normal, continue with regular milk feeds and continue to monitor with reagent strips hourly for 3 hours. If the blood glucose concentration remains low despite 2 milk feeds, start an intravenous infusion. If the blood glucose concentration falls below 1.4 mmol/l at any time, treat for severe hypoglycaemia. If the infant is too small or too ill to tolerate milk feeds, start a 10% intravenous infusion (e.g. Neonatalyte). Monitor the blood glucose concentration with reagent strips and start milk feeds as soon as possible. Remember that mild hypoglycaemia may rapidly progress to severe hypoglycaemia if not correctly treated. Mild hypoglycaemia can usually be corrected with milk feeds. 8-14 How should you treat an infant with severe hypoglycaemia? All infants with a blood glucose concentration below 1.4 mmol/l have severe hypoglycaemia. This is a medical emergency and must be treated immediately. Do not wait for the result of the laboratory measurement before starting treatment. The management of severe hypoglycaemia consists of the following steps: The treatment of choice is to start an intravenous infusion of 10% dextrose (or Neonatalyte) at a drip rate calculated to give 60 ml/kg in the first 24 hours. Infants older than 24 hours can be given a larger volume calculated for their age. A 10% dextrose infusion at 60 ml/kg/24 hours will provide 0.22 mmol (4 mg) glucose/kg/minute which will meet most infants’ energy needs. To increase a 5% to a 10% glucose solution, add 10 ml of 50% dextrose to 100 ml 5 dextrose. Some infants will need a 15 glucose solution, however, to maintain a normal blood glucose concentration. If you cannot rapidly establish a peripheral intravenous line, insert an umbilical vein catheter so that intravenous fluids can be given. Once an intravenous line has been established, give 2 ml/kg of 10% glucose as a bolus. It is not advisable to inject a bolus of 25% or 50% dextrose as it is extremely hypertonic. If the blood glucose concentration is not normal after 15 minutes give a 5 ml bolus of 10% glucose. If the blood glucose concentration still has not returned to normal within a further 15 minutes, give 5 mg hydrocortisone intravenously. Take 5 ml of blood from these infants for glucose and insulin estimation before giving the hydrocortisone. This is very important in identifying the correct cause of the hypoglycaemia. Glucagon 0.3 mg/kg IM or IV can be used if hydrocortisone fails to correct the blood glucose concentration. In an emergency, if you are unable to give intravenous dextrose, give the infant 10 ml/kg breast milk or formula (or cow’s milk if neither is available) by mouth or via a nasogastric tube. You can add 5 ml (a teaspoon) of sugar, or 5 ml of 50% dextrose, per 10 ml feed to increase the energy concentration. Do not give pure 50% dextrose as it will cause vomiting. Start regular milk feeds as soon as possible. Extra sugar can be added to the milk feeds if necessary. As the volume of milk feeds are increased the rate of the intravenous infusion can be reduced. Never suddenly withdraw intravenous dextrose as this may precipitate hypoglycaemia, as commonly happens if the drip infiltrates the tissues. Reduce the drip rate gradually when oral feeds are introduced. Keep the infant warm. Once the blood glucose concentration has returned to normal, monitor the blood glucose concentration hourly until full volume feeds have been established. Repeated or unresponsive hypoglycaemia may be due to a rare metabolic cause and urgent specialist medical advice must be sought. A sample of venous blood should be taken for further investigations. The treatment of severe hypoglycaemia is an intravenous infusion of 10% dextrose. 8-15 How frequently should you measure the blood glucose concentration? The blood glucose concentration should be closely monitored in infants at risk of hypoglycaemia and in infants who have had hypoglycaemia: In most infants at high risk of hypoglycaemia, the blood glucose concentration should be measured hourly with for the first 3 hours, then 2 hourly for the next 3 hours. Thereafter the blood glucose should be monitored every 3 hours until 100 ml/kg/day milk feeds have been established which is usually in 24 to 48 hours. Infants of diabetic mothers should be monitored hourly for the first 6 hours when their risk of hypoglycaemia is greatest. Infants with mild hypoglycaemia should be monitored every 30 minutes until the blood glucose concentration has returned to the normal range. Readings should then be made hourly for 3 hours to ensure that the blood glucose concentration does not fall again. Thereafter, measure the blood glucose concentration every 2 hours until 100 ml/kg milk feeds are established. Infants with severe hypoglycaemia should have their blood glucose concentration measured every 15 minutes until it has increased above 1.4 mmol/l. Then measure the blood glucose concentration as for infants with mild hypoglycaemia. The greater the risk of hypoglycaemia the more frequently the blood glucose concentration should be monitored. 8-16 What is the prognosis after hypoglycaemia? The risk of brain damage depends on the severity, duration and number of hypoglycaemic attacks. The prognosis is worst if the hypoglycaemia has produced clinical signs, especially convulsions. The risk of permanent brain damage is probably low if the hypoglycaemia is asymptomatic. However, asymptomatic hypoglycaemia remains dangerous and must be treated urgently as clinical signs may suddenly develop. 8-17 What is hyperglycaemia? Hyperglycaemia (hyper = high; glycaemia = blood glucose) is defined as a blood glucose concentration above 7.0 mmol/l (126 mg/dl). Usually hyperglycaemia does not cause problems until the blood glucose concentration increases above 10 mmol/l. 8-18 What is the cause of hyperglycaemia? Hyperglycaemia is usually due to a 10% dextrose or Neonatalyte infusion given to a preterm infant during the first few days of life. Some immature infants are not able to remove glucose fast enough from the blood stream. Hyperglycaemia may be caused by a severe intraventricular haemorrhage. The stress of hypoxia or infection may increase or decrease the blood glucose concentration. Transient or permanent neonatal diabetes is a rare cause of hyperglycaemia. 8-19 What are the dangers of hyperglycaemia? A high blood glucose concentration results in a lot of glucose being excreted in the urine (glycosuria), which in turn may cause polyuria and lead to dehydration. Mild glycosuria is common in preterm infants and does not require treatment. Severe hyperglycaemia increases the risk of intraventricular haemorrhage in preterm infants. 8-20 How should you treat hyperglycaemia? The raised blood glucose concentration usually can be lowered into the normal range by simply changing the intravenous solution from Neonatalyte or 10% dextrose to a 5% dextrose solution. Once milk feeds are established, hyperglycaemia usually returns to normal. Case study 1 A term infant is brought to a rural clinic after having been born at home. The infant is cold and wasted but otherwise appears well. A reagent strip reading is between 1.4 and 2.5 mmol/l when the colour is matched against the container. 1. What is your interpretation of the blood glucose concentration? The infant has mild hypoglycaemia. This should be confirmed with a reflectance meter if possible as reading a reagent strip by eye is not very accurate. 2. What is the danger of mild hypoglycaemia? The infant is at high risk of developing severe hypoglycaemia. 3. Why does this term infant have a low blood glucose concentration? Because the infant is cold. Hypothermic infants increase the rate at which they break down glucose in order to produce heat. Eventually the energy stores become depleted and hypoglycaemia may result. In addition this infant is wasted and, therefore, has reduced energy stores. 4. Why is this infant at risk of brain damage? Because the infant has mild hypoglycaemia. This may progress to severe hypoglycaemia if not correctly managed. Remember that even without clinical signs, hypoglycaemia is still dangerous. 5. How would you treat this infant at the clinic? Give the infant a feed of breast milk, formula milk or sweetened cow’s milk. The infant must also be warmed. The blood glucose concentration should have returned to normal in 30 minutes. If not, repeat the feed and arrange urgent transport to the nearest hospital. If the infant develops severe hypoglycaemia, or is to be transported, an infusion with Neonatalyte or 10% dextrose must be started. It is very important to start treatment before referring the infant to hospital. The blood glucose concentration must be carefully monitored during transport. Case study 2 A preterm infant of 1500 g is born in a level I hospital. The infant is nursed in a closed incubator but no feed is given for 2 hours. At 1 hour after birth the Haemo-Glukotest reading with a Reflolux meter is normal but at 2 hours after birth the reading indicates severe hypoglycaemia. The infant is jittery with a poor Moro reflex. 1. Why is this infant hypoglycaemic? The infant is preterm and, therefore, has little energy store. In addition the infant has not been fed for 2 hours after birth. The normal blood glucose concentration at 1 hour indicates that the infant had energy stores to last 1 but not 2 hours. 2. How could the hypoglycaemia have been prevented? Breast or formula feeds via a nasogastric tube or an intravenous infusion should have been started within an hour of delivery. 3. Could the hypoglycaemia have caused the jitteriness and poor Moro reflex? Yes. The brain uses glucose to obtain energy. Therefore, hypoglycaemia interferes with the normal functioning of the brain and may cause both depression of brain function resulting in a poor Moro reflex and overstimulation of the brain resulting in jitteriness. 4. How would you treat this infant? An intravenous infusion of 10% dextrose or Neonatalyte must be started immediately at a rate to give 60 ml/kg/day. Add 2 ml/kg of 10% dextrose as a bolus. Repeat the reagent strip measurement after 15 minutes. If it is still low give a dose of 5 mg hydrocortisone intravenously. Start milk feeds every 2 hours as soon as possible. If the milk feeds are tolerated and the blood glucose concentration returns to normal, then the rate of the 10% dextrose infusion can be slowly reduced. Monitor the blood glucose concentration carefully. 5. Why could this infant not be treated with 5% dextrose orally? Because 5% dextrose does not contain enough glucose to rapidly correct hypoglycaemia. 6. Has this infant already suffered brain damage? It is possible as the infant has symptomatic hypoglycaemia. With immediate treatment there is a good chance that this infant will not suffer permanent brain damage. Case study 3 An infant weighing 4500 g is born to a patient whose diabetes was poorly controlled during pregnancy. The infant is sweating a lot and has a convulsion. The blood glucose concentration is 0 mmol/l. Attempts to give 10% dextrose water via a scalp vein needle fail as the staff cannot find a suitable vein. 1. Why is this infant hypoglycaemic? Because the mother is a poorly controlled diabetic. Excessive glucose crosses the placenta to the fetus and this stimulates the fetal pancreas to secrete excessive insulin. Soon after birth the infant becomes hypoglycaemic as a result of the large amount of insulin still being secreted by the infant’s pancreas. 2. Can hypoglycaemia cause sweating and convulsions? Yes, in both infants and adults hypoglycaemia may present with sweating and convulsions. The convulsions are worrying as they suggest that the function of the brain has been severely affected. 3. What should the staff do if they cannot find a suitable vein? Give 10% dextrose or Neonatalyte via an umbilical vein catheter. 4. What should be done if the hypoglycaemia cannot be corrected with an infusion of 10% dextrose? Give 5 mg hydrocortisone intravenously. 5. How could the hypoglycaemia have been prevented? The maternal diabetes should have been well controlled. As this infant is at very high risk of hypoglycaemia due to the poor diabetic control and high birth weight, milk feeds should have been given straight away and a 10% dextrose or Neonatalyte infusion started. Once feeds are tolerated and the reagent strip readings are normal, the infusion can gradually be slowed. Figure 8-1: The acute management of an infant with hypoglycaemia
OSI Model Tutorial Welcome to the most basic tutorial for networker! Understanding about OSI model is one of the most important tools to help you grasp how networking devices like router, switch, PC… work. Let’s take an example in our real life to demonstrate the OSI model. Maybe you have ever sent a mail to your friend, right? To do it, you have to follow these steps: 1. Write your letter 2. Insert it into an envelope 3. Write information about sender and receiver on that envelope 4. Stamp it 5. Go to the post office and drop it into a mail inbox From the example above, I want to imply we have to go through some steps in a specific order to complete a task. It is also applied for two PCs to communicate with each other. They have to use a predefined model, named OSI, to complete each step. There are 7 steps in this model as listed below: This is also the well-known table of the OSI model so you must take time to learn by heart. A popular way to remember this table is to create a fun sentence with the first letters of each layer. For example: All People Seem To Need Data Processing or a more funny sentence sorted from layer 1 to layer 7: Please Do Not Throw Sausage Pizza Away. There are two notices about this table: 1. First, the table is arranged from top to bottom (numbering from 7 to 1). Each step is called a “layer” so we have 7 layers (maybe we usually call them “layers” to make them more… technical ^^). When a device wants to send information to another one, its data must go from top to bottom layer. But when a device receives this information, it must go from bottom to top to “decapsulate” it. In fact, the reverse action at the other end is very natural in our life. It is very similar when two people communicate via mail. First, the writer must write the letter, insert it into an envelope while the receiver must first open the envelope and then read the mail. The picture below shows the whole process of sending and receiving information. Note: The OSI model layers are often referred to by number than by name (for example, we refer saying “layer 3” to “network layer”) so you should learn the number of each layer as well. 2. When the information goes down through layers (from top to bottom), a header is added to it. This is called “encapsulation” because it is like wrapping an object in a capsule. Each header can be understood only by the corresponding layer at the receiving side. Other layers only see that layer’s header as a part of data. At the receiving side, corresponding header is stripped off in the same layer it was attached. This process is called “decapsulation”. Understand each layer Layer 7 – Application layer This is the closest layer to the end user. It provides the interface between the applications we use and the underlying layers. But notice that the programs you are using (like a web browser – IE, Firefox or Opera…) do not belong to Application layer. Telnet, FTP, email client (SMTP), HyperText Transfer Protocol (HTTP) are examples of Application layer. Layer 6 – Presentation layer This layer ensures the presentation of data, that the communications passing through are in the appropriate form for the recipient. In general, it acts as a translator of the network. For example, you want to send an email and the Presentation will format your data into email format. Or you want to send photos to your friend, the Presentation layer will format your data into GIF, JPG or PNG… format. Layer 5 – Session layer Layer 5 establishes, maintains and ends communication with the receiving device. Layer 4 – Transport layer This layer maintains flow control of data and provides for error checking and recovery of data between the devices. The most common example of Transport layer is Transmission Control Protocol (TCP) and User Datagram Protocol (UDP). Layer 3 – Network layer This layer provides logical addresses which routers will use to determine the path to the destination. In most cases, the logic addresses here means the IP addresses (including source & destination IP addresses). Layer 2 – Data Link Layer The Data Link layer formats the message into a data frame, and adds a header containing the hardware destination and source address to it. This header is responsible for finding the next destination device on a local network. Notice that layer 3 is responsible for finding the path to the last destination (network) but it doesn’t care about who will be the next receiver. It is the Layer 2 that helps data to reach the next destination. This layer is subdivide into 2 sub-layers: logical link control (LLC) and media access control (MAC). The LLC functions include: + Managing frames to upper and lower layers + Error Control + Flow control The MAC sublayer carries the physical address of each device on the network. This address is more commonly called a device’s MAC address. MAC address is a 48 bits address which is burned into the NIC card on the device by its manufacturer. Layer 1 – Physical layer The Physical Layer defines the physical characteristics of the network such as connections, voltage levels and timing. To help you remember the functions of each layer more easily, I created a fun story in which Henry (English) wants to send a document to Charles (French) to demonstrate how the OSI model works. Lastly, I summarize all the important functions of each layer in the table below (please remember them, they are very important knowledge you need to know about OSI model): \|Layer\|\|Description\|\|Popular Protocols\|\|Protocol Data Unit\|\|Devices operate in this layer\| \|Application\|\|+ User interface\|\|HTTP, FTP, TFTP, Telnet, SNMP, DNS…\|\|Data\| \|Presentation\|\|+ Data representation, encryption & decryption\|\| + Video (WMV, AVI…) \|Session\|\|+ Set up, monitor & terminate the connection session\|\|+ SQL, RPC, NETBIOS names…\|\|Data\| \|Transport\|\|+ Flow control (Buffering, Windowing, Congestion Avoidance) helps prevent the loss of segments on the network and the need for retransmission\|\|+ TCP (Connection-Oriented, reliable) + UDP (Connectionless, unreliable) \|Network\|\|+ Path determination + Source & Destination logical addresses + Physical addresses Includes 2 layers: + WAN (HDLC, PPP, Frame Relay…) Encodes and transmits data bits + Electric signals \|+ FDDI, Ethernet\|\|Bit (0, 1)\|\|Hub, Repeater…\| Note: In fact, OSI is just a theoretical model of networking. The practical model used in modern networks is the TCP/IP model. You may think “Hm, it’s just theoretic and has no use in real life! I don’t care!” but believe me, you will use this model more often than the TCP/IP model so take time to grasp it, you will not regret – I promise :)
A subnet mask is defined as a 32-bit address that segregates an IP address into network bits that identify the network and host bits that identify the host device operating on that network. This article explains a subnet mask, how it works, and its benefits to network infrastructure. A subnet mask is a 32-bit address that segregates an IP address into network bits that identify the network and host bits that identify the host device operating on that network. It encapsulates a range of IP addresses that a subnet can use, wherein the subnet refers to a smaller network within a more extensive network. Technically, subnet masks are used internally within a network. Routing devices or switches rely on subnet masks to route data packets to suitable destinations. Data packets that traverse over the internet or any network do not indicate the subnet mask but only reveal the IP address of the destination. However, the routers match this destination IP address to the data packet’s subnet mask to deliver the data packet to the right place. Let’s consider an analogy to understand the subnet mask concept better. Suppose a user named â€˜Davis’ writes a letter to his friend â€˜Tom’. Davis sends this letter to Tom’s office rather than his residence. Tom’s place of employment is a large enterprise with several co-located departments. The administrative team at Tom’s office sorts the mail by department rather than by employee name to ensure that the correspondence isn’t missed and there is no confusion in the process. On receiving Davis’s letter, the team identifies that Tom works in the HR department. As a result, the letter is sent to the HR department instead of Tom. The HR department then hands the letter over to Tom. In the above example, Tom represents an IP address while the HR department serves as a subnet mask. Since the letter was matched to Tom’s department in the initial stages, Davis’s mail was quickly sorted into a group of potential recipients. Without this initial sorting, the administrative team would have to invest more time in looking for the exact location of Tom’s desk, which could have been in any corner of the enterprise building. Now let’s look at a real-world example. A data packet addresses the IP address 22.214.171.124, representing a class C network. Since the IP address is split into a network and host address, here, in a class C network, the network portion is represented by â€˜192.0.4′. Thus, the network routers deliver the data packet to the network identified by 192.0.4. Upon arrival at the right network, the router within the network then consults the routing table for forwarding the packet further. It uses the data packet’s subnet mask of 255.255.255.0 to perform some binary mathematics, observe the device address â€˜16′, and thereby calculate which subnet it should forward the data packet to. On determining the target subnet, it sends the packet to the router that is responsible for delivering data packets within that very subnet. As such, the data packet is eventually delivered to the destination IP address of 126.96.36.199. Representation of subnet masks Subnetting is a process that logically partitions an IP network into multiple subnets. Such network subdivision allows better usage of IPv4 addresses and makes the network’s data routing more secure and efficient. When a new device connects to a network, an IP address is assigned to. Here, the IP address (IPv4) refers to a 32-bit numeric address that has four numbers separated by periods, and each group of numbers within a block is referred to as an octet. The number in each octet ranges from 0 to 255. In such IP addresses, the network and host portions become indistinguishable without the subnet mask. Let’s look at an example: The IP address for a device may be: 11000000. 10101000. 01111011. 10000100 The subnet mask for the IP network above: 11111111. 11111111. 11111111. 00000000 One can represent the IP address and subnet mask as: Subnet masks are vital to the process of subnetting. With minor adjustments in the subnet mask, you can assign the available IP addresses within a network. For example, a household home network has a standard subnet mask of 255.255.255.0. This implies using 254 usable IP addresses within the defined network. In simple words, One can connect up to 254 internet-enabled devices such as phones, computers, IoT gadgets, and others to the home network to access the internet. Moreover, when a device on a network observes the network and host bits on another device’s IP address, it can determine whether the other device is on the same home/business network or online on another network. Thus, devices rely on subnet masks to provide the necessary information to communicate with other devices on the same or outside networks. Subnetting is key to creating fast and efficient computer networks. As businesses worldwide continue to grow, efficient network organization and management are crucial for large firms that intend to expand technologically. Complex networks turn into resilient ones when the traffic has efficient routes to traverse over the network. Without adequate data paths, all network traffic would travel haphazardly over all possible routes, causing traffic congestion and bottlenecks that would degrade the network’s performance. Subnets allow network traffic to pass through a minimum number of routers so that data packets only need to traverse a shorter distance by following mini-routes to reach the target destination within a more extensive network. IP addresses act as an identity for the hardware devices on a network. You can locate a particular device if these IP addresses are organized logically and understandably. That’s where subnetting comes into the picture. It not only helps in localizing network equipment but also aids in maintaining efficiency and order across the network. As computer networks have thousands of interconnected devices, the corresponding IP addresses of all such devices can, in turn, create complex routes for the network traffic to traverse. However, with subnetting, the usage of IP addresses is limited to a few devices. Network engineers can thereby sort data by creating sub-networks, ensuring that the traffic reaches the right place without touching every part of the complex network’s complex routers. As such, the task of engineers is to match each IP address to the corresponding subnet mask. A subnet mask is like an IP address that identifies the network and host parts within the original IP address. This identification helps establish specific routes for sending the data to a particular destination. Thus, the subnet mask serves as a tool that the network routers use to match the data packet’s IP address with the destination’s sub-network. Significance of subnetting Today, computer networks of different sizes are used across the IT industry. These networks are bifurcated into various categories depending on the number of hosts that have access to them. Considering this, IP addresses are divided into classes used by class A networks, class B networks, and class C networks. Class D and E networks also exist; however, they serve other purposes. For example, class D networks are suitable for multicasting tasks, while class E networks are used in the research and development sector. The table below reveals the different network classes, their subnet masks, address range, and the number of hosts that they support. Class A networks can handle hosts in the range of 65,536 to 16 million, class B networks can manage hosts 256 to 65,534, and class C networks can support 254 host addresses. In general scenarios, IP addresses are sufficient for network routers to direct traffic to the correct network. However, when you consider class A networks, it involves millions of connected devices. Routing data traffic to the correct destination can become a time-intensive task as the number of devices increases. This is where subnetting proves to be beneficial. It allows only a certain range of devices within a sub-network to use specific IP addresses. See More: Top 10 Wifi 6 Mesh Routers in 2022 Subnetting gives network administrators better control over their computer networks, including traffic, data packets, subnets, and routers. It boosts the network’s overall performance, enhances its security, and ensures that IP addresses are used efficiently. Let’s dive deeper into some of the critical benefits of subnetting: 1. Efficient data routing Broadcast traffic causes a severe bottleneck on a more extensive network. Here, broadcasting implies that the data packets travel to every node on the network. Subnetting allows you to segregate such broadcast domains into smaller sections. This results in fewer nodes that the broadcast traffic may have to interact with, making data routing efficient and direct. In other words, subnets enable the interaction and communication of multiple devices on different smaller networks simultaneously, thereby reducing the communication traffic over the more extensive network where different instruments interact simultaneously. Let’s consider an analogy here. Suppose 60 people are connected over a conference call on Skype. If all 60 individuals start talking simultaneously, there would only be noise and chaos on the call, making communication inefficient. However, if you split these 60 people into 12 breakout rooms, there’s a high possibility that it may lead to a much more productive and peaceful session. Subnet masks play an important role here as they ensure that the traffic is contained within the defined subnet. As a result, network congestion is avoided, and the network load is also considerably reduced. Moreover, as subnetting limits the distance data packets need to traverse in a network, the data routing activity is carried out effectively. This boosts overall network performance and speed. 2. Enhanced network security For enterprises having more extensive local networks, several connected devices and a significantly high volume of data traffic exist. In such cases, subnets can be beneficial in a security context rather than safeguarding one extensive network. Let’s say hackers attack a smaller subnet. In such a case, only that network segment gets compromised and affected. While the attackers have access only to the devices on that specific subnet, other devices on the more extensive network are not visible to them. This reduces the attack surface as intruders do not gain access to all the devices. A network manager can use small subnets to identify and address external threats by controlling network traffic through route maps, quality of service mechanisms, and network access control lists (ACLs). Here, route map configurations refer to the routing of data packets without relying on routing tables, QoS services prioritize high-performance applications by adjusting network traffic, and ACLs control network traffic to specific subnets. Subnets are essential to such network applications as they enhance overall network security. Subnets also help in isolating legitimate local networks. Moreover, they control access to all devices running on the entire network. As a result, specific files or processes can be secured from unwanted access, and even remote network access can be limited. 3. Prolonged usage of IPv4 addresses With the emergence of the internet, IP addresses were easy to capture. The first version of the â€˜Internet Protocol’ was IPv4, which became a standard communication model in the 1980s for internet users. According to History Computer (Nov. 2021), IPv4 accounted for around 94% of internet traffic. However, as IPv4 addresses were limited, the IP address stock began depleting over time as intelligent devices, personal computers, televisions, speakers, etc., grew in numbers. Considering this scenario, subnetting broadened the usage of a single public IP address. Hence, rather than each device holding a unique IP address, a network can possess multiple IP addresses on one IP network. This implies each device on the network has a portion defining the IP address of the network and a part that specifies the subnet. As such, subnetting facilitated the continued use of IPv4 as an internet standard for an extended period. Large companies employ network administrators and network engineers to subnet their computer networks. This secures their networks from external threats, boosts routing efficiency, preserves public IPv4 addresses, and also enhances network speed and performance. Subnetting invariably makes use of subnet masks to route inbound data traffic to the desired hosts. Irrespective of the size of subnets, subnet masks ensure the smooth and reliable operation of smaller networks. Did this article help you understand the role of subnetting in larger computer networks? Comment below or let us know on FacebookOpens a new window , TwitterOpens a new window , or LinkedInOpens a new window . We’d love to hear from you! MORE ON NETWORKING - What Is WPA (Wi-Fi Protected Access)? Features, Versions, and Importance - What Is FPGA (Field-Programmable Gate Array)? Meaning, Working, and Uses - What Is Network Time Protocol (NTP)? Meaning, Working, Benefits, and Challenges - What Is Beamforming? Working, Techniques, and UsesÂ - OFDMA vs. MU-MIMO: 10 Key Comparisons
Cos function (or cosine function) in a triangle is the ratio of the adjacent side to that of the hypotenuse. The cosine function is one of the three main primary trigonometric functions and it is itself the complement of sine(co+sine). There are various topics that are included in the entire cos concept. Here, the main topics that are focussed include: - Cosine Definition - Cosine Formula - Cosine Table - Cosine Properties With Respect to the Quadrants - Cos Graph - Inverse Cosine (arccos) - Cosine Identities - Cos Calculus - Law of Cosines in Trigonometry - Additional Cos Values - Cosine Worksheet - Trigonometry Related Articles for Class 10 - Trigonometry Related Articles for Class 11 and 12 - Other Trigonometry Related Topics Other Trigonometric Functions \|Sine Function\|\|Tan Function\| \|Cosec (Csc) Function\|\|Sec Function\| In a right-triangle, cos is defined as the ratio of the length of the adjacent side to that of the longest side i.e. the hypotenuse. Suppose a triangle ABC is taken with AB as the hypotenuse and α as the angle between hypotenuse and base. Now, for this triangle, cos α = Adjacent Side/Hypotenuse From the definition of cos, it is now known that it is the adjacent side divided by the hypotenuse. Now, from the above diagram, cos α = AC/AB cos α = b/h Cosine Properties With Respect to the Quadrants It is interesting to note that the value of cos changes according to the quadrants. In the above table, it can be seen that cos 120, 150 and 180 degrees have negative values while cos 0, 30, etc. have positive values. For cos, the value will be positive in the first and the fourth quadrant. \|Degree Range\|\|Quadrant\|\|Cos Function Sign\|\|Cos Value Range\| \|0 to 90 Degrees\|\|1st Quadrant\|\|+ (Positive)\|\|0 < cos(x) < 1\| \|90 to 180 Degrees\|\|2nd Quadrant\|\|– (Negative)\|\|-1 < cos(x) < 0\| \|180 to 270 Degrees\|\|3rd Quadrant\|\|– (Negative)\|\|-1 < cos(x) < 0\| \|270 to 360 Degrees\|\|4th Quadrant\|\|+ (Positive)\|\|0 < cos(x) <1\| The cosine graph or the cos graph is an up-down graph just like the sine graph. The only difference between the sine graph and the cos graph is that sine graph starts from 0 while the cos graph starts from 90 (or π/2). The cos graph given below starts from 1 and falls till -1 and then starts rising again. Arccos (Inverse Cosine) The cos inverse function can be used to measure the angle of any right-angled triangle if the ratio of the adjacent side and hypotenuse is given. The inverse of sine is denoted as arccos or For a right triangle with sides 1, 2, and √3, the cos function can be used to measure the angle. In this, the cos of angle A will be, cos(a)= adjacent/hypotenuse. So, cos(a) = √3/2 Now, the angle “a” will be cos−1(√3/2) Or, a = π/6 = 30° Important Cos Identities - cos2 (x) + sin2 (x) = 1 - cos θ = 1/sec θ - cos (−θ) = cos (θ) - arccos (cos (x)) = x + 2kπ [where k=integer] - Cos (2x) = cos2 (x) − sin2 (x) - cos (θ) = sin (π/2 − θ) Below, all the other trigonometric functions in terms of cos function are also given. Other Trigonometric Functions in Terms of Sine \|Trigonometric Functions\|\|Represented as Sine\| \|tan θ\|\|±√(1-cos2θ)/cos θ\| \|cot θ\|\|±cos θ/√(1-cos2θ)\| \|sec θ\|\|±1/cos θ\| For cosine function f(x) = cos(x), the derivative and the integral will be given as: - Derivative of cos(x), f′ (x) = −sin (x) - Integral of cos(x), ∫f (x) dx = −sin(x) + C) [where C is the constant of integration) Law of Cosines in Trigonometry The law of cosine or cosine rule in trigonometry is a relation between the side and the angles of a triangle. Suppose a triangle with sides a, b, c and with angles A, B, C are taken, the cosine rule will be as follows. According to cos law, the side “c” will be: c2 = a2 + b2 − 2ab cos (C) It is important to be thorough with the law of cosines as questions related to it are common in the examinations. - Law of Sines - Tan Law Additional Cos Values \|Cos 1 Degree is 0.99\|\|Cos 2 Degree is 0.99\| \|Cos 5 Degree is 0.996\|\|Cos 8 Degree is 0.990\| \|Cos 10 Degree is 0.984\|\|Cos 15 Degree is 0.965\| \|Cos 20 Degree is 0.939\|\|Cos 30 Degree is 0.866\| \|Cos 40 Degree is 0.766\|\|Cos 50 Degree is 0.642\| \|Cos 70 Degree is 0.342\|\|Cos 80 Degree is 0.173\| \|Cos 100 Degree is -0.173\|\|Cos 105 Degree is -0.258\| \|Cos 210 Degree is -0.866\|\|Cos 240 Degree is -0.5\| \|Cos 270 Degree is 0\|\|Cos 330 Degree is 0.866\| Cos Questions (Worksheets) - sin (cos-13/5) - In a triangle PQR, PR is 14 cm, QR is 10 cm, and angle RQP is 63 degrees. Calculate angle RPQ and the length of PQ. - In triangle ABC, AB 6 cm, AC is 13 cm, and the angle CAB is 91 degrees. Calculate the length of BC. - Derive the value of cos 60 geometrically. - A ramp is pulled out of the back of a truck. There is a 38 degrees angle between the ramp and the pavement. The distance from the end of the ramp to the back of the truck is 10 feet. Calculate the length of the ramp?
Copyright © 2004 jsd The notion of atom is absolutely central to chemistry, according to any modern (post-1900) understanding of what chemistry is. This is related to the older notion of chemical element. The best way to define things is to start at the bottom and work our way up, step by step. We start with three fundamental particles (proton, neutron, and electron), then define atom, and then define chemical element. For present purposes, we consider protons, neutrons, and electrons to be fundamental particles. They are sufficiently fundamental that it is not worth trying to define them in terms of anything more fundamental. As discussed in reference 1, words acquire meaning from how they are used, not from a pithy dictionary-style definition. In that spirit, it suffices to describe the salient properties of these particles. Each atom has a nucleus consisting of one or more protons and zero or more neutrons. Conventionally, the number of protons is denoted Z, while the number of neutrons is denoted N. Protons and neutrons are both classified as nucleons. (They are the only nucleons you are likely to encounter.) Each proton carries one unit of positive electrical charge. In contrast, neutrons are electrically neutral. As a result, the nucleus carries exactly Z units of positive electrical charge. The number Z is called the proton number or synonymously the atomic number. We name atoms according to atomic number. For example, any atom with Z=1 is called hydrogen by definition, while anything with Z=2 is called helium by definition, et cetera. Any two atoms with the same number of protons (Z) are considered the “same type” of atom, without regard to the number of neutrons (N). This reflects the notion that the chemical properties are determined by Z ... which is true to a decent approximation (but not exactly). The notion of chemical element is a macroscopic notion (in contrast to atoms, which are ultramicroscopic). Specifically, a chemical element is a collection of atoms, all with the same Z value. The periodic table (e.g. reference 2) is arranged in order of atomic number. You can find the name of the element corresponding to a particular Z value, and vice versa, using the periodic table. See reference 3 for details on how to think about the periodic table. If you are going to associate the Z-value with the symbol for an element, the convention is to write it as a subscript to the left of the symbol; for example 2He has Z=2 while 3Li has Z=3. This is of course redundant, since the element-name uniquely specifies the proton number and vice versa. However, sometimes redundancy is good, especially if you don’t have the periodic table memorized or readily accessible. The highest Z value found on earth in any appreciable quantity is Z=92, which we call uranium. Short-lived radioactive elements can be produced artificially, all the way up to Z=116 the last time I checked. We can define the nucleon number to be the number of protons plus the number of neutrons. It is denoted A, so we can write A := Z + N by definition. If you are going to associate the A-value with the symbol for an element, the convention is to write it as a superscript to the left of the symbol; for example 4He has A=4 while 7Li has A=7. There is no corresponding notation for N. There is no need for it, since if you know Z and A you can instantly infer N, namely N = A − Z. There are at least two different definitions for the word atom. This broad definition is particularly convenient when speaking about a collection of atoms, some of which are ionized and some are not. Furthermore, this definition is more-or-less obligatory when speaking about the atoms inside a molecule, where it is usually not possible to keep track of which electrons “belong” to which atom. If we start with a neutral atom and add or subtract some number of electrons, we create an electrically-charged entity called an ion. The word “ion” also applies to electrically charged molecules. For most purposes, when people talk about the size and shape of an isolated atom, they mean the size and shape of the atom’s distribution of electrons. This distribution is a somewhat fuzzy cloud. The details of this distribution are formalized in terms of wavefunctions (also sometimes called orbitals) as discussed in reference 4. Meanwhile, for the atoms inside molecules, any notion of the “size” of an atom is not precise and not particularly useful, because it is not generally possible to keep track of which electrons “belong” to a given atom. Often it is more useful to keep track of the distance between nuclei (rather than atomic “size” per se). Generally this internuclear distance is smaller than you would have guessed based on the “size” of the isolated atom; we can understand by saying there is considerable overlap of the atomic orbitals. Each proton and each neutron has a mass of very nearly 1 dalton. An electron has a much smaller mass, smaller by a factor of approximately 1836. From this you can infer that nearly all the mass of an atom resides in the nucleus. The nucleus is tiny, roughly 100,000 times smaller than the overall size of the atom. Tangential remark: Although electrons are found in atoms, that is not the only place they are found. You should not become too enamored of the idea of electrons being attached to a particular atom. That idea is more-or-less OK for isolated individual atoms, but not otherwise. In molecules, the nuclei share one big cloud of electrons. This is quite spectacular in the case of metals and semiconductors, which can be considered enormous macromolecules, with some electron wavefunctions spread across billions upon billions of atoms. Furthermore, you can have electrons running around in free space, e.g. in electronic amplifier tubes and cathode-ray tube (CRT) displays. In this section, we restrict our attention to ordinary operations involving macroscopic quantities. This means it will be completely impractical to measure quantities by keeping an accurate count of the atoms. To measure the quantity of a macroscopic sample, often the most precise method is to measure its mass. \|Tangential remark: In Europe, kitchen recipes commonly call for ingredients such as flour, sugar, shortening, etc. to be measured by mass, specified in grams or kilograms. This is accurate and convenient, assuming you have a kitchen scale.\|\|Alas, in the US, kitchen recipes virtually always call for such ingredients etc. to be measured by volume. This is often inaccurate and inconvenient. Switching to European-style recipes would not be easy, because most households in the US don’t even have a kitchen scale.\| For many purposes, we want to be able to prepare samples where the number of atoms is controlled with reasonable precision. For example, this includes setting up chemical reactions so that the stoichiometry comes out right. In ordinary chemistry-lab situations, it is not convenient to count the atoms one by one. Instead it is appropriate and conventional to scale things by a factor of Avogadro’s constant, which has the value 6.0221415(10)×1023 particles per mole. (In much of Europe this is called Loschmidt’s number, for good reason, as discussed in section 6.4.) The actual definition is arranged so that one mole of isotopically-pure 12C has a mass of exactly 12 grams. As a consequence, a mole of protons has a mass of approximately 1 gram ... more precisely it’s 1.00727646688(13)g. \|Informally, but for all practical purposes, you can think of the concept of mole as follows: It is just a number. A mole is like a dozen, only much larger. We can speak of a dozen carbon atoms, or a mole of carbon atoms.\|\|The formal SI definition of mole is much more abstract. We don’t need to worry about it for present purposes. It will be discussed in section 8. Note that SI is likely to change the definition in the not-too-distant future.\| Note that the practical definition of mole speaks of particles, not atoms. A mole of oxygen atoms weighs about 16 grams, while a mole of oxygen molecules weighs about 32 grams, because the relevant particle is an oxygen molecule (O2) consisting of two oxygen atoms. To an excellent approximation, the mass of a molecule is the sum of the masses of its constituent atoms. It is traditional in chemistry classes to take this as an exact equality for practical purposes.1 The molar mass of any substance is the average mass per unit number of particles. This concept (and terminology) has a number of advantages: \|Suppose that on average, there are 2.3 children per family.\|\|It is vanishingly unlikely that you will see an “average” family walking down the street with 2.3 children.\| \|The molar mass of monatomic Cl (from natural sources) is 35.5 grams per mole, so on average that’s 35.5 dalton per Cl atom. (See section 4 for a discussion of natural abundances.)\|\|You will never find a Cl atom with mass anywhere near 35.5 dalton. (What you actually find is a mixture containing roughly 75% 35Cl and 25% 37Cl.)\| \|The molar mass of monatomic Br (from natural sources) is 80 grams per mole, so on average that’s 80 dalton per Br atom.\|\|You will never find in nature a Br atom with mass anywhere near 80 dalton. (What you actually find is a mixture containing roughly 50% 79Br and 50% 81Br.)\| Operationally, the molar mass is determined by measuring each isotope using a high resolution mass spectrometer, and then computing the weighted average (weighted by natural abundance). An example of this calculation is shown in section 4. Additional examples can be found in reference 5. Students sometimes question whether it is worth knowing the value of Avogadro’s number or (equivalently) the size of atoms. This is a valid, nontrivial question, but the answer turns out to be yes, for reasons discussed in section 6. It is important to keep in mind that a physical quantity remains the same, no matter what units are used to measure it. For example, the speed of light is the speed of light, no matter whether it is measured in meters per second or furlongs per fortnight. Voltage is voltage, even if it is measured in kilovolts or microvolts. Acreage, otherwise known as area, can be measured in units other than acres. In accordance with this principle, we are not required to measure molar mass in units of grams per mole (although it is commonly convenient to do so). Dimensionally speaking, the molar mass (regardless of units) has the same dimensions as the so-called «atomic mass» or «average atomic mass» ... but molar mass does a much better job of communicating the concept, especially since for most elements there’s no such thing as an «average» atom. In addition to the foregoing argument about dimensions, we can make a point about units: one gram per mole is numerically equal to one dalton per particle. So we have here not just equivalent dimensions, but equivalent units. This makes it particularly easy to switch from “average atomic mass” to molar mass. All you need to do is change the name of the table; you don’t need to change the numerical entries in the table. Here are some units that can be used to measure molar mass: Here are some terms and concepts that you may encounter: The bottle is almost certainly labelled «SiO2» even though the molecules in the bottle are 15 or 20 orders of magnitude bigger than that. The «formula weight» on the label corresponds to the mass of the hypothetical monomer, not the macromolecules. Similar words apply to a bottle of chemically-pure iron filings. Each particle is a macromolecule. The bottle is almost certainly labeled «Fe», even though the molecules in the bottle are many many orders of magnitude larger than that. In any case, whatever you decide the “empirical formula” is, you are better off thinking and speaking in terms of formula mass, or (even better) empirical formula mass. We now turn from discussing macroscopic collections of atoms and molecules to discussing individual atoms and their nuclei. Disclaimer: you shouldn’t need to deal with individual atoms in order to do intro-level chemistry. Almost all chemistry (especially intro-level chemical reaction work) deals with macroscopic samples, i.e. with samples where the atom-count is closer to 1023 than it is to 1. Therefore the molar mass, as given in the periodic table, is sufficient information to let you get on with your work, even though it may be less than sufficient to satisfy your curiosity about individual atoms, and/or about non-chemical processes such as radioactive decay. Recall that an atomic nucleus is composed of Z protons and N neutrons. A particular value of the pair (Z, N) defines our notion of nuclide. (This is analogous to the way a Z-value defined our notion of chemical element.) In addition to the nucleon number (A = Z + N), we should discuss a related concept and some related terminology: \|Baryon number is conserved, even in exotic non-chemical situations where nucleon number is not. That’s because there exist baryons other than nucleons.\|\|In ordinary chem-lab processes, including radioactive decay, nucleons are the only baryons you will encounter, in which case the nucleon number is essentially conserved, because it is essentially equal to the baryon number.\| To denote a nuclide, the conventional notation is to write the A-value as a superscript to the left of the symbol corresponding to the Z-value. For example, 3He has one neutron and two protons, for a total of three nucleons. The neutron number (N) is rarely written down explicitly; you are expected to infer it from the nucleon number (A) and the proton number (Z). Each nuclide (Z, N) is considered an isotope of the corresponding chemical element (Z). For example, 4He is the most-common isotope of He. By extension, two nuclides with the same Z value are called isotopes of each other. For example, 3He is called an isotope of 4He and vice versa.2 Protons and neutrons each have a molar mass close to 1 dalton, and other contributions to the mass of the nuclide are small in comparison. Therefore, for example, 4He will have a molar mass close to 4 grams per mole. \|If you know the nucleon number of a nuclide, you can infer its molar mass to a good approximation. Conversely, if you know the molar mass of a nuclide, you can infer its nucleon number exactly.\|\|If you know the molar mass of a chemical element, do not try to infer “the” nucleon number or even the “typical” nucleon number. It cannot be done reliably. Counterexamples abound, such as chlorine and bromine, as discussed in section 2.1.\| \|Nuclides, yes.\|\|Elements, no.\| The situation for the first few elements is shown in figure 1. For clarity, the numbers in the figure have been rounded off, keeping only enough precision to make the point about molar mass being a weighted average of the nuclide masses. With the exception of the boron abundances, the numbers are known to considerably more precision than this. For details, see the references (section 9). Qualifiers such as “natural” or “naturally-occurring” appear over and over again in this document, because it is possible to obtain samples that don’t have the natural distribution of isotopes. It is easy to buy a mole of 3He, although it is more expensive than ordinary 4He. Similarly it is easy to buy a mole of heavy water (D2O), although it is more expensive than ordinary water. In seawater, there is roughly one deuterium atom for every 6500 hydrogen atoms. You can shift this quite a bit in either direction by fractional distillation or gaseous diffusion. This can even happen inadvertently. The natural product is not always cheaper; natural uranium (which contains about half a percent of 235U) is much more valuable than depleted uranium (from which most of the 235U has been removed). Therefore, if you want to speak clearly, you can’t simply talk about the molar mass of this-or-that element; you need to specify that you’re talking about the molar mass of the naturally occurring element. However, even that isn’t entirely sufficient. It is possible to find different natural sources with different distributions of isotopes. So if you want to be really precise, you need to specify the source: e.g. seawater (not just natural water), or atmospheric nitrogen (not just natural nitrogen). Usually, if you just grab a stock-bottle from the stockroom, the molar mass will be very close to the conventonal “textbook” value, close enough for most purposes. However, for high-precision work, you should double-check the label of the stock-bottle, to make sure the molar mass specified on the label is what you were expecting. In particular, commercially available lithium compounds are sometimes significantly depleted of 6Li, leading to an unnaturally high molar mass (reference 6). The molar mass of a natural sample of a chemical element can be expressed as a weighted average of the isotopes of that element, weighted by their natural abundance. The molar mass of each isotope, along with the natural abundance, can be obtained from the table of nuclides (reference 7), although sometimes more accurate abundance data can be obtained from reference 8. The bromine molar mass computed here is reasonably consistent with the values given in the Los Alamos periodic table (reference 2), namely 79.904(1). Their error bars are twice as large. Perhaps they are using older data, or perhaps they are accounting for sources of uncertainty that I am overlooking. It is worth emphasizing that the molar mass of natural Br is 80, even though the nuclide 80Br has zero natural abundance. It can be created artificially, but it is radioactive with a short half-life, as you can ascertain from the table of nuclides (reference 7). \|Yes, given the masses and abundances of the nuclides, you can compute the molar mass of the element, by a process of averaging.\|\|No, given the molar mass of the element, you cannot reliably undo the averaging to obtain the nucleon numbers, nuclide masses, or abundances.\| For most elements, uncertainty as to the natural abundances is the dominant contribution to the overall uncertainty of the element’s molar mass (far greater than the contribution from the uncertainty in the mass of each isotope). However, there are 21 elements in the periodic table for which only one isotope is found in nature. The molar mass of these elements is known to dramatically greater precision, compared to other elements, because there is no uncertainty as to the natural abundance. Some quantum-mechanical calculations are very easy to do. Let’s see if we can calculate a rough estimate for the size of a hydrogen atom. We anticipate that our answer should come out close to the famous Bohr radius, namely: where 4 π є0 is the constant that appears in Coulomb’s law of electrostatics; ℏ is Planck’s constant, e is the elementary charge; and m is the electron mass. See item 5 for more discussion of these quantities. Our estimate will use little more than dimensional analysis. The electron in the atom can be roughly approximated as a particle in a box, or (equivalently) a wave in a box.3 Some standing-wave wavefunctions for the one-dimensional particle in a box are shown in figure 2. We proceed by applying the following equations. With the possible exception of equation 2a, these equations should be familiar from high-school physics: where k is the wavenumber and Λ is the wavelength. To proceed, we set PE=KE ... by dimensional analysis (or by the virial theorem, if you want to be fancy). We then have which is the same as equation 1 except for an extraneous factor of π2/8. This is as close as one could hope to get by means of dimensional analysis. (Note that Bohr’s formula – equation 1 – was only an approximation to begin with.) Also note that we include an explicit factor of Z, to cover hydrogenic (single-electron) species other than hydrogen, such as He+ and Li++. We can understand what’s happening in the following terms: The electrostatic interaction (equation 2d) keeps the atom from getting too big, while the kinetic energy associated with the stress of bending the wavefunction (equation 2c) keeps the atom from getting too small. It must be emphasized that without the quantum mechanical kinetic energy, the atom would collapse. The electron would spiral down into the nucleus, leaving the atom several orders of magnitude smaller than the observed size. This is just one of many reasons why we say: This is cloned from a proverb about another exceedingly successful theory: Sometimes people ask how we “really” know that atoms exist, how we “really” know the size of atoms, and why we should care. These are nontrivial questions, for reasons discussed in section 6.2. Many things that we see in our daily lives are sensitive to the size of atoms, but the dependence may not be immediately obvious. Ask yourself: If atoms tomorrow were ten times bigger than today, would you notice? How would you notice? What would you look for? Here are some possible answers. The ☞☜ symbol indicates a “hands on” experiment that can be done with simple apparatus. I don’t want to get into a metaphysical debate over whether the bumps seen in figure 3 “are” atoms. It suffices to say that the bumps are in one-to-one correspondence with atoms, and that the spacing of the bumps tells us the spacing of the atoms. A mass spectrometer operates directly on atoms, smallish molecules, and smallish fragments of larger molecules. It classifies them according to their charge-to-mass ratio, to high precision. For example, it can easily distinguish 79Br from 81Br, and tell you that no 80Br is present. There are dozens of different types and subtypes of mass spectrometers. The canonical types look at the curved trajectory of charged particles moving in a magnetic field. See reference 10. It is not hard to get electronics that is sensitive enough to respond to single electrons. From this you can immediately determine the number of elementary charges in a coulomb, thereby connecting the microscopic world to the macroscopic world. Even when you are not clearly seeing individual electrons, you might see shot noise, which is sensitive to the size of electrons. \|Good e-over-m can also be obtained from electrochemistry (electroplating, electrolysis, et cetera).\|\|The classic Millikan experiment will also give you the value of the elementary charge.\| Note that Coulomb’s constant can be determined by measuring a capacitor; Planck’s constant can be determined via the black-body radiation formula and/or via the photoelectric effect; the elementary charge can be measured in various ways as discussed in item 3, and the electron mass can be obtained from e/m data, which in turn can come from electrons moving in a magnetic field. You don’t need to measure all of these things at once, but the point is that you could measure them, so you don’t need to take anything on faith. ☞☜ There is a simple widely-known high-school chemistry experiment that involves HCl diffusing in one direction and NH3 diffusing in the other direction in a tube, roughly 1 meter long and 1 cm in diameter. This (plus some algebra) provides rather decent quantitative information about the size of the molecules involved. With a little more effort, you can do this as a function of pressure, which provides a powerful way of verifying that mean free path and cross section are behaving as advertised. Historical remark: Avogadro died without ever knowing the value of Avogadro’s number, not within several orders of magnitude in either direction. It fell to Loschmidt to make the first serious measurement, based on transport data (speed of diffusion versus speed of sound). ☞☜ Thermal conductivity is rather easy to measure. Take care to prevent convection. ☞☜ There are several ways to measure the viscosity. One amusing way is by looking at the damping of sound waves in a closed resonator. Historical remark: Brownian motion played a role in the history of science, providing some relatively early, relatively convincing evidence for the size of atoms. The medium-small Brownian particle serves as bridge between our macroscopic world and the ultramicroscopic world of atoms and molecules. See reference 14 and reference 15. Observation of Brownian motion is well within the capabilities of high-school or even elementary-school students. Getting from the raw observation to a quantitative determination of the size of molecules requires more analysis than young kids can handle, but the raw data provides at least some glimmer of an appreciation for what is going on in the microscopic and submicroscopic realms. Note that several of the items on this list fall into a pattern: \|In gases, there are a number of first-order properties that don’t tell you much about the size of atoms. These include pressure, temperature, compressibility, speed of sound, et cetera.\|\|There are a number of second-order properties and transport properties that do directly depend on the size of atoms and on the spacing between atoms (or molecules). These include thermal conductivity, viscosity, diffusion, and the fluctuations in various first-order quantities.\| We define the weak atomic hypothesis to be the hypothesis that atoms exist, and have some smallish but nonzero size. That is, we hypothesize that Avogadro’s number “exists” in some vague sense. We consider it large but finite, without bothering to ascertain an accurate value. There are many important chemistry and physics experiments that provide good evidence for the weak atomic hypothesis. They provide evidence that atoms exist, but do not tell us anything about the size of atoms. Examples include: Also, this experiment by itself doesn’t say anything about the number of atoms per molecule. To get that information you need to do additional experiments, perhaps as discussed in the next item. This requires you to get the chemical formulas right. As an example of what can go wrong, if you think the natural oxide of X is XO when in fact it is XO2, you will get the molar mass of X wrong by a factor of two. This law was important in the history of chemistry. It predates the periodic table, and helped lay the groundwork for it. This doesn’t require any notion of stoichiometry, and doesn’t even require you to have a correct chemical formula. That’s important, because almost none of the solids you see around you have a definite formula, i.e. none of them uphold Dalton’s so-called law of multiple proportions. This includes glass, ceramics, most metal objects, most plastic objects, wood, animal hair and tissue, minerals such as feldspar, et cetera. At low temperatures, the law of Dulong and Petit fails. Nowadays the solution is to use something like the Debye model, which works well at low temperatures and correctly reproduces the law of Dulong and Petit at high temperatures. Both these models (Debye and Dulong/Petit) deal only solids and deal only with the part of the specific heat that is due to phonons, i.e. the “lattice” specific heat. They leave out contributions from spin degrees of freedom, electrons, crystallographic phase changes, etc., which are sometimes very significant. Suppose you have established the weak atomic hypothesis. Further suppose you have measured lots of stoichiometric ratios using the methods enumerated above. Then, if you discover the size of one type of atom, you can figure out the size of all the others. The process works like this: The size of one atom plus stoichiometry tells you the size of another, and then you iterate until you have a complete table. By way of contrast to the strong atomic hypothesis (section 6.1) and even the weak atomic hypothesis (section 6.2), there are quite a few things that can be adequately explained in terms of a continuous fluid, without any need to mention atoms. Examples include We use the term hydrodynamic limit or hydrodynamic approximation to refer to situations where the phenomena of interest are well described by macroscopic properties, such as those listed above. Such situations commonly arise when the length-scale of interest is huge compared to the size of particles and huge compared to the spacing between particles. It may be possible to derive and explain the macroscopic properties in terms of atomic theory, but once we have done so (or even if we haven’t), we don’t need to keep track of individual atoms, because the macroscopic properties tell us what we need to know, in the hydrodynamic limit. The hydrodynamic approximation works well in almost all everyday situations, which is not surprising given how small atoms are. For thousands of generations, people were able to live their lives without knowing anything about atoms. Transport properties such as viscosity and diffusion are not included in the list above, because they are in a slightly different category. Without transport properties, the items on the list (indiviually and collectively) do not provide a sufficient basis for ascertaining the size of atoms. In contrast, if you add diffusion and/or viscosity to the list, you then have enough information to estimate the size of atoms, as Loschmidt did (reference 13). On the other hand, if you don’t accept the atomic hypothesis, you can introduce viscosity etc. into the hydrodynamic equations on an ad-hoc macroscopic basis. The equations were known for many years before anybody realized what they implied about atoms. Amedeo Avogadro died without ever knowing the value of Avogadro’s number. If you had guessed a number 100 times too big or 100 times to small, he would have been unable to refute your guess. Johann Loschmidt is generally credited with the first scientific measurement of the size of atoms (reference 13). In much of Europe, the thing we call Avogadro’s number is called Loschmidt’s number, which makes a certain amount of sense. Beware that in the US, the same term, Loschmidt’s number, is on rare occasions used with a different but closely-related meaning, namely the number of particles in one cm3 of gas at standard temperature and pressure. The terms “atomic mass”, “relative atomic mass”, and “atomic weight” are deprecated; use molar mass instead. Any terms involving atomic “weight” are deprecated; use the corresponding notions of mass instead. The terms “mass number” and “atomic mass number” are deprecated; use nucleon number (aka baryon number) instead. The typical periodic table gives you the molar mass, which is sufficient for doing ordinary chem-lab experiments with macroscopic samples. If you are curious about isotopes, the ordinary periodic table does not suffice; you need a chart of the nuclides. If you want the formal SI definition of mole, here it is: 1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol". The advantages and disadvantages of this definition can be summarized as follows: \|The definition given above is a direct quote from the SI document, reference 19.\|\|The SI definition doesn’t explain what they mean by “substance” or “amount of substance”.\| \|The notion of “amount of substance” was important in the history of chemistry. It is a macroscopic 19th-century concept. It predates any knowledge of the numerical value of Avogadro’s number ... just as the macroscopic 19th-century notions of element and compound predate the modern microscopic notions of atom and molecule.\|\|In a modern context, defining a mole as “amount of substance” is less useful, harder to understand, and no more precise, compared to the practical numerical definition given in section 2.1.\| \|Some chemistry teachers vehemently insist on this definition, and object to treating a mole as a number (as we did in section 2.1).\|\|The definition of mole is a moving target. In the metrology community, there are serious efforts toward redefining it to be an exact pure number. (This is analogous to the process whereby the speed of light was redefined to have an exact value.)\| Bottom line: For practical purposes, the modern notions are simpler and in all ways better. English translation: “On the Size of the Air Molecules” J. Chem. Educ. 72 (10), p 870 (1995). Copyright © 2004 jsd
By the end of year 4, children will apply their understanding of maths to solve a wide variety of problems with more than one step and be expected to prove their thinking through pictures, jottings and conversations. They will continue to make connections between different areas of maths and ask their own questions, working in an organised way to find solutions which help them identify common patterns or any errors more easily. Counting and understanding numbers Children will be very familiar with numbers that have up to 4 digits and will be able to order and compare by showing them in different ways such as on a tape measure or using hands-on resources. Using their understanding of place value (how the value of each digit changes depending on its position in the number), children will be able to partition (break and make) numbers in different ways e.g. 2345 = 2000 and 300 and 40 and 5 but could also represent this as 1000 and 1000 and 200 and 100 and 40 and 5 or 2000 and 200 and 145. They will work with numbers securely up to 10,000 and may begin to count beyond in 1s, 10s, 100s and 1000s. They will use this to help them find 10, 100 or 1000 more or less than any given number. They will multiply and divide whole numbers by 10 and 100 and understand that this changes the value of each digit rather than ‘just adding a 0’. They will develop their understanding to decimal hundredths, comparing and ordering these using contexts such as money. Children will also learn about the pattern to find any Roman numeral to 100. Children will develop their expertise when counting forwards and backwards from 0 to include multiples of 6, 7, 9 and 25; decimals with up to 2 places and fractions. They will be able to fluently count in tenths, hundredths and simple fractions. They will develop their understanding of negative numbers through counting backwards through 0. Children will be able to recognise and describe number patterns and relationships including multiples (e.g. 3, 6, 9, 12 are multiples of 3) and factor pairs (e.g. 1 and 12, 2 and 6, 3 and 4 are all factor pairs for 12) for known times tables. Children will develop various strategies for solving +, -, x, ÷ calculations mentally, using jottings when appropriate and for checking that their answers are sensible. Children will be encouraged to share their methods with others to help them see which work best, are quickest and most accurate. Over the course of the year, children will become fluent in all multiplication and division facts up to 12 x 12 and apply these facts to other problems e.g. 232 x 7 = (200 x 7) + (30 x 7) + (2 x 7). Children will use the = sign to demonstrate equal value e.g. 3 x 8 = 48 ÷ 2 and solve missing number problems e.g. 3 x ? = 48÷2. They will explore patterns and rules for the times tables they learn and use pictures and objects to support their understanding. Children will be required to solve problems accurately using the column addition and subtraction methods for numbers with up to 4-digits and explain how the methods work. They will use apparatus to secure their understanding of these. This will include addition and subtraction calculations with different numbers of digits (such as 1286 + 357); and numbers containing 0s (such as 8009 – 3231). They will use formal written methods of short multiplication and short division for two and three digit numbers by a single digit. Children who become very adept at these types of calculations will be stretched through problems such as those containing missing numbers so that they know when, if and why they need to use the methods. Fractions including decimals Children will develop their understanding of fractions by comparing to, or finding a part of, the whole. Through hands-on resources, pictures or jottings, such as a number line, children will add and subtract two fractions with the same denominator (e.g. 2/3 + 2/3). Children will solve problems involving fractions such as ‘find ¾ of 20 litres’ using their knowledge of multiplication and division and through practical equipment. Children secure their understanding that fractions and decimals are different ways of expressing numbers and proportions. Children secure their understanding of place value and decimals to record measurements accurately. They use their understanding of multiplying and dividing by 10, 100 and 1000 to convert between different units of measure of length (km, m, cm, mm), weight (kg, g) and money (£ and p). Children will link their understanding of area to multiplication and describe how to find the perimeter of a rectangle quickly. Children will read and write the time accurately using analogue and digital clocks, including clocks with Roman numerals. They will convert between units of time (hours, minutes and seconds). Children estimate, compare, calculate and solve a variety of problems involving all units of measurement. Children will extend their knowledge of shape to include more unusual quadrilaterals (four-sided shapes) and triangles. They will use increasingly more specific vocabulary such as parallelogram, rhombus and trapezium; scalene and isosceles. They refine their understanding of symmetry and solve problems where the shape is not displayed in its usual way (e.g. it might be on its side). Children find and name different angles and use this information to decide if a shape is regular or irregular. Children describe position and movement on a grid as co-ordinates and will plot points to draw 2-D shapes. Children will complete, read and interpret information on bar charts; they will solve problems that involve finding information in charts, tables and graphs; including time graphs.
Fraction Multiplication (Unlike Denominators) Aligned To Common Core Standard: Grade 5 Fractions - 5.NF.A.1 How Do You Multiply Fractions with Unlike Denominators? One of the four basic arithmetic operations, multiplication, is tricky to understand for kids. However, if we look at this operation closely, there is not must we need to be scared about. When it comes to applying operations between fractions, multiplication is a much more straightforward operation in comparison to addition, subtraction, and division. So, there are two cases of multiplication of fractions. The first one is when both fractions have the same denominator, and the second case is when the fractions do not have the same denominators. While there is not much difference between the multiplication process in both cases, the unlike denominators can scar the students. Use this example to understand how you multiply fractions with unlike denominators. Example: Multiply 3/7 and 5/11 What you need to do here, multiply the numerator of the first fraction with the numerator of the second one. Do the same with the denominators. Multiply the denominator of the first fraction with that of the second fraction. (3×5) / (7×11) = 15/77 If the fraction can be further simplified, you need to reduce it to its simplest form. A collection of worksheets and lessons that shows you how to multiply unlike fractions. Printable Worksheets And Lessons - Multiply Across Step-by-Step Lesson- Some people work on the bottom first and then the top, but it really doesn't matter. - Guided Lesson - Top light fractions that create bottom heavy fractions. - Guided Lesson Explanation - Fractions of fractions sometimes trip up kids. - Horizontal Worksheet 5 Pack -The setup will require you to rewrite them to help make sense. A good habit to get into. - Practice Worksheet - You will find a number of like fractions in these sets - Matching Worksheet - Find the products of the fractions and write the letter. - Multiplying Like Fractions Five Pack - I thought this would be a good place to throw this in. - Fractions of Area Worksheet - Practice writing multiplication sentences. - Fraction and Whole Number Multiplication Worksheet - We ask you to finalize the number as mixed number. - Fraction Multiplication Sentences Practice and Lesson - A unique way to look at things. - Multiplying Fractions By Whole Numbers Lesson and Practice - Breaking fractions into pieces. - Fractions Times Whole Numbers (With Visuals) - Using the images to do the problems makes it much easier. Remember to tell the kids to multiply across the pond and then rewrite your product. - Homework 1 - Multiply the first fraction by the second fraction. - Homework 2 - Try flipping the largest numerator first. - Homework 3 - This time try it the other way around. You have lots of space to work with here. Make sure to use it.
Candidates can download NCERT Exemplar Class 11 Maths Unit 5 from this page. The exemplar has been provided by the National Council of Educational Research & Training (NCERT) and the candidates can check it from below for free of cost. It contains objective, very short answer type, short answer type, and long answer type questions. Along with it, the answer for each question has also been provided. From the NCERT Exemplar Class 11 Maths Unit 5, candidates can understand the level and type of questions that are asked in the exam. NCERT Exemplar Class 11 Maths Unit 5 Complex Numbers and Quadratic Equations NCERT Exemplar Class 11 Maths Unit 5 is for Complex Numbers and Quadratic Equations. The type of questions that will be asked from NCERT Class 11 Maths Unit 5 are displayed in the below provided NCERT Exemplar Class 11 Maths Unit 5. With the help of it, candidates can prepare well for the examination. We know that the square of a real number is always non-negative e.g. 42 = 16 and (– 4)2 = 16. Therefore, square root of 16 is ± 4. What about the square root of a negative number? It is clear that a negative number can not have a real square root. So we need to extend the system of real numbers to a system in which we can find out the square roots of negative numbers. Euler (1707 – 1783) was the first mathematician to introduce the symbol i (iota) for positive square root of – 1 i.e., i = 5.1.1 Imaginary numbers Square root of a negative number is called an imaginary number., for example, 5.1.2 Integral powers of i 5.1.3 Complex numbers a) A number which can be written in the form a + ib, where a, b are real numbers and i = is called a complex number. (b) If z = a + ib is the complex number, then a and b are called real and imaginary parts, respectively, of the complex number and written as Re (z) = a, Im (z) = b. (c) Order relations “greater than” and “less than” are not defined for complex numbers. (d) If the imaginary part of a complex number is zero, then the complex number is known as purely real number and if real part is zero, then it is called purely imaginary number, for example, 2 is a purely real number because its imaginary part is zero and 3i is a purely imaginary number because its real part 5.1.4 Algebra of complex numbers 5.1.5 Addition of complex numbers satisfies the following properties 5.1.6 Multiplication of complex numbers 5.1.8 Conjugate of a complex number 5.1.9 Modulus of a complex number 5.1.10 Properties of modulus of a complex number 5.2 Argand Plane A complex number z = a + ib can be represented by a unique point P (a, b) in the cartesian plane referred to a pair of rectangular axes. The complex number 0 + 0i represent the origin 0 ( 0, 0). A purely real number a, i.e., (a + 0i) is represented by the point (a, 0) on x – axis. Therefore, x-axis is called real axis. A purely imaginary number ib, i.e., (0 + ib) is represented by the point (0, b) on y-axis. Therefore, y-axis is called imaginary axis. Similarly, the representation of complex numbers as points in the plane is known as Argand diagram. The plane representing complex numbers as points is called complex plane or Argand plane or Gaussian plane. 5.2.1 Polar form of a complex number 5.2.2 Solution of a quadratic equation The equations ax 2 + bx + c = 0, where a, b and c are numbers (real or complex, a ≠ 0) is called the general quadratic equation in variable x. The values of the variable satisfying the given equation are called roots of the equation. The quadratic equation ax2 + bx + c = 0 with real coefficients has two roots given by , where D = b2 – 4ac, called the discriminant of the equation. - When D = 0, roots of the quadratic equation are real and equal. When D > 0, roots are real and unequal. Further, if a, b, c ∈ Q and D is a perfect square, then the roots of the equation are rational and unequal, and if a, b, c ∈Q and D is not a perfect square, then the roots are irrational and occur in pair. - When D < 0, roots of the quadratic equation are non real (or complex). Let α, β be the roots of the quadratic equation ax2 + bx + c = 0, then sum of the roots (α + β) = − b/a and the product of the roots ( α . β) = c/a - Let S and P be the sum of roots and product of roots, respectively, of a quadratic equation. Then the quadratic equation is given by x2 – Sx + P = 0. Short Answer Type Questions (Solved Examples) Long Answer Type Questions (Solved Examples) Objective Type Questions (Solved Examples) Short Answer Type Questions (Exercise) Long Answer Type Questions (Exercise) Fill in the Blank Type Questions (Exercise) True or False Type Questions (Exercise) Match Type Questions (Exercise) Other Questions (Exercise) Objective Type Questions (Exercise) Click Here to download NCERT Exemplar Class 11 Maths Unit 5 Complex Numbers and Quadratic Equations. To get fastest exam alerts and government job alerts in India, join our Telegram channel.
NGC 4414, a typical spiral galaxy in the constellation Coma Berenices, is about 55,000 light-years in diameter and approximately 60 million light-years away from Earth. A galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias (γαλαξίας), literally "milky", a reference to the Milky Way galaxy. Examples of galaxies range from dwarfs with as few as ten million (107) stars to giants with a hundred trillion (1014) stars, each orbiting their galaxy's own center of mass. The Antennae Galaxies are undergoing a collision that will result in their eventual merger. Galaxies contain varying amounts of star systems, star clusters and types of interstellar clouds. In between these objects is a sparse interstellar medium of gas, dust, and cosmic rays. Dark matter appears to account for around 90% of the mass of most galaxies. Observational data suggests that supermassive black holes may exist at the center of many, if not all, galaxies. They are thought to be the primary driver of active galactic nuclei found at the core of some galaxies. The Milky Way galaxy appears to harbor at least one such object. The Whirlpool Galaxy (on left), an example of an unbarred spiral galaxy. Galaxies have been historically categorized according to their apparent shape; usually referred to as their visual morphology. A common form is the elliptical galaxy, which has an ellipse-shaped light profile. Spiral galaxies are disk-shaped with dusty, curving arms. Those with irregular or unusual shapes are known as irregular galaxies and typically originate from disruption by the gravitational pull of neighboring galaxies. Such interactions between nearby galaxies, which may ultimately result in a merging, sometimes induce significantly increased incidents of star formation leading to starburst galaxies. Smaller galaxies lacking a coherent structure are referred to as irregular galaxies. Hoag's Object, an example of a ring galaxy There are probably more than 170 billion (1.7 × 1011) galaxies in the observable universe. Most are 1,000 to 100,000 parsecs in diameter and usually separated by distances on the order of millions of parsecs (or megaparsecs). Intergalactic space (the space between galaxies) is filled with a tenuous gas of an average density less than one atom per cubic meter. The majority of galaxies are organized into a hierarchy of associations known as groups and clusters, which, in turn usually form larger superclusters. At the largest scale, these associations are generally arranged into sheets and filaments, which are surrounded by immense voids. NGC 1300, an example of a barred spiral galaxy. Spiral galaxies consist of a rotating disk of stars and interstellar medium, along with a central bulge of generally older stars. Extending outward from the bulge are relatively bright arms. In the Hubble classification scheme, spiral galaxies are listed as type S, followed by a letter (a, b, or c) that indicates the degree of tightness of the spiral arms and the size of the central bulge. An Sa galaxy has tightly wound, poorly defined arms and possesses a relatively large core region. At the other extreme, an Sc galaxy has open, well-defined arms and a small core region. A galaxy with poorly defined arms is sometimes referred to as a flocculent spiral galaxy; in contrast to the grand design spiral galaxy that has prominent and well-defined spiral arms. In spiral galaxies, the spiral arms do have the shape of approximate logarithmic spirals, a pattern that can be theoretically shown to result from a disturbance in a uniformly rotating mass of stars. Like the stars, the spiral arms rotate around the center, but they do so with constant angular velocity. The spiral arms are thought to be areas of high-density matter, or "density waves". As stars move through an arm, the space velocity of each stellar system is modified by the gravitational force of the higher density. (The velocity returns to normal after the stars depart on the other side of the arm.) This effect is akin to a "wave" of slowdowns moving along a highway full of moving cars. The arms are visible because the high density facilitates star formation, and therefore they harbor many bright and young stars. Galactic Center of the Milky Way The word galaxy derives from the Greek term for our own galaxy, galaxias (γαλαξίας), or kyklos galaktikos, meaning "milky circle" for its appearance in the sky. In Greek mythology, Zeus places his son born by a mortal woman, the infant Heracles, on Hera's breast while she is asleep so that the baby will drink her divine milk and will thus become immortal. Hera wakes up while breastfeeding and then realizes she is nursing an unknown baby: she pushes the baby away and a jet of her milk sprays the night sky, producing the faint band of light known as the Milky Way. In the astronomical literature, the capitalized word 'Galaxy' is used to refer to our galaxy, the Milky Way, to distinguish it from the billions of other galaxies. The term Milky Way first appeared in the English language in a story by Chaucer. "See yonder, lo, the Galaxyë Which men clepeth the Milky Wey, For hit is whyt." —Geoffrey Chaucer. The House of Fame, c. 1380. NGC 5866, an example of a lenticular galaxy A lenticular galaxy is a type of galaxy which is intermediate between an elliptical galaxy and a spiral galaxy in galaxy morphological classification schemes. Lenticular galaxies are disk galaxies (like spiral galaxies) which have used up or lost most of their interstellar matter and therefore have very little ongoing star formation. They may, however, retain significant dust in their disks. As a result, they consist mainly of aging stars (like elliptical galaxies). Because of their ill-defined spiral arms, if they are inclined face-on it is often difficult to distinguish between them and elliptical galaxies. Despite the morphological differences, lenticular and elliptical galaxies share common properties like spectral features, scaling relations and both can be considered as early type galaxies which are passively evolving, at least in the local universe.
The findings were presented in papers published by researchers with NASA's Cassini mission to Saturn and work on the Hubble Space Telescope. The microbes could combine the carbon dioxide in water and hydrogen to gain energy. The gas could be a chemical energy source of life, scientists involved with the mission said. The chemical ingredients of life include carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulfur. Cassini project scientist Linda Spilker added that the confirmation - that the chemical energy for life exists within Enceladus' ocean - is an important milestone in mankind's search for habitable worlds beyond Earth. On Earth, such hydrothermal vents support thriving communities of life in complete isolation from sunlight. One of the Saturnian moon's most visible features is its ice plumes - enormous geysers that release water vapor into space. Cassini has found that nearly all of these ingredients are there on Enceladus, a tiny icy moon at a distance of a billion miles away from Saturn. A plume of water had already been observed in the same spot, which is how scientists knew to be watching for it. NASA announced on Thursday that its Cassini spacecraft mission to Saturn has gathered new evidence that there's a chemical reaction taking place under the moon's icy surface that could provide conditions for life. The probe found the hydrogen when it made its last and closest pass through plumes at Enceladus' south pole on October 28, 2015. This new finding is therefore an independent line of evidence supporting the theory of hydrothermal activity taking place in the ocean of Enceladus. Cassini, NASA said, was never created to detect signs of life, but rather to simply record data of Saturn. The original plume was estimated to be about 30 miles (50 km) high, while the newly imaged jet extended about 62 miles (100 km) above the moon's surface. But our planet's mostly liquid surface appears to be an outlier among our system's oceans-most large reservoirs of water exist on planets and moons far from the sun's heat and therefore can exist only beneath a frozen solid crust. That is a tough question to answer, according to Mary Voytek, an astrobiology senior scientist at NASA Headquarters. New observations from NASA's Galileo spacecraft suggests Europa's plume, like the plumes on Enceladus, is associated with warmer temperature readings. The Europa Clipper is set to launch in the 2020s and will make close flybys to Europa to study the oceans there to determine whether or not the same thing is happening there as on Enceladus, and importantly whether or not the moon could possibly support life.
The Mason-Dixon line, also called the Mason and Dixon line or Mason's and Dixon's line, is a demarcation line between four U.S. states, forming part of the borders of Pennsylvania, Maryland, Delaware, and West Virginia (part of Virginia until 1863). It was surveyed between 1763 and 1767 by Charles Mason and Jeremiah Dixon in the resolution of a border dispute involving Maryland, Pennsylvania, and Delaware in Colonial America. The dispute had its origins almost a century earlier in the somewhat confusing proprietary grants by King Charles I to Lord Baltimore (Maryland) and by King Charles II to William Penn (Pennsylvania). The Mason-Dixon line along the southern Pennsylvania border later became informally known as the boundary between the free (Northern) states and the slave (Southern) states. The Virginia portion was the northern border of the Confederacy. This usage especially came to prominence during the debate around the Missouri Compromise of 1820, when drawing boundaries between slave and free territory was an issue. It is still used today in the figurative sense of a line that separates the North and South politically and socially (see Dixie). Maryland's charter of 1632 granted Cecil Calvert land north of the entire length of the Potomac River up to the 40th parallel. A problem arose when Charles II granted a charter for Pennsylvania in 1681. The grant defined Pennsylvania's southern border as identical to Maryland's northern border, but described it differently, as Charles relied on an inaccurate map. The terms of the grant clearly indicate that Charles II and William Penn believed the 40th parallel would intersect the Twelve-Mile Circle around New Castle, Delaware, when in fact it falls north of the original boundaries of the City of Philadelphia, the site of which Penn had already selected for his colony's capital city. Negotiations ensued after the problem was discovered in 1681. A compromise proposed by Charles II in 1682, which might have resolved the issue, was undermined by Penn receiving the additional grant of the "Three Lower Counties" along Delaware Bay, which later became the Delaware Colony, a satellite of Pennsylvania. Maryland considered these lands part of its original grant. The conflict became more of an issue when settlement extended into the interior of the colonies. In 1732 the Proprietary Governor of Maryland, Charles Calvert, 5th Baron Baltimore, signed a provisional agreement with William Penn's sons, which drew a line somewhere in between and renounced the Calvert claim to Delaware. But later, Lord Baltimore claimed that the document he had signed did not contain the terms he had agreed to, and refused to put the agreement into effect. Beginning in the mid-1730s, violence erupted between settlers claiming various loyalties to Maryland and Pennsylvania. The border conflict would be known as Cresap's War. Progress was made after a Court of Chancery ruling affirming the 1732 agreement, but the issue remained unresolved until Frederick Calvert, 6th Baron Baltimore ceased contesting the claims on the Maryland side and accepted the earlier agreements. Maryland's border with Delaware was to be based on the Transpeninsular Line and the Twelve-Mile Circle around New Castle. The Pennsylvania-Maryland border was defined as the line of latitude 15 miles (24 km) south of the southernmost house in Philadelphia (on what is today South Street). As part of the settlement, the Penns and Calverts commissioned the English team of Charles Mason and Jeremiah Dixon to survey the newly established boundaries between the Province of Pennsylvania, the Province of Maryland, and Delaware Colony. In 1779, Pennsylvania and Virginia agreed "To extend Mason's and Dixon's line, due west, five degrees of longitude, to be computed from the river Delaware, for the southern boundary of Pennsylvania, and that a meridian, drawn from the western extremity thereof to the northern limit of the said state, be the western boundary of Pennsylvania for ever." After Pennsylvania abolished slavery in 1781, the western part of this line and the Ohio River became a border between slave and free states, with Delaware retaining slavery until the 13th Amendment was ratified in 1865. Mason and Dixon's actual survey line began to the south of Philadelphia, Pennsylvania, and extended from a benchmark east to the Delaware River and west to what was then the boundary with western Virginia. The surveyors also fixed the boundary between Delaware and Pennsylvania and the approximately north-south portion of the boundary between Delaware and Maryland. Most of the Delaware-Pennsylvania boundary is an arc, and the Delaware-Maryland boundary does not run truly north-south because it was intended to bisect the Delmarva Peninsula rather than follow a meridian. The Maryland-Pennsylvania boundary is an east-west line with an approximate mean latitude of 39°43?20? N (Datum WGS 84). In reality, the east-west Mason-Dixon line is not a true line in the geometric sense, but is instead a series of many adjoining line segments, following a path between latitude 39°43?15? N and 39°43?23? N. The surveyors also extended the boundary line 40 miles (64 km) west of Maryland's western boundary, into territory that was still in dispute between Pennsylvania and Virginia, though this was contrary to their original charter. Mason and Dixon's survey was finished on October 9, 1767, about 31 miles (50 km) east of what is now Pennsylvania's southwest corner. In 1774, commissioners from Pennsylvania and Virginia met to negotiate their boundary, which at the time involved Pennsylvania's southern border west of Maryland and its entire western border. Both sides agreed that Pennsylvania's grant made its western border a tracing of the course of the Delaware River, displaced five degrees (approximately 265 miles) to the west. And both sides thought this would place Fort Pitt in Virginia territory (in fact it would not have). With that in mind, the governor of Pennsylvania argued that, despite the agreement reached with Maryland, Pennsylvania's southern border west of Maryland was still the 39th parallel, about 50 miles (80 km) south of the Mason-Dixon line. Negotiations continued for five years, with a series of proposed lines. In the end, a compromise was reached: the Mason-Dixon line would be extended west to a point five degrees west of the Delaware River. To compensate Pennsylvania for the claimed territory lost, its western boundary would be run due north rather than copying the course of the Delaware River. The Mason-Dixon line was marked by stones every mile 1 mile (1.6 km) and "crownstones" every 5 miles (8.0 km), using stone shipped from England. The Maryland side says "(M)" and the Delaware and Pennsylvania sides say "(P)". Crownstones include the two coats of arms. Today, while a number of the original stones are missing or buried, many are still visible, resting on public land and protected by iron cages. Mason and Dixon confirmed earlier survey work, which delineated Delaware's southern boundary from the Atlantic Ocean to the "Middle Point" stone (along what is today known as the Transpeninsular Line). They proceeded nearly due north from this to the Pennsylvania border. Later, the line was marked in places by additional benchmarks and survey markers. The lines have been resurveyed several times over the centuries without substantive changes to Mason's and Dixon's work. The stones may be a few, to a few hundred, feet east or west of the point Mason and Dixon thought they were: in any event, the line drawn from stone to stone forms the legal boundary. The line was established to end a boundary dispute between the British colonies of Maryland and Pennsylvania/Delaware. Maryland had been granted the territory north of the Potomac River up to the fortieth parallel. Pennsylvania's grant defined the colony's southern boundary as following a 12-mile (radius) circle (19 km) counter-clockwise from the Delaware River until it hit "the beginning of the fortieth degree of Northern latitude." From there the boundary was to follow the fortieth parallel due west for five degrees of longitude. But the fortieth parallel does not, in fact, intersect the 12-mile circle, instead lying significantly farther north. Thus Pennsylvania's southern boundary as defined in its charter was contradictory and unclear. The most serious problem was that the Maryland claim would put Philadelphia, the major city in Pennsylvania, within Maryland. The dispute was peacefully resolved in 1767 when the boundary was fixed as follows: The disputants engaged an expert British team, astronomer Charles Mason and surveyor Jeremiah Dixon, to survey what became known as the Mason-Dixon line. It cost the Calverts of Maryland and the Penns of Pennsylvania £3,512 9/- (equivalent to £455,944 in 2019) to have 244 miles (393 km) surveyed with such accuracy. To them the money was well spent, for in a new country there was no other way of establishing ownership. The Mason-Dixon line is made up of four segments corresponding to the terms of the settlement: The most difficult task was fixing the tangent line, as they had to confirm the accuracy of the transpeninsular line midpoint and the 12-mile circle, determine the tangent point along the circle, and then actually survey and monument the border. They then surveyed the north and arc lines. They did this work between 1763 and 1767. This actually left a small wedge of land in dispute between Delaware and Pennsylvania until 1921.[better source needed] In April 1765, Mason and Dixon began their survey of the more famous Maryland-Pennsylvania line. They were commissioned to run it for a distance of five degrees of longitude west from the Delaware River, fixing the western boundary of Pennsylvania (see the entry for Yohogania County). However, in October 1767, at Dunkard Creek near Mount Morris, Pennsylvania, nearly 244 miles (393 km) west of the Delaware, their Iroquois guides refused to go any further, having reached the border of their lands with the Lenape, with whom they were engaged in hostilities. As a result, the group was forced to quit, and on October 11, they made their final observations, 233 miles (375 km) from their starting point. In 1784, surveyors David Rittenhouse and Andrew Ellicott and their crew completed the survey of the Mason-Dixon line to the southwest corner of Pennsylvania, five degrees from the Delaware River.[note 1] Other surveyors continued west to the Ohio River. The section of the line between the southwestern corner of Pennsylvania and the river is the county line between Marshall and Wetzel counties, West Virginia. The Mason-Dixon line has been resurveyed three times: in 1849, 1900, and in the 1960s. On November 14, 1963, during the bicentennial of the Mason-Dixon line, U.S. President John F. Kennedy opened a newly completed section of Interstate 95 where it crossed the Maryland-Delaware border. It was one of his last public appearances before his assassination in Dallas, Texas. The Delaware Turnpike and the Maryland portion of the new road were later designated as the John F. Kennedy Memorial Highway. Mason and Dixon could only do the work as accurately as they did due to the work of Nevil Maskelyne, some of whose instruments they used. There was keen interest in their work and much communication between the surveyors, Maskelyne and other members of the British Scientific establishment in the Royal Society in Britain, notably Henry Cavendish. During such survey work, it is normal to survey from point to point along the line and then survey back to the starting point, where if there were no errors the origin and re-surveyed position would coincide. Normally the return errors would be random - i.e. the return survey errors compared to the intermediate points back to the start point would be spatially randomly distributed around the start point. Mason and Dixon found that there were larger than expected systematic errors, i.e. non-random errors, that led the return survey consistently being in one direction away from the starting point. When this information got back to the Royal Society members, Henry Cavendish realised that this may have been due to the gravitational pull of the Allegheny Mountains deflecting the theodolite plumb-bobs and spirit levels. Maskelyne then proposed measuring the gravitational force causing this deflection induced by the pull of a nearby mountain upon a plumb-bob in 1772 and sent Mason (who had returned to Britain) on a site survey through central England and Scotland to find a suitable location during the summer of 1773. Mason selected Schiehallion at which to conduct what became known as the Schiehallion experiment, which was carried out primarily by Maskelyne and determined the density of the Scottish mountain. Several years later Cavendish used a very sensitive torsion balance to carry out the Cavendish experiment and determine the average density of Earth. It is unlikely that Mason and Dixon ever heard the phrase "Mason-Dixon line". The official report on the survey, issued in 1768, did not even mention their names. While the term was used occasionally in the decades following the survey, it came into popular use when the Missouri Compromise of 1820 named "Mason and Dixon's line" as part of the boundary between slave territory and free territory. In popular usage to people from the northern United States, the Mason-Dixon line symbolizes a cultural boundary between the North and the South (Dixie). However, for many people who identify as Southern, Maryland is not considered a Southern state, leading to confusion over terminology (for more on Maryland's position as southern or northern, see the Region section of the article on Dixie). Originally "Mason and Dixon's Line" referred to the border between Pennsylvania and Maryland. After Pennsylvania abolished slavery, it served as a demarcation line for the legality of slavery. That demarcation did not extend beyond Pennsylvania because Delaware, then a slave state, extended north and east of the boundary. Also lying north and east of the boundary was New Jersey, where slavery was formally abolished in 1846, but former slaves continued to be "apprenticed" to their masters until the passage of the Thirteenth Amendment to the United States Constitution in 1865. Popular culture contains a multitude of references to the Mason-Dixon line as a general geographic division, or character names evoking it, although a minority of those specifically relate to the line itself. Double run in straight line by helicopter between control spaced at 80 km. Accordingly Mr. Charles Mason, who had been employed on several astronomical occasions by the Royal Society, was appointed to make a tour through the Highlands of Scotland in the summer of the year 1773, taking notice of the principal hills in England which lay in his route either in his going or in his return. The Royal Society agreed to a proposal that it despatch a surveyor, a Mr Charles Mason whom they had previously employed on astronomical projects, all the way to Scotland and back, to survey likely-looking mountains, and to select a suitable mountain - ideally it should be a steep-sided cone, or a wedge with its apex ridge running W - E and with steep faces to N and S, and separated from the nearest neighbours to N and S by low land. Mr Mason selected for them a mountain at "the centre of Scotland", Schiehallion - a wedge, with the summit ridge running nearly W - E, 3547 ft above sea level at its western summit, about 3000 ft at the E-end of the ridge; it presents steep faces to the trench to the N which contains Loch Rannoch and Loch Tummel, and to the deep Gleann Mor to the S. [An approximate altitude for Gleann Mor is 1500 feet, and for the land at the same distance to the north of the ridge is 1600 ft.] In 1772...The proposal was favourably received by the Society, and Mr. Charles Mason was sent to examine various hills in England and Scotland, and to select the most suitable (32). Mason found the two hills referred to by Maskelyne were not suitable; and fixed upon Schehallien in Perthshire as offering the best situation.
1. Powers of 10: looks at multiplying and dividing decimal numbers by 10, 100 and 1000. 2. Multiply and Divide by Powers of 10: looks at multiplying and dividing numbers by 0.1, 0.01, 1/10, 1/100 etc. 3. Both lessons are well differentiated. 4. Now with a newer resource for more able pupils. Part 1: Converting between metric units of length, mass (weight) and capacity. (2022 update) 1. PowerPoint demonstrating converting units 2. Worksheet including a crossnumber (Number crossword) and problem solving and reasoning questions. 3. Answers included on the PowerPoint. Update: Crossword has been fixed. Part 2: Imperial Units Contains examples, conversions and problem solving on the following: Converting between imperial units Converting between imperial and metric units. 1. 1%, 10%, 25% and 50% of amounts 2. 5% and 20% of amounts 3. Multiples of 5% of amounts 4. Problem solving questions included 5. Examples include a visual approach to help pupils fully understand percentages of amounts (bar model) 1. A PowerPoint designed to prompt pupils to fully understand 3D shapes. 2. A worksheet allowing pupils to investigate Euler's Formula. Questions within the worksheet are well differentiated to allow pupils to maximise their progress. Pupils will also investigate Platonic shapes. 3. Pupils will gain a full understanding of Prisms and Pyramids. 4. Pupils will gain knowledge on Polyhedrons and Non-Polyhedrons. Pupils will be able to explain why a Cylinder is not a Prism. 5. All misconceptions are addressed in this lesson. The Radius: Working out the gradient and length of the radius The Tangent: Working out the equation of a tangent and applying it to solve problems Equation of a Circle: Drawing circles from their equations Solving simultaneous equations graphically. Solving simultaneous equations algebraically. 1. A PowerPoint demonstrating the properties of quadrilaterals and how to work interior and external angles of them. 2. A well differentiated worksheet designed to maximise progress. 3. The PowerPoint contains detailed solutions to the worksheet. Worksheet and PowerPoint on Rotation. The PowerPoint shows shapes being rotated including tracing paper being put over the shape. Highly visual. PowerPoint now has a diagnostic quiz at the start to cover prior knowledge. (Use mini white boards) The worksheet has been improved to make it more clear. Introduction to rearranging simple formula including fractions, negatives, squares and square roots. Broken up into 2 lessons. 1 lesson contains a card sort. Lessons include problem solving, STEM questions and answers. 1. PowerPoint demonstrating fractions of amounts (Includes visual examples) 2. Worksheet containing two activities and an NRICH task (Includes visual questions for differentiation) PowerPoint and worksheet designed to allow all pupils make progress and fully understand how to find fractions of amounts. This is done by illustrating the problems on the PPT and having a worksheet that is well differentiated. Complete lesson on using the multiplier method. Starter: Converting percentages to decimals Main 1: Percentages of amounts Main 2: Percentage increase and decrease Key Question: GCSE past paper question (AQA) Each exercise contains reasoning and problem solving Examples and answers included Decimals lessons designed for pupils learning how work with decimal numbers… Highly visual to support pupils understanding of decimal numbers. 1. Place Value and Ordering Decimals (2) 2. Adding and Subtracting Decimal Numbers (£2) 3. Multiplying and Dividing by Powers of 10. (£2) 4. Multiplying and Dividing Decimal Numbers (FREE) 1. Starter on percentages of amounts 2. Mental methods on percentage increase and decrease 3. Calculator method on percentage increase and decrease 4. Examples include the bar model to help pupils understand that the original amount equals 100% Adding and subtracting fractions. 1. Adding and subtracting fractions using diagrams (same denominator) 2. Adding and subtracting fractions with the same denominator. 3. Adding and subtracting fractions with different denominators. 4. Adding and subtracting mixed numbers. 5. Activities include problem solving and RICH tasks. 6. Examples come with diagrams to help pupils gain full understanding. Quadratic sequences at KS3. WALT and WILF Part 1: Using position to term rule to find the first few terms of a quadratic sequence. Part 2: Finding the position to term rule of a quadratic sequence. Part 3: Problem solving and RICH task.
A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value. It is a cross-section of the three-dimensional graph of the function f(x, y) parallel to the x, y plane. In cartography, a contour line (often just called a "contour") joins points of equal elevation (height) above a given level, such as mean sea level. A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness or gentleness of slopes. The contour interval of a contour map is the difference in elevation between successive contour lines. More generally, a contour line for a function of two variables is a curve connecting points where the function has the same particular value. The gradient of the function is always perpendicular to the contour lines. When the lines are close together the magnitude of the gradient is large: the variation is steep. A level set is a generalization of a contour line for functions of any number of variables. Contour lines are curved, straight or a mixture of both lines on a map describing the intersection of a real or hypothetical surface with one or more horizontal planes. The configuration of these contours allows map readers to infer relative gradient of a parameter and estimate that parameter at specific places. Contour lines may be either traced on a visible three-dimensional model of the surface, as when a photogrammetrist viewing a stereo-model plots elevation contours, or interpolated from estimated surface elevations, as when a computer program threads contours through a network of observation points of area centroids. In the latter case, the method of interpolation affects the reliability of individual isolines and their portrayal of slope, pits and peaks. - 1 Types - 1.1 Equidistants (isodistances) - 1.2 Isopleths - 1.3 Meteorology - 1.4 Physical geography and oceanography - 1.5 Geology - 1.6 Environmental science - 1.7 Ecology - 1.8 Social sciences - 1.9 Statistics - 1.10 Thermodynamics, engineering, and other sciences - 1.11 Other phenomena - 2 History - 3 Graphical design - 4 Plan view versus profile view - 5 Labeling contour maps - 6 See also - 7 References - 8 External links Contour lines are often given specific names beginning "iso-" (Ancient Greek: ἴσος isos "equal") according to the nature of the variable being mapped, although in many usages the phrase "contour line" is most commonly used. Specific names are most common in meteorology, where multiple maps with different variables may be viewed simultaneously. The prefix "iso-" can be replaced with "isallo-" to specify a contour line connecting points where a variable changes at the same rate during a given time period. The words isoline and isarithm (ἀριθμός arithmos "number") are general terms covering all types of contour line. The word isogram (γράμμα gramma "writing or drawing") was proposed by Francis Galton in 1889 as a convenient generic designation for lines indicating equality of some physical condition or quantity; but it commonly refers to a word without a repeated letter. An isogon (from γωνία or gonia, meaning 'angle') is a contour line for a variable which measures direction. In meteorology and in geomagnetics, the term isogon has specific meanings which are described below. An isocline (from κλίνειν or klinein, meaning 'to lean or slope') is a line joining points with equal slope. In population dynamics and in geomagnetics, the terms isocline and isoclinic line have specific meanings which are described below. Equidistant is a line of equal distance from a given point, line, polyline. In geography, the word isopleth (from πλῆθος or plethos, meaning 'quantity') is used for contour lines that depict a variable which cannot be measured at a point, but which instead must be calculated from data collected over an area. An example is population density, which can be calculated by dividing the population of a census district by the surface area of that district. Each calculated value is presumed to be the value of the variable at the centre of the area, and isopleths can then be drawn by a process of interpolation. The idea of an isopleth map can be compared with that of a choropleth map. In meteorology, the word isopleth is used for any type of contour line. Meteorological contour lines are based on interpolation of the point data received from weather stations and weather satellites. Weather stations are seldom exactly positioned at a contour line (when they are, this indicates a measurement precisely equal to the value of the contour). Instead, lines are drawn to best approximate the locations of exact values, based on the scattered information points available. Meteorological contour maps may present collected data such as actual air pressure at a given time, or generalized data such as average pressure over a period of time, or forecast data such as predicted air pressure at some point in the future Thermodynamic diagrams use multiple overlapping contour sets (including isobars and isotherms) to present a picture of the major thermodynamic factors in a weather system. An isobar (from βάρος or baros, meaning 'weight') is a line of equal or constant pressure on a graph, plot, or map; an isopleth or contour line of pressure. More accurately, isobars are lines drawn on a map joining places of equal average atmospheric pressure reduced to sea level for a specified period of time. In meteorology, the barometric pressures shown are reduced to sea level, not the surface pressures at the map locations. The distribution of isobars is closely related to the magnitude and direction of the wind field, and can be used to predict future weather patterns. Isobars are commonly used in television weather reporting. Isallobars are lines joining points of equal pressure change during a specific time interval. These can be divided into anallobars, lines joining points of equal pressure increase during a specific time interval, and katallobars, lines joining points of equal pressure decrease. In general, weather systems move along an axis joining high and low isallobaric centers. Isallobaric gradients are important components of the wind as they increase or decrease the geostrophic wind. An isopycnal is a line of constant density. An isoheight or isohypse is a line of constant geopotential height on a constant pressure surface chart. Isohypse and isoheight are simply known as lines showing equal pressure on a map. An isotherm (from θέρμη or thermē, meaning 'heat') is a line that connects points on a map that have the same temperature. Therefore, all points through which an isotherm passes have the same or equal temperatures at the time indicated. An isotherm at 0 °C is called the freezing level. The term was coined by the Prussian geographer and naturalist Alexander von Humboldt, who as part of his research into the geographical distribution of plants published the first map of isotherms in Paris, in 1817. An isogeotherm is a line of equal mean annual temperature. An isocheim is a line of equal mean winter temperature, and an isothere is a line of equal mean summer temperature. Rainfall and air moisture An isoneph is a line indicating equal cloud cover. An isochalaz is a line of constant frequency of hail storms, and an isobront is a line drawn through geographical points at which a given phase of thunderstorm activity occurred simultaneously. Snow cover is frequently shown as a contour-line map. Freeze and thaw An isopectic line denotes equal dates of ice formation each winter, and an isotac denotes equal dates of thawing. Physical geography and oceanography Elevation and depth Contours are one of several common methods used to denote elevation or altitude and depth on maps. From these contours, a sense of the general terrain can be determined. They are used at a variety of scales, from large-scale engineering drawings and architectural plans, through topographic maps and bathymetric charts, up to continental-scale maps. In cartography, the contour interval is the elevation difference between adjacent contour lines. The contour interval should be the same over a single map. When calculated as a ratio against the map scale, a sense of the hilliness of the terrain can be derived. There are several rules to note when interpreting terrain contour lines: - The rule of Vs: sharp-pointed vees usually are in stream valleys, with the drainage channel passing through the point of the vee, with the vee pointing upstream. This is a consequence of erosion. - The rule of Os: closed loops are normally uphill on the inside and downhill on the outside, and the innermost loop is the highest area. If a loop instead represents a depression, some maps note this by short lines radiating from the inside of the loop, called "hachures". - Spacing of contours: close contours indicate a steep slope; distant contours a shallow slope. Two or more contour lines merging indicates a cliff. By counting the number of contours that cross a segment of a stream, the stream gradient can be approximated. Of course, to determine differences in elevation between two points, the contour interval, or distance in altitude between two adjacent contour lines, must be known, and this is normally stated in the map key. Usually contour intervals are consistent throughout a map, but there are exceptions. Sometimes intermediate contours are present in flatter areas; these can be dashed or dotted lines at half the noted contour interval. When contours are used with hypsometric tints on a small-scale map that includes mountains and flatter low-lying areas, it is common to have smaller intervals at lower elevations so that detail is shown in all areas. Conversely, for an island which consists of a plateau surrounded by steep cliffs, it is possible to use smaller intervals as the height increases. An isopotential map is a measure of electrostatic potential in space, often depicted in two dimensions with the electostatic charges inducing that electric potential. The term equipotential line or isopotential line refers to a curve of constant electric potential. Whether crossing an equipotential line represents ascending or descending the potential is inferred from the labels on the charges. In three dimensions, equipotential surfaces may be depicted with a two dimensional cross-section, showing equipotential lines at the intersection of the surfaces and the cross-section. The general mathematical term level set is often used to describe the full collection of points having a particular potential, especially in higher dimensional space. In the study of the Earth's magnetic field, the term isogon or isogonic line refers to a line of constant magnetic declination, the variation of magnetic north from geographic north. An agonic line is drawn through points of zero magnetic declination. An isoporic line refers to a line of constant annual variation of magnetic declination . An isoclinic line connects points of equal magnetic dip, and an aclinic line is the isoclinic line of magnetic dip zero. An isodynamic line (from δύναμις or dynamis meaning 'power') connects points with the same intensity of magnetic force. Besides ocean depth, oceanographers use contour to describe diffuse variable phenomena much as meteorologists do with atmospheric phenomena. In particular, isobathytherms are lines showing depths of water with equal temperature, isohalines show lines of equal ocean salinity, and Isopycnals are surfaces of equal water density. Various geological data are rendered as contour maps in structural geology, sedimentology, stratigraphy and economic geology. Contour maps are used to show the below ground surface of geologic strata, fault surfaces (especially low angle thrust faults) and unconformities. Isopach maps use isopachs (lines of equal thickness) to illustrate variations in thickness of geologic units. In discussing pollution, density maps can be very useful in indicating sources and areas of greatest contamination. Contour maps are especially useful for diffuse forms or scales of pollution. Acid precipitation is indicated on maps with isoplats. Some of the most widespread applications of environmental science contour maps involve mapping of environmental noise (where lines of equal sound pressure level are denoted isobels), air pollution, soil contamination, thermal pollution and groundwater contamination. By contour planting and contour ploughing, the rate of water runoff and thus soil erosion can be substantially reduced; this is especially important in riparian zones. An isoflor is an isopleth contour connecting areas of comparable biological diversity. Usually, the variable is the number of species of a given genus or family that occurs in a region. Isoflor maps are thus used to show distribution patterns and trends such as centres of diversity. In economics, contour lines can be used to describe features which vary quantitatively over space. An isochrone shows lines of equivalent drive time or travel time to a given location and is used in the generation of isochrone maps. An isotim shows equivalent transport costs from the source of a raw material, and an isodapane shows equivalent cost of travel time. Contour lines are also used to display non-geographic information in economics. Indifference curves (as shown at left) are used to show bundles of goods to which a person would assign equal utility. An isoquant (in the image at right) is a curve of equal production quantity for alternative combinations of input usages, and an isocost curve (also in the image at right) shows alternative usages having equal production costs. In statistics, isodensity lines or isodensanes are lines that joint points with the same probability density. Isodensanes are used to display bivariate distributions. Thermodynamics, engineering, and other sciences Various types of graphs in thermodynamics, engineering, and other sciences use isobars (constant pressure), isotherms (constant temperature), isochors (constant specific volume), or other types of isolines, even though these graphs are usually not related to maps. Such isolines are useful for representing more than two dimensions (or quantities) on two-dimensional graphs. Common examples in thermodynamics are some types of phase diagrams. - isochasm: aurora equal occurrence - isochor: volume - isodose: Absorbed dose of radiation - isophene: biological events occurring with coincidence such as plants flowering - isophote: illuminance - mobile telephony: mobile received power and cell coverage area The idea of lines that join points of equal value was rediscovered several times. The oldest known isobath (contour line of constant depth) is found on a map dated 1584 of the river Spaarne, near Haarlem, by Dutchman Pieter Bruinsz. In 1701, Edmond Halley used such lines (isogons) on a chart of magnetic variation. The Dutch engineer Nicholas Cruquius drew the bed of the river Merwede with lines of equal depth (isobaths) at intervals of 1 fathom in 1727, and Philippe Buache used them at 10-fathom intervals on a chart of the English Channel that was prepared in 1737 and published in 1752. Such lines were used to describe a land surface (contour lines) in a map of the Duchy of Modena and Reggio by Domenico Vandelli in 1746, and they were studied theoretically by Ducarla in 1771, and Charles Hutton used them in the Schiehallion experiment. In 1791, a map of France by J. L. Dupain-Triel used contour lines at 20-metre intervals, hachures, spot-heights and a vertical section. In 1801, the chief of the Corps of Engineers, Haxo, used contour lines at the larger scale of 1:500 on a plan of his projects for Rocca d'Aufo. By around 1843, when the Ordnance Survey started to regularly record contour lines in Great Britain and Ireland, they were already in general use in European countries. Isobaths were not routinely used on nautical charts until those of Russia from 1834, and those of Britain from 1838. When maps with contour lines became common, the idea spread to other applications. Perhaps the latest to develop are air quality and noise pollution contour maps, which first appeared in the United States in approximately 1970, largely as a result of national legislation requiring spatial delineation of these parameters. In 2007, Pictometry International was the first to allow users to dynamically generate elevation contour lines to be laid over oblique images. To maximize readability of contour maps, there are several design choices available to the map creator, principally line weight, line color, line type and method of numerical marking. Line weight is simply the darkness or thickness of the line used. This choice is made based upon the least intrusive form of contours that enable the reader to decipher the background information in the map itself. If there is little or no content on the base map, the contour lines may be drawn with relatively heavy thickness. Also, for many forms of contours such as topographic maps, it is common to vary the line weight and/or color, so that a different line characteristic occurs for certain numerical values. For example, in the topographic map above, the even hundred foot elevations are shown in a different weight from the twenty foot intervals. Line color is the choice of any number of pigments that suit the display. Sometimes a sheen or gloss is used as well as color to set the contour lines apart from the base map. Line colour can be varied to show other information. Line type refers to whether the basic contour line is solid, dashed, dotted or broken in some other pattern to create the desired effect. Dotted or dashed lines are often used when the underlying base map conveys very important (or difficult to read) information. Broken line types are used when the location of the contour line is inferred. Numerical marking is the manner of denoting the arithmetical values of contour lines. This can be done by placing numbers along some of the contour lines, typically using interpolation for intervening lines. Alternatively a map key can be produced associating the contours with their values. If the contour lines are not numerically labeled and adjacent lines have the same style (with the same weight, color and type), then the direction of the gradient cannot be determined from the contour lines alone. However, if the contour lines cycle through three or more styles, then the direction of the gradient can be determined from the lines. The orientation of the numerical text labels is often used to indicate the direction of the slope. Plan view versus profile view Most commonly contour lines are drawn in plan view, or as an observer in space would view the Earth's surface: ordinary map form. However, some parameters can often be displayed in profile view showing a vertical profile of the parameter mapped. Some of the most common parameters mapped in profile are air pollutant concentrations and sound levels. In each of those cases it may be important to analyze (air pollutant concentrations or sound levels) at varying heights so as to determine the air quality or noise health effects on people at different elevations, for example, living on different floor levels of an urban apartment. In actuality, both plan and profile view contour maps are used in air pollution and noise pollution studies. Labeling contour maps Labels are a critical component of elevation maps. A properly labeled contour map helps the reader to quickly interpret the shape of the terrain. If numbers are placed close to each other, it means that the terrain is steep. Labels should be placed along a slightly curved line "pointing" to the summit or nadir, from several directions if possible, making the visual identification of the summit or nadir easy. Contour labels can be oriented so a reader is facing uphill when reading the label. Manual labeling of contour maps is a time-consuming process, however, there are a few software systems that can do the job automatically and in accordance with cartographic conventions, called automatic label placement. - Courant, Richard, Herbert Robbins, and Ian Stewart. What Is Mathematics?: An Elementary Approach to Ideas and Methods. New York: Oxford University Press, 1996. p. 344. - Hughes-Hallett, Deborah; McCallum, William G.; Gleason, Andrew M. (2013). Calculus : Single and Multivariable (6 ed.). John wiley. ISBN 978-0470-88861-2. - Merriam Webster - contour line - contour map Merriam Webster - Tracy, John C. Plane Surveying; A Text-Book and Pocket Manual. New York: J. Wiley & Sons, 1907. p. 337. - Davis, John C., 1986, Statistics and data analysis in geology, Wiley ISBN 0-471-08079-9 - Oxford English Dictionary; see also: Nature, 40, 1889, p.651. - Robinson AH (1971). "The genealogy of the isopleth". Cartographic Journal. 8: 49–53. - T. Slocum, R. McMaster, F. Kessler, and H. Howard, Thematic Cartography and Geographic Visualization, 2nd edition, Pearson, 2005, ISBN 0-13-035123-7, p. 272. - ArcGIS, Isopleth: Contours, 2013. - NOAA's National Weather Service, Glossary. - Edward J. Hopkins, Ph.D. (1996-06-10). "Surface Weather Analysis Chart". University of Wisconsin. Retrieved 2007-05-10. - World Meteorological Organisation. "Isallobar". Eumetcal. Retrieved 12 April 2014. - World Meteorological Organisation. "Anallobar". Eumetcal. Retrieved 12 April 2014. - World Meteorological Organisation. "Katallobar". Eumetcal. Retrieved 12 April 2014. - "Forecasting weather system movement with pressure tendency". Chapter 13 - Weather Forecasting. Lyndon State College Atmospheric Sciences. Retrieved 12 April 2014. - DataStreme Atmosphere (2008-04-28). "Air Temperature Patterns". American Meteorological Society. Archived from the original on 2008-05-11. Retrieved 2010-02-07. - Munzar, Jan (1967-09-01). "Alexander Von Humboldt and His Isotherms". Weather. 22 (9): 360–363. doi:10.1002/j.1477-8696.1967.tb02989.x. ISSN 1477-8696. - Sark (Sercq), D Survey, Ministry of Defence, Series M 824, Sheet Sark, Edition 4 GSGS, 1965, OCLC OCLC 27636277. Scale 1:10,560. Contour intervals: 50 feet up to 200, 20 feet from 200 to 300, and 10 feet above 300. - "isoporic line". 1946. Retrieved 2015-07-20. - "Isobel". 2005-01-05. Retrieved 2010-04-25. - Specht, Raymond. Heathlands and related shrublands: Analytical studies. Elsevier. pp. 219–220. - Laver, Michael and Kenneth A. Shepsle (1996) Making and breaking governments pictures. - Fernández, Antonio (2011). "A Generalized Regression Methodology for Bivariate Heteroscedastic Data". Communications in Statistics - Theory and Methods. Taylor and Francis. 40 (4): 601. doi:10.1080/03610920903444011. - Morato-Moreno, Manuel (2017). "Orígenes de la representación topográfica del terreno en algunos mapas hispanoamericanos del s. XVI". Boletín de la Asociación de Geógrafos Españoles. - Thrower, N. J. W. Maps and Civilization: Cartography in Culture and Society, University of Chicago Press, 1972, revised 1996, page 97; and Jardine, Lisa Ingenious Pursuits: Building the Scientific Revolution, Little, Brown, and Company, 1999, page 31. - R. A. Skelton, "Cartography", History of Technology, Oxford, vol. 6, pp. 612-614, 1958. - Colonel Berthaut, La Carte de France, vol. 1, p. 139, quoted by Close. - C. Hutton, "An account of the calculations made from the survey and measures taken at Schehallien, in order to ascertain the mean density of the Earth", Philosophical Transactions of the Royal Society of London, vol. 68, pp. 756-757 - C. Close, The Early Years of the Ordnance Survey, 1926, republished by David and Charles, 1969, ISBN 0-7153-4477-3, pp. 141-144. - T. Owen and E. Pilbeam, Ordnance Survey: Map Makers to Britain since 1791, HMSO, 1992, ISBN 0-11-701507-5. - Imhof, E., "Die Anordnung der Namen in der Karte," Annuaire International de Cartographie II, Orell-Füssli Verlag, Zürich, 93-129, 1962. - Freeman, H., "Computer Name Placement," ch. 29, in Geographical Information Systems, 1, D.J. Maguire, M.F. Goodchild, and D.W. Rhind, John Wiley, New York, 1991, 449-460. \|Wikimedia Commons has media related to Contour lines.\|
Supervised learning is a powerful machine learning technique that enables computers to learn from labeled data. It is used to make predictions or decisions based on input data. The process involves training a model using a dataset with labeled examples, and then using this model to make predictions on new, unseen data. The three steps of supervised learning are training, validation, and testing. In the training step, the model is trained on a large dataset with labeled examples. In the validation step, the model is tested on a separate dataset to see how well it performs. Finally, in the testing step, the model is evaluated on a completely new dataset to see how well it generalizes to new data. This process ensures that the model is accurate and reliable before it is deployed in real-world applications. The three steps of supervised learning are: (1) training the model, (2) testing the model, and (3) validating the model. During the training phase, the model is trained on a labeled dataset to learn the relationship between the input and output variables. Once the model is trained, it is tested on a separate dataset to evaluate its performance. Finally, the model is validated by testing it on a different dataset to ensure that it generalizes well to new data. These three steps are essential for building an accurate and reliable supervised learning model. Understanding Supervised Learning Supervised learning is a type of machine learning where an algorithm learns from labeled data. In this process, the algorithm learns to predict an output based on a given input. The labeled data provides the input-output pairs that the algorithm uses to learn the relationship between the input and output. Supervised learning is a critical component of AI and machine learning. It enables machines to learn from data and make predictions based on that data. It has applications in various fields, including healthcare, finance, and customer service. One of the main advantages of supervised learning is its ability to provide accurate predictions. The algorithm learns from the labeled data, which means it has a basis for making predictions. Additionally, supervised learning can be used for both classification and regression tasks. Classification tasks involve predicting a categorical output, while regression tasks involve predicting a numerical output. Overall, supervised learning is a powerful tool for building predictive models. By understanding the relationship between inputs and outputs, it enables machines to make accurate predictions and improve decision-making processes. Step 1: Data Collection and Preprocessing Importance of Quality Data In supervised learning, the quality of the data used for training is of paramount importance. High-quality data enables the machine learning model to learn more accurately and generalize better to new, unseen data. Conversely, low-quality data can lead to overfitting, where the model performs well on the training data but fails to generalize to new data. Therefore, it is crucial to collect and preprocess data carefully to ensure that it is accurate, relevant, and representative of the problem being solved. Sources of Data for Supervised Learning Supervised learning can be applied to a wide range of problems, from image classification to natural language processing. The data required for supervised learning can be obtained from various sources, including public datasets, private datasets, and real-world data. Public datasets are available from various sources, such as Kaggle, UCI Machine Learning Repository, and Google Dataset Search. Private datasets may be collected by the organization or sourced from third-party providers. Real-world data can be collected through various means, such as user interactions on a website or sensor readings from an IoT device. Data Collection Methods There are various methods for collecting data for supervised learning, depending on the problem being solved and the data available. Some common methods include: - Manual data collection: This involves collecting data manually by human annotators, such as labeling images or transcribing audio recordings. This method is time-consuming and expensive but can provide high-quality data. - Automated data collection: This involves using software tools to collect data automatically, such as web scraping or data extraction from APIs. This method is faster and cheaper than manual data collection but may require preprocessing to ensure data quality. - Data scraping: This involves collecting data from websites or other online sources using web scraping tools. This method can be useful for collecting large amounts of data quickly but may require preprocessing to ensure data quality. - Sensor data collection: This involves collecting data from sensors or other IoT devices. This method can provide real-time data but may require preprocessing to ensure data quality. In summary, collecting data is a critical step in supervised learning, and it is essential to ensure that the data is accurate, relevant, and representative of the problem being solved. The data can be collected from various sources, including public datasets, private datasets, and real-world data, using methods such as manual data collection, automated data collection, data scraping, and sensor data collection. - Cleaning and formatting data - Removing duplicates - Handling categorical variables - Handling numerical variables - Handling missing values and outliers - Imputation methods - Deletion methods - Feature engineering - Feature selection - Feature creation - Feature scaling Preprocessing data is a crucial step in supervised learning. It involves cleaning, formatting, handling missing values and outliers, and feature engineering. Cleaning and formatting data is the first step in preprocessing. This involves removing duplicates, handling categorical variables, and handling numerical variables. The next step is handling missing values and outliers. There are several imputation methods and deletion methods to handle missing values. Outliers can be handled by using robust regression or deleting them. Feature engineering is the final step in preprocessing. This involves selecting features, creating new features, and scaling features. Step 2: Training the Model Choosing an Algorithm Choosing the right algorithm is a crucial step in the training process of supervised learning. The algorithm selected will play a significant role in determining the accuracy and effectiveness of the model. There are various popular supervised learning algorithms that can be used, each with its own unique characteristics and advantages. When selecting an algorithm, it is important to consider the specific problem being addressed, the type of data being used, and the desired outcome. For example, linear regression is a commonly used algorithm for predicting a continuous output variable, while decision trees are often used for classification problems. It is also important to consider the size and complexity of the dataset, as well as the computational resources available. Some algorithms may be more computationally intensive than others, which could impact the speed and efficiency of the training process. In addition to these considerations, it is also important to evaluate the performance of the algorithm using metrics such as accuracy, precision, recall, and F1 score. This will help to ensure that the selected algorithm is appropriate for the specific problem being addressed and will produce accurate and reliable results. Splitting Data into Training and Testing Sets Importance of train-test split Before training a model, it is crucial to split the available data into two separate sets: training and testing. The training set is used to train the model, while the testing set is used to evaluate the model's performance. By doing so, it ensures that the model's performance is not overly optimistic due to the data it was trained on. Techniques for data splitting (e.g., random, stratified) There are different techniques for splitting data into training and testing sets. One common technique is random splitting, where the data is randomly divided into two sets. Another technique is stratified splitting, where the data is divided into strata or groups, and the stratified proportion is maintained in both sets. This technique is particularly useful when the data has a class imbalance, as it ensures that the same proportion of each class is present in both sets. Additionally, there are several rules to consider when splitting the data: - The data should be randomly split, and the random seed should be recorded to ensure reproducibility. - The data should be split into separate sets, not subsets. - The training set should be large enough to capture the underlying patterns in the data. - The testing set should be representative of the data the model will encounter in the real world. By following these rules, data splitting can help to ensure that the model is trained and evaluated accurately and effectively. Training a supervised learning model involves fitting the algorithm to the training data by adjusting the model's parameters to minimize the difference between the predicted outputs and the actual outputs. This process is done using optimization techniques such as gradient descent, which adjust the model's parameters iteratively to minimize the loss function. Gradient descent is an optimization algorithm that adjusts the model's parameters in the direction of the steepest descent of the loss function. It works by computing the gradient of the loss function with respect to the model's parameters and updating the parameters in the opposite direction of the gradient. This process is repeated until the loss function converges to a minimum value. Regularization methods are used to prevent overfitting, which occurs when the model learns the noise in the training data instead of the underlying patterns. Regularization techniques such as L1 and L2 regularization add a penalty term to the loss function to discourage large parameter values, which helps to prevent overfitting. Dropout regularization randomly sets a portion of the model's neurons to zero during training, which helps to prevent overfitting by adding an additional level of noise to the training data. Step 3: Model Evaluation and Deployment Model Evaluation Metrics Evaluating a supervised learning model is a crucial step in the machine learning process, as it allows for assessing the model's performance and identifying areas for improvement. There are several model evaluation metrics that are commonly used in supervised learning, each with its own strengths and weaknesses. In this section, we will explore some of the most popular evaluation metrics and how to choose the appropriate one for a given problem. Accuracy is a commonly used metric for evaluating classification models. It measures the proportion of correctly classified instances out of the total number of instances. While accuracy is a simple and intuitive metric, it may not be the best choice for imbalanced datasets, where one class is significantly larger than the others. In such cases, accuracy can be misleading, as it tends to favor the majority class. Precision is another metric used for evaluating classification models. It measures the proportion of true positives out of the total number of predicted positives. Precision is particularly useful when the cost of false positives is high, such as in medical diagnosis or fraud detection. However, precision does not take into account false negatives, which may be important in some applications. Recall is a metric used for evaluating binary classification models. It measures the proportion of true positives out of the total number of actual positives. Recall is particularly useful when the cost of false negatives is high, such as in spam filtering or detecting rare diseases. However, recall does not take into account false positives, which may be important in some applications. The F1 score is a harmonic mean of precision and recall, and it provides a single score that balances both metrics. The F1 score is particularly useful when precision and recall are both important, and it can be used for both binary and multi-class classification problems. However, the F1 score may not be appropriate when the dataset is imbalanced, as it may give equal weight to all classes, even if one class is much larger than the others. The Receiver Operating Characteristic (ROC) curve is a graphical representation of the trade-off between the true positive rate and the false positive rate of a binary classification model. The ROC curve provides a visual way to compare different models and choose the one with the best trade-off between true positive rate and false positive rate. The area under the ROC curve (AUC) is a common metric for evaluating binary classification models, as it summarizes the performance of the model across different threshold settings. The AUC ranges from 0 to 1, where 1 indicates perfect classification, and 0.5 indicates random guessing. Choosing the appropriate evaluation metric for a given problem depends on the specific context and requirements of the application. In some cases, a single metric may be sufficient, while in others, multiple metrics may be needed to provide a comprehensive evaluation of the model's performance. It is important to carefully consider the strengths and weaknesses of each metric and choose the one that best aligns with the goals and requirements of the problem at hand. Evaluating the Model Evaluating the model is a crucial step in the supervised learning process. The trained model needs to be tested on a separate testing set to determine its performance on unseen data. The evaluation metrics are used to assess the model's performance and to compare it with other models. Testing the Trained Model on the Testing Set The testing set is a separate dataset that has not been used during the training process. It is used to evaluate the model's performance on unseen data. The testing set should be large enough to provide a reliable estimate of the model's performance. The testing set should also be representative of the data that the model will encounter in the real world. Interpreting Evaluation Metrics to Assess Model Performance Evaluation metrics are used to assess the model's performance on the testing set. Some common evaluation metrics include accuracy, precision, recall, F1 score, and AUC-ROC. These metrics provide different insights into the model's performance. For example, accuracy measures the proportion of correct predictions, while precision measures the proportion of true positive predictions among all positive predictions. In addition to these metrics, it is also important to visualize the model's predictions to gain a better understanding of its performance. This can be done by plotting the true positive rate, false positive rate, and threshold as a function of the decision threshold. This plot is known as the ROC curve and provides a visual representation of the trade-off between the true positive rate and the false positive rate. It is also important to evaluate the model's performance on different subgroups of the data. This can help to identify any biases or disparities in the model's performance. Overall, evaluating the model is a critical step in the supervised learning process. It helps to determine the model's performance on unseen data and to identify areas for improvement. Model deployment is the process of integrating the trained model into real-world applications. It is the final step of the supervised learning process and involves deploying the model to production environments. The goal of model deployment is to make the model accessible to end-users and to enable them to make predictions using the model. Integrating the model into real-world applications The first step in model deployment is to integrate the model into real-world applications. This involves packaging the model into a format that can be easily used by other applications. There are several ways to package a model, including using libraries such as TensorFlow or PyTorch. The choice of library depends on the specific requirements of the application. Once the model is packaged, it can be integrated into a variety of applications, including web applications, mobile applications, and desktop applications. The integration process may involve writing code to call the model and display the results to the user. Challenges and considerations for model deployment Model deployment can be challenging and requires careful consideration of several factors. One of the main challenges is ensuring that the model is accurate and performs well in production environments. This may involve fine-tuning the model and retraining it on additional data. Another challenge is managing the performance of the model in production environments. This may involve monitoring the model's performance and making adjustments to ensure that it continues to perform well over time. Finally, model deployment may raise ethical considerations, such as ensuring that the model is fair and does not discriminate against certain groups of people. It is important to carefully consider these issues and address them appropriately. Overall, model deployment is a critical step in the supervised learning process and requires careful consideration of several factors to ensure that the model is accurate, performs well in production environments, and is ethically sound. 1. What are the three steps of supervised learning? Supervised learning is a type of machine learning where the model is trained on labeled data, meaning that the input data has corresponding output data that the model is trying to predict. The three steps of supervised learning are: - Data Preparation: In this step, the data is collected and preprocessed to ensure that it is clean and suitable for the model to learn from. This includes tasks such as removing missing values, handling outliers, and encoding categorical variables. - Model Training: In this step, the model is trained on the labeled data using an algorithm such as linear regression, logistic regression, or neural networks. The goal is to find the best set of parameters that minimize the difference between the predicted output and the actual output. - Model Evaluation: In this step, the model is tested on a separate set of data to evaluate its performance. This helps to determine how well the model generalizes to new data and to identify any potential issues such as overfitting or underfitting. The evaluation metric used depends on the problem and the type of output being predicted, such as accuracy, precision, recall, or F1 score. 2. What is data preparation in supervised learning? Data preparation is the first step in supervised learning, where the raw data is cleaned and preprocessed to make it suitable for the model to learn from. This step is crucial because the quality of the data can have a significant impact on the performance of the model. Data preparation tasks include removing missing values, handling outliers, encoding categorical variables, and scaling numerical features. It is important to carefully consider which preprocessing steps to apply based on the specific problem and the characteristics of the data. 3. What is model training in supervised learning? Model training is the second step in supervised learning, where the model is trained on the labeled data using an algorithm such as linear regression, logistic regression, or neural networks. The goal is to find the best set of parameters that minimize the difference between the predicted output and the actual output. This step involves iteratively adjusting the parameters of the model based on the input data and the desired output until the model can accurately predict the output for new data. The performance of the model is evaluated during training using a loss function, which measures the difference between the predicted output and the actual output. 4. What is model evaluation in supervised learning? Model evaluation is the third step in supervised learning, where the model is tested on a separate set of data to evaluate its performance. This step helps to determine how well the model generalizes to new data and to identify any potential issues such as overfitting or underfitting. The evaluation metric used depends on the problem and the type of output being predicted, such as accuracy, precision, recall, or F1 score. It is important to carefully select the evaluation metric based on the specific problem and the characteristics of the data. Model evaluation provides a way to compare different models and to determine which one performs best on the task at hand.
Most people think of space as a flat sheet: You travel in one direction, and you end up far from your starting point. But a new paper suggests that the universe may in fact be spherical: If you travel far enough in the same direction, you’d end up back where you started. Based on Einstein’s theory of relativity, space can bend into different shapes, so scientists assume the universe must be either open, flat, or closed. Flat is the easiest shape to understand: it is how we experience space in our everyday lives, as a plane in which a beam of light would extend off into infinity. An open universe would be saddle-shaped, with a beam of light bending across the curvature. And a closed universe would be a sphere, with a beam of light eventually looping back around it to meet its origin. In order to tell which shape our universe is, scientists can look at a phenomenon called the cosmic microwave background (CMB). This is the electromagnetic radiation which remains from the Big Bang, also called “relic radiation.” It fills all of space and can be detected with a sufficiently powerful radio telescope. In the new paper, the scientists measured the fluctuations in the CMB using data from the European Space Agency’s Planck space observatory. We know that these fluctuations are related to the amount of dark matter and dark energy in the universe. And although we still can’t detect dark matter or dark energy, we do know approximately how much of each exists. So when the researchers found more strong gravitational lensing of the CMB than would be expected, they knew they had a clue to the shape of the universe. The most obvious explanation for these findings is that the universe is closed, not flat as previously thought. This would be a dramatic finding, to such a degree that the researchers called it a “crisis for cosmology.” However, there are complications which mean we cannot be sure if the universe is definitely closed. For example, the universe is constantly expanding, but researchers disagree on how fast this is happening, making it harder to predict the curvature of the universe. There are also other analyses of Planck data which strongly support the idea of a flat universe. For now, the shape of the universe remains an open question. The research is published in the journal Nature Astronomy. - Astronomers simulate the early universe and the birth of the first galaxies - James Webb researcher reveals how it will investigate the early universe - Researchers have simulated a virtual universe, and you can download it for free - Researchers come up with new method to ‘see’ dark matter - Mars once had rings of its own, new research suggests
The reddish hue of many objects in our solar system's frigid outer reaches may be evidence of complex organic molecules, perhaps even the building blocks of life, new research suggests. Scientists have come up with a computer model to explain the many colors — the reds, whites and blues— found in the Kuiper Belt, the swath of icy bodies circling the sun with Pluto. The model suggests that Kuiper Belt objects have many layers, and that the reds could come from organic materials in a layer near the surface. [Illustration of layered Kuiper Belt object.] If the model is correct, it would support current theories that organic materials might be common in the universe, researchers said. "We're not saying that life is produced in the Kuiper Belt," said physicist John Cooper of NASA's Goddard Space Flight Center in Greenbelt, Md. "But the basic chemistry may start there, as could also happen in similar Kuiper Belt environments elsewhere in the universe, and that is a natural path which could lead toward the chemical evolution of life." Coats of many colors About 1,000 Kuiper Belt objects have been directly imaged so far, and these bodies appear to be a wide range of colors, from red to blue to white, researchers said. Since these objects are so far away — the Hubble Space Telescope sees most of them as just a single pixel of light — scientists had developed few theories to explain the colors. But the new computer model maps out the right combination of materials and space environment that could produce some of those hues. It found that the Kuiper Belt objects likely have many different layers. "This multi-layer model provides a more flexible approach to understanding the diversity of colors," Cooper said. "The model calculates the rate at which energy comes in from radiation and could be causing changes at different depths. So we can define different layers based on that." The layers may have different colors, and could also be dynamic. For example, a deeper layer of relatively pure water ice could erupt to form a new uppermost layer, perhaps accounting for the bright, icy surface of Eris, the largest of the known Kuiper Belt objects. Cooper presented his model in October at the Division for Planetary Sciences meeting of the American Astronomical Society in Pasadena, Calif. The reds and the whites Kuiper Belt objects come in a wide range of colors, sizes and orbits. One group, called the Cold Classical Kuiper Belt, is aligned in nearly the same plane as the planets and has relatively circular orbits. While objects in much of the Kuiper Belt run the color gamut, Cold Classical bodies are consistently reddish, Cooper said. The first thing Cooper's model had to explain was why Kuiper Belt objects don't sport a thick black crust from radiation exposure. He believes that the Cold Classicals formed in a sweet spot where plasma ions from the sun aren't intense enough to overcook the outermost surface. Instead, the plasma ions have just "sandblasted" off the topmost surface layer, which is perhaps a millimeter thick. Additional erosion could come from impacts of tiny dust grains ejected into the Kuiper Belt region when nearby larger objects collide. That means, the model suggests, that the red color must be from the exposed second layer. This second layer may be gently cooked by radiation from interstellar space, according to Cooper. In turn, this cooking effect could transform water ice, carbon, methane, nitrogen and ammonia — the basic substances believed to be on these bodies — into organic molecules containing oxygen and carbon, such as formaldehyde, acetylene and ethane. "If there wasn't any cooking at all, we would just see primordial ice, and the object would appear bright and white," Cooper said. "And if there was too much radiation we would just see black crust." Cooper's layer model can account for white Kuiper Belt objects as well. Beneath the red stuff, a layer of water ice could volcanically erupt through the crust onto the surface, generating bright-white coats. NASA probe to get a close look At this point, the layer model is based on limited data from the Voyager mission that provided information on the energy levels of radiation beyond Neptune. NASA's New Horizons mission spacecraft will pass through the Kuiper Belt region beyond Neptune's orbit in 2014, getting a good look at Pluto and its largest moon Charon in 2015 — and one or two other objects later if all goes well. Cooper hopes New Horizons will pass close enough to another Kuiper Belt object to make detailed observations of its surface, which would help confirm what materials are present. New Horizons can provide additional verification by confirming that the energy distribution and particles in this region of the solar system jibe with what the model requires. If the model is borne out, its findings support the argument that the building blocks of life could be widespread in our solar system and perhaps the universe, researchers said. "When you take the right mix of materials and radiate them, you can produce the most complex species of molecules," Cooper said. "In some cases you may be able to produce the components of life — not just organic materials, but biological molecules such as amino acids." Live Science newsletter Stay up to date on the latest science news by signing up for our Essentials newsletter.
Factors Effecting Quality of Life (QOL) Info: 4778 words (19 pages) Introduction Published: 26th Jan 2022 Tagged: Social Studies Quality of Life (QOL) Quality of life is a broad concept relating in general to the overall level of wellbeing in society. It does not refer solely to the material resources available to individuals or households, but it focuses on enabling people to achieve their goals and choose lifestyle ideal for them. As Robeyns and Veen (2007) wrote, “there is no generally accepted definition of ‘quality of life’. Quality of life has been defined by the World Health Organization (WHO) as individuals’ perception of their life in the context of culture and value system in which they live in relation to the goals, expectations, standards and concerns. QOL refers to those aspects of life and human functions that are considered essential for living a full life. Quality of life interconnects many different elements of life such as social, physical and cultural aspects. Concept of quality of life acknowledges individuals’ need to belong in different places and social groups, as well as to differentiate oneself by pursuing aims and making decisions and choices. Quality of life is also a dynamic concept; values and self-evaluations of life may change over time in response to life and health events and experiences. Each area of quality of life can also have knock on effects on the others. For example, retaining independence and social participation may promote feelings of emotional wellbeing, but are partly dependent on retaining health and adequate finances. These can also be influenced by local transport facilities, type of housing, community resources, and social relationships. Quality of life is multidimensional and its parts affect each other as well as the sum. Models of quality of life The main models of quality of life are - Objective indicator - Subjective indicator - Satisfaction of human needs - Psychological model - Health and functioning model - Social health model - Social cohesion and social capital - Environmental models Objective indicators are standard of living, health and longevity, housing and neighborhood characteristics. These are typically measured with indicators of cost of living, mortality rates, health service provision, education levels, neighborhood structure and density, socio-economic structure and indicators of inequality and crime in the neighborhood. From the World Database of Happiness, which indicated individualization in the society makes citizens to enjoy their lives. Individualization includes people’s capability to choose, opportunities for freedom of political choice, freedom of economic choice and freedom of personal choices. The international data on quality of life has been produced by Mercer Human Resource Consulting (2003) analyzed 39 objective indicators of quality of life in 20 world cities, and which covered political, social, economic and environmental factors; personal safety and health, education, transport and other public services. Subjective indicators are life satisfaction and psychological well-being, morale, individual fulfillment, happiness, measured using indicators of life satisfaction, morale, balance of affect, and self-worth (esteem). Satisfaction of human needs is objective circumstances such as housing, security, food, warmth and opportunities for self-actualization. Needs-based satisfaction model is developed based on Maslow’s (1954) hierarchy. As per Maslow’s theory of self actualization, satisfaction is measured by how much they met the expectations of their life and human needs necessary for maintenance and existence (physiological, safety and security, social and belonging, ego, status and self-esteem, and self actualization). Maslow (1968) further argued that once these basic needs are satisfied, human beings pursue higher needs such as self-actualization, happiness and esteem. It has been argued that human needs are the foundations for quality of life, and hence quality of life can be defined in terms of human needs and the satisfactory fulfillment of those needs. Psychological models are influencing and mediating variables which emphasize personal growth, cognitive competence, efficiency and adaptability, level of dignity, perceived independence; social competence, control , autonomy, self efficacy or self-mastery as well as optimism-pessimism. This model is similar to Bentham’s utilitarian philosophy which regarded well-being as the difference in value between the sum of pleasures of all sorts and the sum of pains of all sorts which a man experienced in a given period of time. Pleasure and satisfaction are insufficient for a good quality of life and a sense of purpose or meaning, self-esteem and self worth are crucial for good Quality of life. It also includes social comparisons-gap relativity models of past experience, present circumstances and aspirations for the future – the individual’s achievement of their expectations, hopes and aspirations, particularly in relation to social comparisons with others. Health and functioning model is measured through the health status. Health and quality of life is highly correlated with self-reported health status and indicators of well-being (Zautra & Hempel, 1984). Good levels of physical and mental functioning and general health status have long been associated with perceived well-being, morale and overall quality of life. Mental health, psychological resources and outlook are also key components of successful ageing and wellbeing (Baltes & Baltes, 1990). It is a direct component of well-being and contributes to a persons basic ability to function in their social roles, to pursue valued activities and goals in life, and to choose the life which they value. Social health model is measured with indicators of social networks, support and activities. Social networks are the identified social relationships that surround an individual, their characteristics and individuals perceptions and valuations of them. Network characteristics include their size, density , boundedness , homogeneity, frequency of contact of members, their multiplexed (number of types of transactions within them), duration and reciprocity. Social support is the interactive process in which emotional, instrumental or financial aid is obtained from network members. Human ecology theory also focuses on the interactions and interdependent relationships between people, and postulates that families are an important resource and a rich environment for individual members (Rettig & Leichtentritt, 1999). Social cohesion and social capital are includes societal, environmental and neighborhood resources. It is measured by objective indicators of indices of crime, pollution, cost of living, shopping facilities, access to areas of scenic quality, cost of owner occupied housing, education facilities, policing, employment levels, wage levels, unemployment levels, climate, access to indoor/outdoor sports, travel to work time, access to leisure facilities, quality of council housing, access to council housing cost of private rented accommodation. Environmental models are concerned with the study of aging in ones place of residence and the importance of designing enabling internal and external environments in order to promote the independence and active social participation to the people. Ideographic are individualized, hermeneutic approaches based on the individuals values, interpretations and perceptions, satisfaction with their position, circumstances and priorities in life. Marital adjustment is also a variable that connected with Quality of life. It may be interchangeably used with subjective well-being. QOL reflects the difference and the gap between the hopes and expectations of a person and one’s present experience. Human adaptation is such that life expectations are usually adjusted so as to lie within the realm of what the individual perceives to be possible. A good quality of life can be said to exist when the hopes of individuals in the marital relations are matched and fulfilled by experience. A good marriage not only produces a satisfied life but it also generates a sense of wellbeing. Social exchange theory postulate that, satisfaction between spouses increases based on attaining the expectations in rewards they receive (Kassin et al., 2008). When partners fail to reach their expectations it generates dissatisfaction in their relationship (Nye, 1982). Marital quality tends to peak in the first few years of marriage and then to decline until midlife. After that point it rises steadily with increasing age and duration of marriage. The process of improving quality of life often requires the sustained collective action of people, and indeed of generations. The quality of life of one person can hardly be traced in isolation, as Putnam demonstrates (2008). Being attracted is the fundamental motive of human being. Research found that people will sacrifice most other goals like getting good education, having a successful carrier or contributing to a better society to before giving up a good relationship (Hammersla and Frease, 1990). Three basic components which involve in intimate relationship are feelings of attachment, affection and love, the fulfillment of psychological needs, interdependence between partners. These components have positive impact in developing and maintaining a relationship. Marriage is the universal social institution. It s established by the human society to control and regulate the sex life of man, it is connected with family. In fact marriage and family are complementary to each other. A marriage is a legally recognized union between two people, generally a man and a woman, in which they are united sexually, cooperate economically, and may give birth to, adopt, or rear children. The union is assumed to be permanent although it may be dissolved by separation or divorce. (Strong, DeVault, & Cohen, 2010). Marriage is documented by law and has legal validity. There are rights and duties of married couple and that is well addressed and enforced by the court of law. There are some procedures if the partners want to split, that is not only untying the relationship but also it concentrated with the assets and liabilities, child caring, custody and maintenance etc. In India, marriage is thought to be for life, and the divorce rate is extremely low. Only 1.1% of marriages in India result in a divorce compared with over 45.8% in the United States, though the Indian figure appears to be rising. With the advancement of time, spread of education and campaigns of human rights activists, divorce has become a way to break free from the marital clutches for many women. Couples facing difficulties in equating their levels of compatibility are now filing for divorce in order to renew their life afresh. In fact, the rate of divorce is rapidly rising in the Indian metropolis. (Chary, 2009; Jones & Ramdas, 2004 & Roberts, 1990) Ingredients of happy and permanent marriage are: similar values, friendship, communication, sexual satisfaction, mutual respect, religious faith (The National Marriage Project and The National Opinion Research Center, 2002, Rutgers University). Ability to take financial responsibility would be an ingredient of successful marriage. It is one aspect which can be a source of conflict and stress among couples. Marriage is not only a private contract, but a social institution of great public value and concern. The advantage of marriage to the society is unique because it is the foundation of the family and the basic building block of the society. It brings significant stability and meaning to human relationships. It is ideal for raising children. It plays an important role in transmitting culture and civilization to future generations. (Coleman, 1994) Some of the important reasons for getting married are: - To love and to be loved - To protect and be cared for - For emotional intimacy which fosters compassion and support - To be socially recognized and give birth to children legally. - To flee from a life of loneliness isolation. - To share responsibilities. - Polygamy, Polyandry, Monogamy, Group marriage (Shankar, 2005) - Bigamy, Same-sex marriage, Cohabitation. In most cultures, monogamy is considered ideal. (Browne, 2011) In Indian society there are mainly three different kinds of marriages: - The arranged marriage, which is managed by the family of the bride and the groom. - The love marriage, solemnized by the choice of the life partners themselves, and, - The love-cum-arrange marriage, where the boy and girl select each other but the marriage is organized by their parents. Whether it is arranged, love or any other kind of marriage, the most valuable thing for the couples is to maintain satisfaction in their married life. In fact, marital satisfaction is an important research theme in all the studies concerning factors contributing to marriage. As marital satisfaction is a variable of this study, it asses the satisfaction level of wives of expatriate husbands. Individual’s most central goals in life is satisfying marriage or relationship, across diverse cultures (Levinger & Huston, 1990). Indeed, marital happiness exceeds satisfaction in other domains (e.g., health, work, or children) as the strongest single predictor of overall life satisfaction. Marital satisfaction is relevant to mental health, general happiness, professional achievement and social interaction. Uniquely, it is a relatively stable attitude and attribute which reflects the individual‘s overall evaluation of the relationship. It depends upon the individual‘s needs, expectations, and desires for the relationship. (Snyder, 2010) Marital satisfaction is a mental state that reflects the perceived benefits and costs of marriage to a particular person. Satisfaction in romantic partnership depends on finding a delicate balance between positive and negative interactions across time (Gottman, 1994). Studies revealed that marital adjustment is problematic in the early years of marriage, as per the data the probability of divorce is highest during the first years of marriage between 2 and 4 years (Kreider & Fields, 2002). Also managing the employment and marriage is problematic to the newlyweds in the early months of marriage, and most of the newlyweds scored in distressed range on marital satisfaction and marital adjustment (Schramm, et al., 2005). Additional sources of problem in the newly married couples are demands from parents & in-laws, religion, education or social class background. In these areas the couples have to compromise so many things, if they fail to compromise it develops the marital distress. Certain lifestyle decision may generate tension. The couple must establish a mutually satisfying sexual relationship. They must carry out an agreement on spending and saving money. They must respond to each other’s sleep patterns, food preferences, work pattern, toilet habit etc. For the better adjustment with the partner psychological commitment is very important. The factors which works to protect the marriage includes - Mutual affection Effective communication and the ability to cope or solve the conflict are essential for the intimacy and high level of satisfaction. Studies found that people with high degree of marital satisfaction report frequent, pleasurable interactions and high degree of disclosure. Disclosure reciprocity means you tell a person what you are thinking about, and that person tells you what he or she thinking aboutassociated with greater relationship satisfaction (Lippert and Prager, 2001). Self disclosure, partner’s disclosure and partner responsiveness are the important predictor of marital satisfaction. In contrast negative interactions and conflicts are associated with distress. Differences in the power between the partners, especially differences in the control of resources and ongoing disagreements about the allocation of resources are underlying source of marital conflict. Three dimensions of conflict are: - Negative communication - Coercive escalation - Different perception of approach Congruence between partners in how they think, they and their partner are approaching the resolution of conflict is significantly related to marital satisfaction where as lack of Congruence is significantly related to marital dissatisfaction and distress (Acitelli, 1997) Criteria for Successful Marriage Areas of agreement that partners will have generally include: a) Friendship: Successful partners develop a significant friendship at the core of their relationship. They genuinely like each other, amuse and comfort one another, and prefer to spend time with each other. b) Role expectations: The partners reach agreement with regards to how household responsibilities are to be divided and how they will behave with each other. c) Emotional intimacy: Successful partners learn to trust each other, to be vulnerable to each other, to laugh together, and to support each other in times of need. d) Sexual expectations: This may further dictate the kinds and patterns of sexual activities that each partner will and will not engage in. As sexual activity is strongly rewarding and bonding for couples, it is best for marriages when partners agree upon sexual expectations and are both satisfied with their lovemaking. e) Vision/Goals: Successful partners agree that they want to pursue the same life paths, values and goals and mutually commit to those paths, values and goals. Examples might include decisions to have children or not, to attend or not to attend religious services, to raise a child in a particular faith, to save or spend money, or to live frugally or extravagantly, etc. (Dombeck, 2006). Loneliness is a complex and usually unpleasant emotional response to isolation or lack of companionship. Loneliness typically includes anxious feelings about a lack of connection or communication with other beings, both in the present and extending into the future. The cognitive perspective assumes that loneliness results from an unacceptable discrepancy between the personal relationships people have and the relationships they would like to have. The notion of a discrepancy between people’s desires and reality suggests that we should examine not only the actual networks of personal relationships but also the preferences people have in this respect to gain insight into differences in feelings of loneliness (Dykstra, 1990) Certain types of relationships within a person’s social network may result in feelings of loneliness is based on the assumption that different types of relationships serve different, more or less unique functions. Based on different type of relationships there two types of loneliness which is the loneliness of social isolation and the loneliness of emotional isolation. The married women were found to suffer from social isolation: though the married women are happy, they lacked a wider circle of friends and acquaintances who could give them a sense of belonging, of companionship, and of being a member of a community. The single parents, most of whom had put an end to an unhappy marriage, felt lonely because they no longer had a partner. They suffer from emotional isolation and the accompanying feelings of desolation and insecurity and of not having someone to turn to (Dykstra and Fokkema, 2007). Social loneliness can be attributed primarily to unfulfilled needs in the wider network of support givers. Emotional loneliness, however, is associated primarily with the absence of a partner, that is, with the absence of an exclusive, close, and intimate tie (Dykstra and Fokkema, 2007). Effects of loneliness Feeling lonely is not mental health problem but loneliness and mental health is correlated. Having mental health problem may leads to feel lonely or feeling lonely may negatively affect the mental health. Chronic loneliness is not only correlated with mental health but also with physical health. The chronic loneliness is associated with the physical problem like stroke; cardiovascular diseases. Marriage is associated with substantially less loneliness; being married was considerably more predictive of loneliness than cohabitation, indicating that companionship alone does not account for the protective nature of marriage. Both marriage and parental status were associated with lower levels of loneliness among men than women; marriage is associated with decreased loneliness independent of two intervening processes: marriage’s association with both health and financial satisfaction (Stack, 1998). Technical advancement changed the structure of entire globe or society. This made different group of people to live together for the purpose of work or because of migration. Changes in the society or the social changes are like any single alteration, modification or transformation in the organization and operation of social activity. As India is a developing country it faces many problems. Unemployment is a major curse to developing country like India. Kerala is the only state of India that has 100 % of literacy rate, and facing lots of unemployment problems. Kerala has higher rate of migrated youth. Unemployment is the main reason for the migration to Gulf countries. Since 1950s people from India are migrating to other countries. After the second half of 1970, it has reached sizable proportion. The number increased in the last few years and it become smaller after the 2008 when international financial crisis began to affect the GCC region. Initial wave of migration usually known as “Gulf boom”, that refers to a large number of people migrating to gulf. In Kerala the period 1972 to 1983 is known as “Kerala Gulf boom”. According to Kerala migration survey 90% of migrants are in Gulf countries out of which 22 lack migrant workers are from Kerala (NOKRA, 2014). People are motivated to migration for better job and prosperity in life. 70% of the migrants are married. Temporariness of the work or the high cost of living in the gulf countries made some of the emigrant to keep their family back home and save money for the future. Impacts of migration Migration or expatriation is like “tipping points”, which means situation that are previously rare becomes dramatically more common. Progress of international migration is very high and significant in the global scape. Broader development processes is both a cause and effect of migration and a fundamental facet of our ever globalizing world. Migration is most common from developing countries to developed countries primarily in the expectation of fast access to healthier economic opportunity. Developed nations are considering migration as a “positive force for development”. As migration increases its impacts becomes visible. Huge buildings, modern household equipments, sophisticated electronic machineries, perfumes and stereos add to the comforts of the families of the migrants. The outfit of family members, ornaments clad, attitude of shopping, etc speaks about it. Children too enjoy the enhanced economic security and get into educational institutions paying huge donations. Though the whole situation appears to be fascinating to the outsiders, the changes are mostly structural in nature. Impact on Families Economical development is the main effect on family; individual can earn drastically higher income and can help the family. The change in living style of the expat and family members of expat is noticeable. As economical changes occur the opportunity of getting higher education and getting higher position in the society will increase. Along with this long term familial separation also takes place, this may cause complicated direct and indirect impact on children and between spouses. Parental Migration Influences Child Development Economical stability is the motivation for migration. Greater investment to a child’s multiple development is based on the family recourses so greater family income can afford greater investment on this. Studies in the West find a strong association between higher household incomes and a variety of child development outcomes. But long term parental absence is the negative outcome of the migration. The impact differs based on the absence of mother or father or significant caretaker. Psychological research has found that parental support is a significant predictor of student’s capacity to deal with stress, anxiety and loss of control. Children with strong parental support do better in school and develop mature psychological traits. They aspire to do good work, experience pleasure in one’s work, and develop both initiative and a sense of control over events, and are better behaved. Environments that destabilize a child’s sense of self control over their life may increase the likelihood of internalizing problems. Research on other contexts in which parents are absent (e.g., single parenthood, divorce, military separation) focus mostly on father absence, which is usually negatively associated with a variety of child level outcomes in developed countries. Children who live in single mother families have been found to have lower academic achievement scores, more likely to suffer from psychological or behavioral problems, and are more likely to drop out of school(Park, Lee & deBrauw, 2010). Impact on Spouse Left Behind Migration has reflective impact on females left behind. These females may be mothers, sisters, daughters or wives. The impact of migration differs from female to female based on the social category and size of their family. The impact leads to be serious and sever in wives left behind. Mainly, the expatriate wives have to take important familial decision in the absence of their spouse. The entire family responsibilities lie on them including disciplining the children. At the same time they have to develop and maintain harmonious relationship with other family members. Thousands of married women are in Kerala lives away from their husbands because of migration. Marriage may be reduced to two-and-a-half months of joy in every two years for the wives and the children hardly get to know their fathers during this period. A prolonged separation in the early period of marriage seriously curtails the marital life of many a young couple. Suppressed sobs and plaintive murmurs linger behind the facade of the luxurious togs and exotic perfumes that make up the world of these women. According to the Kerala migration study these women are hardly equipped to cope up with the separation (Zacharaih, Mathew and Rayan, 2000). Research findings have also shown that women in the migrant households face many tensions, pressures, conflicts and anxieties. These women definitely face problems of loneliness, added responsibilities. The burden and burn out of these women will be doubled when they begin a career of their own. The dual role as a working woman and a care taker at home, that too without support, makes these women depressed and helpless (M.S, 2011). Cite This Work To export a reference to this article please select a referencing stye below: Related ServicesView all Related ContentAll Tags Content relating to: "Social Studies" Social Studies is a field of study that focuses on different aspects of human society. Elements of Social Studies include history, geography, social science, economics, and more. Literature Review on Historical Discontent in Nigeria This chapter reviews literature on the discontents in the Nigerian state as a whole from the historical perspective.... New Social Studies of Childhood Childhood studies, as we know it today, is a multi and inter-disciplinary subject encompassing aspects of psychology, sociology, anthropology, law, politics and economics. 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Monetary Policy - Managing Demand - AS, A-Level - AQA, Edexcel, OCR, IB Last updated 22 Mar 2021 Monetary policy influences the decisions that we make about how much we save, borrow and spend Decisions made by the central banks that operate monetary policy can have a powerful effect on consumers and businesses Changes in interest rates have both demand and supply-side effects What is Money? Money is any asset that is acceptable as a medium of exchange in payment for goods and services. The functions of money are as follows: 1.A medium of exchange used in payment for goods and services 2.A unit of account used to relative measure prices and draw up accounts 3.A standard of deferred payment – for example when using credit to purchase goods and services now but pay for them later 4.A store of value - money holds its value unless there is a situation of accelerating inflation. As the general price level rises, so the internal value of a unit of currency decreases. The media often talks about interest rates going up, or interest rates going doing as if there was one single or unique rate of interest in the economy. That isn't true – indeed there are thousands of different rates in the financial markets – it can get confusing! For example we distinguish between savings rates and borrowing rates, interest rates on secured and unsecured loans and short term and long term interest rates on different forms of savings account. However we find that interest rates tend to move in the same direction. For example if the Bank of England cuts the base rate of interest then we expect to see commercial banks cutting the rates on their loans and lower rates are offered on savings accounts with Banks and Building Societies The Real Rate of Interest - The real rate of interest is important to businesses and consumers when making spending and saving decisions - The real rate of return on savings, for example, is the money rate of interest minus the rate of inflation. So if a saver is receiving a money rate of interest of 6% on his savings, but price inflation is running at 3% per year, the real rate of return on these savings is only + 3%. - Real interest rates become negative when the nominal rate of interest is less than inflation, for example if inflation is 5% and nominal interest rates are 4%, the real cost of borrowing money is negative at -1%.
On this July 4th week, U.S. beachgoers are thronging their way to seaside resorts and parks to celebrate with holiday fireworks. The North Atlantic Bloom: swirling artwork in the sea, phytoplankton bloom each spring southwest of Iceland. Credit: NASA Earth Observatory Across the horizon and miles out to sea toward the north, the Atlantic Ocean's own spring and summer ritual is unfolding: the blooming of countless microscopic plant plankton, or phytoplankton. In what's known as the North Atlantic Bloom, an immense number of phytoplankton burst into color, first "greening" then "whitening" the sea as one species follows another. In research results published in this week's issue of the journal Science, scientists report evidence of what triggers this huge bloom. Whirlpools, or eddies, swirl across the surface of the North Atlantic Ocean sustaining phytoplankton in the ocean's shallower waters where they can get plenty of sunlight to fuel their growth, keeping them from being pushed downward by the ocean's rough surface. The result is a burst of spring and summer color atop the ocean's waters. How important is the bloom to the North Atlantic Ocean and beyond--to the global carbon cycle? Much like forests, springtime blooms of microscopic plants in the ocean absorb enormous quantities of carbon dioxide, emitting oxygen via photosynthesis. Their growth contributes to the oceanic uptake of carbon dioxide, amounting globally to about one-third of the carbon dioxide humans put into the air each year through the burning of fossil fuels. The North Atlantic is critical to this process; it's responsible for more than 20 percent of the ocean's uptake of carbon dioxide. An important scientific question is how this "biological pump" for carbon might change in the future as Earth's climate evolves. In winter, strong winds generate mixing that pushes phytoplankton into deeper waters, robbing them of sunlight but drawing up nutrients from the depths. As winter turns to spring, days are longer and plankton are exposed to more sunlight, fueling their growth. "Our results show that the bloom starts through eddies, even before the sun begins to warm the ocean," says Amala Mahadevan, an oceanographer at the Woods Hole Oceanographic Institution in Massachusetts and lead author of the Science paper. Co-authors of the paper are Eric D'Asaro and Craig Lee of the University of Washington, and Mary Jane Perry of the University of Maine. The National Science Foundation (NSF) funded the research. "Every undergraduate who takes an introductory oceanography course learns about the ecological and climate significance of the North Atlantic Bloom--as well as what causes it," says Don Rice, program director in NSF's Division of Ocean Sciences, which funded the research. "This study reminds us that, when it comes to the ocean, the things we think we know hold some big surprises." The newly discovered mechanism helps explain the timing of the spring and summer bloom, known to mariners and fishers for centuries and clearly visible in satellite images. It also offers a new look at why the bloom has a patchy appearance: it is shaped by eddies that, in essence, orchestrate its formation. Making the discovery was no easy feat. "Working in the North Atlantic Ocean is challenging," says Perry, "but we were able to track a patch of seawater off Iceland and follow the progression of the bloom in a way that hadn't been done before." "Our field work was set up with floats, gliders and research ships that all worked tightly together," adds D'Asaro. "They were in the same area, so we could put together a cohesive picture of the bloom." The scientists focused on phytoplankton known as diatoms. Diatoms live in glass houses--walls made of silica. "When conditions are right, diatom blooms spread across hundreds of miles of ocean," says Lee, "bringing life-sustaining food to sometimes barren waters." In April 2008, Lee, Perry and D'Asaro arrived in a storm-lashed North Atlantic aboard the Icelandic research vessel Bjarni Saemundsson. They launched specially-designed robots in the rough seas. A float that hovered below the water's surface was also deployed. It followed the motion of the ocean, moving around, says D'Asaro, "like a giant phytoplankton." Lurking alongside the float were six-foot-long, teardrop-shaped gliders that dove to depths of up to 1,000 meters. After each dive, the gliders, working in areas 20 to 50 kilometers around the float, rose to the surface, pointed their antennas skyward and transmitted their stored data back to shore. The float and gliders measured the temperature, salinity and velocity of the water, and gathered information about the chemistry and biology of the bloom itself--oxygen, nitrate and the optical signatures of the phytoplankton. Scientists aboard two ships, the Woods Hole-operated research vessel Knorr and Iceland's Bjarni Saemundsson, visited the area four times. Soon after measurements from the float and gliders started coming in, the scientists saw that the bloom had started, even though conditions still looked winter-like. "It was apparent that some new mechanism, other than surface warming, was behind the bloom's initiation," says D'Asaro. To find answers, the researchers needed sophisticated computer modeling. Enter Mahadevan, who then used three-dimensional computer models to look at information collected at sea by Perry, D'Asaro and Lee. She generated eddies in a model, using the north-to-south variation of temperature in the ocean. The model showed that without eddies, the bloom happened several weeks later and didn't have the space and time structures actually observed in the North Atlantic. In future research, the scientists hope to put the North Atlantic Bloom into a broader context. They believe that much could be learned by following the bloom's evolution across an entire year, especially with gliders and floats outfitted with new sensors. The sensors would look at the zooplankton that graze on a phytoplankton smorgasbord. These data could be integrated, say the oceanographers, into models that would offer a more complete story. "What we're learning about eddies is that they're a critical part of life in the ocean," says Perry. "They shape ocean ecosystems in countless ways." Eddies and phytoplankton, the researchers believe, are central to the oceanic cycling of carbon, without which climate on Earth would look very different. "We envision using gliders and floats to make measurements--and models--of ocean physics, chemistry and biology," says D'Asaro, "that span wide regions of the world ocean." And that, says Lee, would spark a new understanding of the sea, all from tiny plankton that each spring and summer bloom by the millions and millions.Media Contacts The National Science Foundation (NSF) is an independent federal agency that supports fundamental research and education across all fields of science and engineering. In fiscal year (FY) 2012, its budget is $7.0 billion. NSF funds reach all 50 states through grants to nearly 2,000 colleges, universities and other institutions. Each year, NSF receives over 50,000 competitive requests for funding, and makes about 11,000 new funding awards. NSF also awards nearly $420 million in professional and service contracts yearly. Cheryl Dybas \| EurekAlert! Treatment of saline wastewater during algae utilization 14.05.2019 \| Jacobs University Bremen gGmbH Plastic gets a do-over: Breakthrough discovery recycles plastic from the inside out 07.05.2019 \| DOE/Lawrence Berkeley National Laboratory A new assessment of NASA's record of global temperatures revealed that the agency's estimate of Earth's long-term temperature rise in recent decades is accurate to within less than a tenth of a degree Fahrenheit, providing confidence that past and future research is correctly capturing rising surface temperatures. The most complete assessment ever of statistical uncertainty within the GISS Surface Temperature Analysis (GISTEMP) data product shows that the annual values... Physicists at the University of Basel are able to show for the first time how a single electron looks in an artificial atom. A newly developed method enables them to show the probability of an electron being present in a space. This allows improved control of electron spins, which could serve as the smallest information unit in a future quantum computer. The experiments were published in Physical Review Letters and the related theory in Physical Review B. The spin of an electron is a promising candidate for use as the smallest information unit (qubit) of a quantum computer. Controlling and switching this spin or... Engineers at the University of Tokyo continually pioneer new ways to improve battery technology. Professor Atsuo Yamada and his team recently developed a... With a quantum coprocessor in the cloud, physicists from Innsbruck, Austria, open the door to the simulation of previously unsolvable problems in chemistry, materials research or high-energy physics. The research groups led by Rainer Blatt and Peter Zoller report in the journal Nature how they simulated particle physics phenomena on 20 quantum bits and how the quantum simulator self-verified the result for the first time. Many scientists are currently working on investigating how quantum advantage can be exploited on hardware already available today. Three years ago, physicists... 'Quantum technologies' utilise the unique phenomena of quantum superposition and entanglement to encode and process information, with potentially profound benefits to a wide range of information technologies from communications to sensing and computing. However a major challenge in developing these technologies is that the quantum phenomena are very fragile, and only a handful of physical systems have been... 29.04.2019 \| Event News 17.04.2019 \| Event News 15.04.2019 \| Event News 24.05.2019 \| Physics and Astronomy 24.05.2019 \| Medical Engineering 24.05.2019 \| Life Sciences
When we solve an algebraic equation, instead of plugging in a given number for the variable, we find a number that, when plugged in for the variable, would make the equation true. Such a number is called a solution to an equation. 58 is a solution to the equation h + 2 = 60, because 58 + 2 = 60. 46 is not a solution to h + 2 = 60, because 46 + 2 does not equal 60. Some equations have more than one solution. For example, 4 and -4 are both solutions to r2 = 16. Most of the equations we will deal with, however, have only one solution. The goal in solving an equation is to get the variable by itself on one side of the equation and a number on the other side of the equation. Generally, the variable will start on one side with operations being performed on it. We must reverse these operations by performing the inverse of each operation. However, we cannot just perform the inverse operation on on e side, because that would change the equation. However, if you perform the same operation on both sides of an equation the equation will not change. Performing an operation on one side of an equation will change the equation and make it false. Given, 5×6 = 30 5×6 = 30×3; 5×6 = 30 while 30×3 = 90 5×6 = 30 + 18; 5×6 = 30 while 30 + 18 = 48 5×6 = 30/10; 5×6 = 30 while 30/10 = 3 Performing the same operation on each side of an equation won't change the equation: Given, 7 + 4 = 11 (7 + 4)×12 = 11×12; both sides equal 132 (7 + 4) + 3 = 11 + 3; both sides equal 14 - (7 + 4) = - 11; both sides equal -11 Herein lies a vital role of solving algebraic equations: whatever operation is carried out on one side of the equal sign in an equation must be carried out on the other side as well. To solve an algebraic equation, reverse all the operations on the variable side of the equation by performing their inverse operations on both sides of the equation.
It can be equivalently thought of as the probability of correctly accepting the alternative hypothesis when the alternative hypothesis is true - that is, the ability of a test to detect an effect, if the effect actually exists. The power is in general a function of the possible distributions, often determined by a parameter, under the alternative hypothesis. As the power increases, the chances of a Type II error occurring decrease. The probability of a Type II error occurring is referred to as the false negative rate (β) and the power is equal to 1−β. The power is also known as the sensitivity. Power analysis can be used to calculate the minimum sample size required so that one can be reasonably likely to detect an effect of a given size. Power analysis can also be used to calculate the minimum effect size that is likely to be detected in a study using a given sample size. In addition, the concept of power is used to make comparisons between different statistical testing procedures: for example, between a parametric and a nonparametric test of the same hypothesis. There is also the concept of a power function of a test, which is the probability of rejecting the null when the null is true. Statistical tests use data from samples to assess, or make inferences about, a statistical population. In the concrete setting of a two-sample comparison, the goal is to assess whether the mean values of some attribute obtained for individuals in two sub-populations differ. For example, to test the null hypothesis that the mean scores of men and women on a test do not differ, samples of men and women are drawn, the test is administered to them, and the mean score of one group is compared to that of the other group using a statistical test such as the two-sample z-test. The power of the test is the probability that the test will find a statistically significant difference between men and women, as a function of the size of the true difference between those two populations. Note power is defined as the probability of finding a difference that does exist, contrary to the likelihood of declaring a difference that does not exist (which is known as a Type I error, or "false positive") Factors influencing power Statistical power may depend on a number of factors. Some of these factors may be particular to a specific testing situation, but at a minimum, power nearly always depends on the following three factors: - the statistical significance criterion used in the test - the magnitude of the effect of interest in the population - the sample size used to detect the effect A significance criterion is a statement of how unlikely a positive result must be, if the null hypothesis of no effect is true, for the null hypothesis to be rejected. The most commonly used criteria are probabilities of 0.05 (5%, 1 in 20), 0.01 (1%, 1 in 100), and 0.001 (0.1%, 1 in 1000). If the criterion is 0.05, the probability of the data implying an effect at least as large as the observed effect when the null hypothesis is true must be less than 0.05, for the null hypothesis of no effect to be rejected. One easy way to increase the power of a test is to carry out a less conservative test by using a larger significance criterion, for example 0.10 instead of 0.05. This increases the chance of rejecting the null hypothesis (i.e. obtaining a statistically significant result) when the null hypothesis is false, that is, reduces the risk of a Type II error (false negative regarding whether an effect exists). But it also increases the risk of obtaining a statistically significant result (i.e. rejecting the null hypothesis) when the null hypothesis is not false; that is, it increases the risk of a Type I error (false positive). The magnitude of the effect of interest in the population can be quantified in terms of an effect size, where there is greater power to detect larger effects. An effect size can be a direct estimate of the quantity of interest, or it can be a standardized measure that also accounts for the variability in the population. For example, in an analysis comparing outcomes in a treated and control population, the difference of outcome means Y − X would be a direct measure of the effect size, whereas (Y − X)/σ where σ is the common standard deviation of the outcomes in the treated and control groups, would be a standardized effect size. If constructed appropriately, a standardized effect size, along with the sample size, will completely determine the power. An unstandardized (direct) effect size will rarely be sufficient to determine the power, as it does not contain information about the variability in the measurements. The sample size determines the amount of sampling error inherent in a test result. Other things being equal, effects are harder to detect in smaller samples. Increasing sample size is often the easiest way to boost the statistical power of a test. The precision with which the data are measured also influences statistical power. Consequently, power can often be improved by reducing the measurement error in the data. A related concept is to improve the "reliability" of the measure being assessed (as in psychometric reliability). The design of an experiment or observational study often influences the power. For example, in a two-sample testing situation with a given total sample size n, it is optimal to have equal numbers of observations from the two populations being compared (as long as the variances in the two populations are the same). In regression analysis and Analysis of Variance, there is an extensive theory, and practical strategies, for improving the power based on optimally setting the values of the independent variables in the model. Although there are no formal standards for power (sometimes referred to as π), most researchers assess the power of their tests using π=0.80 as a standard for adequacy. This convention implies a four-to-one trade off between β-risk and α-risk. (β is the probability of a Type II error; α is the probability of a Type I error, 0.2 and 0.05 are conventional values for β and α). However, there will be times when this 4-to-1 weighting is inappropriate. In medicine, for example, tests are often designed in such a way that no false negatives (Type II errors) will be produced. But this inevitably raises the risk of obtaining a false positive (a Type I error). The rationale is that it is better to tell a healthy patient "we may have found something - let's test further", than to tell a diseased patient "all is well". Power analysis is appropriate when the concern is with the correct rejection, or not, of a null hypothesis. In many contexts, the issue is less about determining if there is or is not a difference but rather with getting a more refined estimate of the population effect size. For example, if we were expecting a population correlation between intelligence and job performance of around .50, a sample size of 20 will give us approximately 80% power (alpha = .05, two-tail) to reject the null hypothesis of zero correlation. However, in doing this study we are probably more interested in knowing whether the correlation is .30 or .60 or .50. In this context we would need a much larger sample size in order to reduce the confidence interval of our estimate to a range that is acceptable for our purposes. Techniques similar to those employed in a traditional power analysis can be used to determine the sample size required for the width of a confidence interval to be less than a given value. Many statistical analyses involve the estimation of several unknown quantities. In simple cases, all but one of these quantities is a nuisance parameter. In this setting, the only relevant power pertains to the single quantity that will undergo formal statistical inference. In some settings, particularly if the goals are more "exploratory", there may be a number of quantities of interest in the analysis. For example, in a multiple regression analysis we may include several covariates of potential interest. In situations such as this where several hypotheses are under consideration, it is common that the powers associated with the different hypotheses differ. For instance, in multiple regression analysis, the power for detecting an effect of a given size is related to the variance of the covariate. Since different covariates will have different variances, their powers will differ as well. Any statistical analysis involving multiple hypotheses is subject to inflation of the type I error rate if appropriate measures are not taken. Such measures typically involve applying a higher threshold of stringency to reject a hypothesis in order to compensate for the multiple comparisons being made (e.g. as in the Bonferroni method). In this situation, the power analysis should reflect the multiple testing approach to be used. Thus, for example, a given study may be well powered to detect a certain effect size when only one test is to be made, but the same effect size may have much lower power if several tests are to be performed. It is also important to consider the statistical power of a hypothesis test when interpreting its results. A test's power is the probability of correctly rejecting the null hypothesis when it is false; a test's power is influenced by the choice of significance level for the test, the size of the effect being measured, and the amount of data available. A hypothesis test may fail to reject the null, for example, if a true difference exists between two populations being compared by a t-test but the effect is small and the sample size is too small to distinguish the effect from random chance. Many clinical trials, for instance, have low statistical power to detect differences in adverse effects of treatments, since such effects are rare and the number of affected patients is very small. A priori vs. post hoc analysis Power analysis can either be done before (a priori or prospective power analysis) or after (post hoc or retrospective power analysis) data are collected. A priori power analysis is conducted prior to the research study, and is typically used in estimating sufficient sample sizes to achieve adequate power. Post-hoc power analysis is conducted after a study has been completed, and uses the obtained sample size and effect size to determine what the power was in the study, assuming the effect size in the sample is equal to the effect size in the population. Whereas the utility of prospective power analysis in experimental design is universally accepted, the usefulness of retrospective techniques is controversial. Falling for the temptation to use the statistical analysis of the collected data to estimate the power will result in uninformative and misleading values. In particular, it has been shown that post-hoc power in its simplest form is a one-to-one function of the p-value attained. This has been extended to show that all post-hoc power analyses suffer from what is called the "power approach paradox" (PAP), in which a study with a null result is thought to show MORE evidence that the null hypothesis is actually true when the p-value is smaller, since the apparent power to detect an actual effect would be higher. In fact, a smaller p-value is properly understood to make the null hypothesis LESS likely to be true. Funding agencies, ethics boards and research review panels frequently request that a researcher perform a power analysis, for example to determine the minimum number of animal test subjects needed for an experiment to be informative. In frequentist statistics, an underpowered study is unlikely to allow one to choose between hypotheses at the desired significance level. In Bayesian statistics, hypothesis testing of the type used in classical power analysis is not done. In the Bayesian framework, one updates his or her prior beliefs using the data obtained in a given study. In principle, a study that would be deemed underpowered from the perspective of hypothesis testing could still be used in such an updating process. However, power remains a useful measure of how much a given experiment size can be expected to refine one's beliefs. A study with low power is unlikely to lead to a large change in beliefs. We study the effect of a treatment on some quantity, and compare research subjects by measuring the quantity before and after the treatment, analyzing the data using a paired t-test. Let and denote the pre-treatment and post-treatment measures on subject i respectively. The possible effect of the treatment should be visible in the differences , which we assume to be independently distributed, all with the same expected value and variance. We proceed by analyzing D as in a one-sided t-test. The null hypothesis will be: (no effect), where denotes the expected value of a quantity. In this case, the alternative is (positive effect). The test statistic is: where n is the sample size, is the average of the and is the sample variance. The null hypothesis is rejected at level 0.05 when where 1.64 is the approximate decision threshold for a level 0.05 test based on a normal approximation to the test statistic, i.e. 1.64 is obtained from the Quantile function (also called inverse Cumulative distribution function) evaluated at 1−0.05=0.95. Now suppose that the alternative hypothesis is true and . Then the power is Since approximately follows a standard normal distribution when the alternative hypothesis is true, the approximate power can be calculated as Note that according to this formula the power increases with the values of the parameter . For a specific value of a higher power may be obtained by increasing the sample size n. It is, of course, not possible to guarantee a sufficient large power for all values of , as may be very close to 0. In fact the minimum (infimum) value of the power is equal to the size of the test, in this example 0.05. However it is of no importance to distinguish between and small positive values. If it is desirable to have enough power, say at least 0.90, to detect values of , the required sample size can be calculated approximately: from which it follows that where is a standard normal quantile; see Probit for an explanation of the relationship between and z-values. Software for Power and Sample Size Calculations Numerous programs are available for performing power and sample size calculations. These include nQuery Advisor, PASS, PS, Russ Lenth's power and sample-size page, GPower (http://www.gpower.hhu.de/), and SAS Power and sample size. A large set of power and sample size routines are included in R and Stata, which are comprehensive statistical packages. The other programs listed above are specialized for these calculations and are easier to use by people who are not familiar with the more general packages. nQuery, PASS, SAS and Stata are commercial products. The other programs listed above are freely available. Limited online statistical power analysis can be conducted within a web browser using WebPower \|Wikiversity has learning materials about Statistical power\| \|\|This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. (January 2010)\| - Ellis, Paul D. (2010). The Essential Guide to Effect Sizes: An Introduction to Statistical Power, Meta-Analysis and the Interpretation of Research Results. United Kingdom: Cambridge University Press. - Ellis, Paul (2010). The Essential Guide to Effect Sizes: Statistical Power, Meta-Analysis, and the Interpretation of Research Results. Cambridge University Press. p. 52. ISBN 978-0521142465. - Tsang, R.; Colley, L.; Lynd, L. D. (2009). "Inadequate statistical power to detect clinically significant differences in adverse event rates in randomized controlled trials". Journal of Clinical Epidemiology 62 (6): 609–616. doi:10.1016/j.jclinepi.2008.08.005. PMID 19013761. - Thomas, L. (1997) Retrospective power analysis. Conservation Biology 11(1):276–280 - Hoenig and Heisey (2001)The Abuse of PowerThe American Statistician 55(1):19-24 - Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). ISBN 0-8058-0283-5. - Aberson, C. L. (2010). Applied Power Analysis for the Behavioral Science. ISBN 1-84872-835-2. - PowerAndSampleSize.com – free, online power and sample size calculators with graphics highlighting sensitivity to input values - PASS – Commercial sample size software from NCSS, LLC - Hypothesis Testing and Statistical Power of a Test - GPower – A free program for Statistical Power Analysis for Mac OS and MS-DOS - Effect Size Calculators Calculate d and r from a variety of statistics. - R/Splus package of power analysis functions along the lines of Cohen (1988) - Examples of all ANOVA and ANCOVA models with up to three treatment factors, including tools to estimate design power - Free A-priori Sample Size Calculator for Multiple Regression from Daniel Soper's Free Statistics Calculators website. Computes the minimum required sample size for a study, given the alpha level, the number of predictors, the anticipated effect size, and the desired statistical power level. - Power calculator from Russ Lenth, University of Iowa
Fractional factorial design This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages)(Learn how and when to remove this template message) In statistics, fractional factorial designs are experimental designs consisting of a carefully chosen subset (fraction) of the experimental runs of a full factorial design . The subset is chosen so as to exploit the sparsity-of-effects principle to expose information about the most important features of the problem studied, while using a fraction of the effort of a full factorial design in terms of experimental runs and resources. In other words, it makes use of the fact that many experiments in full factorial design are often redundant, giving little or no new information about the system. Fractional designs are expressed using the notation lk − p, where l is the number of levels of each factor investigated, k is the number of factors investigated, and p describes the size of the fraction of the full factorial used. Formally, p is the number of generators, assignments as to which effects or interactions are confounded, i.e., cannot be estimated independently of each other (see below). A design with p such generators is a 1/(lp)=l-p fraction of the full factorial design. For example, a 25 − 2 design is 1/4 of a two level, five factor factorial design. Rather than the 32 runs that would be required for the full 25 factorial experiment, this experiment requires only eight runs. In practice, one rarely encounters l > 2 levels in fractional factorial designs, since response surface methodology is a much more experimentally efficient way to determine the relationship between the experimental response and factors at multiple levels. In addition, the methodology to generate such designs for more than two levels is much more cumbersome. The levels of a factor are commonly coded as +1 for the higher level, and −1 for the lower level. For a three-level factor, the intermediate value is coded as 0. To save space, the points in a two-level factorial experiment are often abbreviated with strings of plus and minus signs. The strings have as many symbols as factors, and their values dictate the level of each factor: conventionally, for the first (or low) level, and for the second (or high) level. The points in this experiment can thus be represented as , , , and . The factorial points can also be abbreviated by (1), a, b, and ab, where the presence of a letter indicates that the specified factor is at its high (or second) level and the absence of a letter indicates that the specified factor is at its low (or first) level (for example, "a" indicates that factor A is on its high setting, while all other factors are at their low (or first) setting). (1) is used to indicate that all factors are at their lowest (or first) values. In practice, experimenters typically rely on statistical reference books to supply the "standard" fractional factorial designs, consisting of the principal fraction. The principal fraction is the set of treatment combinations for which the generators evaluate to + under the treatment combination algebra. However, in some situations, experimenters may take it upon themselves to generate their own fractional design. A fractional factorial experiment is generated from a full factorial experiment by choosing an alias structure. The alias structure determines which effects are confounded with each other. For example, the five factor 25 − 2 can be generated by using a full three factor factorial experiment involving three factors (say A, B, and C) and then choosing to confound the two remaining factors D and E with interactions generated by D = AB and E = AC. These two expressions are called the generators of the design. So for example, when the experiment is run and the experimenter estimates the effects for factor D, what is really being estimated is a combination of the main effect of D and the two-factor interaction involving A and B. An important characteristic of a fractional design is the defining relation, which gives the set of interaction columns equal in the design matrix to a column of plus signs, denoted by I. For the above example, since D = AB and E = AC, then ABD and ACE are both columns of plus signs, and consequently so is BDCE. In this case the defining relation of the fractional design is I = ABD = ACE = BCDE. The defining relation allows the alias pattern of the design to be determined. \|Treatment combination\|\|I\|\|A\|\|B\|\|C\|\|D = AB\|\|E = AC\| An important property of a fractional design is its resolution or ability to separate main effects and low-order interactions from one another. Formally, the resolution of the design is the minimum word length in the defining relation excluding (1). The most important fractional designs are those of resolution III, IV, and V: Resolutions below III are not useful and resolutions above V are wasteful in that the expanded experimentation has no practical benefit in most cases—the bulk of the additional effort goes into the estimation of very high-order interactions which rarely occur in practice. The 25 − 2 design above is resolution III since its defining relation is I = ABD = ACE = BCDE. \|I\|\|Not useful: an experiment of exactly one run only tests one level of a factor and hence can't even distinguish between the high and low levels of that factor\|\|21 − 1 with defining relation I = A\| \|II\|\|Not useful: main effects are confounded with other main effects\|\|22 − 1 with defining relation I = AB\| \|III\|\|Estimate main effects, but these may be confounded with two-factor interactions\|\|23 − 1 with defining relation I = ABC\| Estimate main effects unconfounded by two-factor interactions \|24 − 1 with defining relation I = ABCD\| Estimate main effects unconfounded by three-factor (or less) interactions \|25 − 1 with defining relation I = ABCDE\| Estimate main effects unconfounded by four-factor (or less) interactions \|26 − 1 with defining relation I = ABCDEF\| The resolution described is only used for regular designs. Regular designs have run size that equal a power of two, and only full aliasing is present. Nonregular designs are designs where run size is a multiple of 4; these designs introduce partial aliasing, and generalized resolution is used as design criterion instead of the resolution described previously. Example fractional factorial experiment Montgomery gives the following example of a fractional factorial experiment. An engineer performed an experiment to increase the filtration rate (output) of a process to produce a chemical, and to reduce the amount of formaldehyde used in the process. The full factorial experiment is described in the Wikipedia page Factorial experiment. Four factors were considered: temperature (A), pressure (B), formaldehyde concentration (C), and stirring rate (D). The results in that example were that the main effects A, C, and D and the AC and AD interactions were significant. The results of that example may be used to simulate a fractional factorial experiment using a half-fraction of the original 24 = 16 run design. The table shows the 24-1 = 8 run half-fraction experiment design and the resulting filtration rate, extracted from the table for the full 16 run factorial experiment. In this fractional design, each main effect is aliased with a 3-factor interaction (e.g., A = BCD), and every 2-factor interaction is aliased with another 2-factor interaction (e.g., AB = CD). The aliasing relationships are shown in the table. This is a resolution IV design, meaning that main effects are aliased with 3-way interactions, and 2-way interactions are aliased with 2-way interactions. \|A = BCD\| \|B = ACD\| \|C = ABD\| \|D = ABC\| \|AB = CD\| \|AC = BD\| \|BC = AD\| The analysis of variance estimates of the effects are shown in the table below. From inspection of the table, there appear to be large effects due to A, C, and D. The coefficient for the AB interaction is quite small. Unless the AB and CD interactions have approximately equal but opposite effects, these two interactions appear to be negligible. If A, C, and D have large effects, but B has little effect, then the AC and AD interactions are most likely significant. These conclusions are consistent with the results of the full-factorial 16-run experiment. \|A\|\|19.0\|\|A + BCD\| \|B\|\|1.5\|\|B + ACD\| \|C\|\|14.0\|\|C + ABD\| \|D\|\|16.5\|\|D + ABC\| \|A:B\|\|-1.0\|\|AB + CD\| \|A:C\|\|-18.5\|\|AC + BD\| \|A:D\|\|19.0\|\|AD + BC\| Because B and its interactions appear to be insignificant, B may be dropped from the model. Dropping B results in a full factorial 23 design for the factors A, C, and D. Performing the anova using factors A, C, and D, and the interaction terms A:C and A:D, gives the results shown in the table, which are very similar to the results for the full factorial experiment experiment, but have the advantage of requiring only a half-fraction 8 runs rather than 16. \|Coefficient\|\|Estimate\|\|Std. Error\|\|t value\|\|P-value\| - Full Factorial and Fractional Factorial Experiments: Frequently Asked Questions (The Methodology Center, Penn State University) - Fractional Factorial Designs (National Institute of Standards and Technology)
Nucleic acid hybridization is a process in molecular biology where two single-stranded nucleic acids (DNA, RNA) with complementary sequences pair together to form a double-stranded molecule through hydrogen bonding. The strands can be from the same type of nucleic acid or different types (i.e., DNA-RNA or DNA-cDNA). This process is commonly used in various laboratory techniques, such as Southern blotting, Northern blotting, polymerase chain reaction (PCR), and microarray analysis, to detect, isolate, and analyze specific nucleic acid sequences. The hybridization temperature and conditions are critical to ensure the specificity of the interaction between the two strands. A DNA probe is a single-stranded DNA molecule that contains a specific sequence of nucleotides, and is labeled with a detectable marker such as a radioisotope or a fluorescent dye. It is used in molecular biology to identify and locate a complementary sequence within a sample of DNA. The probe hybridizes (forms a stable double-stranded structure) with its complementary sequence through base pairing, allowing for the detection and analysis of the target DNA. This technique is widely used in various applications such as genetic testing, diagnosis of infectious diseases, and forensic science. Viral DNA refers to the genetic material present in viruses that consist of DNA as their core component. Deoxyribonucleic acid (DNA) is one of the two types of nucleic acids that are responsible for storing and transmitting genetic information in living organisms. Viruses are infectious agents much smaller than bacteria that can only replicate inside the cells of other organisms, called hosts. Viral DNA can be double-stranded (dsDNA) or single-stranded (ssDNA), depending on the type of virus. Double-stranded DNA viruses have a genome made up of two complementary strands of DNA, while single-stranded DNA viruses contain only one strand of DNA. Examples of dsDNA viruses include Adenoviruses, Herpesviruses, and Poxviruses, while ssDNA viruses include Parvoviruses and Circoviruses. Viral DNA plays a crucial role in the replication cycle of the virus, encoding for various proteins necessary for its multiplication and survival within the host cell. A viral RNA (ribonucleic acid) is the genetic material found in certain types of viruses, as opposed to viruses that contain DNA (deoxyribonucleic acid). These viruses are known as RNA viruses. The RNA can be single-stranded or double-stranded and can exist as several different forms, such as positive-sense, negative-sense, or ambisense RNA. Upon infecting a host cell, the viral RNA uses the host's cellular machinery to translate the genetic information into proteins, leading to the production of new virus particles and the continuation of the viral life cycle. Examples of human diseases caused by RNA viruses include influenza, COVID-19 (SARS-CoV-2), hepatitis C, and polio. Deoxyribonucleic acid (DNA) is the genetic material present in the cells of organisms where it is responsible for the storage and transmission of hereditary information. DNA is a long molecule that consists of two strands coiled together to form a double helix. Each strand is made up of a series of four nucleotide bases - adenine (A), guanine (G), cytosine (C), and thymine (T) - that are linked together by phosphate and sugar groups. The sequence of these bases along the length of the molecule encodes genetic information, with A always pairing with T and C always pairing with G. This base-pairing allows for the replication and transcription of DNA, which are essential processes in the functioning and reproduction of all living organisms. A base sequence in the context of molecular biology refers to the specific order of nucleotides in a DNA or RNA molecule. In DNA, these nucleotides are adenine (A), guanine (G), cytosine (C), and thymine (T). In RNA, uracil (U) takes the place of thymine. The base sequence contains genetic information that is transcribed into RNA and ultimately translated into proteins. It is the exact order of these bases that determines the genetic code and thus the function of the DNA or RNA molecule. Nucleic acid denaturation is the process of separating the two strands of a double-stranded DNA molecule, or unwinding the helical structure of an RNA molecule, by disrupting the hydrogen bonds that hold the strands together. This process is typically caused by exposure to high temperatures, changes in pH, or the presence of chemicals called denaturants. Denaturation can also cause changes in the shape and function of nucleic acids. For example, it can disrupt the secondary and tertiary structures of RNA molecules, which can affect their ability to bind to other molecules and carry out their functions within the cell. In molecular biology, nucleic acid denaturation is often used as a tool for studying the structure and function of nucleic acids. For example, it can be used to separate the two strands of a DNA molecule for sequencing or amplification, or to study the interactions between nucleic acids and other molecules. It's important to note that denaturation is a reversible process, and under the right conditions, the double-stranded structure of DNA can be restored through a process called renaturation or annealing. A gammaretrovirus is a type of retrovirus, which is a virus that contains RNA as its genetic material and uses the reverse transcriptase enzyme to produce DNA from its RNA genome. Gammaretroviruses are enveloped viruses, meaning they have a lipid membrane derived from the host cell. They are also classified as simple retroviruses because their genome only contains the genes gag, pol, and env. Gammaretroviruses are known to cause diseases in animals, including leukemias and immunodeficiencies. One example of a gammaretrovirus is the feline leukemia virus (FeLV), which can cause a variety of symptoms in cats, including anemia, lymphoma, and immune suppression. Gammaretroviruses have also been implicated in some human diseases, although they are not thought to be major causes of human disease. For example, the human T-cell leukemia virus type 1 (HTLV-1) is a retrovirus that is closely related to gammaretroviruses and can cause adult T-cell leukemia/lymphoma and tropical spastic paraparesis/ HTLV-associated myelopathy (TSP/HAM). It's important to note that the classification of retroviruses has evolved over time, and some viruses that were once classified as gammaretroviruses are now considered to be part of other retrovirus genera. Bacterial DNA refers to the genetic material found in bacteria. It is composed of a double-stranded helix containing four nucleotide bases - adenine (A), thymine (T), guanine (G), and cytosine (C) - that are linked together by phosphodiester bonds. The sequence of these bases in the DNA molecule carries the genetic information necessary for the growth, development, and reproduction of bacteria. Bacterial DNA is circular in most bacterial species, although some have linear chromosomes. In addition to the main chromosome, many bacteria also contain small circular pieces of DNA called plasmids that can carry additional genes and provide resistance to antibiotics or other environmental stressors. Unlike eukaryotic cells, which have their DNA enclosed within a nucleus, bacterial DNA is present in the cytoplasm of the cell, where it is in direct contact with the cell's metabolic machinery. This allows for rapid gene expression and regulation in response to changing environmental conditions. Nucleic acids are biological macromolecules composed of linear chains of nucleotides. They play crucial roles in the structure and function of cells, serving as the primary information-carrying molecules in all known forms of life. The two main types of nucleic acids are deoxyribonucleic acid (DNA) and ribonucleic acid (RNA). DNA is responsible for storing genetic information in a stable form that can be passed down from generation to generation, while RNA plays a key role in translating the genetic code stored in DNA into functional proteins. Each nucleotide consists of a sugar molecule, a phosphate group, and a nitrogenous base. The sugar in DNA is deoxyribose, while in RNA it is ribose. The nitrogenous bases found in both DNA and RNA include adenine (A), guanine (G), and cytosine (C). Thymine (T) is found in DNA, but uracil (U) takes its place in RNA. These nucleotides are linked together by phosphodiester bonds between the sugar of one nucleotide and the phosphate group of another, forming a long, helical structure with backbones made up of alternating sugar and phosphate groups. The sequence of these nitrogenous bases along the nucleic acid chain encodes genetic information in the form of codons, which are sets of three consecutive bases that specify particular amino acids or signals for protein synthesis. This information is used to direct the synthesis of proteins through a process called transcription (converting DNA to RNA) and translation (converting RNA to protein). In summary, nucleic acids are essential biomolecules composed of chains of nucleotides that store, transmit, and express genetic information in cells. They consist of two main types: DNA and RNA, which differ in their sugar type, nitrogenous bases, and functions. Peptide Nucleic Acids (PNAs) are synthetic, artificially produced molecules that have a structure similar to both peptides (short chains of amino acids) and nucleic acids (DNA and RNA). They consist of repeating units called "monomers" made up of a pseudopeptide backbone with nucleobases attached. The backbone is composed of N-(2-aminoethyl)glycine units, which replace the sugar-phosphate backbone found in natural nucleic acids. PNAs are known for their high binding affinity and sequence-specific recognition of DNA and RNA molecules. They can form stable complexes with complementary DNA or RNA strands through Watson-Crick base pairing, even under conditions where normal nucleic acid hybridization is poor. This property makes them valuable tools in molecular biology for various applications such as: 1. Gene regulation and silencing 2. Antisense and antigen technologies 3. Diagnostics and biosensors 4. Study of protein-DNA interactions 5. DNA repair and mutation analysis However, it is important to note that Peptide Nucleic Acids are not naturally occurring molecules; they are entirely synthetic and must be produced in a laboratory setting. An oligonucleotide probe is a short, single-stranded DNA or RNA molecule that contains a specific sequence of nucleotides designed to hybridize with a complementary sequence in a target nucleic acid (DNA or RNA). These probes are typically 15-50 nucleotides long and are used in various molecular biology techniques, such as polymerase chain reaction (PCR), DNA sequencing, microarray analysis, and blotting methods. Oligonucleotide probes can be labeled with various reporter molecules, like fluorescent dyes or radioactive isotopes, to enable the detection of hybridized targets. The high specificity of oligonucleotide probes allows for the precise identification and quantification of target nucleic acids in complex biological samples, making them valuable tools in diagnostic, research, and forensic applications. Biotin is a water-soluble vitamin, also known as Vitamin B7 or Vitamin H. It is a cofactor for several enzymes involved in metabolism, particularly in the synthesis and breakdown of fatty acids, amino acids, and carbohydrates. Biotin plays a crucial role in maintaining healthy skin, hair, nails, nerves, and liver function. It is found in various foods such as nuts, seeds, whole grains, milk, and vegetables. Biotin deficiency is rare but can occur in people with malnutrition, alcoholism, pregnancy, or certain genetic disorders. In the context of medical research, "methods" refers to the specific procedures or techniques used in conducting a study or experiment. This includes details on how data was collected, what measurements were taken, and what statistical analyses were performed. The methods section of a medical paper allows other researchers to replicate the study if they choose to do so. It is considered one of the key components of a well-written research article, as it provides transparency and helps establish the validity of the findings. Bacterial RNA refers to the genetic material present in bacteria that is composed of ribonucleic acid (RNA). Unlike higher organisms, bacteria contain a single circular chromosome made up of DNA, along with smaller circular pieces of DNA called plasmids. These bacterial genetic materials contain the information necessary for the growth and reproduction of the organism. Bacterial RNA can be divided into three main categories: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). mRNA carries genetic information copied from DNA, which is then translated into proteins by the rRNA and tRNA molecules. rRNA is a structural component of the ribosome, where protein synthesis occurs, while tRNA acts as an adapter that brings amino acids to the ribosome during protein synthesis. Bacterial RNA plays a crucial role in various cellular processes, including gene expression, protein synthesis, and regulation of metabolic pathways. Understanding the structure and function of bacterial RNA is essential for developing new antibiotics and other therapeutic strategies to combat bacterial infections. Indicators and reagents are terms commonly used in the field of clinical chemistry and laboratory medicine. Here are their definitions: 1. Indicator: An indicator is a substance that changes its color or other physical properties in response to a chemical change, such as a change in pH, oxidation-reduction potential, or the presence of a particular ion or molecule. Indicators are often used in laboratory tests to monitor or signal the progress of a reaction or to indicate the end point of a titration. A familiar example is the use of phenolphthalein as a pH indicator in acid-base titrations, which turns pink in basic solutions and colorless in acidic solutions. 2. Reagent: A reagent is a substance that is added to a system (such as a sample or a reaction mixture) to bring about a chemical reaction, test for the presence or absence of a particular component, or measure the concentration of a specific analyte. Reagents are typically chemicals with well-defined and consistent properties, allowing them to be used reliably in analytical procedures. Examples of reagents include enzymes, antibodies, dyes, metal ions, and organic compounds. In laboratory settings, reagents are often prepared and standardized according to strict protocols to ensure their quality and performance in diagnostic tests and research applications. In situ hybridization (ISH) is a molecular biology technique used to detect and localize specific nucleic acid sequences, such as DNA or RNA, within cells or tissues. This technique involves the use of a labeled probe that is complementary to the target nucleic acid sequence. The probe can be labeled with various types of markers, including radioisotopes, fluorescent dyes, or enzymes. During the ISH procedure, the labeled probe is hybridized to the target nucleic acid sequence in situ, meaning that the hybridization occurs within the intact cells or tissues. After washing away unbound probe, the location of the labeled probe can be visualized using various methods depending on the type of label used. In situ hybridization has a wide range of applications in both research and diagnostic settings, including the detection of gene expression patterns, identification of viral infections, and diagnosis of genetic disorders. Retroviridae is a family of viruses that includes human immunodeficiency virus (HIV) and other viruses that primarily use RNA as their genetic material. The name "retrovirus" comes from the fact that these viruses reverse transcribe their RNA genome into DNA, which then becomes integrated into the host cell's genome. This is a unique characteristic of retroviruses, as most other viruses use DNA as their genetic material. Retroviruses can cause a variety of diseases in animals and humans, including cancer, neurological disorders, and immunodeficiency syndromes like AIDS. They have a lipid membrane envelope that contains glycoprotein spikes, which allow them to attach to and enter host cells. Once inside the host cell, the viral RNA is reverse transcribed into DNA by the enzyme reverse transcriptase, which is then integrated into the host genome by the enzyme integrase. Retroviruses can remain dormant in the host genome for extended periods of time, and may be reactivated under certain conditions to produce new viral particles. This ability to integrate into the host genome has also made retroviruses useful tools in molecular biology, where they are used as vectors for gene therapy and other genetic manipulations. Fluorescent dyes are substances that emit light upon excitation by absorbing light of a shorter wavelength. In a medical context, these dyes are often used in various diagnostic tests and procedures to highlight or mark certain structures or substances within the body. For example, fluorescent dyes may be used in imaging techniques such as fluorescence microscopy or fluorescence angiography to help visualize cells, tissues, or blood vessels. These dyes can also be used in flow cytometry to identify and sort specific types of cells. The choice of fluorescent dye depends on the specific application and the desired properties, such as excitation and emission spectra, quantum yield, and photostability. Tritium is not a medical term, but it is a term used in the field of nuclear physics and chemistry. Tritium (symbol: T or 3H) is a radioactive isotope of hydrogen with two neutrons and one proton in its nucleus. It is also known as heavy hydrogen or superheavy hydrogen. Tritium has a half-life of about 12.3 years, which means that it decays by emitting a low-energy beta particle (an electron) to become helium-3. Due to its radioactive nature and relatively short half-life, tritium is used in various applications, including nuclear weapons, fusion reactors, luminous paints, and medical research. In the context of medicine, tritium may be used as a radioactive tracer in some scientific studies or medical research, but it is not a term commonly used to describe a medical condition or treatment. Molecular sequence data refers to the specific arrangement of molecules, most commonly nucleotides in DNA or RNA, or amino acids in proteins, that make up a biological macromolecule. This data is generated through laboratory techniques such as sequencing, and provides information about the exact order of the constituent molecules. This data is crucial in various fields of biology, including genetics, evolution, and molecular biology, allowing for comparisons between different organisms, identification of genetic variations, and studies of gene function and regulation. In situ hybridization, fluorescence (FISH) is a type of molecular cytogenetic technique used to detect and localize the presence or absence of specific DNA sequences on chromosomes through the use of fluorescent probes. This technique allows for the direct visualization of genetic material at a cellular level, making it possible to identify chromosomal abnormalities such as deletions, duplications, translocations, and other rearrangements. The process involves denaturing the DNA in the sample to separate the double-stranded molecules into single strands, then adding fluorescently labeled probes that are complementary to the target DNA sequence. The probe hybridizes to the complementary sequence in the sample, and the location of the probe is detected by fluorescence microscopy. FISH has a wide range of applications in both clinical and research settings, including prenatal diagnosis, cancer diagnosis and monitoring, and the study of gene expression and regulation. It is a powerful tool for identifying genetic abnormalities and understanding their role in human disease. Molecular cloning is a laboratory technique used to create multiple copies of a specific DNA sequence. This process involves several steps: 1. Isolation: The first step in molecular cloning is to isolate the DNA sequence of interest from the rest of the genomic DNA. This can be done using various methods such as PCR (polymerase chain reaction), restriction enzymes, or hybridization. 2. Vector construction: Once the DNA sequence of interest has been isolated, it must be inserted into a vector, which is a small circular DNA molecule that can replicate independently in a host cell. Common vectors used in molecular cloning include plasmids and phages. 3. Transformation: The constructed vector is then introduced into a host cell, usually a bacterial or yeast cell, through a process called transformation. This can be done using various methods such as electroporation or chemical transformation. 4. Selection: After transformation, the host cells are grown in selective media that allow only those cells containing the vector to grow. This ensures that the DNA sequence of interest has been successfully cloned into the vector. 5. Amplification: Once the host cells have been selected, they can be grown in large quantities to amplify the number of copies of the cloned DNA sequence. Molecular cloning is a powerful tool in molecular biology and has numerous applications, including the production of recombinant proteins, gene therapy, functional analysis of genes, and genetic engineering. Polymerase Chain Reaction (PCR) is a laboratory technique used to amplify specific regions of DNA. It enables the production of thousands to millions of copies of a particular DNA sequence in a rapid and efficient manner, making it an essential tool in various fields such as molecular biology, medical diagnostics, forensic science, and research. The PCR process involves repeated cycles of heating and cooling to separate the DNA strands, allow primers (short sequences of single-stranded DNA) to attach to the target regions, and extend these primers using an enzyme called Taq polymerase, resulting in the exponential amplification of the desired DNA segment. In a medical context, PCR is often used for detecting and quantifying specific pathogens (viruses, bacteria, fungi, or parasites) in clinical samples, identifying genetic mutations or polymorphisms associated with diseases, monitoring disease progression, and evaluating treatment effectiveness. Viral genes refer to the genetic material present in viruses that contains the information necessary for their replication and the production of viral proteins. In DNA viruses, the genetic material is composed of double-stranded or single-stranded DNA, while in RNA viruses, it is composed of single-stranded or double-stranded RNA. Viral genes can be classified into three categories: early, late, and structural. Early genes encode proteins involved in the replication of the viral genome, modulation of host cell processes, and regulation of viral gene expression. Late genes encode structural proteins that make up the viral capsid or envelope. Some viruses also have structural genes that are expressed throughout their replication cycle. Understanding the genetic makeup of viruses is crucial for developing antiviral therapies and vaccines. By targeting specific viral genes, researchers can develop drugs that inhibit viral replication and reduce the severity of viral infections. Additionally, knowledge of viral gene sequences can inform the development of vaccines that stimulate an immune response to specific viral proteins. RNA-directed DNA polymerase is a type of enzyme that can synthesize DNA using an RNA molecule as a template. This process is called reverse transcription, and it is the mechanism by which retroviruses, such as HIV, replicate their genetic material. The enzyme responsible for this reaction in retroviruses is called reverse transcriptase. Reverse transcriptase is an important target for antiretroviral therapy used to treat HIV infection and AIDS. In addition to its role in viral replication, RNA-directed DNA polymerase also has applications in molecular biology research, such as in the production of complementary DNA (cDNA) copies of RNA molecules for use in downstream applications like cloning and sequencing. DNA restriction enzymes, also known as restriction endonucleases, are a type of enzyme that cut double-stranded DNA at specific recognition sites. These enzymes are produced by bacteria and archaea as a defense mechanism against foreign DNA, such as that found in bacteriophages (viruses that infect bacteria). Restriction enzymes recognize specific sequences of nucleotides (the building blocks of DNA) and cleave the phosphodiester bonds between them. The recognition sites for these enzymes are usually palindromic, meaning that the sequence reads the same in both directions when facing the opposite strands of DNA. Restriction enzymes are widely used in molecular biology research for various applications such as genetic engineering, genome mapping, and DNA fingerprinting. They allow scientists to cut DNA at specific sites, creating precise fragments that can be manipulated and analyzed. The use of restriction enzymes has been instrumental in the development of recombinant DNA technology and the Human Genome Project. Species specificity is a term used in the field of biology, including medicine, to refer to the characteristic of a biological entity (such as a virus, bacterium, or other microorganism) that allows it to interact exclusively or preferentially with a particular species. This means that the biological entity has a strong affinity for, or is only able to infect, a specific host species. For example, HIV is specifically adapted to infect human cells and does not typically infect other animal species. Similarly, some bacterial toxins are species-specific and can only affect certain types of animals or humans. This concept is important in understanding the transmission dynamics and host range of various pathogens, as well as in developing targeted therapies and vaccines. An antigen is any substance that can stimulate an immune response, particularly the production of antibodies. Viral antigens are antigens that are found on or produced by viruses. They can be proteins, glycoproteins, or carbohydrates present on the surface or inside the viral particle. Viral antigens play a crucial role in the immune system's recognition and response to viral infections. When a virus infects a host cell, it may display its antigens on the surface of the infected cell. This allows the immune system to recognize and target the infected cells for destruction, thereby limiting the spread of the virus. Viral antigens are also important targets for vaccines. Vaccines typically work by introducing a harmless form of a viral antigen to the body, which then stimulates the production of antibodies and memory T-cells that can recognize and respond quickly and effectively to future infections with the actual virus. It's worth noting that different types of viruses have different antigens, and these antigens can vary between strains of the same virus. This is why there are often different vaccines available for different viral diseases, and why flu vaccines need to be updated every year to account for changes in the circulating influenza virus strains. Genetic hybridization is a biological process that involves the crossing of two individuals from different populations or species, which can lead to the creation of offspring with new combinations of genetic material. This occurs when the gametes (sex cells) from each parent combine during fertilization, resulting in a zygote with a unique genetic makeup. In genetics, hybridization can also refer to the process of introducing new genetic material into an organism through various means, such as genetic engineering or selective breeding. This type of hybridization is often used in agriculture and biotechnology to create crops or animals with desirable traits, such as increased disease resistance or higher yields. It's important to note that the term "hybrid" can refer to both crosses between different populations within a single species (intraspecific hybrids) and crosses between different species (interspecific hybrids). The latter is often more challenging, as significant genetic differences between the two parental species can lead to various reproductive barriers, making it difficult for the hybrid offspring to produce viable offspring of their own. Micropore filters are medical devices used to filter or sterilize fluids and gases. They are made of materials like cellulose, mixed cellulose ester, or polyvinylidene fluoride with precise pore sizes, typically ranging from 0.1 to 10 micrometers in diameter. These filters are used to remove bacteria, fungi, and other particles from solutions in laboratory and medical settings, such as during the preparation of injectable drugs, tissue culture media, or sterile fluids for medical procedures. They come in various forms, including syringe filters, vacuum filters, and bottle-top filters, and are often used with the assistance of a vacuum or positive pressure to force the fluid through the filter material. Nucleic acid conformation refers to the three-dimensional structure that nucleic acids (DNA and RNA) adopt as a result of the bonding patterns between the atoms within the molecule. The primary structure of nucleic acids is determined by the sequence of nucleotides, while the conformation is influenced by factors such as the sugar-phosphate backbone, base stacking, and hydrogen bonding. Two common conformations of DNA are the B-form and the A-form. The B-form is a right-handed helix with a diameter of about 20 Å and a pitch of 34 Å, while the A-form has a smaller diameter (about 18 Å) and a shorter pitch (about 25 Å). RNA typically adopts an A-form conformation. The conformation of nucleic acids can have significant implications for their function, as it can affect their ability to interact with other molecules such as proteins or drugs. Understanding the conformational properties of nucleic acids is therefore an important area of research in molecular biology and medicine. A cell line is a culture of cells that are grown in a laboratory for use in research. These cells are usually taken from a single cell or group of cells, and they are able to divide and grow continuously in the lab. Cell lines can come from many different sources, including animals, plants, and humans. They are often used in scientific research to study cellular processes, disease mechanisms, and to test new drugs or treatments. Some common types of human cell lines include HeLa cells (which come from a cancer patient named Henrietta Lacks), HEK293 cells (which come from embryonic kidney cells), and HUVEC cells (which come from umbilical vein endothelial cells). It is important to note that cell lines are not the same as primary cells, which are cells that are taken directly from a living organism and have not been grown in the lab. RNA (Ribonucleic Acid) is a single-stranded, linear polymer of ribonucleotides. It is a nucleic acid present in the cells of all living organisms and some viruses. RNAs play crucial roles in various biological processes such as protein synthesis, gene regulation, and cellular signaling. There are several types of RNA including messenger RNA (mRNA), ribosomal RNA (rRNA), transfer RNA (tRNA), small nuclear RNA (snRNA), microRNA (miRNA), and long non-coding RNA (lncRNA). These RNAs differ in their structure, function, and location within the cell. Nucleic acid probes are specialized single-stranded DNA or RNA molecules that are used in molecular biology to identify and detect specific nucleic acid sequences, such as genes or fragments of DNA or RNA. These probes are typically labeled with a marker, such as a radioactive isotope or a fluorescent dye, which allows them to be detected and visualized. Nucleic acid probes work by binding or "hybridizing" to their complementary target sequence through base-pairing interactions between the nucleotides that make up the probe and the target. This specificity of hybridization allows for the detection and identification of specific sequences within a complex mixture of nucleic acids, such as those found in a sample of DNA or RNA from a biological specimen. Nucleic acid probes are used in a variety of applications, including gene expression analysis, genetic mapping, diagnosis of genetic disorders, and detection of pathogens, among others. They are an essential tool in modern molecular biology research and have contributed significantly to our understanding of genetics and disease. Messenger RNA (mRNA) is a type of RNA (ribonucleic acid) that carries genetic information copied from DNA in the form of a series of three-base code "words," each of which specifies a particular amino acid. This information is used by the cell's machinery to construct proteins, a process known as translation. After being transcribed from DNA, mRNA travels out of the nucleus to the ribosomes in the cytoplasm where protein synthesis occurs. Once the protein has been synthesized, the mRNA may be degraded and recycled. Post-transcriptional modifications can also occur to mRNA, such as alternative splicing and addition of a 5' cap and a poly(A) tail, which can affect its stability, localization, and translation efficiency. Nucleic acid amplification techniques (NAATs) are medical laboratory methods used to increase the number of copies of a specific DNA or RNA sequence. These techniques are widely used in molecular biology and diagnostics, including the detection and diagnosis of infectious diseases, genetic disorders, and cancer. The most commonly used NAAT is the polymerase chain reaction (PCR), which involves repeated cycles of heating and cooling to separate and replicate DNA strands. Other NAATs include loop-mediated isothermal amplification (LAMP), nucleic acid sequence-based amplification (NASBA), and transcription-mediated amplification (TMA). NAATs offer several advantages over traditional culture methods for detecting pathogens, including faster turnaround times, increased sensitivity and specificity, and the ability to detect viable but non-culturable organisms. However, they also require specialized equipment and trained personnel, and there is a risk of contamination and false positive results if proper precautions are not taken. 'Escherichia coli' (E. coli) is a type of gram-negative, facultatively anaerobic, rod-shaped bacterium that commonly inhabits the intestinal tract of humans and warm-blooded animals. It is a member of the family Enterobacteriaceae and one of the most well-studied prokaryotic model organisms in molecular biology. While most E. coli strains are harmless and even beneficial to their hosts, some serotypes can cause various forms of gastrointestinal and extraintestinal illnesses in humans and animals. These pathogenic strains possess virulence factors that enable them to colonize and damage host tissues, leading to diseases such as diarrhea, urinary tract infections, pneumonia, and sepsis. E. coli is a versatile organism with remarkable genetic diversity, which allows it to adapt to various environmental niches. It can be found in water, soil, food, and various man-made environments, making it an essential indicator of fecal contamination and a common cause of foodborne illnesses. The study of E. coli has contributed significantly to our understanding of fundamental biological processes, including DNA replication, gene regulation, and protein synthesis. Centrifugation, Density Gradient is a medical laboratory technique used to separate and purify different components of a mixture based on their size, density, and shape. This method involves the use of a centrifuge and a density gradient medium, such as sucrose or cesium chloride, to create a stable density gradient within a column or tube. The sample is carefully layered onto the top of the gradient and then subjected to high-speed centrifugation. During centrifugation, the particles in the sample move through the gradient based on their size, density, and shape, with heavier particles migrating faster and further than lighter ones. This results in the separation of different components of the mixture into distinct bands or zones within the gradient. This technique is commonly used to purify and concentrate various types of biological materials, such as viruses, organelles, ribosomes, and subcellular fractions, from complex mixtures. It allows for the isolation of pure and intact particles, which can then be collected and analyzed for further study or use in downstream applications. In summary, Centrifugation, Density Gradient is a medical laboratory technique used to separate and purify different components of a mixture based on their size, density, and shape using a centrifuge and a density gradient medium. A plasmid is a small, circular, double-stranded DNA molecule that is separate from the chromosomal DNA of a bacterium or other organism. Plasmids are typically not essential for the survival of the organism, but they can confer beneficial traits such as antibiotic resistance or the ability to degrade certain types of pollutants. Plasmids are capable of replicating independently of the chromosomal DNA and can be transferred between bacteria through a process called conjugation. They often contain genes that provide resistance to antibiotics, heavy metals, and other environmental stressors. Plasmids have also been engineered for use in molecular biology as cloning vectors, allowing scientists to replicate and manipulate specific DNA sequences. Plasmids are important tools in genetic engineering and biotechnology because they can be easily manipulated and transferred between organisms. They have been used to produce vaccines, diagnostic tests, and genetically modified organisms (GMOs) for various applications, including agriculture, medicine, and industry. Sensitivity and specificity are statistical measures used to describe the performance of a diagnostic test or screening tool in identifying true positive and true negative results. * Sensitivity refers to the proportion of people who have a particular condition (true positives) who are correctly identified by the test. It is also known as the "true positive rate" or "recall." A highly sensitive test will identify most or all of the people with the condition, but may also produce more false positives. * Specificity refers to the proportion of people who do not have a particular condition (true negatives) who are correctly identified by the test. It is also known as the "true negative rate." A highly specific test will identify most or all of the people without the condition, but may also produce more false negatives. In medical testing, both sensitivity and specificity are important considerations when evaluating a diagnostic test. High sensitivity is desirable for screening tests that aim to identify as many cases of a condition as possible, while high specificity is desirable for confirmatory tests that aim to rule out the condition in people who do not have it. It's worth noting that sensitivity and specificity are often influenced by factors such as the prevalence of the condition in the population being tested, the threshold used to define a positive result, and the reliability and validity of the test itself. Therefore, it's important to consider these factors when interpreting the results of a diagnostic test. Genetic transcription is the process by which the information in a strand of DNA is used to create a complementary RNA molecule. This process is the first step in gene expression, where the genetic code in DNA is converted into a form that can be used to produce proteins or functional RNAs. During transcription, an enzyme called RNA polymerase binds to the DNA template strand and reads the sequence of nucleotide bases. As it moves along the template, it adds complementary RNA nucleotides to the growing RNA chain, creating a single-stranded RNA molecule that is complementary to the DNA template strand. Once transcription is complete, the RNA molecule may undergo further processing before it can be translated into protein or perform its functional role in the cell. Transcription can be either "constitutive" or "regulated." Constitutive transcription occurs at a relatively constant rate and produces essential proteins that are required for basic cellular functions. Regulated transcription, on the other hand, is subject to control by various intracellular and extracellular signals, allowing cells to respond to changing environmental conditions or developmental cues. Oligonucleotides are short sequences of nucleotides, the building blocks of DNA and RNA. They typically contain fewer than 100 nucleotides, and can be synthesized chemically to have specific sequences. Oligonucleotides are used in a variety of applications in molecular biology, including as probes for detecting specific DNA or RNA sequences, as inhibitors of gene expression, and as components of diagnostic tests and therapies. They can also be used in the study of protein-nucleic acid interactions and in the development of new drugs. In a medical context, "hot temperature" is not a standard medical term with a specific definition. However, it is often used in relation to fever, which is a common symptom of illness. A fever is typically defined as a body temperature that is higher than normal, usually above 38°C (100.4°F) for adults and above 37.5-38°C (99.5-101.3°F) for children, depending on the source. Therefore, when a medical professional talks about "hot temperature," they may be referring to a body temperature that is higher than normal due to fever or other causes. It's important to note that a high environmental temperature can also contribute to an elevated body temperature, so it's essential to consider both the body temperature and the environmental temperature when assessing a patient's condition. Temperature, in a medical context, is a measure of the degree of hotness or coldness of a body or environment. It is usually measured using a thermometer and reported in degrees Celsius (°C), degrees Fahrenheit (°F), or kelvin (K). In the human body, normal core temperature ranges from about 36.5-37.5°C (97.7-99.5°F) when measured rectally, and can vary slightly depending on factors such as time of day, physical activity, and menstrual cycle. Elevated body temperature is a common sign of infection or inflammation, while abnormally low body temperature can indicate hypothermia or other medical conditions. In the context of medicine and pharmacology, "kinetics" refers to the study of how a drug moves throughout the body, including its absorption, distribution, metabolism, and excretion (often abbreviated as ADME). This field is called "pharmacokinetics." 1. Absorption: This is the process of a drug moving from its site of administration into the bloodstream. Factors such as the route of administration (e.g., oral, intravenous, etc.), formulation, and individual physiological differences can affect absorption. 2. Distribution: Once a drug is in the bloodstream, it gets distributed throughout the body to various tissues and organs. This process is influenced by factors like blood flow, protein binding, and lipid solubility of the drug. 3. Metabolism: Drugs are often chemically modified in the body, typically in the liver, through processes known as metabolism. These changes can lead to the formation of active or inactive metabolites, which may then be further distributed, excreted, or undergo additional metabolic transformations. 4. Excretion: This is the process by which drugs and their metabolites are eliminated from the body, primarily through the kidneys (urine) and the liver (bile). Understanding the kinetics of a drug is crucial for determining its optimal dosing regimen, potential interactions with other medications or foods, and any necessary adjustments for special populations like pediatric or geriatric patients, or those with impaired renal or hepatic function. Medical Definition of "Herpesvirus 4, Human" (Epstein-Barr Virus) "Herpesvirus 4, Human," also known as Epstein-Barr virus (EBV), is a member of the Herpesviridae family and is one of the most common human viruses. It is primarily transmitted through saliva and is often referred to as the "kissing disease." EBV is the causative agent of infectious mononucleosis (IM), also known as glandular fever, which is characterized by symptoms such as fatigue, sore throat, fever, and swollen lymph nodes. The virus can also cause other diseases, including certain types of cancer, such as Burkitt's lymphoma, Hodgkin's lymphoma, and nasopharyngeal carcinoma. Once a person becomes infected with EBV, the virus remains in the body for the rest of their life, residing in certain white blood cells called B lymphocytes. In most people, the virus remains dormant and does not cause any further symptoms. However, in some individuals, the virus may reactivate, leading to recurrent or persistent symptoms. EBV infection is diagnosed through various tests, including blood tests that detect antibodies against the virus or direct detection of the virus itself through polymerase chain reaction (PCR) assays. There is no cure for EBV infection, and treatment is generally supportive, focusing on relieving symptoms and managing complications. Prevention measures include practicing good hygiene, avoiding close contact with infected individuals, and not sharing personal items such as toothbrushes or drinking glasses. Comparative genomic hybridization (CGH) is a molecular cytogenetic technique used to detect and measure changes in the DNA content of an individual's genome. It is a type of microarray-based analysis that compares the DNA of two samples, typically a test sample and a reference sample, to identify copy number variations (CNVs), including gains or losses of genetic material. In CGH, the DNA from both samples is labeled with different fluorescent dyes, typically one sample with a green fluorophore and the other with a red fluorophore. The labeled DNAs are then co-hybridized to a microarray, which contains thousands of DNA probes representing specific genomic regions. The intensity of each spot on the array reflects the amount of DNA from each sample that has hybridized to the probe. By comparing the ratio of green to red fluorescence intensities for each probe, CGH can detect gains or losses of genetic material in the test sample relative to the reference sample. A ratio of 1 indicates no difference in copy number between the two samples, while a ratio greater than 1 suggests a gain of genetic material, and a ratio less than 1 suggests a loss. CGH is a powerful tool for detecting genomic imbalances associated with various genetic disorders, including cancer, developmental delay, intellectual disability, and congenital abnormalities. It can also be used to study the genomics of organisms in evolutionary biology and ecological studies. RNA probes are specialized biomolecules used in molecular biology to detect and localize specific RNA sequences within cells or tissues. They are typically single-stranded RNA molecules that have been synthesized with a modified nucleotide, such as digoxigenin or biotin, which can be detected using antibodies or streptavidin conjugates. RNA probes are used in techniques such as in situ hybridization (ISH) and Northern blotting to identify the spatial distribution of RNA transcripts within cells or tissues, or to quantify the amount of specific RNA present in a sample. The probe is designed to be complementary to the target RNA sequence, allowing it to bind specifically to its target through base-pairing interactions. RNA probes can be labeled with various reporter molecules, such as radioactive isotopes or fluorescent dyes, which enable their detection and visualization using techniques such as autoradiography or microscopy. The use of RNA probes has proven to be a valuable tool in the study of gene expression, regulation, and localization in various biological systems. An amino acid sequence is the specific order of amino acids in a protein or peptide molecule, formed by the linking of the amino group (-NH2) of one amino acid to the carboxyl group (-COOH) of another amino acid through a peptide bond. The sequence is determined by the genetic code and is unique to each type of protein or peptide. It plays a crucial role in determining the three-dimensional structure and function of proteins. DNA Sequence Analysis is the systematic determination of the order of nucleotides in a DNA molecule. It is a critical component of modern molecular biology, genetics, and genetic engineering. The process involves determining the exact order of the four nucleotide bases - adenine (A), guanine (G), cytosine (C), and thymine (T) - in a DNA molecule or fragment. This information is used in various applications such as identifying gene mutations, studying evolutionary relationships, developing molecular markers for breeding, and diagnosing genetic diseases. The process of DNA Sequence Analysis typically involves several steps, including DNA extraction, PCR amplification (if necessary), purification, sequencing reaction, and electrophoresis. The resulting data is then analyzed using specialized software to determine the exact sequence of nucleotides. In recent years, high-throughput DNA sequencing technologies have revolutionized the field of genomics, enabling the rapid and cost-effective sequencing of entire genomes. This has led to an explosion of genomic data and new insights into the genetic basis of many diseases and traits. Phylogeny is the evolutionary history and relationship among biological entities, such as species or genes, based on their shared characteristics. In other words, it refers to the branching pattern of evolution that shows how various organisms have descended from a common ancestor over time. Phylogenetic analysis involves constructing a tree-like diagram called a phylogenetic tree, which depicts the inferred evolutionary relationships among organisms or genes based on molecular sequence data or other types of characters. This information is crucial for understanding the diversity and distribution of life on Earth, as well as for studying the emergence and spread of diseases. Ribosomal RNA (rRNA) is a type of RNA that combines with proteins to form ribosomes, which are complex structures inside cells where protein synthesis occurs. The "16S" refers to the sedimentation coefficient of the rRNA molecule, which is a measure of its size and shape. In particular, 16S rRNA is a component of the smaller subunit of the prokaryotic ribosome (found in bacteria and archaea), and is often used as a molecular marker for identifying and classifying these organisms due to its relative stability and conservation among species. The sequence of 16S rRNA can be compared across different species to determine their evolutionary relationships and taxonomic positions.
Euclid was the first Greek mathematician who initiated a new way to study Geometry. He is well known for his elements of Geometry. He also made important contributions to the number theory, and one of them is Euclid’s Lemma. A Lemma is a proven statement that is used to prove other statements. Euclid’s division algorithm is based on Euclid’s Lemma. For many years we were using a long division process, but this lemma is a restatement for it. Consider a and b be any two positive integers, unique integers q and r such that If b\|a, then r = 0. Otherwise, r satisfies the stronger inequality 0 < r < b Theorem: Let a and b be any two positive integers then, there exist unique integers q and r such that a = bq + r, 0<= r < b If b\|a, then r = 0. Otherwise, r satisfies the stronger inequality 0 <= r < b Let us consider an Arithmetic Progression ………, a-3b, a - 2b, a - b, a, a + b, a + 2b, a + 3b……. Here the common difference is b and it extends in both directions. Let r is the smallest non-negative term of the arithmetic progression. Then there exists a non- negative integer q such that a - bq = r a = bq + r As, r is the smallest non-negative integer satisfying the above result. Therefore, 0<= r < b Thus, we have a= bq + r, where 0 <= r < b If ‘a’ and ‘b’ are positive integers such that a = bq + r, then every common divisor of ‘a’ and ‘b’, is a common divisor of ‘b’ and ‘r’ and vice versa. Consider positive integers 418 and 33 Taking a bigger number 418 as a and smaller number 33 as b Express the numbers in the form a = bq + r 418 = 33 x 12 +22 Now taking the divisor 33 as a and 22 as b apply Euclid’s Division algorithm to get, 33 = 22 x 1 + 11 Again take 22 as new divisor a and 11 as b apply Euclid’s Division Algorithm to get 22 = 11 x 2 + 0 Since, the remainder = 0 so we cannot proceed further. The last divisor is 11 and we say H.C.F. of 418 and 33 is 11. Euclid Lemma is a theory proposed by Euclid. Euclid lemma is a proven statement used to prove other statements. Example 1: To find HCF of 210 and 55 using Euclid’s division algorithm. Solution: Given integers are 210 and 55. Applying Euclid’s division lemma to 210 and 55 we get, 210 = 55 x 3 + 45………………..(i) Since the remainder 45 is not equal to zero we apply the division lemma to the divisor 55 and remainder 45 to get, 55 =45 x 1 + 10………………….(ii) Now, we apply division lemma to the new divisor 45 and new remainder 10 to get 45 = 10 x 4 + 5…………………….(iii) We now consider the new divisor 10 and the new remainder 5 and apply division lemma to get 10 = 5 x 2 + 0 The remainder at this stage is 0. So the divisor at this stage or the remainder at the previous step is 5 So HCF of 210 and 55 is 5 Example 2: Using Euclid’s Division Algorithm, find the H.C.F of 135 and 225 Solution: Given integers are 135 and 225 Applying Euclid’s division lemma, we get 225 = 135 x 1 + 90 Now taking divisor 135 and remainder 90, we get 135 = 90 x1 + 45 Further taking divisor 90 and remainder 45, we get 90 = 45 x 2 + 0 Now at this stage remainder is 0 so we get 45 as the H.C.F 1.Using Euclid’s division algorithm, find the H.C.F of 196 and 38220. 2.Using Euclid division algorithm find the H.C.F of 441 and 567 1.What is Euclid Division Lemma? The process of dividing one integer by another, in such a way that it produces a question, a remainder which is smaller than the divisor. The question and remainder are unique under some conditions. The basis of the Euclid Division Algorithm is Euclids Division Lemma. We can calculate the highest common factor of two integers using Euclid’s Division Algorithm. Definition:- Euclid’s Division Lemma states that if two positive integers a and b, then there exist two unique integers q and r such that a=bq+r where 0 <= r <= b. 2. What is the difference between the Euclid Division Lemma and Euclid Division Algorithm? The word Lemma is already a proven statement used to prove other statements, whereas the algorithm is the well-defined steps used to solve the problem. We use the Euclid Division Lemma to prove other theorems while Euclid Division Algorithm is used to find the Highest common factor of two positive integers where we apply the Euclid Division Lemma.
Global Forest Maps Forests cover about 30% of the Earth’s surface. Over 1 billion people depend on these forests for their survival because it’s their pharmacy, their fuel, and food for their animals. Forests keep rivers clean. They prevent soil erosion and prevent landslides and avalanches. Plus, they are carbon sinks because they absorb over one-fifth of carbon emissions caused by fossil fuels. But forests are disappearing. Natural causes like disease and forest fires have always existed. Human activities are now the leading cause of deforestation. No other human activity has caused more deforestation than animal agriculture. We have a better spatial understanding because of satellite and mapping technologies. These 4 global forest maps tell a story or our trees. So let’s take a look and start seeing the forest for the trees. 1. NASA’s Forest Heights Map NASA’s Forest Canopy Height map is a first of its kind. It’s unique because it shows the height of trees of the entire planet. Now, NASA didn’t go out in the field and measure every tree height to make this forest map. So how did they do it? All tree heights were derived using satellites orbiting our Earth such as Geoscience Laser Altimeter Systems (GLAS). GLAS is a laser ranging technology. It sends a pulse and measures how long it takes to return to get distance. But GLAS wasn’t the only satellite NASA used. It combined Shuttle Radar Topography Mission (SRTM), MODIS, TRMM and the WorldClim databases. Have you noticed how tree heights are generally taller at the equator? Some trees tower higher than 40 meters in height at the equator. At the poles, the tree canopy is generally shorter. Countries in northern Europe, Canada, and Russia tend to have tree canopy heights less than 20 meters. 2. Global Forest Change Almost one-third of our land is covered in forests. But deforestation is cutting down our forests at about the size of Greece per year. That’s 50 soccer fields every minute. The effects of deforestation are devastating. It increases greenhouse gases and soil erosion. It takes away habitat for wildlife and homes for indigenous groups. How can we quantify deforestation? Landsat is the reigning monarch of historic satellite data. 40 years and counting! Landsat is the longest-running Earth observation mission in history. We could compare a snapshot of Earth from 1972 using Landsat-1 data if we really wanted to. The University of Maryland has carved out the drool-worthy Global Forest Change map solely using Landsat data. The key focus is forest extent and change. Forest is defined as vegetation taller than 5 meters. Forest cover loss and gain are highlighted from 2000-2012. We knew there were red flags for countries like Indonesia, Honduras, and the Philippines and deforestation. On the map, they look like signal flares! On global forest maps like these, it confirms reports and statistics about how these countries sustained great losses in forests. 3. NASA Forest Fires When there’s smoke, there’s fire. And on Earth, there’s something always burning. NASA’s Moderate Resolution Imaging Spectroradiometer (MODIS) keeps a close eye on wildfires around the globe. Whether they’re started by people, lightning strikes or by other means, NASA’s fire maps pinpoint locations of actively burning fires. Are forest fires harmful for the environment? Forest fires are not necessarily bad. They can clear dead underbrush and restore it to good health. In certain ecosystems, plants require periodic burning to reproduce. NASA’s fire maps are animated dating back to 2000 all the way to this year. It’s unbelievable watching the time series animation and watching the flames roar our planet. 4. Global Forest Watch Global Forest Watch is really the mother of all forest monitoring websites. It’s not just one map; it’s a series of forest maps. Each one has cutting-edge algorithms harnessing the power of satellite data and cloud computing. The more you think of it, there’s a lot we don’t know about forests like: - Where are we clearing forests? - Why does it happen? - And who is responsible? Users can dynamically view Landsat’s forest gain/loss data in near real-time. Global Forest Watch takes it a step further showing how forests are being used such as palm oil, mining, logging, etc. It has time animations, forest fire data, and conservation areas. It’s free and simple to use. Governments, businesses, academics, media, and NGOs can gain a wealth of information and ensure sustainability. Global Forest Watch really lets you sit in the driver’s seat and openly explore a goldmine of forest maps and information. Forest maps mean action If an old tree falls in the forest and nobody’s around to hear it, does it make a sound? Near real-time satellite imagery has transformed our global understanding of forests. Satellites deliver timely and accurate information about forest fires, deforestation, canopy height, and even forest disease. Forest maps give users the power to stop harmful forest loss. For example, business managers buying commodities such as palm oil can use near real-time forest maps to see if suppliers are clearing forests they committed to protect. This technology empowers people everywhere to better manage forests. …so if an old tree falls in the forest and nobody’s around to hear it, does it make a sound? With these global forest maps, everyone hears it.
Looking for free content that’s aligned to your standards? You’ve come to the right place! Get Free 2nd Grade Math Content Khan Academy is a nonprofit with thousands of free videos, articles, and practice questions for just about every standard. No ads, no subscriptions – just 100% free, forever. 2.NS Number Sense - 2.NS.1 Count by ones, twos, fives, tens, and hundreds up to at least 1,000 from any given number. - 2.NS.2 Read and write whole numbers up to 1,000. Use words, models, standard form and expanded form to represent and show equivalent forms of whole numbers up to 1,000. - 2.NS.3 Plot and compare whole numbers up to 1,000 on a number line. - 2.NS.4 Match the ordinal numbers first, second, third, etc., with an ordered set up to 30 items. - 2.NS.5 Determine whether a group of objects (up to 20) has an odd or even number of members (e.g., by placing that number of objects in two groups of the same size and recognizing that for even numbers no object will be left over and for odd numbers one object will be left over, or by pairing objects or counting them by 2s). - 2.NS.6 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones (e.g., 706 equals 7 hundreds, 0 tens, and 6 ones). Understand that 100 can be thought of as a group of ten tens—called a “hundred.” Understand that the numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). - 2.NS.7 Use place value understanding to compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. 2.CA Computation and Algebraic Thinking - 2.CA.1 Add and subtract fluently within 100. - 2.CA.2 Solve real-world problems involving addition and subtraction within 100 in situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all parts of the addition or subtraction problem (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Use estimation to decide whether answers are reasonable in addition problems. - 2.CA.3 Solve real-world problems involving addition and subtraction within 100 in situations involving lengths that are given in the same units (e.g., by using drawings, such as drawings of rulers, and equations with a symbol for the unknown number to represent the problem). - 2.CA.4 Add and subtract within 1000, using models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; describe the strategy and explain the reasoning used. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones, and that sometimes it is necessary to compose or decompose tens or hundreds. - 2.CA.5 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal groups. - 2.CA.6 Show that the order in which two numbers are added (commutative property) and how the numbers are grouped in addition (associative property) will not change the sum. These properties can be used to show that numbers can be added in any order. - 2.CA.7 Create, extend, and give an appropriate rule for number patterns using addition and subtraction within 1000. - 2.G.1 Identify, describe, and classify two- and three-dimensional shapes (triangle, square, rectangle, cube, right rectangular prism) according to the number and shape of faces and the number of sides and/or vertices. Draw two-dimensional shapes. - 2.G.2 Create squares, rectangles, triangles, cubes, and right rectangular prisms using appropriate materials. - 2.G.3 Investigate and predict the result of composing and decomposing two- and three-dimensional shapes. - 2.G.4 Partition a rectangle into rows and columns of same-size (unit) squares and count to find the total number of same-size squares. - 2.G.5 Partition circles and rectangles into two, three, or four equal parts; describe the shares using the words halves, thirds, half of, a third of, etc.; and describe the whole as two halves, three thirds, four fourths. Recognize that equal parts of identical wholes need not have the same shape. - 2.M.1 Describe the relationships among inch, foot, and yard. Describe the relationship between centimeter and meter. - 2.M.2 Estimate and measure the length of an object by selecting and using appropriate tools, such as rulers, yardsticks, meter sticks, and measuring tapes to the nearest inch, foot, yard, centimeter and meter. - 2.M.3 Understand that the length of an object does not change regardless of the units used. Measure the length of an object twice using length units of different lengths for the two measurements. Describe how the two measurements relate to the size of the unit chosen. - 2.M.4 Estimate and measure volume (capacity) using cups and pints. - 2.M.5 Tell and write time to the nearest five minutes from analog clocks, using a.m. and p.m. Solve real-world problems involving addition and subtraction of time intervals on the hour or half hour. - 2.M.6 Describe relationships of time, including: seconds in a minute; minutes in an hour; hours in a day; days in a week; and days, weeks, and months in a year. - 2.M.7 Find the value of a collection of pennies, nickels, dimes, quarters and dollars. 2.DA Data Analysis - 2.DA.1 Draw a picture graph (with single-unit scale) and a bar graph (with single-unit scale) to represent a data set with up to four choices (What is your favorite color? red, blue, yellow, green). Solve simple put-together, take-apart, and compare problems using information presented in the graphs.
Basic Physics of Nuclear Medicine/Print version \| This is the print version of Basic Physics of Nuclear Medicine You won't see this message or any elements not part of the book's content when you print or preview this page. Note: current version of this book can be found at http://en.wikibooks.org/wiki/Basic_Physics_of_Nuclear_Medicine Atomic & Nuclear StructureEdit You will have encountered much of what we will cover here in your high school physics. We are going to review this material again below so as to set the context for subsequent chapters. This chapter will also provide you with an opportunity to check your understanding of this topic. The chapter covers atomic structure, nuclear structure, the classification of nuclei, binding energy and nuclear stability. The atom is considered to be the basic building block of all matter. Simple atomic theory tells us that it consists of two components: a nucleus surrounded by an electron cloud. The situation can be considered as being similar in some respects to planets orbiting the sun. From an electrical point of view, the nucleus is said to be positively charged and the electrons negatively charged. From a size point of view, the radius of an atom is about 10-10 m while the radius of a nucleus is about 10-14 m, i.e. about ten thousand times smaller. The situation could be viewed as something like a cricket ball, representing the nucleus, in the middle of a sporting arena with the electrons orbiting somewhere around where the spectators would sit. This perspective tells us that the atom should be composed mainly of empty space. However, the situation is far more complex than this simple picture portrays in that we must also take into account the physical forces which bind the atom together. From a mass point of view the mass of a proton is roughly equal to the mass of a neutron and each of these is about 2,000 times the mass of an electron. So most of the mass of an atom is concentrated in the small region at its core. From an electrical point of view the proton is positively charged and the neutron has no charge. An atom all on its own (if that were possible to achieve!) is electrically neutral. The number of protons in the nucleus of such an atom must therefore equal the number of electrons orbiting that atom. Classification of NucleiEdit The term Atomic Number is defined in nuclear physics as the number of protons in a nucleus and is given the symbol Z. From your chemistry you will remember that this number also defines the position of an element in the Periodic Table of Elements. The term Mass Number is defined as the number of nucleons in a nucleus, that is the number of protons plus the number of neutrons, and is given the symbol A. Note that the symbols here are a bit odd, in that it would prevent some confusion if the Atomic Number were given the symbol A, and the Mass Number were given another symbol, such as M, but its not a simple world! It is possible for nuclei of a given element to have the same number of protons but differing numbers of neutrons, that is to have the same Atomic Number but different Mass Numbers. Such nuclei are referred to as Isotopes. All elements have isotopes and the number ranges from three for hydrogen to over 30 for elements such as caesium and barium. Chemistry has a relatively simple way of classifying the different elements by the use of symbols such as H for hydrogen, He for helium and so on. The classification scheme used to identify different isotopes is based on this approach with the use of a superscript before the chemical symbol to denote the Mass Number along with a subscript before the chemical symbol to denote the Atomic Number. In other words an isotope is identified as: where X is the chemical symbol of the element; A is the "Mass Number," (protons+ neutrons); Z is the "Atomic Number," (number identifying the element on the periodic chart). Let us take the case of hydrogen as an example. It has three isotopes: - the most common one consisting of a single proton orbited by one electron, - a second isotope consisting of a nucleus containing a proton and a neutron orbited by one electron, - a third whose nucleus consists of one proton and two neutrons, again orbited by a single electron. A simple illustration of these isotopes is shown below. Remember though that this is a simplified illustration given what we noted earlier about the size of a nucleus compared with that of an atom. But the illustration is nevertheless useful for showing how isotopes are classified. The first isotope commonly called hydrogen has a Mass Number of 1, an Atomic Number of 1 and hence is identified as: The second isotope commonly called deuterium has a Mass Number of 2, an Atomic Number of 1 and is identified as: The third isotope commonly called tritium is identified as: The same classification scheme is used for all isotopes. For example, you should now be able to figure out that the uranium isotope, , contains 92 protons and 144 neutrons. A final point on classification is that we can also refer to individual isotopes by giving the name of the element followed by the Mass Number. For example, we can refer to deuterium as hydrogen-2 and we can refer to as uranium-236. Before we leave this classification scheme let us further consider the difference between chemistry and nuclear physics. You will remember that the water molecule is made up of two hydrogen atoms bonded with an oxygen atom. Theoretically if we were to combine atoms of hydrogen and oxygen in this manner many, many of billions of times we could make a glass of water. We could also make our glass of water using deuterium instead of hydrogen. This second glass of water would theoretically be very similar from a chemical perspective. However, from a physics perspective our second glass would be heavier than the first since each deuterium nucleus is about twice the mass of each hydrogen nucleus. Indeed water made in this fashion is called heavy water. Atomic Mass UnitEdit The conventional unit of mass, the kilogram, is rather large for use in describing characteristics of nuclei. For this reason, a special unit called the Atomic Mass Unit (amu) is often used. This unit is sometimes defined as 1/12th of the mass of the stable most commonly occurring isotope of carbon, i.e. 12C. In terms of grams, 1 amu is equal to 1.66 x 10-24 g, that is, just over one million, million, million millionth of a gram. The masses of the proton, mp and neutron, mn on this basis are: while that of the electron is just 0.00055 amu. We are now in a position to consider the subject of nuclear stability. From what we have covered so far, we have seen that the nucleus is a tiny region in the centre of an atom and that it is composed of neutrally and positively charged particles. So, in a large nucleus such as that of uranium (Z=92) we have a large number of positively charged protons concentrated into a tiny region in the centre of the atom. An obvious question which arises is that with all these positive charges in close proximity, why doesn't the nucleus fly apart? How can a nucleus remain as an entity with such electrostatic repulsion between the components? Should the orbiting negatively-charged electrons not attract the protons away from the atoms centre? Let us take the case of the helium-4 nucleus as an example. This nucleus contains two protons and two neutrons so that in terms of amu we can figure out from what we covered earlier that the Therefore we would expect the total mass of the nucleus to be 4.03298 amu. The experimentally determined mass of a helium-4 nucleus is a bit less - just 4.00260 amu. In other words there is a difference of 0.03038 amu between what we might expect as the mass of this nucleus and what we actually measure. You might think of this difference as very small at just 0.75%. But remember that since the mass of one electron is 0.00055 amu the difference is actually equivalent to the mass of about 55 electrons. Therefore it is significant enough to wonder about. It is possible to consider that this missing mass is converted to energy which is used to hold the nucleus together; it is converted to a form of energy called Binding Energy. You could say, as with all relationships, energy must be expended in order to maintain them! Like the gram in terms of the mass of nuclei, the common unit of energy, the joule is rather cumbersome when we consider the energy needed to bind a nucleus together. The unit used to express energies on the atomic scale is the electron volt, symbol: eV. One electron volt is defined as the amount of energy gained by an electron as it falls through a potential difference of one volt. This definition on its own is not of great help to us here and it is stated purely for the sake of completeness. So do not worry about it for the time being. Just appreciate that it is a unit representing a tiny amount of energy which is useful on the atomic scale. It is a bit too small in the case of binding energies however and the mega-electron volt (MeV) is often used. Albert Einstein introduced us to the equivalence of mass, m, and energy, E, at the atomic level using the following equation: where c is the velocity of light. It is possible to show that 1 amu is equivalent to 931.48 MeV. Therefore, the mass difference we discussed earlier between the expected and measured mass of the helium-4 nucleus of 0.03038 amu is equivalent to about 28 MeV. This represents about 7 MeV for each of the four nucleons contained in the nucleus. In most stable isotopes the binding energy per nucleon lies between 7 and 9 MeV. There are two competing forces in the nuclei, electrostatic repulsion between protons and the attractive nuclear force between nucleons (protons and neutrons). The electrostatic force is a long range force that becomes more difficult to compensate for as more protons are added to the nucleus. The nuclear force, which arises as the residual strong force (the strong force binds the quarks together within a nucleon), is a short range force that only operates on a very short distance scale (~ 1.5 fm) as it arises from a Yukawa potential. (Electromagnetism is a long range force as the force carrier, the photon, is massless; the nuclear force is a short range force as the force carrier, the pion, is massive). Therefore, larger nuclei tend to be less stable, and require a larger ratio of neutrons to protons (which contribute to the attractive strong force, but not the long-range electrostatic repulsion). For the low Z nuclides the ratio of neutrons to protons is approximately 1, though it gradually increases to about 1.5 for the higher Z nuclides as shown below on the Nuclear Stability Curve. In other words to combat the effect of the increase in electrostatic repulsion when the number of protons increases the number of neutrons must increase more rapidly to contribute sufficient energy to bind the nucleus together. As we noted earlier there are a number of isotopes for each element of the Periodic Table. It has been found that the most stable isotope for each element has a specific number of neutrons in its nucleus. Plotting a graph of the number of protons against the number of neutrons for these stable isotopes generates what is called the Nuclear Stability Curve: Note that the number of protons equals the number of neutrons for small nuclei. But notice also that the number of neutrons increases more rapidly than the number of protons as the size of the nucleus gets bigger so as to maintain the stability of the nucleus. In other words more neutrons need to be there to contribute to the binding energy used to counteract the electrostatic repulsion between the protons. There are about 2,450 known isotopes of the approximately one hundred elements in the Periodic Table. You can imagine the size of a table of isotopes relative to that of the Periodic Table! The unstable isotopes lie above or below the Nuclear Stability Curve. These unstable isotopes attempt to reach the stability curve by splitting into fragments, in a process called Fission, or by emitting particles and/or energy in the form of radiation. This latter process is called Radioactivity. It is useful to dwell for a few moments on the term radioactivity. For example what has nuclear stability to do with radio? From a historical perspective remember that when these radiations were discovered about 100 years ago we did not know exactly what we were dealing with. When people like Henri Becquerel and Marie Curie were working initially on these strange emanations from certain natural materials it was thought that the radiations were somehow related to another phenomenon which also was not well understood at the time - that of radio communication. It seems reasonable on this basis to appreciate that some people considered that the two phenomena were somehow related and hence that the materials which emitted radiation were termed radio-active. We know today that the two phenomena are not directly related but we nevertheless hold onto the term radioactivity for historical purposes. But it should be quite clear to you having reached this stage of this chapter that the term radioactive refers to the emission of particles and/or energy from unstable isotopes. Unstable isotopes for instance those that have too many protons to remain a stable entity are called radioactive isotopes - and called radioisotopes for short. The term radionuclide is also sometimes used. Finally about 300 of the 2,450-odd isotopes mentioned above are found in nature. The rest are man-made, that is they are produced artificially. These 2,150 or so artificial isotopes have been made during the last 100 years or so with most having been made since the second world war. We will return to the production of radioisotopes in a later chapter of this wikibook and will proceed for the time being with a description of the types of radiation emitted by radioisotopes. Multiple Choice QuestionsEdit Click here to access multiple choice questions on atomic and nuclear structure. - Novel Periodic Table - an interactive table providing information about each element. - Marie and Pierre Curie and the Discovery of Polonium and Radium - an historical essay from The Nobel Foundation. - Natural Radioactivity - an overview of radioactivity in nature - includes sections on primordial radionuclides, cosmic radiation, human produced radionuclides, as well as natural radioactivity in soil, in the ocean, in the human body and in building materials - from the University of Michigan Student Chapter of the Health Physics Society. - The Particle Adventure - an interactive tour of the inner workings of the atom which explains the modern tools physicists use to probe nuclear and sub-nuclear matter and how physicists measure the results of their experiments using detectors - from the Particle Data Group at the Lawrence Berkeley National Lab, USA and mirrored at CERN, Geneva. - WebElements - an excellent web-based Periodic Table of the Elements which includes a vast array of data about each element - originally from Mark Winter at the University of Sheffield, England. We saw in the last chapter that radioactivity is a process used by unstable nuclei to achieve a more stable situation. It is said that such nuclei decay in an attempt to achieve stability. So, an alternative title for this chapter is Nuclear Decay Processes. We also saw in the previous chapter that we can use the Nuclear Stability Curve as a means of describing what is going on. So a second alternative title for this chapter is Methods of Getting onto the Nuclear Stability Curve. We are going to follow a descriptive or phenomenological approach to the topic here by describing in a fairly simple fashion what is known about each of the major decay mechanisms. Once again you may have already covered this material in high school physics. But bear with us because the treatment here will help us set the scene for subsequent chapters. Methods of Radioactive DecayEdit Rather than considering what happens to individual nuclei it is perhaps easier to consider a hypothetical nucleus that can undergo many of the major forms of radioactive decay. This hypothetical nucleus is shown below: Firstly we can see two protons and two neutrons being emitted together in a process called alpha-decay. Secondly, we can see that a proton can release a positron in a process called beta-plus decay, and that a neutron can emit an electron in a process called beta-minus decay. We can also see an electron being captured by a proton. Thirdly we can see some energy (a photon) being emitted which results from a process called gamma-decay as well as an electron being attracted into the nucleus and being ejected again. Finally there is the rather catastrophic process where the nucleus cracks in half called spontaneous fission. We will now describe each of these decay processes in turn. This is a very destructive process which occurs in some heavy nuclei which split into 2 or 3 fragments plus some neutrons. These fragments form new nuclei which are usually radioactive. Nuclear reactors exploit this phenomenon for the production of radioisotopes. Its also used for nuclear power generation and in nuclear weaponry. The process is not of great interest to us here and we will say no more about it for the time being. In this decay process two protons and two neutrons leave the nucleus together in an assembly known as an alpha particle. Note that an alpha particle is really a helium-4 nucleus. So why not call it a helium nucleus? Why give it another name? The answer to this question lies in the history of the discovery of radioactivity. At the time when these radiations were discovered we didn't know what they really were. We found out that one type of these radiations had a double positive charge and it was not until sometime later that we learned that they were in fact nuclei of helium-4. In the initial period of their discovery this form of radiation was given the name alpha rays (and the other two were called beta and gamma rays), these terms being the first three letters of the Greek alphabet. We still call this form of radiation by the name alpha particle for historical purposes. Calling it by this name also contributes to the specific jargon of the field and leads outsiders to think that the subject is quite specialized! But notice that the radiation really consists of a helium-4 nucleus emitted from an unstable larger nucleus. There is nothing strange about helium since it is quite an abundant element on our planet. So why is this radiation dangerous to humans? The answer to this question lies with the energy with which they are emitted and the fact that they are quite massive and have a double positive charge. So when they interact with living matter they can cause substantial destruction to molecules which they encounter in their attempt to slow down and to attract two electrons to become a neutral helium atom. An example of this form of decay occurs in the uranium-238 nucleus. The equation which represents what occurs is: Here the uranium-238 nucleus emits a helium-4 nucleus (the alpha particle) and the parent nucleus becomes thorium-234. Note that the Mass Number of the parent nucleus has been reduced by 4 and the Atomic Number is reduced by 2 which is a characteristic of alpha decay for any nucleus in which it occurs. There are three common forms of beta decay: (a) Electron Emission - Certain nuclei which have an excess of neutrons may attempt to reach stability by converting a neutron into a proton with the emission of an electron. The electron is called a beta-minus particle – the minus indicating that the particle is negatively charged. - We can represent what occurs as follows: - where a neutron converts into a proton and an electron. Notice that the total electrical charge is the same on both sides of this equation. We say that the electric charge is conserved. - We can consider that the electron cannot exist inside the nucleus and therefore is ejected. - Once again there is nothing strange or mysterious about an electron. What is important though from a radiation safety point of view is the energy with which it is emitted and the chemical damage it can cause when it interacts with living matter. - An example of this type of decay occurs in the iodine-131 nucleus which decays into xenon-131 with the emission of an electron, that is - The electron is what is called a beta-minus particle. Note that the Mass Number in the above equation remains the same and that the Atomic Number increases by 1 which is characteristic of this type of decay. - You may be wondering how an electron can be produced inside a nucleus given that the simple atomic description we gave in the previous chapter indicated that the nucleus consists of protons and neutrons only. This is one of the limitations of the simple treatment presented so far and can be explained by considering that the two particles which we call protons and neutrons are themselves formed of smaller particles called quarks. We are not going to consider these in any way here other than to note that some combinations of different types of quark produce protons and another combination produces neutrons. The message here is to appreciate that a simple picture is the best way to start in an introductory text such as this and that the real situation is a lot more complex than what has been described. The same can be said about the treatment of beta-decay given above as we will see in subsequent chapters. (b) Positron Emission - When the number of protons in a nucleus is too large for the nucleus to be stable it may attempt to reach stability by converting a proton into a neutron with the emission of a positively-charged electron. - That is not a typographical error! An electron with a positive charge also called a positron is emitted. The positron is the beta-plus particle. - The history here is quite interesting. A brilliant Italian physicist, Enrico Fermi developed a theory of beta decay and his theory predicted that positively-charged as well as negatively-charged electrons could be emitted by unstable nuclei. These particles could be called pieces of anti-matter and they were subsequently discovered by experiment. They do not exist for very long as they quickly combine with a normal electron and the subsequent reaction called annihilation gives rise to the emission of two gamma rays. - Science fiction writers had a great time following the discovery of anti-matter and speculated along with many scientists that parts of our universe may contain negatively-charged protons forming nuclei which are orbited by positively-charged electrons. But this is taking us too far away from the topic at hand! - The reaction in our unstable nucleus which contains one too many protons can be represented as follows: - Notice, once again, that electric charge is conserved on each side of this equation. - An example of this type of decay occurs in sodium-22 which decays into neon-22 with the emission of a positron: - Note that the Mass Number remains the same and that the Atomic Number decreases by 1. (c) Electron Capture - In this third form of beta decay an inner orbiting electron is attracted into an unstable nucleus where it combines with a proton to form a neutron. The reaction can be represented as: - This process is also known as K-capture since the electron is often attracted from the K-shell of the atom. - How do we know that a process like this occurs given that no radiation is emitted? In other words the event occurs within the atom itself and no information about it leaves the atom. Or does it? The signature of this type of decay can be obtained from effects in the electron cloud surrounding the nucleus when the vacant site left in the K-shell is filled by an electron from an outer shell. The filling of the vacancy is associated with the emission of an X-ray from the electron cloud and it is this X-ray which provides a signature for this type of beta decay. - This form of decay can also be recognised by the emission of gamma-rays from the new nucleus. - An example of this type of radioactive decay occurs in iron-55 which decays into manganese-55 following the capture of an electron. The reaction can be represented as follows: - Note that the Mass Number once again is unchanged in this form of decay and that the Atomic Number is decreased by 1. Gamma decay involves the emission of energy from an unstable nucleus in the form of electromagnetic radiation. You should remember from your high school physics that electromagnetic radiation is the biggest physical phenomenon we have so far discovered. The radiation can be characterised in terms of its frequency, its wavelength and its energy. Thinking about it in terms of the energy of the radiation we have very low energy electromagnetic radiation called radio waves, infra-red radiation at a slightly higher energy, visible light at a higher energy still, then ultra-violet radiation and the higher energy forms of this radiation are called X-rays and gamma-rays. You should also remember that these radiations form what is called the Electromagnetic Spectrum. Before proceeding it is useful to pause for a moment to consider the difference between X-rays and gamma-rays. These two forms of radiation are high energy electromagnetic rays and are therefore virtually the same. The difference between them is not what they consist of but where they come from. In general we can say that if the radiation emerges from a nucleus it is called a gamma-ray and if it emerges from outside the nucleus from the electron cloud for example, it is called an X-ray. One final point is of relevance before we consider the different forms of gamma-decay and that is what such a high energy ray really is. It has been found in experiments that gamma-rays (and X-rays for that matter!) sometimes manifest themselves as waves and other times as particles. This wave-particle duality can be explained using the equivalence of mass and energy at the atomic level. When we describe a gamma ray as a wave it has been found useful to use terms such as frequency and wavelength just like any other wave. In addition when we describe a gamma ray as a particle we use terms such as mass and electric charge. Furthermore the term electromagnetic photon is used for these particles. The interesting feature about these photons however is that they have neither mass nor charge! There are two common forms of gamma decay: (a) Isomeric Transition - A nucleus in an excited state may reach its ground or unexcited state by the emission of a gamma-ray. - An example of this type of decay is that of technetium-99m – which by the way is the most common radioisotope used for diagnostic purposes today in medicine. The reaction can be expressed as: - Here a nucleus of technetium-99 is in an excited state, that is, it has excess energy. The excited state in this case is called a metastable state and the nucleus is therefore called technetium-99m (m for metastable). The excited nucleus looses its excess energy by emitting a gamma-ray to become technetium-99. (b) Internal Conversion - Here the excess energy of an excited nucleus is given to an atomic electron, e.g. a K-shell electron. Decay schemes are widely used to give a visual representation of radioactive decay. A scheme for a relatively straight-forward decay is shown below: This scheme is for hydrogen-3 which decays to helium-3 with a half-life of 12.3 years through the emission of a beta-minus particle with an energy of 0.0057 MeV. A scheme for a more complicated decay is that of caesium-137. This isotope can decay through through two beta-minus processes. In one which occurs in 5% of disintegrations a beta-minus particle is emitted with an energy of 1.17 MeV to produce barium-137. In the second which occurs more frequently (in the remaining 95% of disintegrations) a beta-minus particle of energy 0.51 MeV is emitted to produce barium-137m – in other words a barium-137 nucleus in a metastable state. The barium-137m then decays via isomeric transition with the emission of a gamma-ray of energy 0.662 MeV. The general method used for decay schemes is illustrated in the diagram on the right. The energy is plotted on the vertical axis and atomic number on the horizontal axis – although these axes are rarely displayed in actual schemes. The isotope from which the scheme originates is displayed at the top – X in the case above. This isotope is referred to as the parent. The parent loses energy when it decays and hence the products of the decay referred to as daughters are plotted at a lower energy level. The diagram illustrates the situation for common forms of radioactive decay. Alpha-decay is illustrated on the left where the mass number is reduced by 4 and the atomic number is reduced by 2 to produce daughter A. To its right the scheme for beta-plus decay is shown to produce daughter B. The situation for beta-minus decay followed by gamma-decay is shown on the right side of the diagram where daughters C and D respectively are produced. Multiple Choice QuestionsEdit Click here to access multiple choice questions on radioactive decay. - Basics about Radiation – overview of the different types of ionising radiation from the Radiation Effects Research Foundation – a cooperative Japan-United States Research Organization which conducts research for peaceful purposes. - Radiation and Life – from the World Nuclear Association website. - Radiation and Radioactivity – a self-paced lesson developed by the University of Michigan's Student Chapter of the Health Physics Society, with sections on radiation, radioactivity, the atom, alpha radiation, beta radiation and gamma radiation. The Radioactive Decay LawEdit We covered radioactive decay from a phenomenological perspective in the last chapter. In this chapter we consider the topic from a more general analytical perspective. The reason for doing this is so that we can develop a form of thinking which will help us to understand what is going on in a quantitative, mathematical sense. We will be introduced to concepts such as the Decay Constant and the Half Life as well as units used for the measurement of radioactivity. You will also have a chance to develop your understanding by being brought through three questions on this subject. The usual starting point in most forms of analysis in physics is to make some assumptions which simplify the situation. By simplifying the situation we can dispose of irrelevant effects which tend to complicate matters but in doing so we sometimes make the situation so simple that it becomes a bit too abstract and apparently hard to understand. For this reason we will try here to relate the subject of radioactive decay to a more common situation which we will use as an analogy and hopefully we will be able to overcome the abstract feature of the subject matter. The analogy we will use here is that of making popcorn. So think about putting some oil in a pot, adding the corn, heating the pot on the cooker and watching what happens. You might also like to try this out while considering the situation! For our radioactive decay situation we first of all consider that we have a sample containing a large number of radioactive nuclei all of the same kind. This is our unpopped corn in the pot for example. Secondly we assume that all of the radioactive nuclei decay by the same process be it alpha, beta or gamma-decay. In other words our unpopped corn goes pop at some stage during the heating process. Thirdly take a few moments to ponder on the fact that we can only really consider what is going on from a statistical perspective. If you look at an individual piece of corn, can you figure out when it is going to pop? Not really. You can however figure out that a large number of them will have popped after a period of time. But its rather more difficult to figure out the situation for an individual piece of corn. So instead of dealing with individual entities we consider what happens on a larger scale and this is where statistics comes in. We can say that the radioactive decay is a statistical one-shot process, that is when a nucleus has decayed it cannot repeat the process again. In other words when a piece of corn has popped it cannot repeat the process. Simple! In addition as long as a radioactive nucleus has not decayed the probability for it doing so in the next moment remains the same. In other words if a piece of corn has not popped at a certain time the chance of it popping in the next second is the same as in the previous second. The bets are even! Let us not push this popcorn analogy too far though in that we know that we can control the rate of popping by the heat we apply to the pot for example. However as far as our radioactive nuclei are concerned there is nothing we can do to control what is going on. The rate at which nuclei go pop (or decay, in other words) cannot be influenced by heating up the sample. Nor by cooling it for that matter or by putting it under greater pressures, by changing the gravitational environment by taking it out into space for instance, or by changing any other aspect of its physical environment. The only thing that determines whether an individual nucleus will decay seems to be the nucleus itself. But on the average we can say that it will decay at some stage. The Radioactive Decay LawEdit Let us now use some symbols to reduce the amount of writing we have to do to describe what is going on and to avail ourselves of some mathematical techniques to simplify the situation even further than we have been able to do so far. Let us say that in the sample of radioactive material there are N nuclei which have not decayed at a certain time, t. So what happens in the next brief period of time? Some nuclei will decay for sure. But how many? On the basis of our reasoning above we can say that the number which will decay will depend on overall number of nuclei, N, and also on the length of the brief period of time. In other words the more nuclei there are the more will decay and the longer the time period the more nuclei will decay. Let us denote the number which will have decayed as dN and the small time interval as dt. So we have reasoned that the number of radioactive nuclei which will decay during the time interval from t to t+dt must be proportional to N and to dt. In symbols therefore: the minus sign indicating that N is decreasing. Turning the proportionality in this equation into an equality we can write: where the constant of proportionality, λ, is called the Decay Constant. Dividing across by N we can rewrite this equation as: So this equation describes the situation for any brief time interval, dt. To find out what happens for all periods of time we simply add up what happens in each brief time interval. In other words we integrate the above equation. Expressing this more formally we can say that for the period of time from t = 0 to any later time t, the number of radioactive nuclei will decrease from N0 to Nt, so that: This final expression is known as the Radioactive Decay Law. It tells us that the number of radioactive nuclei will decrease in an exponential fashion with time with the rate of decrease being controlled by the Decay Constant. Before looking at this expression in further detail let us review the mathematics which we used above. First of all we used integral calculus to figure out what was happening over a period of time by integrating what we knew would occur in a brief interval of time. Secondly we used a calculus relationship that the where ln x represents the natural logarithm of x. And thirdly we used the definition of logarithms that when Now, to return to the Radioactive Decay Law. The Law tells us that the number of radioactive nuclei will decrease with time in an exponential fashion with the rate of decrease being controlled by the Decay Constant. The Law is shown in graphical form in the figure below: The graph plots the number of radioactive nuclei at any time, Nt, against time, t. We can see that the number of radioactive nuclei decreases from N0 that is the number at t = 0 in a rapid fashion initially and then more slowly in the classic exponential manner. The influence of the Decay Constant can be seen in the following figure: All three curves here are exponential in nature, only the Decay Constant is different. Notice that when the Decay Constant has a low value the curve decreases relatively slowly and when the Decay Constant is large the curve decreases very quickly. The Decay Constant is characteristic of individual radionuclides. Some like uranium-238 have a small value and the material therefore decays quite slowly over a long period of time. Other nuclei such as technetium-99m have a relatively large Decay Constant and they decay far more quickly. It is also possible to consider the Radioactive Decay Law from another perspective by plotting the logarithm of Nt against time. In other words from our analysis above by plotting the expression: in the form Notice that this expression is simply an equation of the form y = mx + c where m = -l and c = ln N0. As a result it is the equation of a straight line of slope -l as shown in the following figure. Such a plot is sometimes useful when we wish to consider a situation without the complication of the direct exponential behaviour. Most of us have not been taught to think instinctively in terms of logarithmic or exponential terms even though many natural phenomena display exponential behaviours. Most of the forms of thinking which we have been taught in school are based on linear changes and as a result it is rather difficult for us to grasp the Radioactive Decay Law intuitively. For this reason an indicator is usually derived from the law which helps us think more clearly about what is going on. This indicator is called the Half Life and it expresses the length of time it takes for the radioactivity of a radioisotope to decrease by a factor of two. From a graphical point of view we can say that when: the time taken is the Half Life: Note that the half-life does not express how long a material will remain radioactive but simply the length of time for its radioactivity to halve. Examples of the half lives of some radioisotopes are given in the following table. Notice that some of these have a relatively short half life. These tend to be the ones used for medical diagnostic purposes because they do not remain radioactive for very long following administration to a patient and hence result in a relatively low radiation dose. \|Radioisotope\|\|Half Life (approx.)\| \|238U\|\|4.51 x 109 years\| But they do present a logistical problem when we wish to use them when there may not be a radioisotope production facility nearby. For example suppose we wish to use 99mTc for a patient study and the nearest nuclear facility for making this isotope is 5,000 km away. The production facility could be in Sydney and the patient could be in Perth for instance. After making the isotope at the nuclear plant it would be decaying with a half life of 6 hours. So we put the material on a truck and drive it to Sydney airport. The isotope would be decaying as the truck sits in Sydney traffic then decaying still more as it waits for a plane to take it to Perth. Then decaying more as it is flown across to Perth and so on. By the time it gets to our patient it will have substantially reduced in radioactivity possibly to the point of being useless for the patient's investigation. And what about the problem if we needed to use 81mKr instead of 99mTc for our patient? You will see in another chapter of this book that logistical challenges such as this have given rise to quite innovative solutions. More about that later! You can appreciate from the table above that other isotopes have a very long half lives. For example 226Ra has a half life of over 1,500 years. This isotope has been used in the past for therapeutic applications in medicine. Think about the logistical problems here. They obviously do not relate to transporting the material from the point of production to the point of use. But they relate to how the material is kept following its arrival at the point of use. We must have a storage facility so that the material can be kept safely for a long period of time. But for how long? A general rule of thumb for the quantities of radioactivity used in medicine is that the radioactivity will remain significant for about 10 half lives. So we would have to have a safe environment for storage of the 226Ra for about 16,000 years! This storage facility would have to be secure from many unforeseeable events such as earthquakes, bombing etc. and be kept in a manner which our children's, children's children can understand. A very serious undertaking indeed! Relationship between the Decay Constant and the Half LifeEdit On the basis of the above you should be able to appreciate that there is a relationship between the Decay Constant and the Half Life. For example when the Decay Constant is small the Half Life should be long and correspondingly when the Decay Constant is large the Half Life should be short. But what exactly is the nature of this relationship? We can easily answer this question by using the definition of Half Life and applying it to the Radioactive Decay Law. Once again the law tells us that at any time, t: and the definition of Half Life tells us that: We can therefore re-write the Radioactive Decay Law by substituting for Nt and t as follows: These last two equations express the relationship between the Decay Constant and the Half Life. They are very useful as you will see when solving numerical questions relating to radioactivity and usually form the first step in solving a numerical problem. Units of RadioactivityEdit The SI or metric unit of radioactivity is named after Henri Becquerel, in honour of his discovery of radioactivity, and is called the becquerel with the symbol Bq. The becquerel is defined as the quantity of radioactive substance that gives rise to a decay rate of 1 decay per second. In medical diagnostic work 1 Bq is a rather small amount of radioactivity. Indeed it is easy to remember its definition if you think of it as a buggerall amount of radioactivity. For this reason the kilobecquerel (kBq) and megabecquerel (MBq) are more frequently used. The traditional unit of radioactivity is named after Marie Curie and is called the curie, with the symbol Ci. The curie is defined as the amount of radioactive substance which gives rise to a decay rate of 3.7 x 1010 decays per second. In other words 37 thousand, million decays per second which as you might appreciate is a substantial amount of radioactivity. For medical diagnostic work the millicurie (mCi) and the microcurie (µCi) are therefore more frequently used. Why two units? It in essence like all other units of measurement depends on what part of the world you are in. For example the kilometer is widely used in Europe and Australia as a unit of distance and the mile is used in the USA. So if you are reading an American textbook you are likely to find the curie used as the unit of radioactivity, if you are reading an Australian book it will most likely refer to becquerels and both units might be used if you are reading a European book. You will therefore find it necessary to know and understand both units. Multiple Choice QuestionsEdit Click here to access an MCQ on the Radioactive Decay Law. Three questions are given below to help you develop your understanding of the material presented in this chapter. The first one is relatively straight-forward and will exercise your application of the Radioactive Decay Law as well as your understanding of the concept of Half Life. The second question is a lot more challenging and will help you relate the Radioactive Decay Law to the number of radioactive nuclei which are decaying in a sample of radioactive material. The third question will help you understand the approach used in the second question by asking a similar question from a slightly different perspective. (a) The half-life of 99mTc is 6 hours. After how much time will 1/16th of the radioisotope remain? (b) Verify your answer by another means. - (a) Starting with the relationship we established earlier between the Decay Constant and the Half Life we can calculate the Decay Constant as follows: - Now applying the Radioactive Decay Law, - we can re-write it in the form: - The question tells us that N0 has reduced to 1/16th of its value, that is: - which we need to solve for t. One way of doing this is as follows: - So it will take 24 hours until 1/16th of the radioactivity remains. - (b) A way in which this answer can be verified is by using the definition of Half Life. We are told that the Half Life of 99mTc is 6 hours. Therefore after six hours half of the radioactivity remains. - Therefore after 12 hours a quarter remains; after 18 hours an eighth remains and after 24 hours one sixteenth remains. And we arrive at the same answer as in part (a). So we must be right! - Note that this second approach is useful if we are dealing with relatively simple situations where the radioactivity is halved, quartered and so on. But supposing the question asked how long would it take for the radioactivity to decrease to a tenth of its initial value. Deduction from the definition of half life is rather more difficult in this case and the mathematical approach used for part (a) above will yield the answer more readily. Find the radioactivity of a 1 g sample of 226Ra given that t1/2: 1620 years and Avogadro's Number: 6.023 x 1023. - We can start the answer like we did with Question 1(a) by calculating the Decay Constant from the Half Life using the following equation: - Note that the length of a year used in converting from 'per year' to 'per second' above is 365.25 days to account for leap years. In addition the reason for converting to units of 'per second' is because the unit of radioactivity is expressed as the number of nuclei decaying per second. - Secondly we can calculate that 1 g of 226Ra contains: - Thirdly we need to express the Radioactive Decay Law in terms of the number of nuclei decaying per unit time. We can do this by differentiating the equation as follows: - The reason for expressing the result above in absolute terms is to remove the minus sign in that we already know that the number is decreasing. - We can now enter the data we derived above for λ and N: - So the radioactivity of our 1 g sample of radium-226 is approximately 1 Ci. - This is not a surprising answer since the definition of the curie was originally conceived as the radioactivity of 1 g of radium-226! What is the minimum mass of 99mTc that can have a radioactivity of 1 MBq? Assume the half-life is 6 hours and that Avogadro's Number is 6.023 x 1023. - Starting again with the relationship between the Decay Constant and the Half Life: - Secondly the question tells us that the radioactivity is 1 MBq. Therefore since 1 MBq = 1 x 106 decays per second, - Finally the mass of these nuclei can be calculated as follows: - In other words a mass of just over five picograms of 99mTc can emit one million gamma-rays per second. The result reinforces an important point that you will learn about radiation protection which is that you should treat radioactive materials just like you would handle pathogenic bacteria! Units of Radiation MeasurementEdit This is the fourth chapter of a wikibook entitled Basic Physics of Nuclear Medicine. After that rather long and detailed chapter we have just finished we will now proceed at a more leisurely pace for a short treatment of some of the more common units of measurement used in this field. Before we do so however it is useful to consider the typical radiation environment. By doing so we will gain an appreciation of the various quantities that can be measured before considering the units which are used to express such measurements. So, we will first of all consider a typical radiation situation and then go on to consider the various units of measurement. A Typical Radiation SituationEdit A typical radiation set-up is shown in the figure below. Firstly there is a source of radiation, secondly a radiation beam and thirdly some material which absorbs the radiation. So the quantities which can be measured are associated with the source, the radiation beam and the absorber. This type of environment could be one where the radiation from the source is used to irradiate a patient (that is the absorber) for diagnostic purposes where we would place a device behind the patient for producing an image or for therapeutic purposes where the radiation is intended to cause damage to a specific region of a patient. It is also a situation where we as an absorber may be working with a source of radiation. The Radiation SourceEdit When the radiation source is a radioactive one the quantity that is typically measured is the radioactivity of the source. We saw in the previous chapter that the units used to express radioactivity are the becquerel (SI unit) and the curie (traditional unit). The Radiation BeamEdit The characteristic of a radiation beam that is typically measured is called the Radiation Exposure. This quantity expresses how much ionisation the beam causes in the air through which it travels. We will see in the following chapter that one of the major things that happens when radiation encounters matter is that ions are formed – air being the form of matter it encounters in this case. So the radiation exposure produced by a radiation beam is expressed in terms of the amount of ionisation which occurs in air. A straight-forward way of measuring such ionisation is to determine the amount of electric charge which is produced. You will remember from your high school physics that the SI unit of electric charge is the coulomb. The SI unit of radiation exposure is the coulomb per kilogram – and is given the symbol C kg-1. It is defined as the quantity of X- or gamma-rays such that the associated electrons emitted per kilogram of air at standard temperature and pressure (STP) produce ions carrying 1 coulomb of electric charge. The traditional unit of radiation exposure is the roentgen, named in honour of Wilhelm Roentgen (who discovered X-rays) and is given the symbol R. The roentgen is defined as the quantity of X- or gamma-rays such that the associated electrons emitted per kilogram of air at STP produce ions carrying 2.58 x 10-4 coulombs of electric charge. So 1 R is a small exposure relative to 1 C kg-1 – in fact it is 3,876 times smaller. Note that this unit is confined to radiation beams consisting of X-rays or gamma-rays. Often it is not simply the exposure that is of interest but the exposure rate, that is the exposure per unit time. The units which tend to be used in this case are the C kg-1 s-1 and the R hr-1. Energy is deposited in the absorber when radiation interacts with it. It is usually quite a small amount of energy but energy nonetheless. The quantity that is measured is called the Absorbed Dose and it is of relevance to all types of radiation be they X- or gamma-rays, alpha- or beta-particles. The SI unit of absorbed dose is called the gray, named after a famous radiobiologist, LH Gray, and is given the symbol Gy. The gray is defined as the absorption of 1 joule of radiation energy per kilogram of material. So when 1 joule of radiation energy is absorbed by a kilogram of the absorber material we say that the absorbed dose is 1 Gy. The traditional unit of absorbed dose is called the rad, which supposedly stands for Radiation Absorbed Dose. It is defined as the absorption of 10-2 joules of radiation energy per kilogram of material. As you can figure out 1 Gy is equal to 100 rad. There are other quantities derived from the gray and the rad which express the biological effects of such absorbed radiation energy when the absorber is living matter – human tissue for example. These quantities include the Equivalent Dose, H, and the Effective Dose, E. The Equivalent Dose is based on estimates of the ionization capability of the different types of radiation which are called Radiation Weighting Factors, wR, such that where D is the absorbed dose. The Effective Dose includes wR as well as estimates of the sensitivity of different tissues called Tissue Weighting Factors, wT, such that where the summation, Σ, is over all the tissue types involved. Both the Equivalent Dose and the Effective Dose are measured in derived SI units called sieverts (Sv). Let us pause here for a bit to ponder on the use of the term dose. It usually has a medical connotation in that we can say that someone had a dose of the 'flu, or that the doctor prescribed a certain dose of a drug. What has it to do with the deposition of energy by a beam of radiation in an absorber? It could have something to do with the initial applications of radiation in the early part of the 20th century when it was used to treat numerous diseases. As a result we can speculate that the term has stayed in the vernacular of the field. It would be much easier to use a term like absorbed radiation energy since we are talking about the deposition of energy in an absorber. But this might make the subject just a little too simple! Specific Gamma Ray ConstantEdit A final quantity is worth mentioning with regard to radiation units. This is the Specific Gamma-Ray Constant for a radioisotope. This quantity is an amalgam of the quantities we have already covered and expresses the exposure rate produced by the gamma-rays emitted from a radioisotope. It is quite a useful quantity from a practical viewpoint when we are dealing with a radioactive source which emits gamma-rays. Supposing you are using a gamma-emitting radioactive source (for example 99mTc or 137Cs) and you will be standing at a certain distance from this source while you are working. You most likely will be interested in the exposure rate produced by the source from a radiation safety point of view. This is where the Specific Gamma-Ray Constant comes in. It is defined as the exposure rate per unit activity at a certain distance from a source. The SI unit is therefore the and the traditional unit is the These units of measurement are quite cumbersome and a bit of a mouthful. It might have been better if they were named after some famous scientist so that we could call the SI unit 1 smith and the traditional unit 1 jones for example. But again things are not that simple! The Inverse Square LawEdit Before we finish this chapter we are going to consider what happens as we move our absorber away from the radiation source. In other words we are going to think about the influence of distance on the intensity of the radiation beam. You will find that a useful result emerges from this that has a very important impact on radiation safety. The radiation produced in a radioactive source is emitted in all directions. We can consider that spheres of equal radiation intensity exist around the source with the number of photons/particles spreading out as we move away from the source. Consider an area on the surface of one of these spheres and assume that there are a certain number of photons/particles passing though it. If we now consider a sphere at a greater distance from the source the same number of photons/particles will now be spread out over a bigger area. Following this line of thought it is easy to appreciate that the radiation intensity, I will decrease with the square of the distance, r from the source, i.e. This effect is known as the Inverse Square Law. As a result if we double the distance from a source, we reduce the intensity by a factor of two squared, that is 4. If we triple the distance the intensity is reduced by a factor of 9, that is three squared, and so on. This is a very useful piece of information if you are working with a source of radiation and are interested in minimising the dose of radiation you will receive. - Radiation and Risk – covers the effect of radiation, how risks are determined, comparison of radiation with other risks and radiation doses. - Radiation Effects Overview – results of studies of victims of nuclear bombs including early effects on survivors, effects on the in utero exposed, and late effects on the survivors – from the Radiation Effects Research Foundation, a cooperative Japan-United States Research Organization. - The Radiation and Health Physics Home Page – all you ever wanted to know about radiation but were afraid to ask....with hundreds of WWW links – from the Student Chapter of the Health Physics Society, University of Michigan containing sections on general information, regulatory Information, professional organizations and societies, radiation specialties, health physics research and education. - What You Need to Know about Radiation – to protect yourself to protect your family to make reasonable social and political choices – covers sources of radiation and radiation protection – by Lauriston S. Taylor. Interaction of Radiation with MatterEdit We have focussed in previous chapters on the source of radiation and the types of radiation. We are now in a position to consider what happens when this radiation interacts with matter. Our main reason for doing this is to find out what happens to the radiation as it passes through matter and also to set ourselves up for considering how it interacts with living tissue and how to detect radiation. Since all radiation detectors are made from some form of matter it is useful to first of all know how radiation interacts so that we can exploit the effects in the design of such detectors in subsequent chapters of this wikibook. Before we do this let us first remind ourselves of the physical characteristics of the major types of radiation. We have covered this information in some detail earlier and it is summarised in the table below for convenience. We will now consider the passage of each type of radiation through matter with most attention given to gamma-rays because they are the most common type used in nuclear medicine. One of the main effects that you will notice irrespective of the type of radiation is that ions are produced when radiation interacts with matter. It is for this reason that it is called ionizing radiation. about 8,000 times lighter less than the velocity of light 3 x 108 m/s in free space Before we start though you might find an analogy useful to help you with your thinking. This analogy works on the basis of thinking about matter as an enormous mass of atoms (that is nuclei with orbiting electrons) and that the radiation is a particle/photon passing through this type of environment. So the analogy to think about is a spaceship passing through a meteor storm like you might see in a science-fiction movie where the spaceship represents the radiation and the meteors represent the atoms of the material through which the radiation is passing. One added feature to bring on board however is that our spaceship sometimes has an electric charge depending on the type of radiation it represents. We can see from the table above that alpha-particles have a double positive charge and we can therefore easily appreciate that they will exert considerable electrostatic attraction on the outer orbital electrons of atoms near which they pass. The result is that some electrons will be attracted away from their parent atoms and that ions will be produced. In other words ionizations occur. We can also appreciate from the table that alpha-particles are quite massive relative to the other types of radiation and also to the electrons of atoms of the material through which they are passing. As a result they travel in straight lines through matter except for rare direct collisions with nuclei of atoms along their path. A third feature of relevance here is the energy with which they are emitted. This energy in the case of alpha-particles is always distinct. For example 221Ra emits an alpha-particle with an energy of 6.71 MeV. Every alpha-particle emitted from this radionuclide has this energy. Another example is 230U which emits three alpha-particles with energies of 5.66, 5.82, 5.89 MeV. Finally it is useful to note that alpha-particles are very damaging biologically and this is one reason why they are not used for in-vivo diagnostic studies. We will therefore not be considering them in any great detail in this wikibook. We can see from the table that beta-particles have a negative electric charge. Notice that positrons are not considered here since as we noted in chapter 2 these particles do not last for very long in matter before they are annihilated. Beta-minus particles last considerably longer and are therefore the focus of our attention here. Because of their negative charge they are attracted by nuclei and repelled by electron clouds as they pass through matter. The result once again without going into great detail is ionization. The path of beta-particles in matter is often described as being tortuous, since they tend to ricochet from atom to atom. A final and important point to note is that the energy of beta-particles is never found to be distinct in contrast to the alpha-particles above. The energies of the beta-particles from a radioactive source forms a spectrum up to a maximum energy – see figure below. Notice from the figure that a range of energies is present and features such as the mean energy, Emean, or the maximum energy, Emax, are quoted. The question we will consider here is: why should a spectrum of energies be seen? Surely if a beta-particle is produced inside a nucleus when a neutron is converted into a proton, a single distinct energy should result. The answer lies in the fact that two particles are actually produced in beta-decay. We did not cover this in our treatment in chapter 2 for fear of complicating things too much at that stage of this wikibook. But we will cover it here briefly for the sake of completeness. The second particle produced in beta-decay is called a neutrino and was named by Enrico Fermi. It is quite a mysterious particle possessing virtually no mass and carrying no charge, though we are still researching its properties today. The difficulty with them is that they are very hard to detect and this has greatly limited our knowledge about them so far. The beta-particle energy spectrum can be explained by considering that the energy produced when a neutron is converted to a proton is shared between the beta-particle and the anti-neutrino. Sometimes all the energy is given to the beta-particle and it receives the maximum energy, Emax. But more often the energy is shared between them so that for example the beta-particle has the mean energy, Emean and the neutrino has the remainder of the energy. Finally it is useful to note that beta-particles are quite damaging biologically and this is one reason why they are not used for in-vivo diagnostic studies. We will therefore not consider them in any great detail in this wikibook. Since we have been talking about energies above, let us first note that the energies of gamma-rays emitted from a radioactive source are always distinct. For example 99mTc emits gamma-rays which all have an energy of 140 keV and 51Cr emits gamma-rays which have an energy of 320 keV. Gamma-rays have many modes of interaction with matter. Those which have little or no relevance to nuclear medicine imaging are: and will not be described here. Those which are very important to nuclear medicine imaging, are the Photoelectric Effect and the Compton Effect. We will consider each of these in turn below. Note that the effects described here are also of relevance to the interaction of X-rays with matter since as we have noted before X-rays and gamma-rays are essentially the same entities. So the treatment below is also of relevance to radiography. - When a gamma-ray collides with an orbital electron of an atom of the material through which it is passing it can transfer all its energy to the electron and cease to exist – see figure below. On the basis of the Principle of Conservation of Energy we can deduce that the electron will leave the atom with a kinetic energy equal to the energy of the gamma-ray less that of the orbital binding energy. This electron is called a photoelectron. - Note that an ion results when the photoelectron leaves the atom. Also note that the gamma-ray energy is totally absorbed in the process. - Two subsequent points should also be noted. Firstly the photoelectron can cause ionisations along its track in a similar manner to a beta-particle. Secondly X-ray emission can occur when the vacancy left by the photoelectron is filled by an electron from an outer shell of the atom. Remember that we came across this type of feature before when we dealt with Electron Capture in chapter 2. - This type of effect is somewhat akin to a cue ball hitting a coloured ball on a pool table. Here a gamma-ray transfers only part of its energy to a valance electron which is essentially free – see figure below. Notice that the electron leaves the atom and may act like a beta-particle and that the gamma-ray deflects off in a different direction to that with which it approached the atom. This deflected or scattered gamma-ray can undergo further Compton Effects within the material. - Note that this effect is sometimes called Compton Scattering. The two effects we have just described give rise to both absorption and scattering of the radiation beam. The overall effect is referred to as attenuation of gamma-rays. We will investigate this feature from an analytical perspective in the following chapter. Before we do so, we'll briefly consider the interaction of radiation with living matter. It is well known that exposure to ionizing radiation can result in damage to living tissue. We've already described the initial atomic interactions. What's important in radiation biology is that these interactions may trigger complex chains of biomolecular events and consequent biological damage. We've seen above that the primary means by which ionizing radiations lose their energy in matter is by ejection of orbital electrons. The loss of orbital electrons from the atom leaves it positively charged. Other interaction processes lead to excitation of the atom rather than ionization. Here, an outer valence electron receives sufficient energy to overcome the binding energy of its shell and moves further away from the nucleus to an orbit that is not normally occupied. This type of effect alters the chemical force that binds atoms into molecules and a regrouping of the affected atoms into different molecular structures can result. That is, excitation is an indirect method of inducing chemical change through the modification of individual atomic bonds. Ionizations and excitations can give rise to unstable chemical species called free radicals. These are atoms and molecules in which there are unpaired electrons. They are chemically very reactive and seek stability by bonding with other atoms and molecules. Changes to nearby molecules can arise because of their production. But, let's go back to the interactions themselves for the moment..... In the case of X- and gamma-ray interactions, the energy of the photons is usually transferred by collisions with orbital electrons, e.g. via photoelectric and Compton effects. These radiations are capable of penetrating deeply into tissue since their interactions depend on chance collisions with electrons. Indeed, nuclear medicine imaging is only possible when the energy of the gamma-rays is sufficient for complete emission from the body, but low enough to be detected. The interaction of charged particles (e.g. alpha and beta particles), on the other hand, can be by collisions with atomic electrons and also via attractive and repulsive electrostatic forces. The rate at which energy is lost along the track of a charged particle depends therefore on the square of the charge on that particle. That is, the greater the particle charge, the greater the probability of it generating ion pairs along its track. In addition, a longer period of time is available for electrostatic forces to act when a charged particle is moving slowly and the ionization probability is therefore increased as a result. The situation is illustrated in the following figure where tracks of charged particles in water are depicted. Notice that the track of the relatively massive α-particle is a straight line, as we've discussed earlier in this chapter, with a large number of interactions (indicated by the asterisks) per unit length. Notice also that the tracks for electrons are tortuous, as we've also discussed earlier, and that the number of interactions per unit length is considerably less. The Linear Energy Transfer (LET) is defined as the energy released per unit length of the track of an ionizing particle. A slowly moving, highly charged particle therefore has a substantially higher LET than a fast, singly charged particle. An alpha particle of 5 MeV energy and an electron of 1 MeV energy have LETs, for instance, of 95 and 0.25 keV/μm, respectively. The ionization density and hence the energy deposition pattern associated with the heavier charged particle is very much greater than that arising from electrons, as illustrated in the figure above. The energy transferred along the track of a charged particle will vary because the velocity of the particle is likely to be continuously decreasing. Each interaction removes a small amount of energy from the particle so that the LET gradually increases along a particle track with a dramatic increase (called the Bragg Peak) occurring just before the particle comes to rest. The International Commission on Radiation Units and Measurements (ICRU) suggest that lineal energy is a better indicator of relative biological effectiveness (RBE). Although lineal energy has the same units as LET (e.g. keV/μm), it is defined as the: Since the microscopic deposition of energy may be quite anisotropic, lineal energy should be a more appropriate measure of potential damage than that of LET. The ICRU and the ICRP have accordingly recommended that the radiation effectiveness of a particular radiation type should be based on lineal energy in a 1 μm diameter sphere of tissue. The lineal energy can be calculated for any given radiation type and energy and a Radiation Weighting Factor, (wR) can then be determined based on the integrated values of lineal energy along the radiation track. All living things on this planet have been exposed to ionizing radiation since the dawn of time. The current situation for humans is summarized in the following table: \|Source\|\|Effective Dose (mSv/year)\|\|Comment\| About 100,000 cosmic ray neutrons and 400,000 secondary cosmic rays penetrate our bodies every hour – and it increases with altitude! Over 200 million gamma-rays pass through our body every hour from sources such as soil and building materials About 15 million 40K atoms and about 7,000 natural uranium atoms disintegrate inside our bodies every hour, primarily from our diet \|Radon and other gases\|\| About 30,000 atoms disintegrate inside our lungs every hour as a result of breathing The sum total of this Natural Background Radiation is about 2.5 mSv per year, with large variations depending on altitude and dietary intake as well as geological and geographical location. Its generally considered that repair mechanisms exist in living matter and that these can be invoked following radiation damage at the biomolecular level. These mechanisms are likely to have an evolutionary basis arising as a response to radiation fluxes generated by natural background sources over the aeons. Its also known that quite considerable damage to tissues can arise at quite higher radiation fluxes, even at medical exposures. Cell death and transformations to malignant states can result leading to latent periods of many years before clinical signs of cancer or leukemia, for instance, become manifest. Further treatment of this vast field of radiation biology however is beyond our scope here. Practical Radiation SafetyEdit Radiation hazards arise since nuclear medicine involves the handling of radioactive materials. Although this risk may be small, it remains important to keep occupational exposures as low as reasonably achievable. Essential practices for achieving this aim include: - Maintaining a comprehensive record of all radioactive source purchases, usage, movement and storage. - Ensuring that any Codes of Safe Practice are adhered to and develop sensible written protocols and working rules for handling radioisotopes. - Protocols for dealing with minor contamination incidents of the environment or of staff members must be established. Remember that no matter how good work practices are, minor accidents or incidents involving spillage of radioisotopes can take place. - Storage of radioactive sources in a secure shielded environment. Specially dedicated facilities are required for the storage, safe handling, manipulation and dispensing of unsealed radioactive sources. Storage areas should be designed for both bulk radioisotope and radioactive waste. Furthermore, radioactive patients should be regarded as unsealed sources. - Adequate ventilation of any work area. This is particularly important to minimize the inhalation of Technigas and potentially volatile radioisotopes such as I-125 and I-131. It is preferable to use fume hoods when working with volatile materials. - Benches should be manufactured with smooth, hard impervious surfaces with appropriate splash-backs to allow ready decontamination following any spillage of radioisotopes. Laboratory work should be performed in stainless steel trays lined with absorbent paper. - Excretion of radioactive materials by patients may be via faeces, urine, saliva, blood, exhaled breath or the skin. Provision to deal with any or all of these potential pathways for contamination must be made. - Provision for collection and possible storage of both liquid and solid radioactive waste may be necessary in some circumstances. Most short-lived, water soluble liquid waste can be flushed into the sewers but longer lived isotopes such as I-131 may have to be stored for decay. Such waste must be adequately contained and labelled during storage. - Ensure that appropriate survey monitors are available to determine if any contamination has occurred and to assist in decontamination procedures. Routine monitoring of potentially contaminated areas must be performed. - Ensure that all potentially exposed staff are issued with individual personnel monitors. - Protective clothing such as gowns, smocks, overboots and gloves should be provided and worn to prevent contamination of the personnel handling the radioactivity. In particular, gloves must be worn when administering radioactive materials orally or intravenously to patients. It should be noted that penetration of gloves may occur when handling some iodine compounds so that wearing a second pair of gloves is recommended. In any event, gloves should be changed frequently and discarded ones treated as radioactive waste. - Eating and drinking of food, smoking, and the application of cosmetics is prohibited in laboratories in which unsealed sources are utilized. - Mouth pipetting of any radioactive substance is totally prohibited. - Precautions should be taken to avoid punctures, cuts, abrasions and any other open skin wounds which otherwise might allow egress of radiopharmaceuticals into the blood stream. - Always ensure that there is a net benefit resulting from the patient procedure. Can the diagnosis or treatment be made by recourse to an alternative means using non ionizing radiation? - Ensure that all staff, including physicians, technologists, nurses and interns and other students, who are involved in the practice of nuclear medicine receive the relevant level of training and education appropriate to their assigned tasks. The training program could be in the form of seminars, refresher courses and informal tutorials. - A substantive Quality Assurance (QA) program should be implemented to ensure that the function of the Dose Calibrator, Gamma Camera, computer and other ancillary equipment is optimized. The potential hazards to staff in a nuclear medicine environment include: - Milking the 99mTc generator, drawing up and measuring the quantity of radioisotope prior to administration. - Delivering the activity to the patient by injection or other means and positioning the now radioactive patient in the imaging device. - Removing the patients from the imaging device and returning them to the ward where they may continue to represent a radiation hazard for some time. For Tc-99m, a short-lived radionuclide the hazard period will be only a few hours but for therapeutic isotopes the hazardous period may be several days. - Disposal of radioactive waste including body fluids, such as blood and urine, but also swabs, syringes, needles, paper towels etc. - Cleaning up the imaging area after the procedure. The table below lists the dose rates from patients having nuclear medicine examinations. In general, the hazards from handling or dealing with radioactive patients arise in two parts: - External hazard: This will be the case when the radioisotope emits penetrating gamma-rays. Usually, this hazard can be minimised by employing shielding and sensible work practices. - Radioactive contamination: This is potentially of more concern as it may lead to the inhalation or ingestion of radioactive material by staff. Possible sources of contamination are radioactive blood, urine and saliva, emanating from a patient, or airborne radioactive vapour. Sensible work practices, which involve high levels of personal hygiene, should ensure that contamination is not a major issue. One of the most common nuclear medicine diagnostic procedures is the bone scan using the isotope Tc-99m. The exposure rate at 1 metre from a typical patient will peak at approximately 3 μSv per hour immediately after injection dropping steadily because of radioactivity decay and through excretion so that after 2 hours it will be about 1.5 μSv per hour. Neglecting any further excretion, the total exposure received by an individual, should that person stand one meter from the patient for the whole of the first 24 hours, would be ~17 μSv. For a person at 3 meters from the patient this number would reduce to 1.7 μSv and for a distance of 5 metres it would be ~0.7 μSv. These values have been estimated on the basis of the inverse square law. Patients should be encouraged to drink substantial quantities of liquid following their scan, as this will improve excretion and aid in minimizing not only their radiation dose but also that of nursing staff. Attenuation of Gamma-RaysEdit We covered the interaction of gamma-rays with matter from a descriptive viewpoint in the previous chapter and we saw that the Compton and Photoelectric Effects were the major mechanisms. We will consider the subject again here but this time from an analytical perspective. This will allow us to develop a more general understanding of the phenomenon. Note that the treatment here also refers to the attenuation of X-rays since, as we noted before gamma-rays and X-rays are essentially the same physical entities. Our treatment begins with a description of a simple radiation experiment which can be performed easily in the laboratory and which many of the early pioneers in this field did. We will then build on the information obtained from such an experiment to develop a simple equation and some simple concepts which will allow us generalise the situation to any attenuation situation. The experiment is quite simple. It involves firing a narrow beam of gamma-rays at a material and measuring how much of the radiation gets through. We can vary the energy of the gamma-rays we use and the type of absorbing material as well as its thickness and density. The experimental set-up is illustrated in the figure below. We refer to the intensity of the radiation which strikes the absorber as the incident intensity, I0, and the intensity of the radiation which gets through the absorber as the transmitted intensity, Ix. Notice also that the thickness of the absorber is denoted by x. From what we covered in the previous chapter we can appreciate that some of the gamma-rays will be subjected to interactions such as the Photoelectric Effect and the Compton Effect as they pass through the absorber. The transmitted gamma-rays will in the main be those which pass through without any interactions at all. We can therefore expect to find that the transmitted intensity will be less than the incident intensity, that is But by how much you might ask. Before we consider this let us denote the difference between Ix and I0 as ∆I, that is Effect of Atomic NumberEdit - Let us start exploring the magnitude of ∆I by placing different absorbers in turn in the radiation beam. What we would find is that the magnitude of ∆I is highly dependent on the atomic number of the absorbing material. For example we would find that ∆I would be quite low in the case of an absorber made from carbon (Z=6) and very large in the case of lead (Z=82). - We can gain an appreciation of why this is so from the following figure: - The figure illustrates a high atomic number absorber by the large circles which represent individual atoms and a low atomic number material by smaller circles. The incident radiation beam is represented by the arrows entering each absorber from the left. Notice that the atoms of the high atomic number absorber present larger targets for the radiation to strike and hence the chances for interactions via the Photoelectric and Compton Effects is relatively high. The attenuation should therefore be relatively large. - In the case of the low atomic number absorber however the individual atoms are smaller and hence the chances of interactions are reduced. In other words the radiation has a greater probability of being transmitted through the absorber and the attenuation is consequently lower than in the high atomic number case. - With respect to our spaceship analogy used in the previous chapter the atomic number can be thought of as the size of individual meteors in the meteor cloud. - If we were to precisely control our experimental set-up and carefully analyse our results we would find that: - Therefore if we were to double the atomic number of our absorber we would increase the attenuation by a factor of two cubed, that is 8, if we were to triple the atomic number we would increase the attenuation by a factor of 27, that is three cubed, and so on. - It is for this reason that high atomic number materials (e.g. Pb) are used for radiation protection. Effect of DensityEdit - A second approach to exploring the magnitude of ∆I is to see what happens when we change the density of the absorber. We can see from the following figure that a low density absorber will give rise to less attenuation than a high density absorber since the chances of an interaction between the radiation and the atoms of the absorber are relatively lower. In addition, the density determines the transmission coefficient as it relates to the sample, since the lower the density, the higher the transmission coefficient due to the porous nature of the material. - So in our analogy of the spaceship entering a meteor cloud think of meteor clouds of different density and the chances of the spaceship colliding with a meteor. Effect of ThicknessEdit - A third factor which we could vary is the thickness of the absorber. As you should be able to predict at this stage the thicker the absorber the greater the attenuation. Effect of Gamma-Ray EnergyEdit - Finally in our experiment we could vary the energy of the gamma-ray beam. We would find without going into it in any great detail that the greater the energy of the gamma-rays the less the attenuation. You might like to think of it in terms of the energy with which the spaceship approaches the meteor cloud and the likelihood of a slow spaceship getting through as opposed to a spaceship travelling with a higher energy. We will consider a mathematical model here which will help us to express our experimental observations in more general terms. You will find that the mathematical approach adopted and the result obtained is quite similar to what we encountered earlier with Radioactive Decay. So you will not have to plod your way through any new maths below, just a different application of the same form of mathematical analysis! Let us start quite simply and assume that we vary only the thickness of the absorber. In other words we use an absorber of the same material (i.e. same atomic number) and the same density and use gamma-rays of the same energy for the experiment. Only the thickness of the absorber is changed. From our reasoning above it is easy to appreciate that the magnitude of ∆I should be dependent on the radiation intensity as well as the thickness of the absorber, that is for an infinitesimally small change in absorber thickness: the minus sign indicating that the intensity is reduced by the absorber. Turning the proportionality in this equation into an equality, we can write: where the constant of proportionality, μ, is called the Linear Attenuation Coefficient. Dividing across by I we can rewrite this equation as: So this equation describes the situation for any tiny change in absorber thickness, dx. To find out what happens for the complete thickness of an absorber we simply add up what happens in each small thickness. In other words we integrate the above equation. Expressing this more formally we can say that for thicknesses from x = 0 to any other thickness x, the radiation intensity will decrease from I0 to Ix, so that: This final expression tells us that the radiation intensity will decrease in an exponential fashion with the thickness of the absorber with the rate of decrease being controlled by the Linear Attenuation Coefficient. The expression is shown in graphical form below. The graph plots the intensity against thickness, x. We can see that the intensity decreases from I0, that is the number at x = 0, in a rapid fashion initially and then more slowly in the classic exponential manner. The influence of the Linear Attenuation Coefficient can be seen in the next figure. All three curves here are exponential in nature, only the Linear Attenuation Coefficient is different. Notice that when the Linear Attenuation Coefficient has a low value the curve decreases relatively slowly and when the Linear Attenuation Coefficient is large the curve decreases very quickly. The Linear Attenuation Coefficient is characteristic of individual absorbing materials. Some like carbon have a small value and are easily penetrated by gamma-rays. Other materials such as lead have a relatively large Linear Attenuation Coefficient and are relatively good absorbers of radiation: \|Absorber\|\|100 keV\|\|200 keV\|\|500 keV\| The materials listed in the table above are air, water and a range of elements from carbon (Z=6) through to lead (Z=82) and their Linear Attenuation Coefficients are given for three gamma-ray energies. The first point to note is that the Linear Attenuation Coefficient increases as the atomic number of the absorber increases. For example it increases from a very small value of 0.000195 cm-1 for air at 100 keV to almost 60 cm-1 for lead. The second point to note is that the Linear Attenuation Coefficient for all materials decreases with the energy of the gamma-rays. For example the value for copper decreases from about 3.8 cm-1 at 100 keV to 0.73 cm-1 at 500 keV. The third point to note is that the trends in the table are consistent with the analysis presented earlier. Finally it is important to appreciate that our analysis above is only strictly true when we are dealing with narrow radiation beams. Other factors need to be taken into account when broad radiation beams are involved. Half Value LayerEdit As with using the Half Life to describe the Radioactive Decay Law an indicator is usually derived from the exponential attenuation equation above which helps us think more clearly about what is going on. This indicator is called the Half Value Layer and it expresses the thickness of absorbing material which is needed to reduce the incident radiation intensity by a factor of two. From a graphical point of view we can say that when: the thickness of absorber is the Half Value Layer: The Half Value Layer for a range of absorbers is listed in the following table for three gamma-ray energies: \|Absorber\|\|100 keV\|\|200 keV\|\|500 keV\| The first point to note is that the Half Value Layer decreases as the atomic number increases. For example the value for air at 100 keV is about 35 meters and it decreases to just 0.12 mm for lead at this energy. In other words 35 m of air is needed to reduce the intensity of a 100 keV gamma-ray beam by a factor of two whereas just 0.12 mm of lead can do the same thing. The second thing to note is that the Half Value Layer increases with increasing gamma-ray energy. For example from 0.18 cm for copper at 100 keV to about 1 cm at 500 keV. Thirdly note that relative to the data in the previous table there is a reciprocal relationship between the Half Value Layer and the Linear Attenuation Coefficient, which we will now investigate. Relationship between μ and the HVLEdit As was the case with the Radioactive Decay Law, where we explored the relationship between the Half Life and the Decay Constant, a relationship can be derived between the Half Value Layer and the Linear Attenuation Coefficient. We can do this by using the definition of the Half Value Layer: and inserting it in the exponential attenuation equation, that is: These last two equations express the relationship between the Linear Attenuation Coefficient and the Half Value Layer. They are very useful as you will see when solving numerical questions relating to attenuation and frequently form the first step in solving a numerical problem. Mass Attenuation CoefficientEdit We implied above that the Linear Attenuation Coefficient was useful when we were considering an absorbing material of the same density but of different thicknesses. A related coefficient can be of value when we wish to include the density, ρ, of the absorber in our analysis. This is the Mass Attenuation Coefficient which is defined as the: The measurement unit used for the Linear Attenuation Coefficient in the table above is cm-1, and a common unit of density is the g cm-3. You might like to derive for yourself on this basis that the cm2 g-1 is the equivalent unit of the Mass Attenuation Coefficient. Two questions are given below to help you develop your understanding of the material presented in this chapter. The first one is relatively straight-forward and will exercise your application of the exponential attenuation equation. The second question is a lot more challenging and will help you relate exponential attenuation to radioactivity and radiation exposure. How much aluminium is required to reduce the intensity of a 200 keV gamma-ray beam to 10% of its incident intensity? Assume that the Half Value Layer for 200 keV gamma-rays in Al is 2.14 cm. - The question phrased in terms of the symbols used above is: - We are told that the Half Value Layer is 2.14 cm. Therefore the Linear Attenuation Coefficient is - Now combining all this with the exponential attenuation equation: - we can write: - So the thickness of aluminium required to reduce these gamma-rays by a factor of ten is about 7 cm. This relatively large thickness is the reason why aluminium is not generally used in radiation protection - its atomic number is not high enough for efficient and significant attenuation of gamma-rays. - You might like to try this question for the case when Pb is the absorber - but you will need to find out the Half Value Layer for the 200 keV gamma-rays yourself! - Here's a hint though: have a look at one of the tables above. - And here's the answer for you to check when you've finished: 2.2 mm. - In other words a relatively thin thickness of Pb is required to do the same job as 7 cm of aluminium. A 105 MBq source of 137Cs is to be contained in a Pb box so that the exposure rate 1 m away from the source is less than 0.5 mR/hour. If the Half Value Layer for 137Cs gamma-rays in Pb is 0.6 cm, what thickness of Pb is required? The Specific Gamma Ray Constant for 137Cs is 3.3 R hr-1 mCi-1 at 1 cm. - This is a fairly typical question which arises when someone is using radioactive materials. We wish to use a certain quantity of the material and we wish to store it in a lead container so that the exposure rate when we are working a certain distance away is below some level for safety reasons. We know the radioactivity of the material we will be using. But its quoted in SI units. We look up a reference book to find out the exposure rate for this radioisotope and find that the Specific Gamma Ray Constant is quoted in traditional units. Just as in our question! - So let us start by getting our units right. The Specific Gamma Ray Constant is given as: - This is equal to: - which is equal to: - on the basis of the Inverse Square Law. This result expressed per becquerel is - since 1 mCi = 3.7 x 107 Bq. And therefore for 105 MBq, the exposure rate is: - That is the exposure rate 1 meter from our source is 891.9 mR hr-1. - We wish to reduce this exposure rate according to the question to less than 0.5 mR hr-1 using Pb. - You should be able at this stage to use the exponential attenuation equation along with the Half Value Layer for these gamma-rays in Pb to calculate that the thickness of Pb required is about 6.5 cm. - Mucal on the Web - an online program which calculates x-ray absorption coefficients - by Pathikrit Bandyopadhyay, The Center for Synchrotron Radiation Research and Instrumentation at the Illinois Institute of Technology. - Tables of X-Ray Mass Attenuation Coefficients - a vast amount of data for all elements from National Institute of Science & Technology, USA. Gas-Filled Radiation DetectorsEdit We have learned in the last two chapters about how radiation interacts with matter and we are now in a position to apply our understanding to the detection of radiation. One of the major outcomes of the interaction of radiation with matter is the creation of ions as we saw in Chapter 5. This outcome is exploited in gas-filled detectors as you will see in this chapter. The detector in this case is essentially a gas, in that it is the atoms of a gas which are ionised by the radiation. We will see in the next chapter that solids can also be used as radiation detectors but for now we will deal with gases and be introduced to detectors such as the Ionization Chamber and the Geiger Counter. Before considering these specific types of gas-filled detectors we will first of all consider the situation from a very general perspective. As we noted above the radiation interacts with gas atoms in this form of detector and causes ions to be produced. On the basis of what we covered in Chapter 5 it is easy to appreciate that it is the Photoelectric and Compton Effects that cause the ionisations when the radiation consists of gamma-rays with energies useful for diagnostic purposes. There are actually two particles generated when an ion is produced - the positive ion itself and an electron. These two particles are collectively called an ion pair. The detection of the production of ion pairs in the gas is the basis upon which gas detectors operate. The manner in which this is done is by using an electric field to sweep the electrons away to a positively charged electrode and the ions to a negatively charged electrode. Let us consider a very simple arrangement as shown in the following figure: Here we have two electrodes with the gas between them. Something like a capacitor with a gas dielectric. The gas which is used is typically an inert gas, for example argon or xenon. The reason for using an inert gas is so that chemical reactions will not occur within the gas following the ionisations which could change the characteristics of our detector. A dc voltage is placed between the two electrodes. As a result when the radiation interacts with a gas atom the electron will move towards the positive electrode and the ion will move towards the negative electrode. But will these charges reach their respective electrodes? The answer is obviously dependent on the magnitude of the dc voltage. For example if at one extreme we had a dc voltage of a microvolt (that is, one millionth of a volt) the resultant electric field may be insufficient to move the ion pair very far and the two particles may recombine to reform the gas atom. At the other extreme suppose we applied a million volts between the two electrodes. In this case we are likely to get sparks flying between the two electrodes - a lightning bolt if you like - and our detector might act something like a neon sign. Somewhere in between these two extremes though we should be able to provide a sufficient attractive force for the ion and electron to move to their respective electrodes without recombination or sparking occurring. We will look at this subject in more detail below. Before we do let us see how the concept of the simple detector illustrated above is applied in practice. The gas-filled chamber is generally cylindrical in shape in real detectors. This shape has been found to be more efficient than the parallel electrode arrangement shown above. A cross-sectional view through this cylinder is shown in the following figure: The positive electrode consists of a thin wire running through the centre of the cylinder and the negative electrode consists of the wall of the cylinder. In principle we could make such a detector by getting a section of a metal pipe, mounting a wire through its centre, filling it with an inert gas and sealing the ends of the pipe. Actual detectors are a little bit more complex however but let us not get side-tracked at this stage. We apply a dc voltage via a battery or via a dc voltage supply and connect it as shown in the figure using a resistor, R. Now, assume that a gamma-ray enters the detector. Ion pairs will be produced in the gas - the ions heading towards the outer wall and the electrons heading towards the centre wire. Let us think about the electrons for a moment. When they hit the centre wire we can simply think of them as entering the wire and flowing through the resistor to get to the positive terminal of the dc voltage supply. These electrons flowing through the resistor constitute an electric current and as a result of Ohm's Law a voltage is generated across the resistor. This voltage is amplified by an amplifier and some type of device is used to register the amplified voltage. A loud-speaker is a fairly simple device to use for this purpose and the generation of a voltage pulse is manifest by a click from the loud-speaker. Other display devices include a ratemeter which displays the number of voltage pulses generated per unit time - something like a speedometer in a car - and a pulse counter (or scaler) which counts the number of voltage pulses generated in a set period of time. A voltage pulse is frequently referred to in practice as a count and the number of voltage pulses generated per unit time is frequently called the count rate. DC Voltage DependenceEdit If we were to build a detector and electronic circuit as shown in the figure above we could conduct an experiment that would allow us to explore the effect of the dc voltage on the magnitude of the voltage pulses produced across the resistor, R. Note that the term pulse height is frequently used in this field to refer to the magnitude of voltage pulses. Ideally, we could generate a result similar to that illustrated in the following figure: The graph illustrates the dependence of the pulse height on the dc voltage. Note that the vertical axis representing the pulse height is on a logarithmic scale for the sake of compressing a large linear scale onto a reasonably-sized graph. The experimental results can be divided into five regions as shown. We will now consider each region in turn. - Region A Here Vdc is relatively low so that recombination of positive ions and electrons occurs. As a result not all ion pairs are collected and the voltage pulse height is relatively low. It does increase as the dc voltage increases however as the amount of recombination reduces. - Region B Vdc is sufficiently high in this region so that only a negligible amount of recombination occurs. This is the region where a type of detector called the Ionization Chamber operates. - Region C Vdc is sufficiently high in this region so that electrons approaching the centre wire attain sufficient energy between collisions with the electrons of gas atoms to produce new ion pairs. Thus the number of electrons is increased so that the electric charge passing through the resistor, R, may be up to a thousand times greater than the charge produced initially by the radiation interaction. This is the region where a type of detector called the Proportional Counter operates. - Region D Vdc is so high that even a minimally-ionizing particle will produce a very large voltage pulse. The initial ionization produced by the radiation triggers a complete gas breakdown as an avalanche of electrons heads towards and spreads along the centre wire. This region is called the Geiger-Müller Region, and is exploited in the Geiger Counter. - Region E Here Vdc is high enough for the gas to completely breakdown and it cannot be used to detect radiation. We will now consider features of the Ionisation Chamber and the Geiger Counter in more detail. The ionisation chamber consists of a gas-filled detector energised by a relatively low dc voltage. We will first of all make an estimate of the voltage pulse height generated by this type of detector. We will then consider some applications of ionisation chambers. When a beta-particle interacts with the gas the energy required to produce one ion pair is about 30 eV. Therefore when a beta-particle of energy 1 MeV is completely absorbed in the gas the number of ion pairs produced is: The electric charge produced in the gas is therefore If the capacitance of the ionisation chamber (remember that we compared a gas-filled detector to a capacitor above) is 100 pF then the amplitude of the voltage pulse generated is: Because such a small voltage is generated it is necessary to use a very sensitive amplifier in the electronic circuitry connected to the chamber. We will now learn about two applications of ionisation chambers. The first one is for the measurement of radiation exposures. You will remember from Chapter 4 that the unit of radiation exposure (be it the SI or the traditional unit) is defined in terms of the amount of electric charge produced in a unit mass of a air. An ionization chamber filled with air is the natural instrument to use for such measurements. The second application is the measurement of radioactivity. The ionisation chamber used here is configured in what is called a re-entrant arrangement (see figure below) so that the sample of radioactive material can be placed within the detector using a holder and hence most of the emitted radiation can be detected. The instrument is widely referred to as an Isotope Calibrator and the trickle of electric current generated by such a detector is calibrated so that a reading in units of radioactivity (for example MBq or mCi) can be obtained. Most well-run Nuclear Medicine Departments will have at least one of these devices so that doses of radioactivity can be checked prior to administration to patients. Here are some photographs of ionisation chambers designed for various applications: We saw earlier that the Geiger Counter operates at relatively high dc voltages (for example 400-900 volts) and that an avalanche of electrons is generated following the absorption of radiation in the gas. The voltage pulses produced by this detector are relatively large since the gas effectively acts as an amplifier of the electric charge produced. There are four features of this detector which we will discuss. The first is that a sensitive amplifier (as was the case with the Ionization Chamber) is not required for this detector because of the gas amplification noted above. The second feature results from the fact that the generation of the electron avalanche must be stopped in order to reform the detector. In other words when a radiation particle/photon is absorbed by the gas a complete gas breakdown occurs which implies that the gas is incapable of detecting the next particle/photon which enters the detector. So in the extreme case one minute we have a radiation detector and the following moment we do not. A means of stopping the electron avalanche is therefore required - a process called Quenching. One means of doing this is by electronically lowering the dc voltage following an avalanche. A more widely used method of quenching is to add a small amount of a quenching gas to the inert gas. For example the gas could be argon with ethyl alcohol added. The ethyl alcohol is in vapour form and since it consists of relatively large molecules energy which would in their absence give rise to sustaining the electron avalanche is absorbed by these molecules. The large molecules act like a brake in effect. Irrespective of the type of quenching used the detector is insensitive for a small period of time following absorption of a radiation particle/photon. This period of time is called the Dead Time and this is the third feature of this detector which we will consider. Dead times are relatively short but nevertheless significant - being typically of the order of 200-400 µs. As a result the reading obtained with this detector is less than it should be. The true count rate, T, can be obtained using the following equation: where A is the (actual) reading and τ is the dead time. Some instruments perform this calculation automatically. The fourth feature to note about this detector is the dependence of its performance on the dc voltage. The Geiger-Müller Region of our figure above is shown in more detail below: Notice that it contains a plateau where the count rate obtained is independent of the dc voltage. The centre of this plateau is where most detectors are operated. It is clear that the count rate from the detector is not affected if the dc voltage fluctuates about the operating voltage. This implies that a relatively straight-forward dc voltage supply can be used. This feature coupled with the fact that a sensitive amplifier is not needed translates in practice to a relatively inexpensive radiation detector. - Inside a smoke detector - about the ion chamber used in smoke detectors - from the How Stuff Works website. - Ionisation Chambers - a brief description from the Triumf Safety Group. - Radiation and Radioactivity - a self-paced lesson developed by the University of Michigan's Student Chapter of the Health Physics Society with a section on gas filled detectors. - The Geiger Counter - a brief overview from the NASA Goddard Space Flight Center, USA. The second type of radiation detector we will discuss is called the scintillation detector. Scintillations are minute flashes of light which are produced by certain materials when they absorb radiation. These materials are variously called fluorescent materials, fluors, scintillators or phosphors. If we had a radioactive source and a scintillator in the lab we could darken the room, move the scintillator close to the source and see the scintillations. These small flashes of light might be green or blue or some other colour depending on the scintillator. We could also count the number of flashes produced to gain an estimate of the radioactivity of the source, that is the more flashes of light seen the more radiation present. The scintillation detector was possibly the first radiation detector discovered. You might have heard the story of the discovery of X-rays by Wilhelm Roentgen in 1895. He was working one evening in his laboratory in Wurzburg, Germany with a device which fired a beam of electrons at a target inside an evacuated glass tube. While working with this device he noticed that some platino-barium cyanide crystals, which he just happened to have close by, began to glow – and that they stopped glowing when he switched the device off. Roentgen had accidentally discovered a new form of radiation. He had also accidentally discovered a scintillator detector. Although scintillations can be seen we have a more sophisticated way of counting and measuring them today by using some form of photodetector. We will learn about the construction and mode of operation of this type of detector in this chapter. In addition, we will see how it can be used not just for detecting the presence of ionizing radiation but also for measuring the energy of that radiation. Before we do however it is useful to note that scintillators are very widely used in the medical radiations field. For example the X-ray cassette used in radiography contains a scintillator (called an intensifying screen) in close contact with a photographic film. A second example is the X-ray Image Intensifier used in fluoroscopy which contains scintillators called phosphors. Scintillators are also used in some CT Scanners and as we will see in the next chapter, in the Gamma Camera and PET Scanner. Their application is not limited to the medical radiations field in that scintillators are also used as screens in television sets and computer monitors and for generating light in fluorescent tubes – to mention just two common applications. What other applications can you think of? So scintillators are a lot more common than you might initially think and you will therefore find the information presented here useful to you not just for your studies of nuclear medicine. Some fluorescent materials are listed in the following table. Thallium-activated sodium iodide, NaI(Tl) is a crystalline material which is widely used for the detection of gamma-rays in scintillation detectors. We will be looking at this in more detail below. Another crystalline material sodium-activated caesium iodide, CsI(Na) is widely used for X-ray detection in devices such as the X-ray image intensifier. Another one called calcium tungstate, CaWO4 has been widely used in X-ray cassettes although this substance has been replaced by other scintillators such as lanthanum oxybromide in many modern cassettes. \|p-terphenyl in toluene\|\|liquid\| \|p-terphenyl in polystyrene\|\|plastic\| Notice that some scintillation materials are activated with certain elements. What this means is that the base material has a small amount of the activation element present. The term doped is sometimes used instead of activated. This activating element is used to influence the wavelength (colour) of the light produced by the scintillator. Silver-activated zinc sulphide is a scintillator in powder form and p-terphenyl in toluene is a liquid scintillator. The advantage of such forms of scintillators is that the radioactive material can be placed in close contact with the scintillating material. For example if a radioactive sample happened to be in liquid form we could mix it with a liquid scintillator so as to optimise the chances of detection of the emitted radiation and hence have a very sensitive detector. A final example is p-terphenyl in polystyrene which is a scintillator in the form of a plastic. This form can be easily made into different shapes like most plastics and is therefore useful when detectors of particular shapes are required. A scintillation crystal coupled to a photomultiplier tube (PMT) is illustrated in the following figure. The overall device is typically cylindrical in shape and the figure shows a cross-section through this cylinder: The scintillation crystal, NaI(Tl) is very delicate and this is one of the reasons it is housed in an aluminium casing. The inside wall of the casing is designed so that any light which strikes it is reflected downwards towards the PMT. The PMT itself consists of a photocathode, a focussing grid, an array of dynodes and an anode housed in an evacuated glass tube. The function of the photocathode is to convert the light flashes produced by radiation attenuation in the scintillation crystal into electrons. The grid focuses these electrons onto the first dynode and the dynode array is used for electron multiplication. We will consider this process in more detail below. Finally the anode collects the electrons produced by the array of dynodes. The electrical circuitry which is typically attached to a PMT is shown in the next figure: It consists of a high voltage supply, a resistor divider chain and a load resistor, RL. The high voltage supply generates a dc voltage, Vdc which can be up to 1,000 volts. It is applied to the resistor divider chain which consists of an array of resistors, each of which has the same resistance, R. The function of this chain of resistors is to divide up Vdc into equal voltages which are supplied to the dynodes. As a result voltages which increase in equal steps are applied to the array of dynodes. The load resistor is used so that an output voltage, Vout can be generated. Finally the operation of the device is illustrated in the figure below: The ionizing radiation produces flashes of light in the scintillation crystal. This light strikes the photocathode and is converted into electrons. The electrons are directed by the grid onto the first dynode. Dynodes are made from certain alloys which emit electrons when their surface is struck by electrons with the advantage that more electrons are emitted than are absorbed. A dynode used in a PMT typically emits between two and five electrons for each electron which strikes it. So when an electron from the photocathode strikes the first dynode between two and five electrons are emitted and are directed towards the second dynode in the array (three are illustrated in the figure). This electron multiplication process is repeated at the second dynode so that we end up with nine electrons for example heading towards the third dynode. An electron avalanche therefore develops so that a sizeable number of electrons eventually hits the anode at the bottom of the dynode chain. These electrons flow through the load resistor, RL and constitute an electric current which according to Ohm's Law generates a voltage, Vout which is measured by electronic circuitry (which we will describe later). A number of photographs of devices based on scintillation detection are shown below: The important feature of the scintillation detector is that this output voltage, Vout is directly proportional to the energy deposited by the radiation in the crystal. We will see what a useful feature this is below. Before we do so we will briefly analyze the operation of this device. A simple mathematical model will be presented below which will help us get a better handle on the performance of a scintillation detector. We will do this by quantifying the performance of the scintillator, the photocathode and the dynodes. Let's use the following symbols to characterize each stage of the detection process: - m: number of light photons produced in crystal - k: optical efficiency of the crystal, that is the efficiency with which the crystal transmits light - l: quantum efficiency of the photocathode, that is the efficiency with which the photocathode converts light photons to electrons - n: number of dynodes - R: dynode multiplication factor, that is the number of secondary electrons emitted by a dynode per primary electron absorbed. Therefore the charge collected at the anode is given by the following equation: where e: the electronic charge. For example supposing a 100 keV gamma-ray is absorbed in the crystal. The number of light photons produced, m, might be about 1,000 for a typical scintillation crystal. A typical crystal might have an optical efficiency, k, of 0.5 – in other words 50% of the light produced reaches the photocathode which might have a quantum efficiency of 0.15. A typical PMT has ten dynodes and let us assume that the dynode multiplication factor is 4.5. This amount of charge is very small. Even though we have used a sophisticated photodetector like a PMT we still end up with quite a small electrical signal. A very sensitive amplifier is therefore needed to amplify this signal. This type of amplifier is generally called a pre-amplifier and we will refer to it again later. We noted above that the voltage measured across the resistor, RL, is proportional to the energy deposited in the scintillation crystal by the radiation. Let us consider how the radiation might deposit its energy in the crystal. Let us consider a situation where gamma-rays are detected by the crystal. We learnt in Chapter 5 that there were two interaction mechanisms involved in gamma-ray attenuation – the Photoelectric Effect and the Compton Effect. You will remember that the Photoelectric Effect involves the total absorption of the energy of a gamma-ray, while the Compton Effect involves just partial absorption of this energy. Since the output voltage of a scintillation detector is proportional to the energy deposited by the gamma-rays it is reasonable to expect that Photoelectric Effects in the crystal will generate distinct and relatively large output voltages and that Compton Effects will result in lower output voltages. The usual way of presenting this information is by plotting a graph of the count rate versus the output voltage pulse height as shown in the following figure: This plot illustrates what is obtained for a monoenergetic gamma-emitting radioisotope, for example 99mTc – which, as we have noted before emits a single gamma-ray with an energy of 140 keV. Before we look at it in detail remember that we noted above that the output voltage from this detector is proportional to the energy deposited by the radiation in the crystal. The horizontal axis can therefore be used to represent the output voltage or the gamma-ray energy. Both of these quantities are shown in the figure to help with this discussion. In addition note that this plot is often called a Gamma-Ray Energy Spectrum. The figure above contains two regions. One called the Photopeak and the other called the Compton Smear. The Photopeak results because of Photoelectric absorption of the gamma-rays from the radioactive source – remember that we are dealing with a monoenergetic emitter in this example. It consists of a peak representing the gamma-ray energy (140 keV in our example). If our radioisotope emitted gamma-rays of two energies we would have two photopeaks in our spectrum and so on. Notice that the peak has a statistical spread. This has to do with how good our detector is and we will not get into any detail about it here other than to note that the extent of this spread is a measure of the quality of our detector. A high quality (and more expensive!) detector will have a narrower statistical spread in the photopeaks which it measures. The other component of our spectrum is the Compton Smear. It represents a range of output voltages which are lower than that for the Photopeak. It is therefore indicative of the partial absorption of the energy of gamma-rays in the crystal. In some Compton Effects a substantial scattering with a valence electron can occur which gives rise to relatively large voltage pulses. In other Compton Effects the gamma-ray just grazes off a valence electron with minimal energy transfer and hence a relatively small voltage pulse is generated. In between these two extremes are a range of scattering events involving a range of energy transfers and hence a range of voltage pulse heights. A 'smear' therefore manifests itself on the gamma-ray energy spectrum. It is important to note that the spectrum illustrated in the figure is simplified for the sake of this introductory discussion and that actual spectra are a little more complex – see figure below for an example: You will find though that your understanding of actual spectra can easily develop on the basis of the simple picture we have painted here. It is also important to appreciate the additional information which this type of radiation detector provides relative to a gas-filled detector. In essence gas-filled detectors can be used to tell us if any radiation is present as well as the amount of that radiation. Scintillation detectors also give us this information but they tell us about the energy of this radiation as well. This additional information can be used for many diverse applications such as the identification of unknown radioisotopes and the production of nuclear medicine images. Let us stay a little bit longer though with the fundamental features of how scintillation detectors work. The photopeak of the Gamma-Ray Energy Spectrum is generally of interest in nuclear medicine. This peak is the main signature of the radioisotope being used and its isolation from the Compton Smear is normally achieved using a technique called Pulse Height Analysis. Pulse Height AnalysisEdit This is an electronic technique which allows a spectrum to be acquired using two types of circuitry. One circuit is called a Lower Level Discriminator which only allows voltages pulses through it which are higher than its setting. The other is called an Upper Level Discriminator which only allows voltage pulses though which are lower than its setting. The result of using both these circuits in combination is a variable-width window which can be placed anywhere along a spectrum. For example if we wished to obtain information from the photopeak only of our simplified spectrum we would place the discrimination controls as shown in the following figure: A final point to note here is that since the scintillation detector is widely used to obtain information about the energies of the radiation emitted from a radioactive source it is frequently referred to as a Scintillation Spectrometer. Types of scintillation spectrometer fall into two basic categories – the relatively straight-forward Single Channel Analyser and the more sophisticated Multi-Channel Analyser. The Single Channel Analyser is the type of instrument we have been describing so far in this discussion. A block diagram of the instrument is shown below: It consists of a scintillation crystal coupled to a photomultiplier tube which is powered by a high voltage circuit (H.V.). The output voltages are initially amplified by a sensitive pre-amplifier (Pre-Amp) as we noted above before being amplified further and conditioned by the amplifier (Amp). The voltage pulses are then in a suitable form for the pulse height analyser (P.H.A.) – the output pulses from which can be fed to a Scaler and a Ratemeter for display of the information about the portion of the spectrum we have allowed to pass through the PHA. The Ratemeter is a display device just like the speedometer in a car and indicates the number of pulses generated per unit time. The Scaler on the other hand usually consists of a digital display which shows the number of voltage pulses produced in a specified period of time. We can illustrate the operation of this circuitry by considering how it might be used to generate a Gamma-Ray Energy Spectrum. What we would do is set up the LLD and ULD so as to define a narrow window and place this to pass the lowest voltage pulses produced by the detector through to the Scaler and Ratemeter. In other words we would place a narrow window at the extreme left of the spectrum and acquire information about the lowest energy gamma-ray interactions in the crystal. We would then adjust the LLD and ULD settings to acquire information about the interactions of the next highest energy. We would proceed in this fashion to scan the whole spectrum. A more sophisticated detector circuit is illustrated in the following figure: It is quite similar to that in the previous figure with the exception that the PHA, Scaler and Ratemeter are replaced by a Multi-Channel Analyser and a computer. The Multi-Channel Analyser (MCA) is a circuit which is capable of setting up a large number of individual windows to look at a complete spectrum in one go. The MCA might consist of 1024 individual windows for example and the computer might consist of a personal computer which can acquire information simultaneously from each window and display it as an energy spectrum. The computer generally contains software which allows us to manipulate the resultant information in a variety of ways. Indeed the 137Cs spectrum shown above was generated using this approach. Nuclear Medicine Imaging SystemsEdit Topics we have covered in this wikibook have included radioactivity, the interaction of gamma-rays with matter and radiation detection. The main reason for following this pathway was to bring us to the subject of this chapter: nuclear medicine imaging systems. These are devices which produce pictures of the distribution of radioactive material following administration to a patient. The radioactivity is generally administered to the patient in the form of a radiopharmaceutical – the term radiotracer is also used. This follows some physiological pathway to accumulate for a short period of time in some part of the body. A good example is 99mTc-tin colloid which following intravenous injection accumulates mainly in the patient's liver. The substance emits gamma-rays while it is in the patient's liver and we can produce an image of its distribution using a nuclear medicine imaging system. This image can tell us whether the function of the liver is normal or abnormal or if sections of it are damaged from some form of disease. Different radiopharmaceuticals are used to produce images from almost every region of the body: \|Part of the Body\|\|Example Radiotracer\| \|Lung (Ventilation)\|\|133Xe gas\| \|Liver\|\|99mTc-Tin (or Sulphur) Colloid\| \|Spleen\|\|99mTc-Damaged Red Blood Cells\| Note that the form of information obtained using this imaging method is mainly related to the physiological functioning of an organ as opposed to the mainly anatomical information which is obtained using X-ray imaging systems. Nuclear medicine therefore provides a different perspective on a disease condition and generates additional information to that obtained from X-ray images. Our purpose here is to concentrate on the imaging systems used to produce the images. Early forms of imaging system used in this field consisted of a radiation detector (a scintillation detector for example) which was scanned slowly over a region of the patient in order to measure the radiation intensity emitted from individual points within the region. One such device was called the Rectilinear Scanner. Such imaging systems have been replaced since the 1970s by more sophisticated devices which produce images much more rapidly. The most common of these modern devices is called the Gamma Camera and we will consider its construction and mode of operation below. A review of recent developments in this technology for cardiac applications can be found in Slomka et al (2009). The basic design of the most common type of gamma camera used today was developed by an American physicist, Hal Anger and is therefore sometimes called the Anger Camera. It consists of a large diameter NaI(Tl) scintillation crystal which is viewed by a large number of photomultiplier tubes. A block diagram of the basic components of a gamma camera is shown below: The crystal and PM Tubes are housed in a cylindrical shaped housing commonly called the camera head and a cross-sectional view of this is shown in the figure. The crystal can be between about 25 cm and 40 cm in diameter and about 1 cm thick. The diameter is dependent on the application of the device. For example a 25 cm diameter crystal might be used for a camera designed for cardiac applications while a larger 40 cm crystal would be used for producing images of the lungs. The thickness of the crystal is chosen so that it provides good detection for the 140 keV gamma-rays emitted from 99mTc – which is the most common radioisotope used today. Scintillations produced in the crystal are detected by a large number of PM tubes which are arranged in a two-dimensional array. There are typically between 37 and 91 PM tubes in modern gamma cameras. The output voltages generated by these PM tubes are fed to a position circuit which produces four output signals called ±X and ±Y. These position signals contain information about where the scintillations were produced within the crystal. In the most basic gamma camera design they are fed to a cathode ray oscilloscope (CRO). We will describe the operation of the CRO in more detail below. Before we do so we should note that the position signals also contain information about the intensity of each scintillation. This intensity information can be derived from the position signals by feeding them to a summation circuit (marked ∑ in the figure) which adds up the four position signals to generate a voltage pulse which represents the intensity of a scintillation. This voltage pulse is commonly called the Z-pulse which, following pulse height analysis, (PHA) is fed as the unblank pulse to the CRO. So we end up with four position signals and an unblank pulse sent to the CRO. Let us briefly review the operation of a CRO before we continue. The core of a CRO consists of an evacuated tube with an electron gun at one end and a phosphor-coated screen at the other end. The electron gun generates an electron beam which is directed at the screen and the screen emits light at those points struck by the electron beam. The position of the electron beam can be controlled by vertical and horizontal deflection plates and with the appropriate voltages fed to these plates the electron beam can be positioned at any point on the screen. The normal mode of operation of an oscilloscope is for the electron beam to remain switched on. In the case of the gamma camera the electron beam of the CRO is normally switched off – it is said to be blanked. When an unblank pulse is generated by the PHA circuit the electron beam of the CRO is switched on for a brief period of time so as to display a flash of light on the screen. In other words the voltage pulse from the PHA circuit is used to unblank the electron beam of the CRO. So where does this flash of light occur on the screen of the CRO? The position of the flash of light is dictated by the ±X and ±Y signals generated by the position circuit. These signals as you might have guessed are fed to the deflection plates of the CRO so as to cause the unblanked electron beam to strike the screen at a point related to where the scintillation was originally produced in the NaI(Tl) crystal. Simple! The gamma camera can therefore be considered to be a sophisticated arrangement of electronic circuits used to translate the position of a flash of light in a scintillation crystal to a flash of light at a related point on the screen of an oscilloscope. In addition the use of a pulse height analyser in the circuitry allows us to translate the scintillations related only to photoelectric events in the crystal by rejecting all voltage pulses except those occurring within the photopeak of the gamma-ray energy spectrum. Let us summarise where we have got to before we proceed. A radiopharmaceutical is administered to the patient and it accumulates in the organ of interest. Gamma-rays are emitted in all directions from the organ and those heading in the direction of the gamma camera enter the crystal and produce scintillations (note that there is a device in front of the crystal called a collimator which we will discuss later). The scintillations are detected by an array of PM tubes whose outputs are fed to a position circuit which generates four voltage pulses related to the position of a scintillation within the crystal. These voltage pulses are fed to the deflection circuitry of the CRO. They are also fed to a summation circuit whose output (the Z-pulse) is fed to the PHA and the output of the PHA is used to switch on (that is, unblank) the electron beam of the CRO. A flash of light appears on the screen of the CRO at a point related to where the scintillation occurred within the NaI(Tl) crystal. An image of the distribution of the radiopharmaceutical within the organ is therefore formed on the screen of the CRO when the gamma-rays emitted from the organ are detected by the crystal. What we have described above is the operation of a fairly traditional gamma camera. Modern designs are a good deal more complex but the basic design has remained much the same as has been described. One area where major design improvements have occurred is the area of image formation and display. The most basic approach to image formation is to photograph the screen of the CRO over a period of time to allow integration of the light flashes to form an image on photographic film. A stage up from this is to use a storage oscilloscope which allows each flash of light to remain on the screen for a reasonable period of time. The most modern approach is to feed the position and energy signals into the memory circuitry of a computer for storage. The memory contents can therefore be displayed on a computer monitor and can also be manipulated (that is processed) in many ways. For example various colours can be used to represent different concentrations of a radiopharmaceutical within an organ. The use of digital image processing is now widespread in nuclear medicine in that it can be used to rapidly and conveniently control image acquisition and display as well as to analyse an image or sequences of images, to annotate images with the patient's name and examination details, to store the images for subsequent retrieval and to communicate the image data to other computers over a network. The essential elements of a modern gamma camera are shown in the next figure. Gamma rays emitted by the patient pass through the collimator and are detected within the camera head, which generates data related to the location of scintillations in the crystal as well as to the energy of the gamma rays. This data is then processed on-the-fly by electronic hardware which corrects for technical factors such as spatial linearity, PM tube drift and energy response so as to produce an imaging system with a spatially-uniform sensitivity and distortion-free performance. A multichannel analyzer (MCA) is used to display the energy spectrum of gamma rays which interact inside the crystal. Since these gamma rays originate from within the patient, some of them will have an energy lower than the photopeak as a result of being scattered as they travel through the patient's tissues – and by other components such as the patient table and structures of the imaging system. Some of these scattering events may involve just glancing interactions with free electrons, so that the gamma rays lose only a small amount of energy. These gamma rays may have an energy just below that of the photopeak so that their spectrum merges with the photopeak. The photopeak for a gamma camera imaging a patient therefore contains information from spatially-correlated, unattenuated gamma rays (which is the information we want) and from spatially-uncorrelated, scattered gamma rays. The scattered gamma rays act like a variable background within the true photopeak data and the effect is that of a background haze in gamma camera images. While scatter may not be a significant problem in planar scintigraphy, it has a strong bearing on the fidelity of quantitative information derived from gamma camera images and is a vital consideration for accurate image reconstruction in emission tomography. It is the unattenuated gamma rays (also called the primary radiation) that contain the desired information, because of their direct dependence on radioactivity. The scatter situation is illustrated in more detail in the figure below, which shows estimates of the primary and scatter spectra for 99mTc in patient imaging conditions. Such spectral estimates can be generated using Monte Carlo methods. It is seen in the figure that the energy of the scattered radiation forms a broad band, similar to the Compton Smear described previously, which merges into and contributes substantially to the detected photopeak. The detected photopeak is therefore an overestimate of the primary radiation. The extent of this overestimate is likely to be dependent on the specific imaging situation because of the different thicknesses of tissues involved. It is clear however that the scatter contribution within the detected photopeak needs to be accounted for if an accurate measure of radioactivity is required. One method of compensating for the scatter contribution is illustrated in the figure below and involves using data from a lower energy window as an estimate for subtraction from the photopeak, i.e. where k is a scaling factor to account for the extent of the scatter contribution. This approach to scatter compensation is referred to as the Dual-Energy Window (DEW) method. It can be implemented in practice by acquiring two images, one for each energy window, and subtracting a fraction (k) of the scatter image from the photopeak image. For the spectrum shown above, it can be seen that the scaling factor, k, is about 0.5, but it should be appreciated that its exact value is dependent on the scattering conditions. Gamma cameras which use the DEW method therefore generally provide the capability of adjusting k for different imaging situations. Some systems use a narrower scatter window than that illustrated, e.g. 114-126 keV, with a consequent increase in k to about 1.0, for instance. A host of other methods of scatter compensation have also been developed. These include more complex forms of energy analysis such as the Dual-Photopeak and the Triple-Energy Window techniques, as well as approaches based on deconvolution and models of photon attenuation. An excellent review of these developments is provided in Zaidi & Koral (2004). Some photographs of gamma cameras and related devices are shown below: We will continue with our description of the gamma camera by considering the construction and purpose of the collimator. The collimator is a device which is attached to the front of the gamma camera head. It functions something like a lens used in a photographic camera but this analogy is not quite correct because it is rather difficult to focus gamma-rays. Nevertheless in its simplest form it is used to block out all gamma rays which are heading towards the crystal except those which are travelling at right angles to the plane of the crystal: The figure illustrates a magnified view of a parallel-hole collimator attached to a crystal. The collimator simply consists of a large number of small holes drilled in a lead plate. Notice that gamma-rays entering at an angle to the crystal get absorbed by the lead and that only those entering along the direction of the holes get through to cause scintillations in the crystal. If the collimator was not in place these obliquely incident gamma-rays would blur the images produced by the gamma camera. In other words the images would not be very clear. Most gamma cameras have a number of collimators which can be fitted depending on the examination. The basic design of these collimators is the same except that they vary in terms of the diameter of each hole, the depth of each hole and the thickness of lead between each hole (commonly called the septum thickness). The choice of a specific collimator is dependent on the amount of radiation absorption that occurs (which influences the sensitivity of the gamma camera), and the clarity of images (that is the spatial resolution) it produces. Unfortunately these two factors are inversely related in that the use of a collimator which produces images of good spatial resolution generally implies that the instrument is not very sensitive to radiation. Other collimator designs beside the parallel hole type are also in use. For example a diverging hole collimator produces a minified image and converging hole and pin-hole collimators produce a magnified image. The pin-hole collimator is illustrated in the following figure: It is typically a cone-shaped device with its walls made from lead. A cross-section through this cone is shown in the figure. It operates in a similar fashion to a pin-hole photographic camera and produces an inverted image of an object – an arrow is used in the figure to illustrate this inversion. This type of collimator has been found useful for imaging small objects such as the thyroid gland. A representative selection of nuclear medicine images is shown below: The form of imaging which we have been describing is called Planar Imaging. It produces a two-dimensional image of a three-dimensional object. As a result images contain no depth information and some details can be superimposed on top of each other and obscured or partially obscured as a result. Note that this is also a feature of conventional X-ray imaging. The usual way of trying to overcome this limitation is to take at least two views of the patient, one from the front and one from the side for example. So in chest radiography a posterio-anterior (PA) and a lateral view can be taken. And in a nuclear medicine liver scan an antero-posterior (AP) and lateral scan are acquired. This limitation of planar X-ray imaging was overcome by the development of the CAT Scanner about 1970 or thereabouts. CAT stands for Computerized Axial Tomography or Computer Assisted Tomography and today the term is often shortened to Computed Tomography or CT scanning (the term tomography comes from the Greek word tomos meaning slice). Irrespective of its exact name the technique allows images of slices through the body to be produced using a computer. It does this in essence by taking X-ray images at a number of angles around the patient. These slice images show the third dimension which is missing from planar images and thus eliminate the problem of superimposed details. Furthermore images of a number of successive slices through a region of the patient can be stacked on top of each other using the computer to produce a three-dimensional image. Clearly CT scanning is a very powerful imaging technique relative to planar imaging. The equivalent nuclear medicine imaging technique is called Emission Computed Tomography. We will consider two implementations of this technique below. Single Photon Emission Computed Tomography (SPECT)Edit - This SPECT technique uses a gamma camera to record images at a series of angles around the patient. These images are then subjected to a form of digital image processing called Image Reconstruction in order to compute images of slices through the patient. - The Back Projection reconstruction process is illustrated below. Let us assume for simplicity that the slice through the patient actually consists of a 2x2 voxel array with the radioactivity in each voxel given by A1...A4: - The first projection, P1, is imaged from the right and the second projection, P2, from the right oblique and so on. The back projection process involves firstly adding the projections to each other as shown below: - and then normalising the summed (or superimposed) projections to generate an estimate of the radioactivity in each voxel. Since this process can generate streaking artefacts in reconstructed images, the projections are generally filtered prior to back projection, as described in a later chapter, with the overall process referred to as Filtered Back Projection (FBP): - An alternative image reconstruction technique is called Iterative Reconstruction, a successive approximation technique. The Maximum-Likelihood Expectation-Maximisation (ML-EM) algorithm is widely applied where a division process is used to compare the actual and estimated projections, as shown below: - One cycle of data through this processing chain is referred to as one iteration. Sixteen or more iterations can be required in order to generate an adequate reconstruction and, as a result, computation times can be rather long. The Ordered-Subsets Expectation-Maximisation (OS-EM) algorithm can be used to substantially reduce the computation time by utilising a limited number of projections (called subsets) in a sequential fashion within the iterative process. Noise generated during the reconstruction process can be reduced, for example, using a Gaussian filter built into the reconstruction calculations or applied as a post-filter: - Images generated using different iterations, subsets and filtration settings can be found in an online book. - A comparison of these image reconstruction techniques is shown below for a slice through a ventilation scan of a patient's lungs: - The gamma camera is typiclly rotated around the patient in order to acquire the images. Modern gamma cameras which are designed specifically for SPECT scanning can consist of two camera heads mounted parallel to each other with the patient in between. The time required to produce images is therefore reduced by a factor of about two. In addition some SPECT gamma cameras designed for brain scanning have three camera heads mounted in a triangular arrangement. - A wide variety of strategies can be used for the acquisition and processing of SPECT images. Positron Emission Tomography (PET)Edit - You will remember from chapter 2 that positrons can be emitted from radioactive nuclei which have too many neutrons for stability. You will also remember that positrons do not last for very long in matter since they will quickly encounter an electron and a process called annihilation results. In the process the positron and electron vanish and their energy is converted into two gamma-rays which are emitted at roughly 180o degrees to each other. The emission is often referred to as two back-to-back gamma-rays and they each have a discrete energy of 0.51 MeV. - So if we administer a positron-emitting radiopharmaceutical to a patient an emitted positrons can annihilate with a nearby electron and two gamma-rays will be emitted in opposite directions. These gamma-rays can be detected using a ring of radiation detectors encircling the patient and tomographic images can be generated using a computer system. The detectors are typically specialised scintillation devices which are optimised for detection of the 0.51 MeV gamma-rays. This ring of detectors, associated apparatus and computer system are called a PET Scanner: - The locations of positron decays within the patient are highlighted by the solid circles in the above diagram. In addition only a few detectors are shown in the diagram for reasons of clarity. Each detector around the ring is operated in coincidence with a bank of opposing detectors and the annihilation gamma-rays thus detected are used to build up a single profile. - It has also been found that gamma cameras fitted with thick crystals and special collimators can be used for PET scanning. - The radioisotopes used for PET scanning include 11C, 13N, 15O and 18F. These isotopes are usually produced using an instrument called a cyclotron. In addition these isotopes have relatively short half lives. PET scanning therefore needs a cyclotron and associated radiopharmaceutical production facilities located close by. We will consider cyclotrons in the next chapter of this wikibook. - Standardized Uptake Value (SUV) is a semi-quantitative index used in PET to express the uptake of a radiopharmaceutical in a region of interest of a patient's scan. Its typically calculated as the ratio of the radioactivity in the region to the injected dose, corrected for body weight. It should be noted that the SUV is influenced by several major sources of variability and it therefore should not be used as a quantitative measure. - A number of photographs of a PET scanner are shown below: Images reconstructed using different settings of subsets and iterations for iterative reconstruction are shown below: - Slomka PJ, Patton JA, Berman DS & Germano G, 2009. Advances in technical aspects of myocardial perfusion SPECT imaging. Journal of Nuclear Cardiology, 16(2), 255–76. - Maher KP, 2016. Iterations, Subsets & Gaussian Filtration, 3rd Edition (Bookemon.com] - Centre for Positron Emission Tomography at the Austin & Repatriation Medical Centre, Melbourne with sections on what PET is, current facilities, projects & research and a PET image library Production of RadioisotopesEdit Most of the radioisotopes found in nature have relatively long half lives. They also belong to elements which are not handled well by the human body. As a result medical applications generally require the use of radioisotopes which are produced artificially. We have looked at the subject of radioactivity in earlier chapters of this wikibook and have then progressed to cover the interaction of radiation with matter, radiation detectors and imaging systems. We return to sources of radioactivity in this chapter in order to learn about methods which are used to make radioisotopes. The type of radioisotope of value to nuclear medicine imaging should have characteristics which keep the radiation dose to the patient as low as possible. For this reason they generally have a short half life and emit only gamma-rays - that is no alpha-particle or beta-particle emissions. From an energy point of view the gamma-ray energy should not be so low that the radiation gets completely absorbed before emerging from the patient's body and not too high that it is difficult to detect. For this reason most of the radioisotopes used emit gamma-rays of medium energy, that is between about 100 and 200 keV. Finally since the radioisotope needs to be incorporated into some form of radiopharmaceutical it should also be capable of being produced in a form which is amenable to chemical, pharmaceutical and sterile processing. The production methods we will consider are nuclear fission, nuclear bombardment and the radioisotope generator. We were introduced to spontaneous fission in chapter 2 where we saw that a heavy nucleus can break into a number of fragments. This disintegration process can be induced to occur when certain heavy nuclei absorb neutrons. Following absorption of a neutron such nuclei break into smaller fragments with atomic numbers between about 30 and 65. Some of these new nuclei are of value to nuclear medicine and can be separated from other fission fragments using chemical processes. In this method of radioisotope production charged particles are accelerated up to very high energies and caused to collide into a target material. Examples of such charged particles are protons, alpha particles and deuterons. New nuclei can be formed when these particles collide with nuclei in the target material. Some of these nuclei are of value to nuclear medicine. An example of this method is the production of 22Na where a target of 24Mg is bombarded with deuterons, that is: 24Mg + 2H → 22Na + 4He. A deuteron you will remember from chapter 1 is the second most common isotope of hydrogen, that is 2H. When it collides with a 24Mg nucleus a 22Na nucleus plus an alpha particle is produced. The target is exposed to the deuterons for a period of time and is subsequently processed chemically in order to separate out the 22Na nuclei. The type of device commonly used for this method of radioisotope production is called a cyclotron. It consists of an ion gun for producing the charged particles, electrodes for accelerating them to high energies and a magnet for steering them towards the target material. All arranged in a circular structure. This method is widely used to produce certain short-lived radioisotopes in a hospital or clinic. It involves obtaining a relatively long-lived radioisotope which decays into the short-lived isotope of interest. A good example is 99mTc which as we have noted before is the most widely used radioisotope in nuclear medicine today. This isotope has a half-life of six hours which is rather short if we wish to have it delivered directly from a nuclear facility. Instead the nuclear facility supplies the isotope 99Mo which decays into 99mTc with a half life of about 2.75 days. The 99Mo is called the parent isotope and 99mTc is called the daughter isotope. So the nuclear facility produces the parent isotope which decays relatively slowly into the daughter isotope and the daughter is separated chemically from the parent at the hospital/clinic. The chemical separation device is called, in this example, a 99mTc Generator: It consists of a ceramic column with 99Mo adsorbed onto its top surface. A solution called an eluent is passed through the column, reacts chemically with any 99mTc and emerges in a chemical form which is suitable for combining with a pharmaceutical to produce a radiopharmaceutical. The arrangement shown in the figure on the right is called a Positive Pressure system where the eluent is forced through the ceramic column by a pressure, slightly above atmospheric pressure, in the eluent vial. The ceramic column and collection vials need to be surrounded by lead shielding for radiation protection purposes. In addition all components are produced and need to be maintained in a sterile condition since the collected solution will be administered to patients. Finally an Isotope Calibrator is needed when a 99mTc Generator is used to determine the radioactivity for preparation of patient doses and to check whether any 99Mo is present in the collected solution. Operation of a 99m-Tc GeneratorEdit Suppose we have a sample of 99Mo and suppose that at time there are nuclei in our sample and nothing else. The number of 99Mo nuclei decreases with time according to radioactive decay law as discussed in Chapter 3: where is the decay constant for 99Mo. Thus the number of 99Mo nuclei that decay during a small time interval is given by Since 99Mo decays into 99mTc, the same number of 99mTc nuclei are formed during the time period . At a time , only a fraction of these nuclei will still be around since the 99mTc is also decaying. The time for 99mTc to decay is given by . Plugging this into radioactive the decay law we arrive at: Now we sum up the little contributions . In other words we integrate over in order to find the number , that is the number of all 99mTc nuclei present at the time : Finally solving this integral we find: The figure below illustrates the outcome of this calculation. The horizontal axis represents time (in days), while the vertical one represents the number of nulcei present (in arbitrary units). The green curve illustrates the exponential decay of a sample of pure 99mTc. The red curve shows the number of 99mTc nuclei present in a 99mTc generator that is never eluted. Finally, the blue curve shows the situation for a 99mTc generator that is eluted every 12 hours. Photographs taken in a nuclear medicine hot lab are shown below: - Concerns over Molybdenum Supplies – news from 2008 compiled by the British Nuclear Medicine Society. - Cyclotron Java Applet – a Java-based interactive demonstration of the operation of a cyclotron from GFu-Kwun Hwang, Dept. of Physics, National Taiwan Normal University, Virtual Physics Laboratory. - Nuclear Power Plant Demonstration – a Java-based interactive demonstration of controlling a nuclear reactor. Also contains nuclear power Information links. - ANSTO – information about Australia's nuclear organization. - Medical Valley – contains information on what nuclear medicine is, production of nuclear pharmaceuticals, molybdenum and technetium – from The Netherlands Energy Research Foundation Petten. Chapter Review: Atomic & Nuclear StructureEdit - The atom consists of two components - a nucleus (positively charged) and an electron cloud (negatively charged); - The radius of the nucleus is about 10,000 times smaller than that of the atom; - The nucleus can have two component particles - neutrons (no charge) and protons (positively charged) - collectively called nucleons; - The mass of a proton is about equal to that of a neutron - and is about 1,840 times that of an electron; - The number of protons equals the number of electrons in an isolated atom; - The Atomic Number specifies the number of protons in a nucleus; - The Mass Number specifies the number of nucleons in a nucleus; - Isotopes of elements have the same atomic number but different mass numbers; - Isotopes are classified by specifying the element's chemical symbol preceded by a superscript giving the mass number and a subscript giving the atomic number; - The atomic mass unit is defined as 1/12th the mass of the stable, most commonly occurring isotope of carbon (i.e. C-12); - Binding energy is the energy which holds the nucleons together in a nucleus and is measured in electron volts (eV); - To combat the effect of the increase in electrostatic repulsion as the number of protons increases, the number of neutrons increases more rapidly - giving rise to the Nuclear Stability Curve; - There are ~2450 isotopes of ~100 elements and the unstable isotopes lie above or below the Nuclear Stability Curve; - Unstable isotopes attempt to reach the stability curve by splitting into fragments (fission) or by emitting particles/energy (radioactivity); - Unstable isotopes <=> radioactive isotopes <=> radioisotopes <=> radionuclides; - ~300 of the ~2450 isotopes are found in nature - the rest are produced artificially. Chapter Review: Radioactive DecayEdit - Fission: Some heavy nuclei decay by splitting into 2 or 3 fragments plus some neutrons. These fragments form new nuclei which are usually radioactive; - Alpha Decay: Two protons and two neutrons leave the nucleus together in an assembly known as an alpha-particle; - An alpha-particle is a He-4 nucleus; - Beta Decay - Electron Emission: Certain nuclei with an excess of neutrons may reach stability by converting a neutron into a proton with the emission of a beta-minus particle; - A beta-minus particle is an electron; - Beta Decay - Positron Emission: When the number of protons in a nucleus is in excess, the nucleus may reach stability by converting a proton into a neutron with the emission of a beta-plus particle; - A beta-plus particle is a positron; - Positrons annihilate with electrons to produce two back-to-back gamma-rays; - Beta Decay - Electron Capture: An inner orbital electron is attracted into the nucleus where it combines with a proton to form a neutron; - Electron capture is also known as K-capture; - Following electron capture, the excited nucleus may give off some gamma-rays. In addition, as the vacant electron site is filled, an X-ray is emitted; - Gamma Decay - Isomeric Transition: A nucleus in an excited state may reach its ground state by the emission of a gamma-ray; - A gamma-ray is an electromagnetic photon of high energy; - Gamma Decay - Internal Conversion: the excitation energy of an excited nucleus is given to an atomic electron. Chapter Review: The Radioactive Decay LawEdit - The radioactive decay law in equation form; - Radioactivity is the number of radioactive decays per unit time; - The decay constant is defined as the fraction of the initial number of radioactive nuclei which decay in unit time; - Half Life: The time taken for the number of radioactive nuclei in the sample to reduce by a factor of two; - Half Life = (0.693)/(Decay Constant); - The SI Unit of radioactivity is the becquerel (Bq) - 1 Bq = one radioactive decay per second; - The traditional unit of radioactivity is the curie (Ci); - 1 Ci = 3.7 x 1010 radioactive decays per second. Chapter Review: Units of Radiation MeasurementEdit - Exposure expresses the intensity of an X- or gamma-ray beam; - The SI unit of exposure is the coulomb per kilogram (C/kg); - 1 C/kg = The quantity of X- or gamma-rays such that the associated electrons emitted per kg of air at STP produce in air ions carrying 1 coulomb of electric charge; - The traditional unit of exposure is the roentgen (R); - 1 R = The quantity of X- or gamma-rays such that the associated electrons emitted per kg of air at STP produce in air ions carrying 2.58 x 10-4 coulombs of electric charge; - The exposure rate is the exposure per unit time, e.g. C/kg/s; - Absorbed dose is the radiation energy absorbed per unit mass of absorbing material; - The SI unit of absorbed dose is the gray (Gy); - 1 Gy = The absorption of 1 joule of radiation energy per kilogram of material; - The traditional unit of absorbed dose is the rad; - 1 rad = The absorption of 10-2 joules of radiation energy per kilogram of material; - The Specific Gamma-Ray Constant expresses the exposure rate produced by the gamma-rays from a radioisotope; - The Specific Gamma-Ray Constant is expressed in SI units in C/kg/s/Bq at 1 m; - Exposure from an X- or gamma-ray source follows the Inverse Square Law and decreases with the square of the distance from the source. Chapter Review: Interaction of Radiation with MatterEdit - exert considerable electrostatic attraction on the outer orbital electrons of atoms near which they pass and cause ionisations; - travel in straight lines - except for rare direct collisions with nuclei of atoms in their path; - energy is always discrete. - Beta-Minus Particles: - attracted by nuclei and repelled by electron clouds as they pass through matter and cause ionisations; - have a tortuous path; - have a range of energies; - range of energies results because two particles are emitted - a beta-particle and a neutrino. - energy is always discrete; - have many modes of interaction with matter; - important interactions for nuclear medicine imaging (and radiography) are the Photoelectric Effect and the Compton Effect. - Photoelectric Effect: - when a gamma-ray collides with an orbital electron, it may transfer all its energy to the electron and cease to exist; - the electron can leave the atom with a kinetic energy equal to the energy of the gamma-ray less the orbital binding energy; - a positive ion is formed when the electron leaves the atom; - the electron is called a photoelectron; - the photoelectron can cause further ionisations; - subsequent X-ray emission as the orbital vacancy is filled. - Compton Effect: - A gamma-ray may transfer only part of its energy to a valence electron which is essentially free; ** gives rise to a scattered gamma-ray; - is sometimes called Compton Scatter; - a positive ion results; - Attenuation is term used to describe both absorption and scattering of radiation. Chapter Review: Attenuation of Gamma-RaysEdit - Attenuation of a narrow-beam of gamma-rays increases as the thickness, the density and the atomic number of the absorber increases; - Attenuation of a narrow-beam of gamma-rays decreases as the energy of the gamma-rays increases; - Attenuation of a narrow beam is described by an equation; - the Linear Attenuation Coefficient is defined as the fraction of the incident intensity absorbed in a unit distance of the absorber; - Linear attenuation coefficients are usually expressed in units of cm-1; - the Half Value Layer is the thickness of absorber required to reduce the intensity of a radiation beam by a factor of 2; - Half Value Layer = (0.693)/(Linear Attenuation Coefficient); - the Mass Attenuation Coefficient is given by the linear attenuation coefficient divided by the density of the absorber; - Mass attenuation coefficients are usually expressed in units of cm2 g-1. Chapter Review: Gas-Filled DetectorsEdit - Gas-filled detectors include the ionisation chamber, the proportional counter and the Geiger counter; - They operate on the basis of ionisation of gas atoms by the incident radiation, where the positive ions and electrons produced are collected by electrodes; - An ion pair is the term used to describe a positive ion and an electron; - The operation of gas-filled detectors is critically dependent on the magnitude of the applied dc voltage; - The output voltage of an ionisation chamber can be calculated on the basis of the capacitance of the chamber; - A very sensitive amplifier is required to measure voltage pulses produced by an ionisation chamber; - The gas in ionisation chambers is usually air; - Ionisation chambers are typically used to measure radiation exposure (in a device called an Exposure Meter) and radioactivity (in a device called an Isotope Calibrator); - The total charge collected in a proportional counter may be up to 1000 times the charge produced initially by the radiation; - The initial ionisation triggers a complete gas breakdown in a Geiger counter; - The gas in a Geiger counter is usually an inert gas; - The gas breakdown must be stopped in order to prepare the Geiger counter for a new event by a process called quenching; - Two types of quenching are possible: electronic quenching and the use of a quenching gas; - Geiger counters suffer from dead time, a small period of time following the gas breakdown when the counter is inoperative; - The true count rate can be determined from the actual count rate and the dead time using an equation; - The value of the applied dc voltage in a Geiger counter is critical, but high stability is not required. Chapter Review: Scintillation DetectorsEdit - NaI(Tl) is a scintillation crystal widely used in nuclear medicine; - The crystal is coupled to a photomultiplier tube to generate a voltage pulse representing the energy deposited in the crystal by the radiation; - A very sensitive amplifier is needed to measure such voltage pulses; - The voltages pulses range in amplitude depending on how the radiation interacts with the crystal, i.e. the pulses form a spectrum whose shape depends on the interaction mechanisms involved, e.g. for medium-energy gamma-rays used in in-vivo nuclear medicine: the Compton effect and the Photoelectric effect; - A Gamma-Ray Energy Spectrum for a medium-energy, monoenergetic gamma-ray emitter consists (simply) of a Compton Smear and a Photopeak; - Pulse Height Analysis is used to discriminate the amplitude of voltage pulses; - A pulse height analyser (PHA) consists of a lower level discriminator (which passes voltage pulses which are than its setting) and an upper level discriminator (which passes voltage pulses lower than its setting); - The result is a variable width window which can be placed anywhere along a spectrum, or used to scan a spectrum; - A single channel analyser (SCA) consists of a single PHA with a scaler and a ratemeter; - A multi-channel analyser (MCA) is a computer-controlled device which can acquire data from many windows simultaneously. Chapter Review: Nuclear Medicine Imaging SystemsEdit - A gamma camera consists of a large diameter (25-40 cm) NaI(Tl) crystal, ~1 cm thick; - The crystal is viewed by an array of 37-91 PM tubes; - PM tubes signals are processed by a position circuit which generates +/- X and +/- Y signals; - These position signals are summed to form a Z signal which is fed to a pulse height analyser; - The +/- X, +/- Y and discriminated Z signals are sent to a computer for digital image processing; - A collimator is used to improve the spatial resolution of a gamma-camera; - Collimators typically consist of a Pb plate containing a large number of small holes; - The most common type is a parallel multi-hole collimator; - The most resolvable area is directly in front of a collimator; - Parallel-hole collimators vary in terms of the number of holes, the hole diameter, the length of each hole and the septum thickness - the combination of which affect the sensitivity and spatial resolution of the imaging system; - Other types include the diverging-hole collimator (which generates minified images), the converging-hole collimator (which generates magnified images) and the pin-hole collimator (which generates magnified inverted images); - Conventional imaging with a gamma camera is referred to as Planar Imaging, i.e. a 2D image portraying a 3D object giving superimposed details and no depth information; - Single Photon Emission Computed Tomography (SPECT) produces images of slices through the body; - SPECT uses a gamma camera to record images at a series of angles around the patient; - The resultant data can be processed using Filtered Back Projection and Iterative Reconstruction; - SPECT gamma-cameras can have one, two or three camera heads; - Positron Emission Tomography (PET) also produces images of slices through the body; - PET exploits the positron annihilation process where two 0.51 MeV back-to-back gamma-rays are produced; - If these gamma-rays are detected, their origin will lie on a line joining two of the detectors of the ring of detectors which encircles the patient; - A Time-of-Flight method can be used to localise their origin; - PET systems require on-site or nearby cyclotron to produce short-lived radioisotopes, such as C-11, N-13, O-15 and F-18. Chapter Review: Production of RadioisotopesEdit - Naturally-occurring radioisotopes generally have long half lives and belong to relatively heavy elements - and are therefore unsuitable for medical diagnostic applications; - Medical diagnostic radioisotopes are generally produced artificially; - The fission process can be exploited so that radioisotopes of interest can be separated chemically from fission products; - A cyclotron can be used to accelerate charged particles up to high energies so that they to collide into a target of the material to be activated; - A radioisotope generator is generally used in hospitals to produce short-lived radioisotopes; - A technetium-99m generator consists of an alumina column containing Mo-99, which decays into Tc-99m; - Saline is passed through the generator to elute the Tc-99m - the resulting solution is called sodium pertechnetate; - Both positive pressure and negative pressure generators are in use; - An isotope calibrator is needed when a Tc-99m generator is used in order to determine the activity for preparation of patient doses and to test whether any Mo-99 is present in the collected solution. 1. Discuss the process of radioactive decay from the perspective of the nuclear stability curve. 2. Describe in detail FOUR common forms of radioactive decay. 3. Give the equation which expresses the Radioactive Decay Law, and explain the meaning of each of its terms. 4. Define each of the following: - (a) Half life; - (b) Decay Constant; - (c) Becquerel. 5. A sample of radioactive substance is found to have an activity of 100 kBq. Its radioactivity is measured again 82 days later and is found to be 15 kBq. Calculate: - (a) the half-life; - (b) the decay constant. 6. Define each of the following radiation units: - (a) Roentgen; - (b) Becquerel; - (c) Gray. 7. Estimate the exposure rate at 1 metre from a 100 MBq source of radioactivity which has a Specific Gamma Ray Constant of 50 mR per hour per MBq at 1 cm. 8. Briefly describe the basic principle of operation of gas-filled radiation detectors. 9. Illustrate using a graph how the magnitude of the voltage pulses from a gas-filled radiation detector varies with applied voltage and identify on the graph the regions associated with the operation of Ionisation Chambers and the Geiger Counters. 10. Describe the construction and principles of operation of a scintillation spectrometer. 11. Discuss the components of the energy spectrum from a monoenergetic, medium energy gamma- emitting radioisotope obtained using a scintillation spectrometer on the basis of how the gamma-rays interact with the scintillation crystal. 12. Describe the construction and principles of operation of a Gamma Camera. 13. Compare features of three types of collimator which can be used with a Gamma Camera. Nuclear Medicine is a fascinating application of nuclear physics. The first ten chapters of this wikibook are intended to support a basic introductory course in an early semester of an undergraduate program. They assume that students have completed decent high school programs in maths and physics and are concurrently taking subjects in the medical sciences. Additional chapters cover more advanced topics in this field. Our focus in this wikibook is the diagnostic application of Nuclear Medicine. Therapeutic applications are considered in a separate wikibook, "Radiation Oncology". Note that this WikiBooks is well past its use-by date. Some of the basic physics might still be of relevance, but the technologies and applications chapters need substantial updating. A companion wikibook on the Basic Physics of Digital Radiography is also available. - Atomic & Nuclear Structure - Radioactive Decay - The Radioactive Decay Law - Units of Radiation Measurement - Interaction of Radiation with Matter - Attenuation of Gamma-Rays - Gas-Filled Radiation Detectors - Scintillation Detectors - Nuclear Medicine Imaging Systems - Computers in Nuclear Medicine - Fourier Methods - X-Ray CT in Nuclear Medicine - PACS and Advanced Image Processing - Three-Dimensional Visualization Techniques - Patient Dosimetry - Production of Radioisotopes - Chapter Review - Dynamic Studies in Nuclear Medicine - Deconvolution Analysis - Sonography & Nuclear Medicine - MRI & Nuclear Medicine - Dual-Energy Absorptiometry The principal author of this text is grateful for the expert editorial assistance of Dirk Hünniger during his German translation of the text and his contribution to the section on the Operation of a 99m-Tc Generator. - Applied Imaging Technology, 4th Ed., JCP Heggie, NA Liddell & KP Maher (St Vincent's Hospital Melbourne, 2001) - Basic Science of Nuclear Medicine, 2nd Ed., RP Parker, PHS Smith, DM Taylor (Churchill Livingstone, 1984) - Computed Tomography: Fundamentals, System Technology, Image Quality, Applications, 3rd Ed., WA Kalender (Wiley, 2000) - Introduction to Nuclear Physics, H Enge (Addison-Wesley, 1966) - Magnetic Resonance in Medicine, 4th Ed., PA Rinck (Blackwell, 2001) - Nuclear Medicine in Urology & Nephrology, 2nd Ed., HJ Testa, PH O'Reilly & RA Shields (Butterworth-Heinemann, 1986) - Physics in Nuclear Medicine, JA Sorenson and ME Phelps (Grune & Stratton, 1980) - Radioisotope Techniques in Clinical Research and Diagnosis, N Veall and H Vetter (Butterworths, 1958) - Radionuclide Techniques in Medicine, JM McAlister (Cambridge University Press, 1979).
All machines works according to the mechanical conditions which calculates as per our instructions and gives us accurate output. These mechanical conditions are calculated under certain measurable systems which contains special laws, formulas, and rules. We had already learn the three axis in our chart and graph diagrams but do you know that is been taught as per the rules of the system integrated with it. One such system is the mechanical system which proves the correct and exact coordinates of the machine to work accurately. In Algebra, a coordinate system is a system which utilizes one or more figures, or coordinates, to distinctively conclude the location of a point or other geometric component on a space. The regulation of the coordinates is important and they are sometimes recognized by their location as in "the x coordinate". The coordinates are taken to be valid numbers in basic mathematics, but may be intricate figures. In mathematics and physics, the right-hand rule is a common term for considering information reunion for vectors in 3 dimensions. When selecting three vectors that must be at right angles to each other, there are two separate resolutions. This can be seen by holding your hands together, palm up, with the fingers warped. If the curl of your fingers characterizes a rotary motion from the first axis to the second, then the third axis can point any along your right thumb or your left thumb. Same way the machine such as Milling machines and Router has this method of resolution with making out the three basic axis X, Y, and Z axis. Here each axis has its own rule which coordinates to the system of the right hand rule. This rule relates with the MCS (mechanical coordinate system) where the coordinates origin in a stable location. This is manually set to make the formula work for the system of the machine. Let’s see an example of the system relating to the machine: Milling is the machining process of using rotating shears to eliminate substance from a work piece moving ahead in a direction at an angle with the axis of the tool. It covers a broad selection of diverse procedure and equipment, on balance from minute individual fraction to huge, processes. It is one of the most normally used processes in industry and mechanism shops today for machining piece to accurate dimension and forms. Here how the mechanism works the angle formed with the axis of the tool and generates the way of working system to give the best production as per the industry demand. This manual tool change systemhelps the machine to work on the position, direction as well as the motion. The accurate comes with the physical dimension of the parts and the overall body of the machine for which it is intend to make for. 1 Main Street Cell: 123 456 789
A Brief history of Einstein’s special theory of relativity. The main conclusions of Einstein’s special theory of relativity are the Lorentz transformation equations. They are called the “Lorentz transformation equations,” because they had already been discovered, before Einstein’s first paper, by H. A. Lorentz, taking a Newtonian approach. That is where I will pick up the story about the Einsteinian revolution in physics, since spatiomaterialism is merely following in the footsteps of Lorentz. What I will call the four “Lorentz distortions”are sufficient to explain all the of the predictions by which Einstein’s special theory of relativity has been confirmed. Lorentz. By 1887, some eighteen years before Einstein’s paper, Michelson and Morley had made experiments that showed that light has the same velocity relative to any object, regardless of its own motion. What made their result puzzling was the Newtonian assumption that the medium in which light propagates is a “luminiferous ether,” a very subtle kind of material substance that was supposed to be at rest in absolute space. Given that the velocity of light is everywhere the same relative to absolute space, they expected that the velocity of light, as measured from a material object, to vary with that object’s own velocity in absolute space—just as the velocity of ripples propagating in a pond arrive faster (or slower), when a boat is moving toward them (or away from them). Michelson and Morley used an interferometer, which compares the two-way velocities of light in perpendicular directions; that is, light is reflected back from mirrors in perpendicular directions and the signals are compared to see if one is lagging behind the other. They made measurements at various points in the Earth’s orbit around the sun, where the Earth should have different velocities in absolute space. On a moving object, the time it takes for light to travel both to and from a distant mirror in the direction of absolute motion should be different from the time it takes to travel an equal distance in the transverse direction. The margins of error were small enough, given the velocity of light and the velocity of the Earth in its orbit around the sun, that it should have been possible for their interferometer to detect absolute velocity. But Michelson and Morley failed to detect any difference at all in the time it took light to travel the same distance in perpendicular directions. Absolute motion could not be detected. Length contraction. The Michelson-Morley result was surprising, but even before Einstein published his special theory in 1905, Lorentz had proposed a Newtonian explanation of it. Lorentz showed, in 1895, that their result could be explained physically, if the motion of such an apparatus in absolute space caused its length to shrink in the direction of motion as a function of its velocity by a factor of . Lorentz argued that this length contraction is a real physical change in the material object that depends on its motion relative to absolute space. The equation was L=Lo, where Lo was the length at absolute rest. The shrinkage had been proposed independently by George F. Fitzgerald in 1889 and hence became known as the “Lorentz-Fitzgerald contraction”. Lorentz tried to explain the length contraction physically, as an effect of motion through a stagnant ether on the electrostatic forces among its constituent, charged particles. But he could just as well have taken it to be a law of physics, making the Lorentz-Fitzgerald contraction the discovery of a new, basic physical law. (An ontological explanation of it will be suggested in the last section of this discussion of the special theory of relativity.) Lorentz also described the length contraction as a mathematical transformation between the coordinates of a reference frame based on the moving material object and the coordinates of a reference frame at absolute rest. Lorentz started with the Galilean transformation by which Newtonians would obtain the spatial coordinates used on an object in uniform motion in the x-direction, or x’ = x - vt, and combining that with the length contraction he had discovered, he came up with the transformation equation, for obtaining the spatial coordinates on the moving material object. Time dilation. There is, however, another distortion that material objects undergo as a function of their absolute motion. That is a slowing down of clocks (and physical processes generally) at the same rate as the length contractions, or the so-called "time dilation," which took somewhat longer for Lorentz to discover. The Galilean transformation for time in Newtonian physics is simply t = t' , because Newtonian physics assumes that time is the same everywhere. But by using transformation equations to describe the distortions in material objects, Lorentz found that he had to introduce a special equation for transforming time: t’ = t - vx/c2 (Goldberg, p. 94). The new factor in the transformation equation, vx/c2, implied that time on the moving frame varies with location in that frame. Lorentz called it "local time," but he did not attribute any physical significance to it. "Local time" is not compatible with the belief in absolute space and time, and Lorentz described it as “no more than an auxiliary mathematical quantity” (Torretti, p. 45, 85), insisting that his transformation equations were merely “an aid to calculation” (Goldberg, p. 96). The slowing down of physical processes is called “time dilation.” Lorentz discovered this distortion by tinkering with various ways of calculating the coordinates used on inertial reference frames in relative motion. Thus, it is natural to describe time dilation as the slowing down of clocks on the moving reference frame. It was included in the final version of Lorentz's explanation, now called the “Lorentz transformation equations.” (Lorentz 1904) Those equations contained not only the length contraction and transformation for “local time”, but also the implication that clocks on moving frames are slowed down at the same rate as lengths are contracted (that is, ). The final Lorentz equation for time transformation included both the variation in local time and time dilation: . Though Lorentz took the distortions that he discovered in fast-moving material objects to be laws of nature, he did not think that they were basic. He thought they were effects of motion on the interactions between electrons and the ether which could be explained by his electronic theory of matter, and he saw explaining this effect as the the main challenge to Newtonian physics. The transformation equations themselves never seemed puzzling to Lorentz, because he never took them to more than just a mathematical aid to calculation. Poincaré. H. Poincaré thought he saw more clearly what Lorentz had discovered than Lorentz himself. As early as 1895, Poincaré had expressed dissatisfaction with Lorentz’s piecemeal approach, introducing one modification of the laws of Newtonian physics after another in order to account for different aspects of the phenomenon discovered by Michelson and Morley. Instead of such ad hoc modifications, he urged the recognition of what he called a “principle of relativity” to cover all the phenomena involved in fast-moving objects. As Poincaré put it in 1904, the principle of relativity requires that “the laws of physical phenomena should be the same for an observer at rest or for an observer carried along in uniform movement of translation, so that we do not and cannot have any means of determining whether we actually undergo a motion of this kind” (from Torretti, 83). A principle of relativity like this had, in effect, been affirmed by Newton himself, when he admitted that his laws of motion depend, not on the absolute velocities of material objects, but only on their relative velocities. That is, Newton had already denied that absolute rest could be detected by mechanical experiments. It seemed that absolute motion could be detected only when Maxwell had discovered that light could be explained as an electromagnetic wave. Thus, Poincaré saw Lorentz's discovery of distortions in fast-moving material objects as a way of extending Newton’s principle of relativity to cover electromagnetic phenomena. Understanding how the undetectability of absolute motion could be a result of the distortions that Lorentz had discovered, he referred to Lorentz theory as “Lorentz’s principle of relativity” even after Einstein had published his special theory and Lorentz himself was attributing the principle of relativity to Einstein (Torretti 85, Goldberg 212, and Holton 178). Indeed, Poincaré joined Lorentz in the attempt to explain the Lorentz distortions by the motion of material objects through absolute space, also expecting to find their cause in the dynamics of electrons; he also thought that motion through the ether caused material objects to shrink in the direction of motion and natural clocks to slow down by the exact amount required to mask their motion, as implied by Lorentz’s transformation equations (Goldberg 94-102, Torretti 38-47). Furthermore, Poincaré apparently thought that what Lorentz said about those equations in his 1904 work answered his own demand that it be a “demonstration of the principle of relativity with a single thrust” (Goldberg 214-15). Lorentz's explanation of the distortions was not, however, a complete explanation of the principle of relativity. There are really two quite different aspects of the phenomenon described by the principle of relativity, and Lorentz had explicitly explained only one of them. What Lorentz’s electron theory of matter (and Poincaré’s own refinements of it) explained physically were the Lorentz distortions in material objects with absolute velocity. That explained the negative outcome of the Michelson-Morley experiment: the contraction of lengths in the direction of motion and the slowing down of clocks as a function of motion through absolute space does make it physically impossible to detect absolute motion on a moving object by measuring the velocity of light relative to it. And that is one way in which inertial reference frames are empirically equivalent, because it holds of measurements made using any material object in uniform motion as one's reference frame, regardless of its motion through absolute space. But there is more to the principle of relativity than explaining the null result of the Michelson-Morley experiment. The transformation equations that Lorentz constructed to describe the effects of absolute motion on material objects predict the outcomes of other experiments, such as attempts to measure directly the lengths of high-velocity measuring rods and the rate at which high-velocity clocks are ticking away. Though such experiments are more difficult to perform, they are conceivable, and Lorentz's equations do make predictions about them: moving measuring rods will be shrunken in the direction of motion and moving clocks will be slowed down. That suggests another way of detecting absolute motion. One might compare measuring rods or clocks that are moving at a whole range different velocities with one another and take the one with the longest measuring rods and quickest clocks to be closest to absolute rest. Hence, the principle of relativity would be false. It is not possible, however, to detect absolute rest in this way, and as it happens, its impossibility is also predicted by Lorentz's theory, because he formulated his description of the Lorentz distortions in terms of transformation equations. Transformation equations are equations for transforming the coordinates obtained by using one material objects as a frame of reference into the coordinates obtained by using another material object as a frame of reference, and to be consistent, they must work both ways. That is, it must be possible to obtain the original coordinates by applying the transformation equations to the transformed coordinates. Thus, whatever distortions observers at absolute rest may find in material objects with a high absolute velocity will also be found by observers in absolute motion in material objects that are at absolute rest. The recognition that Lorentz's theory, being formulated in terms of transformation equations, implied that all such inertial reference frames are empirically equivalent is presumably what led Poincaré to proclaim that Lorentz had finally explained the truth of the principle of relativity. Absolute rest and motion cannot be detected from any inertial reference frame. Lorentz's theory was not, however, an adequate explanation of the principle of relativity, for there is still something puzzling about the empirical equivalence entailed by the symmetry of the Lorentz transformation equations. Lorentz meant his transformation equations to be a way of describing the length contraction and time dilation in material objects with absolute motion, for that would explain the Michelson-Morley experiment, that is, why absolute motion cannot be detected by measuring the velocity of light in different directions. But since the transformation equations describe a symmetry between the members of any pair of inertial reference frames, they imply that observers using a fast-moving material object as the basis of their reference frame would observe a length contraction in measuring rods that were at absolute rest and a time dilation in clocks at absolute rest. That makes it impossible to detect absolute rest or motion by comparing different inertial reference frames with one another. But it is puzzling, because it is hard to see how both views could be true at the same time, that is, how two measuring rods passing one another at high velocity could both be shorter than the other and how two clocks passing by one another could both be going slower than the other. In other words, Lorentz's theory does not really give a physical explanation of what Poincaré called the "principle of relativity." What entails the truth of the principle of relativity is the description of the Lorentz distortions in terms of transformation equations; the inability to detect absolute rest and motion by comparing inertial frames with one another comes from the symmetrical relationship that transformation equations represent as holding between the members of any pair of inertial reference frames. That symmetry is not physically possible, at least, not in the sense of "physical" that Lorentz had in mind when he tried to explain the distortions as occurring to material objects because of their motion in absolute space. If inertial frames are material objects in absolute space, then their measuring rods cannot both be shorter than the other and their clocks cannot both be slower. As we shall see, what enables Lorentz's transformation equations to predict the symmetry of distortions is the "local time" factor in the time equation, vx/c2, which Lorentz insisted was just an "aid to calculation." It represents the readings that would be given by clocks on a moving reference frame that have been synchronized by using light signals between them as if they were all at absolute rest, that is, on the assumption that the one-way velocity of light is the same both ways along the pathway between any two clocks (as required by Einstein's definition of simultaneity at a distance). That assumption is false, as Lorentz understood these phenomena, and clocks on the moving inertial frame would be mis-synchronized. It can be shown, as we shall see, that this way of mis-synchronizing clocks on a moving frame combines with the Lorentz distortions that the moving frame is actually suffering to make it appear that its own Lorentz distortions are occurring in the reference frame at absolute rest (or moving more slowly). This is a physical explanation, given how the other frame's measuring rods and clocks are measured. But it is an explanation of the principle of relativity that reveals it to be the description of a mere appearance. Though there is an empirical equivalence among inertial frames, a physicist who accepted Lorentz's Newtonian assumptions would insist that it has a deeper physical explanation. It was not Lorentz, however, but Poincaré who declared that Lorentz had explained the truth of the principle of relativity, and Poincaré's acceptance of Lorentz's explanation as adequate may have been colored by his own philosophical commitment to conventionalism. Poincaré viewed the choice between Euclidean or non-Euclidean geometry as conventional, and he argued that convention is also what raised inertia and the conservation of energy to the status of principles that could not be empirically falsified. Poincaré's acceptance of the principle of relativity should probably be understood in the context of this more or less Kantian skepticism about knowing the real nature of what exists. Considering how the standard of simultaneity at a distance varies from one inertial reference frame to another (depending on the "local time" factor in the Lorentz transformation equations), the principle of relativity could also be seen as a conventional truth. Poincaré's pronouncement that Lorentz's theory had explained the principle of relativity could not have set well with Lorentz himself. Lorentz may have continued to call it "Einstein's principle of relativity" because he realized that it was not explained by his theory about how spatial and temporal distortions are caused in material objects by their absolute motion. What is responsible for the principle of relativity is the symmetry in pairs of inertial frames entailed by his equations being transformation equations. If the distortions didn’t hold symmetrically in any pair inertial frames, it would be possible to detect absolute rest and motion. But to my knowledge, Lorentz never argued explicitly that what he called "local time" on the moving material object (that is, vx/c2 in the time equation) represents a mis-synchronization of clocks on the moving frame that causes the moving frame's own Lorentz distortions to appear to be occurring in the other inertial reference frame. The Newtonian explanation of all the relevant phenomena did not, therefore, have an adequate defender. Lorentz was more concerned to find an adequate physical explanation of the distortions he had discovered in material objects, and Poincaré was more interested in defending conventionalism. That is the Newtonian context in which Einstein's special theory of relativity won the day. Einstein. Einstein took a dramatically different approach from both Lorentz and Poincaré. Instead of taking the principle of relativity to be an empirical hypothesis that could be explained physically by deeper, Newtonian principles, or as a conventional truth, Einstein raised the principle of relativity to the status of a postulate, which was not to be explained at all, but rather accepted as basic and used to explain other phenomena (Zahar 90-2). The mathematical elegance of Einstein's explanation of these phenomena is stunning. From the premise that all inertial reference frames are empirically equivalent, he derived a description of how two different inertial reference frames would appear to each other; that is, he deduced the Lorentz transformation equations. Einstein's new approach can be seen most clearly by considering the structure of his argument. It is represented below in a diagrammatic form. The Principle of Relativity \|The laws of nature apply the same way on all inertial frames.\| \|The Light Postulate\|\|The velocity of light is the same on all inertial frames.\| \|The Definition of Simultaneity at a Distance\|\|The local event halfway through the period required for light to travel to the distant event and back is simultaneous with the distant event.\| \|To obtain the second frame's coordinates from the first frame:\|\|To obtain the first frame's coordinates from the second frame:\| \|Lorentz transformation equations (kinematic phenomena)\|\| \|Relativistic increase in mass (dynamic phenomena)\|\| The assumption that inertial frames are all empirically equivalent takes the form of three premises in Einstein’s argument: the Principle of Relativity, the Light Postulate, and Einstein's Definition of Simultaneity at a Distance (see table). Einstein's principle of relativity holds, with Poincaré, that the laws of nature hold in the same way on every inertial reference frame. That allowed Einstein to assume that Maxwell's laws of electromagnetism hold universally, and he considered what would be true of two different inertial frames in the same world. But in order to deduce the Lorentz transformation equations, Einstein also had to assume that that the velocity of light is the same relative to every inertial frame (the light postulate) and, accordingly, that simultaneity at a distance is defined on each reference frame as if the velocity of light is the same both to and back from a distance object. What Einstein deduced from these premises are the “Lorentz transformation equations,” that is, equations for transforming the coordinates of any given inertial reference frame into those of any other. The Lorentz transformation equations imply that any material object moving relative to any other inertial frame at a velocity approaching that of light will appear to suffer the Lorentz distortions: its clocks (and all physical processes) will be slowed down, and its measuring rods (and all material objects) will be shortened in the direction of its motion—both by the same amount, , which is a function of its velocity in the observer’s reference frame. Einstein also inferred from these kinematic distortions and his principle of relativity that the mass of objects moving in an inertial frame increases at the same rate, making three distortions altogether. That dynamical implication is the source of Einstein's most famous equations, E = mc2. It should be emphasized that there are really two sets of transformation equations. It may not seem that way, because Einstein's conclusion is often stated as just one of the two sets of equations listed above, making it look mathematically simpler. But that formulation overlooks a mathematical detail and thereby obscures what Einstein's conclusion is about. Though the Lorentz transformation is exactly the same both ways between the members of any pair of inertial reference frames, it requires two, non-identical sets of transformation equations, because their relative velocity has the opposite sign for each observer. That is, the two coordinate systems are set up so that their origins coincide when t = 0 and t' = 0, and since they are moving in opposite directions, the relative velocity is v for one of them and -v for the other. Thus, in order for the transformation to be symmetrical, one set of transformation equations has to have the opposite sign for the second factor in the numerator of the equations for space and time. Since this seems to be a mere technicality, the conclusions of Einstein’s argument are usually represented as a single set of Lorentz transformation equations (the first set in the above table). Duplication is avoided by introducing a special mathematical symbol to make the single set of equations represent both transformations in any pair of inertial frames. Thus, Einstein's conclusion seems more like just another universal law of nature. But this is just homage to the Pythagorean ideal of mathematical simplicity, which obscures the fact that Einstein's theory is, in the first instance, about the symmetry that holds between the members of every pair of inertial frames. It should also be emphasized that Einstein's theory is about how reference frames are related, and only indirectly about the material objects on which they are based. Though it does have implications concerning the relationship between material objects with a high relative velocity, that relationship is described by way of a mathematical transformation that holds between the reference frames based on them. Inertial reference frames are based on material objects that are not being accelerated, and what makes the material object a reference frame is that it is used as the basis for a coordinate system by which the locations and times of events throughout the universe can be measured. (For this purpose, it is useful to think of an inertial reference frame as a grid of rigid bars extending wherever needed in space with synchronized clocks located everywhere.) Notice that Einstein's three premises are all about reference frames based on material objects. Indeed, his definition of simultaneity prescribes how clocks must be synchronized to set up such a reference frame. The light postulate makes explicit the assumption about the velocity of light on which his definition of simultaneity is based. And the principle of relativity states that all the laws of physics will hold the same way within that reference frame as every other one, that is, will make correct predictions about what happens in that reference frame. Einstein derives conclusions from his premises by assuming that there are two different inertial reference frames in the world and figuring out how they must appear to one another. Since his premises are about their reference frames, it is hardly surprising that his conclusion is about a mathematical transformation between their coordinates. Indirectly, however, Einstein's conclusion is a description of how material objects with different constant velocities are related to one another as parts of the same world, since the reference frames in question are based on material objects. But to see Einstein's conclusion as a description of how material objects are related in space is to take Lorentz's approach. For Lorentz, these same transformation equations were just a mathematically convenient way of describing from the absolute frame the spatial and temporal distortions that occur in material objects with a high velocity in absolute space. By calling his argument a theory of relativity, Einstein emphasized that his theory is about the empirical equivalence of all inertial reference frames, not the relationship between the material objects on which they are based. Observers on each inertial reference frame have their own view of the relationship between the material objects involved, but they are different views, and it is their views that are related by the Lorentz transformation equations. The symmetry of the relationship between their reference frames is what is crucial for Einstein, because that is what rules out any way of detecting absolute rest or motion by comparing inertial frames to one another and ensures that there is nothing to distinguish one inertial frame from another except their velocities relative to one another. The Lorentz distortions in material objects are, however, a consequence of the Lorentz transformation equations that Einstein deduced. And if one does follow Lorentz, interpreting them as a way of describing the material objects on which the inertial reference frames are based, then the Lorentz transformation equations lead to paradoxes, as I have already suggested. Those equations imply that observers using any given inertial reference frame will find the Lorentz distortions occurring in the material objects on which the other inertial reference frame is based, and thus, the symmetry of the transformation for any pair of inertial frames leads to paradoxes. Consider two inertial frames in motion relative to one another. From the first frame it appears that clocks on the second frame are slowed down. That would make sense, if from the second frame, it appeared that first-frame clocks were speeded up. But special relativity implies that it also appears from the second frame that clocks on the first frame are slowed down. That is, the distortions are symmetrical on Einstein’s theory, not the reverse of one another, as one might expect. And if the Lorentz distortions are really symmetrical, it is inconceivable that the two inertial frames are just material objects moving relative to one another in absolute space, because in absolute space, there can’t be two clocks next to one another both of which are actually going slower than the other. If one assumes that Einstein's theory is describing material objects, one must give up the assumption that those objects are located in absolute space. They are, of course, parts of the same world, but they must be related to one another in some other way. The same problem arises from the symmetry of the length contraction and relativistic mass increase, for there cannot be two measuring rods passing one another in space that are both shorter than the other. Nor can there be two material objects both be more massive than the other. It is simply not possible for material objects located in absolute space. None of this should be a surprise, however, because even the Light Postulate itself is incompatible with absolute space (or at least, with the assumption that light has a fixed velocity relative to absolute space). Though Newtonian physics had taken absolute space to contain the medium in which light propagates, Einstein assumed that the velocity of light relative to every object is the same, regardless of their own velocities relative to other objects in the world. Thus, Einstein held that the velocity of light would be the same in both members of any pair of inertial frames. This is not possible, if electromagnetic waves propagate through (an ether in) absolute space, like waves in water, for the motion of an object through waves propagating in space would change the velocity of those waves relative to the object—just as the motion of a row boat through ripples propagating in a pond changes the velocity of those ripples relative to the boat. Taken as a description of the relationship between material objects in space, therefore, Einstein's special theory of relativity leads to paradoxes. But Einstein was not discouraged by these paradoxes. He was not thinking of inertial reference frames as material objects that are related in space, that is, in absolute space, or a space that is the same for both material objects. He was making a more abstract, mathematical argument and, in the process, giving physics a new standpoint from which to explain all physical processes. That Einstein's basic approach is different from Lorentz's can be seen in what made Einstein curious about these phenomena in the first place. It was not the Michelson-Morley experiment, but rather something peculiar about the connection between classical mechanics and Maxwell’s theory of electromagnetism (Zahar 99-100). Einstein realized that even though Maxwell’s theory was standardly interpreted as referring to absolute space, absolute space was not needed in order to explain electromagnetic phenomena. For example, a conductor moving through a magnetic field at absolute rest moves electrons exactly the same way as if it were at absolute rest and the magnetic field were moving. That is what suggested the principle of relativity to Einstein, and though from it he derived the same transformation equations that Lorentz had proposed in 1904, Einstein claimed not to know about Lorentz's 1904 work. By raising the principle of relativity to the status of a postulate, Einstein was assuming, in effect, that the deepest truth that can be known about the nature of space and time is that inertial frames are all empirically equivalent. And by relying on the predictions of measurements derived from that principle to justify his theory, Einstein had the support of the positivists, who dominated philosophy of science at that time. Indeed, Einstein admits to having been influenced by Ernst Mach at the time of his first paper on special relativity. To positivists, the paradoxes mentioned above about two clocks both going slower than the other and two measuring rods both shorter than the other are not real problems, but merely theoretical problems. Theoretical propositions that could not be spelled out in terms of observations were dismissed as "metaphysical," as if theories were mere instruments for making predictions. That attitude could be taken about the aforementioned paradoxes, because there is never any occasion in which two clocks can be directly observed both going slower than the other (or two measuring rods observed both shorter than the other). Observations are made from one inertial reference frame or another, and if both members of some pair of inertial frames are observed from a third reference frame, their clocks and measuring rods do not appear this way because of the Lorentz distortions that are introduced by its own velocity relative to them. Though when taken as a description of material objects, the special theory of relativity is incompatible with the existence of absolute space, Einstein did not attempt to use its implications to show that absolute space does not exist. He was making a mathematical argument to show that accepted theories in Newtonian physics, which did assume the existence of absolute space, could all be replaced by theories that do not mention absolute rest or motion at all. All he explicitly claimed was that physics does not require an “absolutely stationary space” and that the notion of a “‘luminiferous ether’ will prove to be superfluous” because the “phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the ideas of absolute rest” (Einstein, 1923 p. 37). It could be argued, therefore, that Einstein was merely imitating empiricist skepticism about theoretical entities generally by casting doubt on the reality of absolute space. As it turned out, Einstein's theory proved to be remarkably successful in making surprising predictions of new experiments. For example, unstable particles have longer half-lives when moving at velocities approaching that of light. Clocks flown around the earth are indeed slowed down compared to clocks that stayed at home. The most famous new prediction of special relativity, E = mc2, has been confirmed repeatedly. It is a consequence of the relativistic increase in mass, which Einstein first pointed out, and without it, high energy physics as we know it today would be inconceivable. Finally, the equations of special relativity have become (after Dirac) the foundation of quantum field theory as well as Einstein’s theory of gravitation. The Lorentz transformation is now so basic to physics that “covariance” (or “Lorentz covariance”) is taken as a constraint on all possible laws of physics. To be sure, Newtonian physicists complained about the loss of intuitive understanding that came with the acceptance of Einstein's way of explaining these phenomena. It was no longer possible to construct in ordinary spatial imagination a picture of the nature of the world. But that objection did not detract from the predictive success of Einstein's theory, and the Einsteinian revolution made the capacity of mathematical arguments to make surprising predictions of precise measurements the establishment criterion for accepting theories in contemporary physics. But physics is not just mathematics. A theory in physics is generally thought to be true when it corresponds to what exists, and if the special theory of relativity does not correspond to material objects in absolute space, we want to know what it does correspond to. The success in making surprising predictions of what happens by which Einstein's theory has been confirmed means that it corresponds to regularities that hold of change in the world, but it is natural to want to know the nature of what exists that makes those regularities true. The answer given by contemporary physics is spacetime, and it was Minkowski that has made that answer possible. Minkowski. In 1908, Minkowski offered a mathematically elegant way of representing what is true from all inertial frames, according to Einstein’s special theory of relativity, using only the coordinates of any single inertial frame. His was a “graphic method” which he said allows us to “visualize” what is going on. The key to his diagram was to represent time in the same way as space, and that is what has led to the belief that what exists is not space and time, but rather spacetime. In Minkowski’s “spacetime diagrams”, time is represented as a fourth dimension perpendicular to the three dimensions of space (though when comparing two inertial frames, the spatial dimensions can be reduced to one by a suitable orientation of their coordinate frames). A material object at rest in space is represented, therefore, as a line running parallel to the time axis, and a material object with a constant, non-zero velocity is represented by a line inclined slightly in the direction of motion. Units for measuring time and space are usually chosen so that the path of light in spacetime (the “light-line”, t = x/c) bisects the time and space axes, making the “basic unit” of distance how far light travels in a unit of time. Since the second frame of reference is based on a moving object, we can think of the tilted line representing its pathway as its time axis. From such a moving reference frame, the location of an object at rest in the first frame (such as one always located at its origin) would change relative to the moving frame. So far, this diagram of space and time would be acceptable in classical Newtonian physics, because it represents a so-called Galilean transformation for the coordinates of moving reference frames (in which distances in space would be related as x' = x – VT, where v is their relative velocity in the x-direction.) What Minkowski discovered was that the Lorentz transformation for moving reference frames could be represented by tilting the space line of the moving frame equally in the opposite direction and lengthening the units of time and space. That is, the time-line and the space-line of the moving frame are inclined symmetrically around the pathway of light. (See the comparison of the Newtonian Diagram of Space and Time and Minkowski's Spacetime Diagram.) In either the Newtonian or Minkowski's diagram, every point represents the location of a possible event in space and time (called a “world-point”), and superimposing a second reference frame makes it possible to give such coordinates in either reference frame. From the coordinates for any event in the first reference frame, we can simply read off the coordinates for the same event in the moving reference frame, and vice versa. In the case of event E, for example, the coordinates in the first frame are (2,1), and in Minkowski's diagram, they are (1.3,0.3). All possible reference frames can be represented in this way, each with a different tilt to its time-axis representing its velocity relative to the first. The two reference frames in the Newtonian diagram have a very simple relationship, because time coordinates are the same for both reference frames and there is no change in the units of either time or space. But Minkowski's spacetime diagram represents the Lorentz transformation, and not only are the units of time and space different, but the space-line of the moving reference frame is inclined relative to the first reference frame. Minkowski’s spacetime diagram yields the same coordinates for the second reference frame that are obtained from the Lorentz transformation equations deduced by Einstein. Thus, it predicts that measurements of the second inertial frame will reveal its clocks to be slowed down and its measuring rods to be contracted in the x-direction. But since the Lorentz transformation works both ways, it is possible to start with the second (tilted) reference frame and obtain coordinates for events in the first reference frame. Thus, it predicts that the moving observers will detect Lorentz distortions occurring in the first frame. This symmetry about the relationship between inertial reference frames makes it impossible to single out any particular frame as being at absolute rest by comparing reference frames with one another. Minkowski's spacetime diagram may seem to mitigate the paradoxes resulting from the symmetry of the relationship between members of any pair of inertial reference frames, because it enables us to "picture" two clocks both ticking away slower than the other and two measuring rods both shorter than the other. It is just a result of how the inertial reference frames are related to one another. But this wonderful power of Minkowski's spacetime diagram to represent these puzzling phenomena would not be possible, if the space-lines of different reference frames had the same slope. The inclined orientation of the space-line of the second inertial frame relative to the first frame is crucial to representing the Lorentz transformation, and it represents a disagreement between inertial observers about simultaneity at a distance. That is, observers using different inertial reference frames will disagree about which events at a distance are simultaneous with the origins of their systems when they pass by one another. That is the source of all the ontological problems with the belief in spacetime. Though it is possible to interpret Minkowski's spacetime diagram as just a useful mathematical device for predicting the measurements that would be made on different inertial frames, that is what the Lorentz transformation equations already do. The historical significance of Minkowski's diagram is that it enables us to "picture" what exists in a world where Einstein's special theory of relativity is the deepest truth about the world. Thus, it leads to the belief in spacetime (that is, "spatiotemporalism," as I called it in Spatiomaterialism, or "substantivalism about spacetime," as it is called in the literature.) The belief in spacetime comes from realism about special relativity. Scientific realism holds that theories in physics are true in the sense of corresponding to what exists, and spacetime is what must exist, if Einstein's special theory of relativity is the deepest truth about the real nature of what exists as far as space and time are concerned. With regard to space and time, Newtonian realists would say that what their theories correspond to is absolute space and absolute time, that is, to a three dimensional space all of whose parts exists at the present moment and endure simultaneously through time. But that is not what Einstein's special theory of relativity corresponds to, because it implies that observers on all possible inertial reference frames are equally correct about the times and places of the events that occur in the world, even though they disagree about the simultaneity of events at a distance. What all the different inertial observers say about the times and places of events can, however, be true at the same time, only if what exists is represented by Minkowski's spacetime diagram. Thus, spacetime is the natural answer to the question about what corresponds to Einstein's special theory of relativity. According to realists about special relativity, what exists is spacetime, a four-dimensional entity that contains time as a dimension and, thus, is not itself in time. Though Einstein may merely have been arguing in the spirit of the empiricist skepticism that prevailed in philosophy at that time, Minkowski made it possible to give a realist interpretation of Einstein’s special theory. His spacetime diagram showed how Einstein's theory could be interpreted as a description of what really exists in the case of space and time. Minkowski must have realized that he was giving a realist interpretation of Einstein's special theory of relativity when he introduced his spacetime diagrams; he said (Minkowski 75) that “space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality”. In any case, later in the twentieth century, when logical positivism gave way to scientific realism, Einstein’s skepticism about absolute space, if that is what it was, spawned the belief in the existence of spacetime. Indeed, regardless what Einstein may have believed in 1905, he apparently came to agree that what he had discovered was spacetime. (See Einstein 1966, pp. 205-8). Scientific realism is, however, a way of letting science determine one's ontology. That is not the best way to decide which ontological theory to accept, because the empirical method that science follows is to infer to the best efficient-cause explanation, and that may not be the best ontological-cause explanation. But we can see how realism led to an ontology based on spacetime. Einstein's special theory of relativity was a better efficient-cause explanation of the relevant phenomena than Lorentz's way of defending his transformation equations, because it made all the same precise predictions of measurements, but in a mathematically simpler way. As an efficient-cause explanation, however, all that Einstein's special theory requires is an empirical equivalence of inertial reference frames. It assumes that inertial frames are experimentally indistinguishable from one another, and it derives a description about how they must appear to one another as parts of the same world (where Maxwell's laws of electromagnetism hold). That relationship is described by the Lorentz equations for transforming their coordinates into one another, and it is represented by Minkowski's spacetime diagram. But Einstein's was a mathematical argument, and no mechanism or cause of the empirical equivalence was given. A realist interpretation of special relativity goes beyond mere empirical equivalence and holds that inertial frames are all ontologically equivalent. If special relativity is the literal and deepest truth about the world, then what observers on all possible inertial reference frames believe must be true at the same time. That is to hold, not merely that no experiment can distinguish any one inertial frame from all the others as the absolute frame, but that there is nothing about the nature of any inertial frame that makes it stand out from all the others. That means, among other things, that no assertion made by observers on one inertial frame can be true unless the same kind of assertion made by observers on every other inertial frame is also true. (Nor can any assertion made on one inertial frame be false unless the same kind of assertion made on every other inertial frame is also false.) The virtue of Minkowski's spacetime diagram is that it enables us to "picture" what exists in a world where inertial reference frames are all ontologically equivalent. Though it may still be unclear what spacetime is, Minkowski's diagram does allow us to believe that all possible reference frames are related to what exists in the same way, for it accommodates all possible standards of simultaneity at a distance. But they can all correspond to what exists only if the world is a four-dimensional entity all of whose parts in both space and time exist in the same way. It is clear that this ontological equivalence of inertial frames is incompatible with absolute space and time, because if space and time were absolute, one inertial frame would be singled out ontologically from all possible inertial frames. Only one of all possible inertial frames would have the correct standard of simultaneity. Its location in space and time could be shared by observers on many other inertial frames, but none of their claims about which distant events are simultaneous with their shared here and how would correspond to what exists. Einsteinians do not use the term "ontological equivalence" to describe the relationship between different inertial reference frames, but that is what the belief in spacetime comes to. Most philosophers of space and time simply take it for granted that they must accept "substantivalism" about spacetime in order to interpret the special theory as a description of the real nature of what exists. To believe in spacetime is to accept an ontology that is fundamentally different from Lorentz's Newtonian view, and the difference can be seen in what each implies about the nature of material objects. Newtonian physicists assumed that material objects are substances that endure through time. They had to believe in absolute time, because the endurance theory of substances presupposes that only the present exists, or "presentism." (If the world is everything that exists, then objects that exist at only one moment in their histories must exist at the same time, for otherwise they would not be parts of the same world.) And since Newtonian physicists believed that material objects are all related to one another by (consistent) spatial relations, they were also forced to believe in absolute space. In a natural world, absolute time entails absolute space. Hence, the Newtonian world was made up of material objects in three dimensional space that endured through time. Spacetime, on the other hand, is a four-dimensional entity. What exists is spacetime and all the events that are located in spacetime. Since time is an aspect of its essential structure, a spacetime world cannot endure through time. Thus, spacetime points and spacetime events must all exist in the same way independently of one another, if they exist at all. There are no material objects in a spacetime world, at least, not in the way that Lorentz believed. There are only the spacetime events that seem to make up the histories of so-called material objects. Thus, what is ordinarily called a "material object" is just a continuous series of spacetime events in spacetime. Its real nature is represented accurately by a “world line” in a spacetime diagram, because each spacetime event making up the history of a "material object" has an existence that is distinct from all the others, just as one point on a line exists distinctly from every other point on the line. In short, whereas a material object in a Newtonian world exists only at each moment as it is present, but is identical across time, a so-called material object in a spacetime world is a continuous series of spacetime events, each of which exists eternally as a distinct part of the world. This is the difference between the endurance and perdurance theory of substances, and between the presentist and eternalist theory about time and existence. Scientific realists sometimes assume that they can believe that Einstein's special theory of relativity corresponds to what exists without denying that they are themselves substances that endure through time by holding that only objects at a distance from themselves must exist the same way at all different moments in their histories. But that is not possible, if they believe that the truth of Einstein's special theory means that it corresponds to what exists for every observer. If Einstein's theory is universally true, then it must be true for inertial observers located elsewhere in the universe, and the only way that different inertial observes at a distance from us can all be correct about which moment in our local history is simultaneous with their passing by one another is if the moments in our local history all exist in the same way. We must perdure, rather than endure, because we are material objects at a distance for inertial observers elsewhere in the universe. What Minkowski's “union” of space and time means ontologically is, therefore, that presentism is false. The denial of presentism is such a serious obstacle to an ontological explanation of the world that, in Spatiomaterialism, we were led to reject spacetime substantivalism (or "spatiotemporalism"), promising to justify it later by showing how it is possible for space and time to be absolute, despite the Einsteinian revolution. That is the argument we take up in the next section. But first, let us consider briefly why physics has ignored the ontological problems with eternalism. What explains the ascendancy of the belief in spacetime is, once again, the empirical method of science and the physicists' addiction to mathematics as a means of practicing it. Behind Minkowski's spacetime diagram lies an elegant equation that has proved to be irresistibly attractive. Minkowski provided a method of constructing in our own spacetime coordinate frame the spacetime coordinate frame that would be used by observers on an object moving relative to us. We may call their world-line the “moving timeline” (t = x/v), because it will be the time axis that moving observers use for their spacetime coordinate frame. Minkowski formulated the conclusion of Einstein’s special theory as an equation that describes a hyperboloid in four dimensional spacetime: 12 = c2t2 - x2 - y2 - z2. (When we orient our x-axis in the direction of the others’ motion, we can ignore the other two dimensions and it reduces to 12 = c2t2 - x2.) (It is the red curve in the diagram depicting how Minkowski's spacetime diagram is constructed.) The intersection of Minkowski’s hyperboloid curve with our time-axis is the unit of time in our frame (t = 1), and the unit of distance (in “basic units”) is the distance in our frame that light travels during that period of time (x = 1). The moving timeline (the time-axis of the moving spacetime frame) also intersects the curve described by Minkowski’s equation, and the distance of that point along our time-axis is the length of a unit of time on the moving coordinate frame according to our clocks. As the diagram shows, moving clocks are slowed down in our frame. The other axis of the moving spacetime frame, the “moving space-line”, is also deduced from Minkowski’s equation. Moving space-lines all have the same slope as the tangent to Minkowski’s curve at the point of the moving timeline’s intersection with his curve. (Its slope is v/c2; the points on any line with this slope are simultaneous in the moving spacetime frame.) Finally, the unit of distance on the moving space-line is how far light travels in the moving frame during a unit of time on the moving frame. Inertial frames are all equivalent on Minkowski’s theory, as on Einstein’s, since Minkowski’s equation determines precisely the same hyperbola in every moving inertial frame constructed this way in our own spacetime coordinate frame. That is, their hyperbolas all coincide. In particular, the same procedure on the moving coordinate frame, using the same equation (and taking the velocity to be -v along the x'-axis), produces the original coordinate frame. Or more abstractly, Minkowski’s equation can be generalized as a measure, s, of the separation between any two events that is the same in every inertial frame, despite variations in their coordinates for particular events: s2 = c2t2 - x2 - y2 - z2. In Minkowski’s equation, the parallel between the representation of space and time is remarkable. Time would be just another spatial dimension, except that it lacks a minus sign (and needs the velocity of light, c, to make units of time commensurable with distance). Indeed, that is how Minkowski includes relativistic mass increase. His equations’s form can be used to state the laws of nature that hold true in every inertial frame. In “four vector physics”, or “covariant” formulations of laws of physics, the energy of an object, E, takes the place of time and the three dimensions of momentum, p, take the place of the three spatial dimensions, so that the objects’ rest mass, m0, rather than the separation, is what is the same about the object in all inertial frames: mo2c4 = E2 - px2c2 - py2c2 - pz2c2. The mathematics of four vector physics is so elegant and suggestive about the relationship of energy and momentum that it is not surprising that physicists now find themselves committed to the belief in spacetime. By comparison with Lorentz’s ad hoc attempts to patch up classical physics in the wake of the Michelson-Morley experiment, Einstein’s argument was astonishingly simple and elegant, making it seem that Einstein had a deeper insight into these phenomena. And since Minkowski provided a diagram that made it possible to represent what special relativity implies about the world independently of particular reference frames, it is hardly surprising that the belief in spacetime has become the orthodox ontology in physics and the philosophy of science. The acceptance of Einstein’s special theory of relativity involved, however, a remarkable change in the empirical method of physics, for it involved the abandonment of the requirement that explanations in physics be intuitively intelligible. To follow the empirical method is to infer to the best efficient-cause explanation. Even in classical physics, theories were highly mathematical and confirmation was most convincing when they predicted surprising, quantitatively precise measurements. But since classical physicists still believed in absolute space and time, they also expected the best scientific theories to be intuitively intelligible, in the sense that it was possible to think coherently about what was happening in spatial imagination. But intuitive intelligibility was no longer possible when the best scientific theory required giving up the belief in absolute space and time. That was undeniably a loss, but physicists felt that they had to grow up and recognize that their deepest commitment was to judging the best theory by which is the simplest and most complete prediction of measurements. Since this came from mathematical theories, abandoning the requirement that physical explanations be intuitively intelligible left them addicted to mathematics. This is because the velocity of light relative to the object in motion is different in opposite directions, and going one way the whole distance at the lower (relative) velocity takes more extra time than it can make up coming back over the same distance at the higher (relative) velocity. Though the path back and forth is spatially symmetric, the effect of the velocity of light relative to the frame on the time of travel accumulates per unit time, and so the signal loses more time than it gains. The equation was L=Lo, where Lo was the length at absolute rest. The shrinkage had been proposed independently by George F. Fitzgerald in 1889 and hence became known as the “Lorentz-Fitzgerald contraction”. Relevant portions of Lorentz’s 1985 monograph and 1904 theory are reprinted in Lorentz, et al, (1923, pp. 3-84). See Stanley Goldberg (1984, p. 98) and Roberto Torretti (1983, pp. 45-6). Hereafter, these works are referred to as “Goldberg” or “Torretti”, with page numbers. “Holton” refers to Holton (1973). “Zahar” refers to Zahar (1989). The discovery of the Lorentz distortions was complicated by the fact that there are other effects of absolute motion on material objects, besides those that are directly related to the Michelson-Morley experiment. These are the “first-order” effects of motion in space (which vary as v/c, rather than as v2/c2, or “second order” effects), such as the way telescopes must be inclined slightly in the direction of motion in order to intercept light from overhead stars (much as umbrellas must be inclined slightly forward in walking through rain to keep raindrops from hitting one’s body). First order effects (including the effects on the index of refraction) had previously been explained by the “ether drag” hypothesis (that the motion of material objects drags the ether along with them), but Lorentz abandoned it . Lorentz’s explanation of length contraction assumed that the ether is totally unaffected by the motion of material objects through it, and he had no explanation of such first order effects except to state transformation equations by which one could obtain the coordinates used on the moving object from those used at absolute rest. Goldberg, pp. 88-92; Torretti, pp. 41-45
A Graph is A Portrait - A Graph Is A Stylized Picture. - A graph is a stylized picture. It shows how a first set of numbers is acted upon by a rule to create a second set of numbers Just as the Impressionists used points to paint a picture, mathematicians use points to produce their graph. Though an Impressionists' points blurr to create the picture, the mathematician's points are drawn as accurately as possible. A mathematician's blank canvas is a coordinate plane. - Remember, a graph is a stylized picture produced to display how one set of numbers is related to another. The blank canvas is the coordinate plane -- the stylized element. [See COORDINATE PLANE]. - Look carefully at the blank canvas, the coordinate plane. Half way from the top to the bottom of the picture is a line, a number line [see NUMBER LINE], which acts as a base line Every point on the line is named by a real number These are numbers which may be acted upon by the rule. If the rule acts upon a number on this line and results in a real number, a point will be placed on the canvas on, above, or below this number. If the rule does not act upon this number or if the result of the action is not a real number, no point is placed on the canvas. The exact location of the point is determined by the rule. The vertical number line [see Y-AXIS] is the scale used to place the point. - Portrait of a Function -- The Graph of - Mathematicians know what this graph looks like without having to see it on paper, on a calculator, or on a computer screen. Beginning math students might be required to generate the curve -- draw the graph -- create the portrait. [If you wish to see how this is done, complete this jump.] Here, we'll simply see how this is indeed a stylized picture which conveys how the domain is acted upon by the rule to produce the range. We'll consider only a few of the many points graphed. - Look at the graph of . - Notice that on the left there are no points anywhere on the canvas. This is because the results of performing the rule, square roots of the numbers, -1, -2, -3, -4, are numbers which are not real numbers - A student who has not yet learned about imaginary numbers would simply say, "You can't graph a point because you can't take the square root of a negative number." - Look again at the graph. On, above, or below all other points (numbers) on the horizontal axis, there is a point; the exact location of the number used. There is a point 1 unit above the 1 on the x-axis because the square root of 1 is 1. There is a point about 1.4 units above the 2 on the x-axis because the square root of 2 is about 1.4. - What Is A Graph? - A graph is a means of summarizing or representing what a relation does. - If one knows the graph, one knows how the relation behaves. - Once a graph is drawn, as in statistical data collection or experimentation in a science class, it suggests what relation might exist between the two sets of numbers and permit a possible expression to be written. - Just as a picture, a graph is worth a thousand words. This is a page from the dictionary MATH SPOKEN HERE!, published in 1995 by MATHEMATICAL CONCEPTS, inc., ISBN: 0-9623593-5-1. You are hereby granted permission to make ONE printed copy of this page and its picture(s) for your PERSONAL and not-for-profit use. \|© 2005, Agnes Azzolino \|
The basic principle behind the particle accelerator is simple: Collide things together at high energy and detect what comes out. In 1909, Ernest Rutherford discovered that the atom consists of a tiny, massive, positively charged nucleus surrounded by a billowy cloud of light electrons 10,000 times as large. To understand the structure of this atomic nucleus, scientists have developed various "probes" in the years since—the most useful being the electrically neutral neutron and a variety of electrically charged particles. As the neutron is not repelled by the nuclear charge, low-velocity ones do fine as probes (see nuclear fission). Charged particles, however, penetrate best when they are highly energetic. Pumping up the energy of such probes is the role of the particle accelerator. The very first high-energy probes were provided by nature, in terms of the alpha, beta, and gamma rays of radioactive elements. In fact, Rutherford used the high-energy alphas from radium as a probe to establish his model of the atom. Although cosmic rays have been (and still are) used as probes—the positron was discovered in this way—almost all the advances in particle physics have been made using man-made accelerators with ever-increasing power. As the power of the probes increased, a plethora of particles were discovered, developing into what was called a "particle zoo." Eventually, they were all organized according to a system called the Standard Model. In the atom bomb, matter is turned into energy; in a high-energy particle accelerator, energy is turned into matter. A particle accelerator uses electric fields to propel electrically charged particles to high speeds and to contain them. An ordinary CRT television set is a simple form of an accelerator. There are two basic types of accelerators: linear and circular. Both designs have limitations. The longer a linear accelerator is, the higher the energy that can be imparted, so the limits are set by the practical length. In a circular design, the length is unbounded. The limits here arise because making electrical charges go in circles causes them to shed energy. As they speed up, more energy is shed, until eventually they shed energy just as quickly as it can be pumped in. In a linear accelerator (linac), particles are accelerated in a straight line with a target of interest at one end. Linear high-energy accelerators use a linear array of plates (or drift tubes) to which an alternating high-energy field is applied. As the particles approach a plate, they are accelerated towards it by an opposite polarity charge applied to the plate. As they pass through a hole in the plate, the polarity is switched so that the plate now repels them and they are then accelerated by it towards the next plate. Normally a stream of "bunches" of particles are accelerated, so a carefully controlled AC voltage is applied to each plate to continuously repeat this for each bunch. As the particles approach the speed of light, the switching rate of the electric fields becomes so high that they operate at microwave frequencies, and so RF cavity resonators are used in higher energy machines instead of simple plates. DC accelerator types capable of accelerating particles to speeds sufficient to cause nuclear reactions are Cockcroft-Walton generators, or voltage multipliers, which convert AC to high voltage DC, or Van de Graaff generators that use static electricity carried by belts. The largest and most powerful particle accelerators, such as the RHIC, the LHC (scheduled to start operation in 2008) and the Tevatron, are used for experimental particle physics. Particle accelerators can also produce proton beams, which can produce "proton-heavy" research or medical isotopes, as opposed to the "neutron-heavy" ones made in fission reactors. An example of this type of machine is LANSCE at Los Alamos. Everyday examples of particle accelerators are those found in television sets and X-ray generators. Low-energy accelerators, such as cathode ray tubes and X-ray generators, use a single pair of electrodes with a DC voltage of a few thousand volts between them. In an X-ray generator, the target itself is one of the electrodes. A low-energy particle accelerator, called an ion implanter, is used in the manufacture of integrated circuits. Linacs are very widely used. They are also used to provide an initial low-energy kick to particles before they are injected into circular accelerators. The longest linac in the world is the Stanford Linear Accelerator, SLAC, which is 3 km (2 miles) long. SLAC is an electron-positron collider. Linear accelerators are also widely used in medicine, for radiotherapy and radiosurgery. Medical grade Linacs accelerate electrons using a klystron and a complex bending magnet arrangement, which produces a beam of 6-30 million electron-volt (MeV) energy. The electrons can be used directly or they can be collided with a target to produce a beam of X-rays. The reliability, flexibility, and accuracy of the radiation beam produced has largely supplanted the older use of Cobalt-60 therapy as a treatment tool. Tandem electrostatic accelerators In a tandem accelerator, the negatively charged ion gains energy by attraction to the very high positive voltage at the geometric center of the pressure vessel. When it arrives at the center region known as the high voltage terminal, some electrons are stripped from the ion. The ion then becomes positive and accelerated away by the high positive voltage. Thus, this type of accelerator is called a "tandem" accelerator. The accelerator has two stages of acceleration, first pulling and then pushing the charged particles. An example of a tandem accelerator is ANTARES (Australian National Tandem Accelerator for Applied Research). In the circular accelerator, particles move in a circle until they reach sufficient energy. The particle track is typically bent into a circle using electromagnets. The advantage of circular accelerators over linear accelerators is that the ring topology allows continuous acceleration, as the particle can transit indefinitely. Another advantage is that a circular accelerator is relatively smaller than a linear accelerator of comparable power (i.e. a linac would have to be extremely long to have the equivalent power of a circular accelerator). Depending on the energy and the particle being accelerated, circular accelerators suffer a disadvantage in that the particles emit synchrotron radiation. When any charged particle is accelerated, it emits both electromagnetic radiation and secondary emissions. As a particle traveling in a circle is always accelerating towards the center of the circle, it continuously radiates towards the tangent of the circle. This radiation is called synchrotron light and depends highly on the mass of the accelerating particle. For this reason, many high energy electron accelerators are linacs. The shedding of energy by electrical particles forced to curve is called synchrotron radiation. The tighter the curve, the greater the energy shed, which is why circular accelerators are as large as possible, minimizing the curvature. Some circular accelerators have been built to deliberately generate radiation (called synchrotron light) as X-rays, for example, the Diamond Light Source being built at the Rutherford Appleton Laboratory in England or the Advanced Photon Source at Argonne National Laboratory in Illinois. High-energy X-rays are useful for X-ray spectroscopy of proteins or X-ray absorption fine structure (XAFS). Synchrotron radiation is more powerfully emitted by lighter particles, so these accelerators are invariably electron accelerators. Synchrotron radiation allows for better imaging as researched and developed at SLAC's SPEAR. In contrast, particle physicists are increasingly using more massive particles, such as protons (or nuclei), in their accelerators to get to higher energies. These particles are composites of quarks and gluons, which makes analyzing the results of their interactions much more complicated, and also of much scientific interest. History of cyclotrons The earliest circular accelerators were cyclotrons, invented in 1929 by Ernest O. Lawrence at the University of California, Berkeley. Cyclotrons have a single pair of hollow, D-shaped plates to accelerate the particles and a single dipole magnet to curve the track of the particles. The particles are injected in the center of the circular machine and spiral outwards towards the circumference. Another type of circular accelerator, invented in 1940 for accelerating electrons, is the Betatron. Cyclotrons reach an energy limit because of the relativistic effects at high energies whereby particles become more difficult to accelerate. Though the special theory of relativity precludes matter from traveling faster than the speed of light in a vacuum, the particles in an accelerator normally travel very close to the speed of light. In high-energy accelerators, there is a diminishing return in speed as the particle approaches the speed of light. Therefore particle physicists do not generally think in terms of speed, but rather in terms of a particle's energy, usually measured in electron volts (eV), instead. Cyclotrons can no longer accelerate protons when they have reached an energy of about 10 million electron volts (10 MeV), because the protons get out of phase with the driving electric field. They continue to spiral outward to a larger radius but, as explained above, no longer gain enough speed to complete the larger circle as quickly. They are nevertheless useful for "lower energy" applications. There are ways for compensating for this to some extent—namely the synchrocyclotron and the isochronous cyclotron. To make the energies even higher, to billions of electron volts (GeV), it is necessary to use a synchrotron. This is an accelerator in which the particles are contained in a donut-shaped tube, called a storage ring. The tube has many magnets distributed around it to focus the particles and curve their tracks around the tube, and microwave cavities similarly distributed to accelerate them. The size of Lawrence's first cyclotron was a mere 4 inches (100 mm) in diameter. Fermilab has a ring with a beam path of 4 miles (6 km). The largest circular accelerator ever built was the LEP synchrotron at CERN, with a circumference 26.6 kilometers, which was an electron/positron collider. It has been dismantled and the underground tunnel is being reused for a proton/proton collider called the LHC. The aborted Superconducting Supercollider (SSC) in Texas would have had a circumference of 87 km. Construction was started but it was subsequently abandoned well before completion. Very large circular accelerators are invariably built in underground tunnels a few meters wide to minimize the disruption and cost of building such a structure on the surface, and to provide shielding against the intense synchrotron radiation. Current accelerators such as the Spallation Neutron Source, incorporate superconducting cryomodules. The Relativistic Heavy Ion Collider, and upcoming Large Hadron Collider also make use of superconducting magnets and RF cavity resonators to accelerate particles. Targets and detectors The output of a particle accelerator can generally be directed towards multiple lines of experiments, one at a given time, by means of a deviating electromagnet. This makes it possible to operate multiple experiments without needing to move things around or shutting down the entire accelerator beam. Except for synchrotron radiation sources, the purpose of an accelerator is to generate high-energy particles for interaction with matter. This is usually a fixed target, such as the phosphor coating on the back of the screen (in the case of a television tube); a piece of uranium in an accelerator designed as a neutron source; or a tungsten target for an X-ray generator. In a linac, the target is simply fitted to the end of the accelerator. The particle track in a cyclotron is a spiral outwards from the center of the circular machine, so the accelerated particles emerge from a fixed point, just as in a linear accelerator. For synchrotrons, the situation is more complex. Particles are accelerated to the desired energy. Then, a fast-acting dipole magnet is used to switch the particles out of the circular synchrotron tube and towards the target. A variation commonly used for particle physics research is a collider, also called a "storage ring collider." Two circular synchrotrons are built in close proximity—usually on top of each other and using the same magnets (which are then of more complicated design to accommodate both beam tubes). Bunches of particles travel in opposite directions around the two accelerators and collide at intersections between them. This can increase the energy enormously; whereas in a fixed-target experiment the energy available to produce new particles is proportional to the square root of the beam energy, in a collider the available energy is linear. At present, the highest energy accelerators are all circular colliders, but it is likely that limits have been reached in respect of compensating for synchrotron radiation losses for electron accelerators, and the next generation will probably be linear accelerators 10 times the current length. An example of such a next generation electron accelerator is the 40 km long International Linear Collider, due to be constructed between 2015-2020. As of 2005, it is believed that plasma wakefield acceleration in the form of electron-beam "afterburners" and standalone laser pulsers will provide dramatic increases in efficiency within two to three decades. In plasma wakefield accelerators, the beam cavity is filled with a plasma (rather than vacuum). A short pulse of electrons or laser light either constitutes or immediately trails the particles that are being accelerated. The pulse disrupts the plasma, causing the charged particles in the plasma to integrate into and move toward the rear of the bunch of particles that are being accelerated. This process transfers energy to the particle bunch, accelerating it further, and continues as long as the pulse is coherent. Energy gradients as steep as 200 GeV/m have been achieved over millimeter-scale distances using laser pulsers and gradients approaching 1 GeV/m are being produced on the multi-centimeter-scale with electron-beam systems, in contrast to a limit of about 0.1 GeV/m for radio-frequency acceleration alone. Existing electron accelerators such as SLAC could use electron-beam afterburners to greatly increase the energy of their particle beams, at the cost of beam intensity. Electron systems in general can provide tightly collimated, reliable beams; laser systems may offer more power and compactness. Thus, plasma wakefield accelerators could be used—if technical issues can be resolved—to both increase the maximum energy of the largest accelerators and to bring high energies into university laboratories and medical centers. Black hole production In the next few decades, the possibility of black hole production at the highest energy accelerators may arise, if certain predictions of superstring theory are accurate. If they are produced, it is thought that black holes would evaporate extremely quickly via Hawking radiation. However, the existence of Hawking radiation is controversial. It is also thought that an analogy between colliders and cosmic rays demonstrates collider safety. If colliders can produce black holes, cosmic rays (and particularly ultra-high-energy cosmic rays) should have been producing them for eons, and they have yet to harm earth. - ↑ Matthew Wright and Early Wright, Riding the Plasma Wave of the Future. Symmetry: Dimensions of Particle Physics (Fermilab/SLAC). - ↑ B.N. Briezman, et al, Self-Focused Particle Beam Drivers for Plasma Wakefield Accelerators. Retrieved October 9, 2007. - ↑ ESI Special Topics, An Interview with Dr. Steve Giddings. Retrieved October 9, 2007. - ↑ Adam D. Helfer, Do black holes radiate? Rept. Prog. Phys. 66:943. Retrieved October 9, 2007. ReferencesISBN links support NWE through referral fees - Wiedemann, Helmut. 2007. Particle Accelerator Physics. New York: Springer. ISBN 3540490434 - Wille, Klaus and Jason McFall. 2001. The Physics of Particle Accelerators: An Introduction. New York: Oxford University Press. ISBN 0198505493 - Wilson, E.J.N. 2001. An Introduction to Particle Accelerators. New York: Oxford University Press. ISBN 0198508298 All links retrieved November 18, 2022. - Particle accelerator research - Particle Accelerators around the world. - Panofsky, Wolfgang K.H. 1997. The Evolution of Particle Accelerators & Colliders. Stanford. - Kestenbaum, David. 2007. Massive Particle Accelerator Revving Up. NPR. - RTFTechnologies.org Electrostatic Particle Accelerator. New World Encyclopedia writers and editors rewrote and completed the Wikipedia article in accordance with New World Encyclopedia standards. This article abides by terms of the Creative Commons CC-by-sa 3.0 License (CC-by-sa), which may be used and disseminated with proper attribution. Credit is due under the terms of this license that can reference both the New World Encyclopedia contributors and the selfless volunteer contributors of the Wikimedia Foundation. 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Presentation on theme: "Physics Subject Area Test MECHANICS: KINEMATICS."— Presentation transcript: Physics Subject Area Test MECHANICS: KINEMATICS To simplify the concept of motion, we will first consider motion that takes place in one direction. One example is the motion of a commuter train on a straight track. To measure motion, you must first choose a frame of reference. A frame of reference is a system for specifying the precise location of objects in space and time. In the train example, any station along the route. Displacement is a change in position. Displacement is not always equal to the distance traveled. The SI unit of displacement is the meter, m. ∆ x = x f -x i Displacement – final position – initial position Displacement is not always equal to the distance traveled. Example: If a gecko starts at an initial position of 20 cm and moves to the 80 cm mark, then retreats back to the 50 cm mark as its final position, How far has the gecko traveled? What is its displacement? The gecko traveled 90 cm, but its displacement is 30 cm. In general, right (east) is positive as well as upward (north) and left (west) is negative as well as downward (south). Average velocity is the total displacement divided by the time interval during which the displacement occurred. In SI, the unit of velocity is meters per second abbreviated as m/s. Consider a trip to a friend’s house 370 km to the west (negative direction) along a straight highway. If you left at 10 AM and arrived at 3 PM, what is your average velocity? This is your average. You did not travel at 74 km/h at every moment. Velocity is not the same as speed. Velocity describes motion with both direction and a numerical value (magnitude). Speed has no direction, only magnitude. Average speed is equal to the total distance traveled divided by the time interval. Consider an object whose position-time graph is not a straight line, but a curve. We obtain different average velocities depending on the time interval. The instantaneous velocity is the velocity of the object at a specific point in the object’s path The instaneous velocity can be determined by measuring the slope of the line that is tangent to that point on the diatance-vs-time graph. Acceleration – Rate at which velocity changes over time An object accelerates if its speed, direction or both change. Acceleration has direction and magnitude. Acceleration is a vector quantity. Acceleration has the dimensions of length divided by time squared. SI units are m/s 2 Remember we have (m/s)/s = m/s 2 Acceleration A bus slows down with an average acceleration of -1.8 m/s 2. How long does it take the bus to slow down from 9.0 m/s to a complete stop? Consider a train moving to the right, so that the displacement and velocity are positive. The slope of the velocity-time graph is the average acceleration. When the velocity in the positive direction is increasing, the acceleration is positive, as at A. When the velocity is constant, there is no acceleration, as at B. When the velocity in the positive direction is decreasing, the acceleration is negative, as at C. When velocity changes by the same amount during each time interval, acceleration is constant. The relationships between displacement, time, velocity, and constant acceleration are expressed by the equations shown on the next slide. These equations apply to any object moving with constant acceleration. These equations use the following symbols: A racing car reaches a speed of 42 m/s. It begins a uniform negative acceleration, using its parachute and braking system, and comes to a complete rest 5.5 s later. Find the distance that the car travels during braking. * A scalar is only a magnitude (length) (Example: Temperature, time, mass) * A vector has magnitude and direction (Example: displacement = 10 m East, Velocity= 50 mph west) * A vector will be symbolized by the “letter” with an arrow over it. The arrow indicates direction. * Vectors are equal if they have the same units, magnitude, and direction. * A vector can be moved anywhere parallel to itself. * To add vectors they must have the same units. * Tip-to -tail method put them head to tail and connect them so you end up with a triangle. * Parallelogram Method- (put them tail to tail) make vectors parallel and draw a line making 2 triangles * Resultant Vector * The resultant vector is the sum of a given set of vectors * Tip to tail- subtract by putting vector in the opposite direction * If you change the sign of a vector it is not the same vector. It is a new vector. * A – B does not equal B - A * A component is a part * It is useful to use rectangular components * These are the projections of the vector along the x- and y-axes * The x-component of a vector is the projection along the x-axis * The y-component of a vector is the projection along the y-axis * Then, The Pythagorean Theorem can only be used with right triangles! When its not 90 0 R 2 = A 2 + B 2 – 2AB(COSӨ) * Find the magnitude of the sum of a 15 km displacement and a 25 km displacement when the angle between them is 90 0 and when the angle between them is (a) Find the horizontal and vertical components of the 100m displacement of a superhero who flies from the top of a tall building at an angle of (b) (b) Suppose instead the superhero leaps in the other direction along a displacement vector B to the top of a flagpole where the displacement components are given B x = -25m and B Y =10.0m. Find the magnitude and direction of the displacement vector. * A GPS receiver indicates that your home is 15.0 km and 40 0 north of west, but the only path through the woods leads directly north. If you follow the path 5.0 km before it opens into a field, how far, and in what direction, would you have to walk to reach your home? * R= * Ө = 158’ Resolving a Vector Into Components +x +y A AxAx AyAy The horizontal, or x-component, of A is found by A x = A cos The vertical, or y-component, of A is found by A y = A sin By the Pythagorean Theorem, A x 2 + A y 2 = A 2 Every vector can be resolved using these formulas, such that A is the magnitude of A, and is the angle the vector makes with the x- axis. Each component must have the proper “sign” according to the quadrant the vector terminates in. Analytical Method of Vector Addition 1. Find the x- and y-components of each vector. A x = A cos =A y = A sin = B x = B cos = B y = B sin = C x = C cos =C y = C sin = 2. Sum the x-components. This is the x-component of the resultant. Rx =Rx = 3. Sum the y-components. This is the y-component of the resultant. R y = Pythagorean Theorem 4. Use the Pythagorean Theorem to find the magnitude of the resultant vector. R x 2 + R y 2 = R 2 * A roller coaster moves 215 ft horizontally and then rises 130 ft at an angle of above the horizontally. Next, it travels 125 ft at an angle of below the horizontal. Find the roller coaster’s displacement from its starting point to the end of this movement. * A quarter back takes the ball from the line of scrimmage, runs backwards for 15.0 yards, then runs sideways parallel to the line of scrimmage for 15.0 yards. At this point, he throws a 60.0 yard forward pass straight downfield, perpendicular to the line of scrimmage. What is the magnitude of the football’s resultant displacement? Vector Multiplication DOT PRODUCT scalar product A ∙ B A ∙ B = AB cosφ The product of the 2 vectors and the cosine of the angle between them A ∙ B = (A x i + A y j) (B x i + B y j) = A x B x i ∙ i + A x B y i ∙ j + A y B x j ∙ i + A y B y j ∙ j i.i = j.j = k.k = 1 and i.j = j.i = i.k = k.i = j.k = k.j = 0 A ∙ B = A x B x i ∙ i + A y B y j ∙ j With 3 dimension: A ∙ B = A x B x i ∙ i + A y B y j ∙ j + A z B z k ∙ k CROSS PRODUCT vector product A x B The product of the 2 vectors and the sine of the angle between them A x B is not the same as B x A … the direction is opposite i x i = j x j = k x k = 0 i x j = k j x k = I k x i = j a x b = (a 2 b 3 – a 3 b 2 ) i + (a 3 b 1 – a 1 b 3 ) j + (a 1 b 2 - a 2 b 1 ) k kij * Two vectors in component forms are written as : In evaluating the product, we make use of the fact that multiplication of the same unit vectors gives the value of 0, while multiplication of two different unit vectors result in remaining vector with appropriate sign. Finally, the vector product evaluates to vector terms : * Moving in the x and y direction * A projectile is an object shot through the air. This occurs in a parabola curve. Object dropped Object thrown up Object thrown at an angle projectile- any object that moves through the air or through space, acted on only by gravity (and air resistance, if any) The vertical acceleration of a projectile is caused by gravity, so a y = -9.8 m/s 2 Parabolic Trajectory * g remains constant (g= -9.8m/s 2) * a in the x direction is 0 because gravity is not acting on it. * Neglect air resistance * Neglect the effects of the earths rotation Projectiles launched horizontally To find how far the ball falls, you use the formula. y =v iy t + 1/2gt 2 1 st second- 5m After 2 seconds- 20m After 3 seconds- 45m The curved path of a projectile produced is a parabola (caused by both horizontal motion and vertical motion. It must accelerate only in the vertical direction) * The projectile will experience two: * Accelerations (a x = o and a Y = -9.8m/s 2 ) * Velocities * Displacements Upwardly Launched Projectiles When a projectile is launched at an upward angle, it follows a curved path and finally hits the ground because of gravity. The Vertical distance a cannonball falls below “imaginary path if no gravity” is the same vertical distance it would fall if it were dropped from rest & had been falling for the same amount of time. * Draw a free body diagram with a coordinate system. * Divide the information into x and y components * Look at your formulas and decided which one(s) to use. Objects that have been thrown will have a horizontal velocity that stays the same (no horizontal acceleration a x = 0m/s 2) So v fx =v ix in the second formula and third formulas under horizontal motion. (X) Horizontal (Y) Vertical x f- x i = v ix t + ½ a x t 2 y f -y i = v iy t + ½ a y t 2 v fx = v ix + a x t v fy = v iy + a y t v fx 2 - v ix 2 = 2a x (x f- x i ) v fy 2 = v iy 2 + 2a y (y f -y i ) This equation only works when y f and y i are both the same magnitude a = 2v iy t If a ball is thrown up in the air from a moving truck, where will it land? (Ignore air resistance) In front of the truck, behind the truck, or back in the truck Where will a package land if it is released from a plane? Behind the plane, in front of the plane below the plane What is the horizontal distance covered by an arrow that was shot through the air at a 60 0 angle with a velocity of 55 m/s? Given v = 55m/s v ix =27.5 m/s v iy =47.6m/s a x =0 a y =-9.8m/s 2 t=? d x =? Solve V xi = cos 60(55m/s)=27.5 m/s V iy = sin60(55m/s)=47.6m/s v fy =v iy +a y t d x = V ix t (we need time) m/s dydy V ix d x 0 = 47.6m/s m/s 2 t -47.6m/s = -9.8m/st 4.86 s =t d x = 27.5 m/s(9.7s) d x = m Total time in the air 4.86s x 2 = 9.7s Need to find time first! To find x dist: x = v 0x t * Frames of Reference Observers using different frames of reference may measure different displacements or velocities for an object in motion Relative Velocities the difference between the velocities relative to some common point * Relative Motion: Suppose you are on a train platform as the train rushes through the station without stopping. Someone on board the train is pitching a ball, throwing it has hard as they can towards the back of the train. If the train’s speed is 60 mph and the pitcher is capable of throwing at 60 mph, what is the speed of the ball as you see it from the platform? * A boat heading due north crosses a river with a speed of 10.0 km/h. The water in the river has a speed of 5.0 km/h due east. Moving frame of reference In general we have (a)Determine the velocity of the boat. (b)If the river is 3.0 km wide how long does it take to cross it? Conservation of Linear Momentum Completely Inelastic Collision Velocity of Center of Mass
What is coordinate geometry? In mathematics each and every point or any figure plane or anything has a specific position in space. To locate a point we require proper coordinates of the point. And these coordinate represent the position of the point. Here we will learn about the geometries through the coordinates. The determination of the coordinates of any figure, plane or any point in space and application of the various geometries on these figures is called as Coordinate Geometry. Below are some basics related to Coordinate Geometry: Distance Formula x-coordinate, or abscissa. y-coordinate, or ordinate. (x, 0), and of a point on the y-axis are of the form (0, y). Let us consider two points in the Cartesian plane P and Q. The coordinates of P(x1,y1) and Q(x2,y2). Then the distance between the two points P and Q will be given by the Distance Formula PQ =√ [(x2-x1 )2 + (y2-y1)2] OR (PQ)2 = (x2-x1 )2 + (y2-y1)2 x-coordinate, or abscissa. y-coordinate, or ordinate. (x, 0), and of a point on the y-axis are of the form (0, y). Let us consider two points in the Cartesian plane P and Q. The coordinates of P(x1,y1) and Q(x2,y2). Then the distance between the two points P and Q will be given by the Distance Formula PQ =√ [(x2-x1 )2 + (y2-y1)2] OR (PQ)2 = (x2-x1 )2 + (y2-y1)2 Solution: Since the point is on X axis let us assume it’s coordinates is (x,0). Therefore, on using the distance formula we get, (2-x)2 + (-5-0)2 = (-2-x)2+ (9-0)2 (On squaring both the sides) 4+x2-4x + 25 = 4+x2+4 x + 81 8x = 56 and hence, x = 7. Therefore, the point (7,0) is the point on X axis equidistant from the above two points. Let us suppose two points A(x1,y1 ) and B(x2,y2) on the Cartesian plane. If any point P(x,y) divides the line segment AB in the ratio m:n then the coordinates of P(x,y) cab be find using the section formula: When division is internal: x = (mx2+ nx1 ) / (m+n) and y = (my2+ ny1 ) / (m+n) When division is external: x = (mx2- nx1 ) / (m-n) and y = (my2-ny1 ) / (m-n) Here an important point is to be remembered that if P is the mid-point of the line segment AB, then the value of both m and n will be that is the ratio will be 1:1 Example 2: Find the coordinates of the point which divides the line segment AB in half where A(-2,2) and B(2,8). Solution: Let us assume the coordinates of the point to be (x,y) and here m:n = 1:1. So by using the Section Formula we get: x = [(1 x 2) + (1 x -2)] / (1+1) and y = [ (1 x 8) +(1 x2)] / (1+1) x = 0 and y = 5 Hence the point (0,5) divides the line AB into half. Area of Triangle We all know the very basic formula to calculate the area of a triangle whose bas e and height is given by: Area = x Base x Height We also know the other method to calculate the area of the triangle by using the Heron’s Formula. But here in coordinate geometry we are going to learn another formula or way to calculate the area of a triangle: Let us suppose three points in the Cartesian plane A(x1,y1 ) B(x2,y2) and C(x3,y3) . Hence the area of the triangle ABC formed by joining these three points will be given by: Area = ½ [ x1(y2 -y3) + x2(y3 -y1) + x3(y1 –y2)] Example 3: Find the area of the triangle with vertices (1,1) (2,2) and (3,3). Solution: By using the formula we get Area = ½[1(2 – 3) + 2(3-1) + 3(1-2)] = 0. Here the area of triangle is 0, which means these three do not form a triangle which means they are collinear. Hence we can check whether three points are collinear or not bye finding the area of the triangle and if it comes to be 0 then they are collinear otherwise not. Q1) Find the distance between two points A(4,5) and B(5,-8). Q2) Show that the points A(0,-1), B(-2,3), C(6,7), D(8,3) are the vertices of a square. Q3) Find the point on y axis which is equidistant from the point (5,5) and (3,-2). Q4) Find the coordinates of the point P which divides the line segment A(3,4) and B(8,2) in the ratio 2:3. Q5) Find the area of the triangle with vertices (5,4) , (7,1) and (4,2). - Distance formula can be used to calculate the distance between two points on a Cartesian plane. - Section Formula is used to find the division ratio which a point makes on any line segment. - If we have given three points then we can also calculate the area of the triangle formed. - If the area comes out to be 0 we can predict that these three points are collinear. This helps us a lot in further investigations of the figures which you will learn in higher classes.
Definition and Principles of Communication Communication – as we grow up, our family, then society –teaches us how to speak then read and write. Through this practices, communication became integrated in our lives. It then became a basic human activity that enable us to connect with each other (Langley, 2006). Communication – is a complex process. • To be able to understand how it happens, we would need to dissect its characteristics and elements. Mark Twain – sums up communication nicely, “The difference between a good word and the right word is the same as the difference between a lightning bug and lightning.” (Dean Brenner, Marni Lane). Learning how to be good communicator opens a lot of opportunity for us in relationships, career, and fulfilling our goals and dreams. Communication started years ago with some of our ancestors surviving through drawings, sounds, and gestures. Along with the evolution of civilizations various mediums of communication also emerged. Through time, technology became integrated in our language processes and description. Communication, originated in the Latin word communicare – meaning to share, unite or join, can be defined as the process by which people share ideas or thoughts which can be understood by another through a chosen medium. These said medium can either be verbal and non-verbal channels. In a nutshell, it is to send and receive messages using a channel. Principles of Communication Before we delve in to oral communication, let us first through the principles of communication. Knowing these would make it easier for us to understand how to properly and adequately communicate with others. Definition and Principles of Communication The process of communication makes you either the sender or receiver. By taking one of the roles above, you will activate your schemata, background, or experiences. Schemata or schemas provide a basis on how we relate to ideas concepts, and events based on past experiences. Prior experiences give meaning to conveyed messages. Having no previous experience nor ides will only resort pronouncing or sounding the words. No experience of any communicative act will trigger views, feelings or ideas. 2. Interpretive act Communication is an interpretative act. The exact meaning of the message being transmitted is known only by the sender or speaker. The sender has the absolute idea of what the meaning of the message is. The receiver can only interpret, guess or infer based on how it appeals to his/her sense of hearing. 3. Communication is Active, forceful and powerful In a communicative act, there will always be different effects to the participants. Any message conveyed may have various interpretations because of cultural, ideological, and environmental factors. What is rude in one culture can be perceived as something acceptable in another. For example, in western countries, calling an adult not related to you by their first name is acceptable; yet in the Philippines, this is rude. You need to use their titles or (i.e. Attorney, Miss, Mrs., teacher, etc.) general terms showing respect (i.e. auntie, kuya, Tito, etc.) when you call refer to them or call them by their name. 4. Communication is Symbolic Signs, symbols, letters, graphs, pictures, etc. are concrete objects that stands for represents an idea. Non-verbal communication, on the other hand, expresses ideas through gestures, voice pitch, posture, facial expression, time, and space. 5. Communication always result in something Two or more persons usually participate in any communicative act. One sends the message while another reacts to the message. As a transactional process, communication creates an effect on the involved parties. It will elicit either a verbal or non-verbal response. 6. Communication is irreversible The adage “Think you click” suggests that you go over idea before posting it on your social networks or messages. The same concept should also be applied to the other form of communication. With Oral communications, the moment you utter the words to convey your message already creates an impact to listeners. Attempts to reverse, restore, or recreate the original mood or setting before these words were spoken would be irrevocable. The discipline of mulling over your thoughts before translating them into words can help avoid any instances which may cause problems directly or indirectly. 7. Communication is contextual Ideas exchanges between the sender and the receiver involves communication setting like time, occasion, purpose or manner of communication. Consider cultural differences when communicating to avoid any negative impact due to the effects of the factors above. 8. Communication is Progressive Communication is a process you learn from birth and continues to evolve as time passes by. Communicative competence is not learned in one sitting. You go through different levels as you strive to improve your abilities to interact with other people. 9. Communication is a process Several stages of communication take place when people convey and exchange ideas with one another. Each stage differs from other. Elements or components work in a coordinated manner the complete the process. 10. Communication is ethical A Communicative event is expected to follow rules, values, and beliefs agreed upon by members of society. These standards determine which cultural group you belong to. Going against these conventions make interaction with others wrong or unethical. E.g.: In Russia Don’t give a thumbs-up sign-in and other hand gesture facts. 11. Communication is Influenced by technology and media Communication in the current age of technology is characterized by the instant, real-time exchange of knowledge, messages, and services. The rapid speed of communication influences how people construct their messages and what platform the use to send their messages. Why we need to study Oral Communication? Oral communication competence – both in listening and speaking – is mandatory to the success of a person academically, professionally, and in their personal lives. Poor listening skills lead to people being unable to absorb and understand instructions. This issue intensifies as they respond incorrectly or inappropriately because of deplorable speaking skills. Being able to articulate your ideas and opinions adds value to one’s self. Skills in oral communication transcends the academic and professional setting. Competence in listening and speaking can also contribute to personal fulfillment. • Communicare – to join, share, receive or divide with/ out • Contextual – Depending on or relating to circumstances that form a setting of an event, idea of statement to clarify a meaning. • Ethical – Pertaining to moral; To what is right and wrong; conforms to imposed standards or rules and regulations • Process – A series of steps or activities that leads to a result • Progressive – Continuous improvement. • Schemata – A mental framework of preconceived ideas that are based on experiences and interactions which shape how the world is seen and understood. • Scrutinize – To examine, inspect thoroughly. Diaz, Rafaela Hernandez. (2014). Speech and Oral Communication for College Students, Revised Edition. Quezon City: National Book Store Kinds of Communication Learning these kinds of communication will greatly aid you in becoming more aware of how to create more emphasis or to tone down when transmitting your messages you receive. To get an overview of the two main kinds of communication, refers to the illustration below. Non-verbal communication transmits messages without relying on language or speech. It uses audio signals or visual signals to communicate a message. Kinesics is the language of the body. Notice how our body movements and facial expressions add visuals. You may know a friend or an acquaintance who is entertaining to watch when telling a story because of the gestures or facial twitches. This friend is practicing this form of non-verbal communication. Proxemics is the language of space. Distance and space are devices that can also be used to convey meaning. The relationship of people can be determine by observing the distance they maintain from each other. Personal Space Distances Intimate Zone <8’’ Personal Zone 8’’-5ft Social Zone 5-10ft Public Zone 10-25ft However, one must also consider other factors when deciphering the relationship between people from other cultures. For example, Americans are naturally more aggressive in nature when it comes to positioning themselves when talking to others, on the contrary, and English person will maintain a relatively farther distance as compared to the American. Haptics is the language of touch. This nonverbal communication reveals feelings and culture. If you have ever heard of the saying mother’s touch, it illustrates how someone can feel loved just through touching. Another example is when friends bump fists to show that they acknowledge another person’s idea or they absolutely agree on something. At work, it’s also important to remember that there are rules to follow when communicating with your superiors or colleagues. There is such thing as Professional-functional touch, which is used to communicate emotions of manager to their team members. Chronemics is the language in time. This shows the interrelatedness of time and communication. A way in which one perceives and values time, structures time, and reacts to time frame communication. Across cultures, time perception plays a large role in the nonverbal communication process. An example can be what they call Filipino time. During events, Filipinos allegedly come at least an hour or two late, thus, foreigners usually complain about the practice of Filipino time since foreigners, especially Americans, usually arrive on time. This goes to show that Filipinos and foreigners may have a different understanding of what “on time” really means. The language of look-appearance, The way a person looks reflects on his/her status or position, mood, culture, taste, and grooming. As with working, certain companies require a specific look amongst their employees, say a brand ambassador for make-up brand versus a brand ambassador for a laundry soap. Artifactual communication is the language of objects. “Artifactual communication is the aesthetic coding and decoding of symbols or representations. The coding and decoding is subjectively interpreted with culture in mind in order to establish cautious generalizations) about individual who adorns themselves with an artifacts. Artifacts and the representation, merely approximations. Objects, colors, body modifications, and environments make up criteria that may constitute artifacts. (2002. Rudrow, K.) Paralanguage refers to various nonverbal cues we can hear in our voice. This elements are the following: a. Vocal Quality – refers to the how pleasant or unpleasant a person’s voice sounds. Voice quality is usually referred to as the timbre or tone color. As with communicating, emotions play a role. b. Pitch – lowness or highness of tone. People vary in the pitch of their voice although it can be observed that nervousness, fright, and sometimes excitement may raise the pitch of the voice, on the other hand, sadness or disappointment makes the pitch lower (2008, Flores and Lopez). c. Tempo – how fast or slow someone speaks. d. Volume – describes the force of the voice or how loud or soft it goes. e. Junctures – breaks or pauses applied at the end of utterances or between thoughts. Verbal communication uses written or spoken language to transmit information or messages. It involves sound production; utterance of words phrases and sentences through speech. There are five basic features of human language: 1. Phonology – studies the system of sound in language including how sounds is organized and structured to convey meaning. 2. Semantics – deal with meaning of words, phrases, and sentences in a language. Semantics “explains different connotations (associated meaning) and denotations (dictionary meaning words)”. 3. Morphology – studies the information of words. Words can be divided into two categories: content words and function words. 4. Syntax – is when one studies how words are put together to form grammatically correct sentences in language. 5. Pragmatics – touches on how language is used. It is how words can be interpreted in various scenarios. How many basic features does the human language have? 5 from the exam. But it should be 13 normally. I made mistakes here. Process and Elements of Communication To be able to understand how communication happens, always remember that communication is a two-way process. Always remember that for every message sent to the receiver, we must expect a feedback or response either through non-verbal or verbal medium. Process of Communication The communication process pertains to the steps through which communication takes place between the sender and the receiver in an under stable manner. It is dynamic in nature rather than a static occurrence. The diagram above shows the communication process and the details are as follow: Elements of Communication The sender (source) is an individual, group, or organization who initiates the communication. All communication begins with the sender. The sender is the source of information for a target receiver or audience. The first step the sender does involves the encoding process. This process translates the ideas or concepts into the coded message that will be communicated. The symbols can take on different forms like languages, words, or gestures. The message is the idea or information being conveyed by the sender to the receiver or listener. It includes content, structure, and style. To start sending the message, the sender uses a channel which is also known as a medium. It is the method used to deliver the message. Most channels are either oral or written but, as technology evolves, visual channels are becoming more common. Usual channels include the television, radio, telephone/mobile phone, etc. The message begins with the decoding stage when the appropriate channel is selected. Decoding is executed by the receiver. Once the message is received and reviewed, it is sent to the brain to be interpreted to appoint meaning to it. Successful communication occurs when the receiver correctly interprets the sender’s message. The receiver is the individual or individuals to whom the message is directed. All interpretations by the receiver are influenced by their experiences, attitudes, knowledge, skills, perceptions, and culture. Picture the next scene. Shelly is a shy student who says little inside the classroom. She may feel a bit nervous when her teacher asked her. Feedback is a key element of the communication process since it allows the sender to review the effectiveness of the message. It may be in the form of a spoken comment, along sigh, a written message, a smile, or some other action. Without a feedback, the sender cannot confirm that the receiver has interpreted the message correctly. Certain barriers are present throughout the communication process. Some usual barriers include the use of an inappropriate channel, incorrect grammar, provocative words, words that conflict with body language, and technical jargon. Noise is also another common barrier. Noise can occur during any stage of the process. Noise is essentially anything that distorts a message by interfering with the communication process. Noise can take many forms, including a radio playing in the background, another person trying to enter your conversation, and any other distractions that prevent the receiver from paying attention. Forms of Communication When we talk about communication, we usually think of sending messages to another person; however, communicating with one’s self is also possible. It is the first level of communication we experience. The prefix intra means “within”. We experience this kind of communication when we meditate, analyze, think, study, and talk to one’s self. You talk to yourself when you are about to make a decision and you argue or try to persuade yourself. Sometimes you also do this when you’re rehearsing a message you intend to send to others.Talking to yourself is normal and necessary. You are simply engaging in intrapersonal communication. The study of this form of communication is not that popular; yet, awareness of this form of communication can greatly enhance the quality of life. 2. Dyadic Communication – is when two people communicate. Communication may take place through the phone, SMS messaging or face-to-face such as interviews, dialogues or ordinary conversations. It is through interpersonal communication that you establish, maintain, restore and/or end relationships. At this level of communication, you learn about others and hopefully, you learn about yourself as well. 3. Small Group Communication – happens when more than three people are involved. This is simply an enlarged group which usually happens to solve problems. Examples of this are conferences, business meetings, symposiums and team meetings inside the classroom. 4. Public Communication – happens between one and several other people. This large group type of communication usually happens in public speaking. In public speaking, the speaker addresses the audience to persuade, inform, entertain, or do all of three. Just like the other forms, this kind of communication requires knowledge and good communication skills from the speaker. 5. Mass Communication – happens when you communicate to an extremely large audience. It is usually mediated by audio and/or visual means. The purposes are to entertain, persuade and/or inform. Media and technology are used to reach a large audience in a variety of ways today. Examples of mass communication media are television, radio, newspapers, recordings, movies, magazines, comics, billboards, computers, and the internet. As seen in the image above, the newscaster is communicating to his audience via the radio, television, and YouTube. The process of communication can be studied through the communication models. These communication models are conceptual models. Conceptual models aid in simplifying the explanation of how something works. As mentioned in the previous module, communication is a process and to be able to understand how the process works, we will utilize the communication models below. Linear Communication Models The linear model was the first kind of model that experts have made to understand the process of communication. This kind of model has improved and has been updated through the years. Characteristics of the linear model are the following: 1. Unidirectional – The linear model is a unidirectional model. It is a one-way communication. The speaker sends messages to the receiver with or without effect. Senders can only transmit messages while receivers can only receive the messages and no feedback is expected to happen. Communication may not happen in turns – thus, the lack of feedback is seen in this model. This applies to mass communication. 2. Simple – This model presents a simple communication act. If you look at the figure below, you will observe that it doesn’t look like a process. Instead, it looks like the transmission of one-way causality, which is conveying of only a cause and effect. There is only the beginning and the end and there is no interchanging of roles between the sender and receiver. 3. Persuasion not Mutual understanding – This model promotes one-way direction of communication which promotes advice and influence rather than understanding from both receiver and sender. Again, the emphasis is on the lack of feedback. 4. Values psychological over social effects: This model focuses more on the psychological effects (such as understanding the messages) rather than the social effects (like building the relationship amongst the communicators). There is no assurance that the message was effective because the receiver is only concerned with the delivery of the message and will now know the effect on the receiver/s because of the lack of feedback. The Shannon-Weaver model, also known as the Information Theory model, was primarily developed to illustrate transmission of electronic information back in 1948. This conceptual model has six elements: a. Information source / Sender: The Sender / Information Source chooses the message /s to be communicated to the receiver and the channel to use and sends the message. b. Transmitter / Encoder: This changes the message into a signal then sends it over the communication channel c. Channel – This is the medium the sender uses to transmit the message /s d. Receptor / Decoder – This does the opposite of the Encoder. It decodes the message sent over the channel. e. Receiver / Destination – The receiver is the person or group of people who must get the message. The receiver can then provide a feedback which will then reverse their roles. f. Noise – Noise is a kind of disturbance coming from people, the environment, internal knowledge, beliefs, etc. which hinders the receiver from getting and understanding the message. An example how this model explains this process: The sender can be you and the receiver can be your friend. The channel you will use is your mobile network. The encoder is your mobile network company and decoder is the receiver’s smartphone. When you try to send SMS message to your friend and your friend receives only parts of the message due to disruption of mobile signal, that is the noise. B. Berlo’s SMCR model David Berlo conceptualized the Sender-Message-Channel-Receiver (SMCR) model during the sixties. He postulated this model from the Shannon-Weaver Information Theory model and emphasized on the encoding and decoding parts of the process. Berlo’s model has 4 components: Sender, Message, Channel, and Receiver. He stated that each of the components are affected by many factors. a. Communication Skills – of sender and receiver plays significant role in the process. Communication skills include writing, speaking, listening, presenting, reading, etc. If the sender is not good in communicating, the message might be lost in the process of transmittal. b. Attitudes – The attitude of the sender and receiver also plays a part in the process. The sender’s attitude towards others, himself / herself, and the environment cab affect the meaning of the message. c. Knowledge – Knowledge of the sender and receiver on the subject matter makes the sender and effective communicator. If the sender is familiar with the subject or topic at hand, it adds value and impact to the message. d. Social System - Belief, religions, social status, values and other social factors can affect how the sender communicates the message and how the receiver understands it. The situation and place or environment where it happens are also part of this element. e. Culture – Cultural difference can make it difficult to communicate. Some culture may accept something while the other may find it offensive. Culture may also be under social systems. a. Content – the content is the entirety of the message – it covers the beginning until the end. b. Elements – These are what comprise the message. This includes gestures, body language, language, Haptics, etc. Content is accompanied by elements c. Treatment is how the message is conveyed. It is how you package your message. d. Structure refers to the arrangement of elements in the content of the message. Arrangement of elements affects the affectivity and impact of the message. e. Code – is the form in which the message will be sent. Message can be sent in the form of the videos, spoken word, text, culture etc. Improper use of a code may still lead to miscommunication. 3. Channel – simply means the use of the five senses. a.Hearing is when you use your ears to get the message. b. Seeing when eyes are used, the sense of sight is activated. c.Touching communication through touching is also possible. d. Smelling smell can also be used as a channel for communication. The smell of something burning can communicate the danger of fire nearby. e. Taste can also be channel of communication. The tongue has millions of tastes buds that can be used to decipher. 4. Receiver – the receiver and the sender have the same elements. You can refer to the description above. a. Communication Skills d. Social System Transactional Communication Models The transactional models are communication models that illustrate how the sender and receiver take turns in conveying and receiver messages. We call the sender and receiver “communicators”. Their roles are reversed each time sending and receiving messages occur at the same time. For this kind of communication model we will scrutinize the Helix model. Dance’s Helix Model The Helical model of communication was conceptualized in 1967 by Frank Dance. A helix is “an object having a three-dimensional shape like that of a wire wound uniformly around a cylinder or cone” like a corkscrew or coil that grows bigger and bigger as it moves up. The Helix communication model illustrates how the development and growth communication or communicative actions will always be based on previous experiences or behaviors. “That communication while moving forward is at the same time coming back to itself and being affected by its past behavior…” (Dance, 1967). This model shows how the knowledge base of a person deepens and expands throughout life. This model also shows that a person’s understanding of a message or thought is influenced by external and internal factors that are learned throughout life. To better illustrate how this works, refer to the illustration and example below. As babies, the only way we can communicate was through crying. Babies cry when they are hungry, scared, uncomfortable or startled. When babies cry, their parents will give them what they want – milk, a change of diapers, or be rocked to sleep. As they grow up they continue to use crying as a language in their toddler years but they also learn how to speak during these years. So aside from crying to get what they want, they also communicate using the vocabulary they learn. As they grow older, their vocabulary increases and they learn to utilize not only words but non-verbal cues to communicate what they want or need to others. This build-up of experiences to send and receive messages can be explained by the helical model of communication. Interactive Communication Model Interactive communication model, also known as convergence model, emphasizes the coding and decoding components of the process. It also focuses on the cycle of message exchanges between the sender and receiver. The source of the message will need to encode the message while the receiver will need to decode the message. These messages will always be affected by the “field of experience” – these are communication patterns rising from the factors such as psychological, social, cultural, societal or situational experiences or gained knowledge. This model also takes into consideration noise as a form of barrier in communication. Schramm’s communication model is an example of an interactive communication model. Schramm’s Communication Model Schramm’s model has the following components: a. Sender (transmitter) – sends the message b. Encoder – converts the message into codes before sending c. Decoder – gets the encoded message then converts it into the language understandable by the receiver d. Interpreter – tries to understand and analyze the message. Message is considered received after interpretation is done and message is understood. Interpreter and receiver are the same. e. Receiver – gets the message. Decoding and interpreting is also part of his/her role f. Message – data sent by the sender and information that the receiver gets. g. Feedback – process where in receiver responds to the received message h. Medium or media – channel used to send the message. i. Noise – interference disruptions during the process. This is also created when the intended meaning sent by the sender is different from what was interpreted by the receiver. j. *Field of experience – patterns which affect the communication process. This can be from society, culture, situations, psychological or sociological events or experiences of the sender and receiver. Schramm’s communication model states the communication is a never ending process. This model emphasizes the encoding and decoding parts of the process. It suggests that the role of the receiver and sender will eventually switch each other as they continue the exchange of the messages. Feedback is seen as an important part of this model to ensure that communication takes place. The field of experience affects the messages being exchanged. It means that the background of the persons involved in communication process plays a role in how they interpret the messages received or how they encode the messages they will be sending.This model can be used in Interpersonal and Intrapersonal communication. A simple example of how this happens in real life: : You are the sender and your friend is the receiver. The communication is initiated by the sender. The message is first processed in the sender’s brain then sent to the mount to be transmitted. The message is then delivered to your friend through language, your voice, symbols, and non-verbal cues. While sharing the message you may encounter disruptions or noise. Your friend will in turn try to understand the message and will react or give feedback accordingly. This process repeats until one of them ends process. Conceptual Models – A representation of a system, concept or abstract idea which can be help in making it understandable and easier to simulate or imitate. Helix – a smooth curve just like spring which goes upwards also comes downwards. The rise of the internet and the improvement of transportation and technology made it possible for us to get know our fellow humans from other countries. We are now living in a period where traveling from one place to another is easier than before and communication has become swift that we have found ways to work with other people from different time zones and regions. As our world becomes smaller in a sense that we get to touch base faster and more frequently than before, we will then be more exposed to various cultures from different points in the world. Culture is the accumulated learned behavior of a group of people. It is the way of life of people that they accept without thinking and it is passed along from generation to another through imitation and communication. Culture doesn’t have to be from another country, it can also be observed from people living in the same country but from different regions or states or even groups of people coming from different schools, religion or even family. Intercultural communication involves communicating with another person or group of people coming from a background or community who does not share your beliefs, tradition, symbolism, or values. This kind of communication should be done in mindful way to be able to engage each other properly and effectively. Aspects of Intercultural communication There are five basic elements or aspects to remember when participating in an intercultural or cross-cultural communication. These elements are: 1. Cultural Identity – As mentioned earlier, culture is the sum of the beliefs, traditions, values, symbols and practices of a group of people (Mulvaney, 2005). Different culture can be seen within a community; say, culture in rural areas versus urban areas, We can even observe different culture from another family who lives next door to us. An example of culture difference: Chinese families teach children early on the value of handling money well as they want their children to focus more on business, math’s, and sciences. Also, it is part of their culture to be transparent when it comes to money matters. (Lee-Chua, 2012) (Li, 2008). On the other hand, Filipinos shy away from talking about money with their family as it is taboo. Money is often a topic avoided as it brings misunderstanding. (Rapisura, 2016). 2. Gender role – Gender is a social construct and is not synonymous to sex, which refers to the anatomical differences between male and female. Gender roles are learned and taught by culture. A culture’s language reflects the social roles of men and women. An example can be calling an assertive girl “bossy” and calling an assertive boy “a leader”. Immediately you can observe the negative connotation of term “bossy” – that is usually used to describe women in a patriarchal society. Male language is often direct, commanding, and assertive while female language should be polite, collaborative and nurturing. 3. Age identity – This refers not only to their biological age but it is also about how they think and feel about themselves as they age. Age identity influences one’s self-image, language use, personality, attitude and communication with others. We consider that some children can be mature and not all adults are responsible and matured. We may have dealt with cases wherein old people usually generalize that teenagers as brash and impulsive even if this is not true. Moreover, older people specially those have reached their 50s to be fragile and slow. In other instances, advertisements use-span-related role identities can be used to trigger affect to a certain period. An example can be the infamous McDonald’s commercial aptly titled, “Lolo” (Notz, 2002). This commercial showed the relationship of “Karen” the granddaughter and her grandfather who were eating at McDonald’s. This commercial became popular as it showcases the relationship of the brand with the relationship of the two characters. 4. Social Status. Social Status is determined and assigned according to income, titles possessions, etc. Social classes in other cultures also differ from one another. General speaking, the lower classes usually work blue collar jobs or manage their own businesses. Perception of a person’s status affects how the people around her communicate. In the Philippines, the use of the English language, with the slight twang, projects an elite social status. As Tolentino (2011) stated in an interview with The Guidon, a student publication, English proficiency of Ateneans is”…a marker of a kind of elitism in the country”. Showing this kind of language proficiency insinuates a wealthy background even if the student comes from the middle or lower classes and subsists on scholarships. 5. Religion. Religion is defined by Geertz, an anthropologist, as “ (1) a system which acts to (2) establish powerful, pervasive, and long-lasting moods and motivations in men by (3) formulating conceptions of a general order of existence and (4) clothing these conceptions with such an aura of factuality that (5) the moods and motivations seem uniquely realistic.” Religious identity is when someone sees themselves as a member of a religious group and may be active or inactive in practicing their rituals and customs. Religion plays a big part in the lifestyle of a person and seen as sacred and important. Thus, religious issues and prejudices should be handled respectfully. Why is it important to learn more about cross-cultural communication? At this day and age travel has become easier and the internet have made cultures more exposed and accessible. To be able to communicate with another person from another country, religion, social status, and gender means to be able to have a smooth and harmonious relationship. Problems in intercultural communication To be able to avoid intercultural miscommunication, one must be able to identify first the problems that need to be addressed. The following are the problems that usually arise in intercultural communication: 1. Ethnocentrism is the term applied to ethnic bias. This term comes from the word “ethnos” meaning nation and the word “center”. This is the conscious or unconscious worldview coming from a person’s own perspective which establishes an archetype or rating of other groups in reference to the ideal of his or her own group. This kind of worldview often results to the inadequate understanding of other cultures and judging other groups according to the preference of the group they belong in which often leads to assertion of the inherent inferiority of other groups. “Tunnel vision” is the idiom used for ethnocentrism. An example of ethnocentrism in the Philippines can be observed during the 2017 Bar exam results. When the results of the bar exam were posted online on social media, the comments section became a platform where people questioned the results, some even saying that they do not know the schools where the top examinees came from since these schools were not from Metro Manila. One netizen even questioned the integrity of a Dumaguete based law school. This behavior clearly shows how Manilenos see provincial schools and students subpar to those coming from NCR. They exhibit the superiority of those coming from Manila. 2. Stereotyping is the generation “made about a group of people underestimating their culture” (Baraceros and Lintao). Stereotyping assumes members of a group of people share the same characteristics. When one stereotypes, you judge how person behaves or looks based on what you believe about the group where they belong. One of the usual stereotyping we hear are about women. Women are still being boxed by society when it comes to reading children. It is expected that women should have children in a certain age range while men are given the chance to do whatever they want until whatever age. That women must always prioritize building a family rather than building their own career. This stereotype is still rampant until now even if a lot of groups around the world have strived for equality in gender roles. Another kind of stereotype can be seen in local television series. Usually women protagonists have long straight hair while antagonist women have short or curly/wavy hair. Another thing to observe is how rich families are usually seen in formal clothes even if they’re inside their house and will not be attending any formal event. These stereotypes are very far from real rich families who dress simply when going out or even dress in plain house clothes when they are inside their house. 3. Prejudice is when one has a negative preconceived notion, feeling, or attitude against a cultural group. These assumptions are often made even if there is a little or no interaction with this said group at all. An example can be the prejudice towards Muslims. In Manila, it can be observed that Catholics are wary of Muslims. The author has observed how their neighbors are always hesitant or reserved when interacting with their Muslim neighbor. Rarely did anyone talk to their Muslim neighbors during events or gatherings. This prejudice usually comes from how Muslims are portrayed by media thus when one encounters a Muslim in society, their prejudice for this certain group kicks in. How to Avoid intercultural miscommunication? With these three problems in mind, how exactly do we ensure that we communicate effectively and properly with people from other cultures? 1. Delay attributing meaning – Non-verbal communication plays a big role in avoiding intercultural communication breakdown. Avoid interpreting non-verbal signals made by a person from another culture until you have read and studied their culture adequately. When visiting another place, say a province or country, study their culture before the trip and try to learn more about their non-verbal cues. An example can be when attending church service with Iglesia ni Kristo. Men and women cannot sit together in one side even if they are already married. Women are also expected to wear dress or skirt during service. Another example can be you give your business card in Japan. In Japan, you are expected to hold your business card with both hands and to bow when you give it to someone. The business card must be turned towards the receiver. The receiver, on the other hand, must also receive the business card with both hands with head bowed slightly and must display the card for the duration of the meeting. 2. Develop awareness of your non-verbal communication – Be mindful of how you use your face, gestures, body language, and voice when communicating. Understanding how certain cultures react to certain body language can smoothen and make the experience with other cultures pleasurable. Be aware of your voice, of your fidgeting or even the space you allot when communicating with people from other cultures. A thumbs up sign in Filipino means you “approve” or you’re okay or you agree. While in other countries such as Middle East the thumbs up sign is almost equivalent to giving someone the middle finger. 3. Check whether non-verbal messages correspond to verbal messages. It is given that you will not be able to understand the language of another group or culture immediately so you have to be very observant and persistent in listening when you communicate with them. Sometimes misinterpretation can happen when the verbal and non-verbal messages come in conflict with each other. Paying attention and being very mindful of how a person speaks or reacts can give you clues if you really are communicating with each other. Blue collar jobs – Work that requires manual labor Identity – A category or social group which is assumed to insinuate sameness or connection, such as gender, age, or nationality, or nationality, or to a large scale a sense of self to which the specific identity categorizes are assumed to contribute. White Collar Jobs – Work that is done inside an office or cubicle or an administrative job Week 7 Learning Activity Team collaboration inside the classroom is what form of communication? Group Communication A problem solving meeting belongs to what form of communication? Group Communication Listening to Spotify ads shows what form of communication? Mass Communication How many forms of communication are there? 5 You are trying to decide if you want to take Medicine or Engineering, what kind of communication is happening? Intrapersonal Communication Listening – is a skill usually taken for granted especially since we normally consider ourselves to be good listeners already. Just like eloquence, listening is important achieving effective communication. Thus, it is crucial to develop this skill. Listening helps us stay focused on the message being sent, aids in comprehension, and may improve or at the least maintain our relationships with other people. Listening is the most basic kind of communicating activity that we do daily. Ang (2009), a researcher, said that we spend 45% of our time listening and that 90% of the information we gather are retained and received through our eyes and ears. It was stated in studies that “the level of our listening effectiveness is only about 50%” which means that we do not receive and understand the entirety of the message. “But” you may argue, “I heard what my teacher said”. There is a difference between listening and hearing. Hearing is when we refer to the plain act of receiving sounds. While listening is a process where we use our sensory experiences or our background knowledge to recognize, interpret spoken or verbal language to satisfy a need. So, when you say that you “heard” your teacher it means you just received the sound of her voice but if you really understood and put meaning to the content of the sound she made, that is when you can say you “listened” to your teacher. The very main goal of listening is get what the speaker has to say about a subject; however, listening is get what the speaker has to say about a subject; however, listening should not just be focused on the content. Listening must also be about structure, or organization of the topic (Galero Tejero). Hearing is a natural process (psychological) of receiving aural and visual stimuli Hearing is the passive phase of speech reception. Good hearing is needed for effective listening. Good hearing is NOT synonymous to good listening. Listening is more than hearing; it is a SKILL that needs to be developed. Listening is the active phase of speech reception. Listening is a sub-process of communication that involves not only hearing Listening constitutes understanding and remembering. We are equipped with the sense of hearing; however, even if we are exposed to the same sounds, we attach different meanings to them. This is because we are individually different from each other. Each one of us is different in terms of character traits, gender, cultural knowledge, age, physical make up, and so on. These differences are the reasons why various meaning can be assigned to a sound. To be able to be a good communicator, you must also be aware of these different reasons why a sound can have different meanings to different people. Understanding much about listening can often help in building social relationships, determine traits of people, perform professional duties, and many more. Models of Listening 1. Active listening requires effort and concentration on the listener’s part. Listening to lectures, discussions, or conferences. This action demands your full attention and concentration so you can understand the message. a. In critical or persuasive listening, it is important to understand the message based on evidence or proof presented by the speaker/ sender to prove their point. With this kind of listening, it is important to determine the differences of ideas to look in to the condition or state of the object of the talk and other aspects in order to get more information before deciding if you agree or disagree with them. This kind of listening leads to reflective thinking, thinking that requires to inquire and investigative on the values, reason of things before considering them valuable or meritorious. Reflective thinking hinders you from automatically agreeing with the speaker. b. In discriminative or instructional listening we “listen to derive information, facts, ideas and principles.” This kind of listening is used in class discussions, business meetings and conferences where you hear people discuss their observations, opinions, feelings, and thought about the things that interest them. With this kind of listening, it is important to determine the differences of ideas, to look in to the condition or state of the object of the talk in order to get instructions or information. 2. Passive Listening does not rely on focus or effort. This usually happens when you do something else while listening. Simultaneously listening to two sounds divide your attention which leads to superficial or nonchalant listening. This also happens when you listen to while away your time or when you try to ease up from stress. An example can be listening to the radio while you talk to a parent. a. Emphatic or therapeutic listening: This kind of listening is something that you do to relieve yourself from anxiety and tension. You listen as an output of pent-up emotions. This kind of listening does not necessarily have to be something you do to analyze, appreciate or judge. b. In appreciative listening or emotional, we “listen for pleasure, entertainment or enjoyment.” The moment you find happiness and enjoyment in listening to a particular sound that you do it over and over again repeatedly in an engaged manner, that is already appreciated listening. Barriers to Listening In a perfect world, we would all be great listeners thus understanding every message being sent to us. However, the reality is we deal with certain situations or preconceived notions as barriers in listening. 1. Noise – this is any kind of sensory stimuli that affects the transmission of messages. It can dampen or boost your speaking engagements depending on how you deal with them or utilize them. a. External – these are kinds of noise that come from physical objects such as the radio, roosters outside your house, temperature of the room, uncomfortable chair, taste of food, etc. that disturbs and prevents you from giving your complete focus and attention to what you’re listening to. b. Internal - these are emotional or mental distractions that interfere with you attention while listening. Daydreaming, prejudice against the speaker, anticipating and predicting what will come up next can affect your focus. Understanding yourself – preconceived notions about yourself will prevent you from getting the entirety of the message. How you feel about the speaker and the topic also affects how you listen to someone. If you see yourself superior to the speaker, you will have a hard time listening to them because you tend to mentally contradict their messages or criticize them in your mind. If you find the topic boring, you tend to space out and just hear certain parts which catches your interest- this is also called selective hearing. Understanding others – these are about the preconceived notions or beliefs about others. You judge the speaker according to voice quality, gestures, appearance or social standing. These actions and thoughts affect how you listen to the speaker. You become preoccupied in criticizing the way they look or sound which makes you either an attentive listener or someone who totally disregards the messages coming from this speaker. Extrinsic Noise - Hot or cold room, Noisy neighbors, Uncomfortable chair, Jeeps and buses outside windows, Classmates fidgeting with his pen, Old air conditioner, Poor motivation of speaker, Speaker’s style, Amount of information transmitted. Intrinsic Noise – Feeling of pain or hunger, family problem, financial problem, fear of teacher, sleeplessness, constant self-focus, eagerness to talk, Lack of information or knowledge of the topic, Beliefs. Listening is a fundamental component in communication. Practicing habits in improving your listening skills not only make you a more competent member of the workforce or school, it enhances your relationships with yourself and with other people. Business magazines such as Forbes and Success magazine still discuss the importance of practicing good listening habits to improve or maintain relationships at work and in business. 1. Stop Talking “If we were supposed to talk more than we listen, we would have two tongues and one ear.” Mark Twain When somebody is talking, stop talking, do not interrupt and let them finish what they are saying. It is rude to talk while somebody else is speaking. Let the other person finish first then you can provide your feedback. If it’s not your turn to speak, respect the speaker and respect your role as the listener. 2. Concentrate on your task: Listening Refrain from thinking about anything else other than what the speaker is talking about. Relax and take in what is being said. Do not think about your existing problems, pending tasks or favorite television series. Discipline your mind in focusing only on one task at a time. “ The mind is easily distracted by other thoughts” so start practicing good habits in listening. 3. Don’t criticize the speaker – there may be times where your dislike how your speaker looks, dress or sound, but you have to remember that the message she will be sharing or giving is more important. Help make the speaker feel at ease by nodding or using gestures to encourage them. Also, maintain eye contact – this shows that you are attentively listening and that you understand what is being communicated. 4. Remove Distractions: Focus on what is being said. Avoid shuffling papers, tapping your pen on the table or fidgeting too much. These actions not only distract you from listening but it also distracts the speaker and might communicate that you are bored or feeling hostile against him or her. 5. Avoid emotional reactions: Empathize. Be courteous and respect the speaker by thinking not about yourself but putting yourself in their shoes. See the topic from their perspective and disregard what you’ve heard about the topic while listening. If you disagree on some point, let the speaker finish first before you voice your opinion or feedback about the message. Keep an open mind. 6. Be Patient – If the speaker pauses, don’t interrupt. Put yourself in their shoes, sometimes it takes a bit of time to construct your thoughts and verbalize them so let them finish what they are saying. 7. Guard against prejudice. Try to avoid focusing on annoying mannerisms or how they look like. Be impartial and disregard any distractions coming from their appearance or sound. Focus on the message not how they delivered the message to you. If the speaker comes from a different background, let go of your preconceived idea about their culture and pay extra attention only to what they are saying. Make sure to take note of non-verbal cues. 8. Focus on main points – This may take some time to practice: sort through how they verbalized the message and focus on the main point of their message. There is no need to remember everything word for word. Just focus on the ideas that you pick up from them. 9. Take down notes – Develop your own system of note taking to make it second nature as you listen. Taking down notes is very different from taking dictation. Dictation entails word for word transcription while taking down notes may be more on using your own words as to how you understood topic. Practice on getting the main idea of the message. 10. Watch for verbal and non-verbal communication – Listening does not only make use of sense of hearing, it actually utilizes all of our senses. Look out for non-verbal cues such as gestures, facial expressions, and eye movements. These non-verbal cues either add value or contradict what the speaker is saying verbally. Non-verbal communication also signals how confident or nervous the speaker is, which may affect how you perceive the message. Always remember that in order for the communication process to happen, we should be mindful of our roles, both as speaker and receiver. In order to be effective in any competency we should build up our skills in listening as it is the foundation of other competencies. Selective hearing increases our chances of understanding someone. Which culture is more rigid with time? Which Mcdonald’s commercial was used as an example in the module? Why are Chinese kids ahead of Filipinos when it comes to Math? It is part of their culture The anthropologist who gave the definition of religion in the module: Which culture is more rigid with time? Low context cultures do not tolerate being rejected Selective hearing increases our chances of understanding someone. What are the main problems in intercultural communication? b. Prejudice, ethnocentrism, and stereotyping There are four kinds of noise that affect the communication process. List them down. c. external noise, internal noise, semantic noise, factual noise. High context cultures are more tolerant of being rejected. Your cousins can have a different culture from you. In the Philippines, where the majority is brow skinned, fair skin is equated to beauty and wealth. What kind of intercultural problem is this? Ethnocentrism can also happen when someone from Mindanao is discriminated by someone rom Luzon. It's okay to think about what you want to tell your friend while she's talking to you. Who said that filipinos avoid talking about money? b. Vince RApisura Listening and Hearing are the same. Noise only happens internally. Which culture is more analytical and requires more verbal cues? What problem is encountered every time this old adage is relayed to children: " Wag kang makulit, sige ka, kukunin ka nung bumbay". a. All of the answers correct When you use your own knowledge in interpreting the sent data and you find out that your preconceived notions and the meaning of the message are not compatible, which kind of noise is present? a. internal noise Roosters crowing at 2 a.m is an extrinsic noise. Why are Chinese kids ahead of Filipinos when it comes to Math? a. It is part of their culture There is no need to understand yourself when listening. The anthropologists who gave the definition of religion in the module Listening is when we receive sounds. What problem is encountered every time we hear this thought: " Why wear clothes that show too much skin if you're not interested in attracting men to think of lustful thoughts about you?!" Noise only happens externally. Which culture can cancel schedules or appointments due to personal and social responsibilities? You're trying to listen to your teacher but you keep on remembering the fun night you had with your friends. When the teacher called you to recite and you did not hear what the question was, what kind of noise was present? b. internal noise Roosters crowing at 2 a.m is an intrinsic noise. Hearing is synonymous to listening. This is any kind of stimuli to our senses which affects how messages are conveyed. True or False: These are the 11 principles of communication - schemata drive, interpretative act, communication is active, forceful or powerful, symbolic, result in something, reversible, contextual, progressive, process, ethical, and influenced by media. In the movie Harry Potter, they never say the name of Voldemort and called him "He-Who-Must-Not-Be-Named". Which principle of communication can be observed in this practice? a. active and powerful Barriers and Strategies in communication What is Effective Communication Effective communication happens when the receiver does not only get the message but he or she must truly understand it. Effectively communicating with ones’ self or other can be hindered because of communication barriers. These barriers, however, are not permanent and can be dealt with accordingly. To be able to provide a solution, we must first learn to identify these barriers. Barriers in Communication a. Language Barrier – English is not our native language; thus, we are called second language learners. As a second language learners, there will be times when misinterpretation happens – this may be caused using terminologies or nuances that are not familiar to us; thus, creating confusion between the sender and receiver of the message. Keep in mind that misinterpretation can also happen even if we use our native tongue. Again, terms or jargons used may be the root of this issue. Learning Activity 7 Madeline’s father died the night before her college entrance exam. She was so distraught with what is happening she snapped at her classmate who asked her to move closer to the person in front of her while she was lining up to get in the testing room. Mateo, a three year old boy, went to the playground with his dad, Chuck. Mateo started playing on the slide. Another boy on the playground started following Mateo and trying to imitate what he was doing. After a few rounds of going up and down the slide, the boy would always race Mateo and would go on the slide first. Mateo remained patient until the boy shoved him to the side while scrambling up the stairs up the slide. Chuck saw everything and even if he was really angry inside, he calmly walked towards Mateo. He asked Mateo if he was fine, the boy just nodded while balling his fist. Chuck picked up Mateo and carried him back to their house. Before Mateo can burst out in tears, Chuck hugged him tightly and told him “you’re okay, anak, that was very brave of you”. Mateo hugged his father back and tried to smile. What communication strategy was used to comfort the little boy? c. Pay attention to nonverbal cues and keep emotions at bay. Tessa and Jayson were married and were living together in a small house. They agreed that household chores must be shared between them. One day, Tessa came home really tired from work. She cooked dinner and waited for Jayson to get home. Once Jayson was home, while eating dinner, Jayson’s boss called and told him to go online in an hour for an emergency meeting. Jayson hurriedly finished his food and put the dishes on the sink. He expected that Tessa would clean up the dishes. A few hours later, when they were both getting ready to go to bed, Tessa was not talking to him and kept silent even if he was initiating a conversation. The next morning, Jayson found the dirty dishes stacked on the sink. He called out Tessa and she got angry and hurriedly stormed out of their house. Jason was so mad he didn’t bother cleaning up. They both went to work angry at each other thinking that the other person was being unfair and was not following the rules they set. What barrier of communication transpired in this situation? e. Systemic / Systematic Resistance to believing in alternative medicine f. attitudinal barriers Talking about dogs to someone who hates animals The correct answer is: attitudinal barriers Which function of communication is used when you go for a job interview? Negative motivation results to? c. All of the answers correct What is communication anxiety? d. When a person is afraid to speak in front of a group Motivation is always a positive experience. When you express your grief over a relative who died, which function of communication can you use? a. Avoidance of speaking in groups, public speaking or even in interpersonal situations Creating a travel Vlog on Youtube Laughing with a friend c. Communicating to connect This chapter's title a. Functions of Communication What is the result of positive motivation? b. No correct answer Negative motivation results to? c. All of the answers correct Changing how you talk depending on who you are talking to. c. Emotional expression b. 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\|nth root (√)\| Subtraction is a mathematical operation that represents the operation of removing objects from a collection. It is signified by the minus sign (−). For example, in the picture on the right, there are 5 − 2 apples—meaning 5 apples with 2 taken away, which is a total of 3 apples. Therefore, 5 − 2 = 3. Besides counting fruits, subtraction can also represent combining other physical and abstract quantities using different kinds of objects including negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices. Subtraction follows several important patterns. It is anticommutative, meaning that changing the order changes the sign of the answer. It is not associative, meaning that when one subtracts more than two numbers, the order in which subtraction is performed matters. Subtraction of 0 does not change a number. Subtraction also obeys predictable rules concerning related operations such as addition and multiplication. All of these rules can be proven, starting with the subtraction of integers and generalizing up through the real numbers and beyond. General binary operations that continue these patterns are studied in abstract algebra. Performing subtraction is one of the simplest numerical tasks. Subtraction of very small numbers is accessible to young children. In primary education, students are taught to subtract numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer. - 1 Notation and terminology - 2 Of integers and real numbers - 3 Properties - 4 Units of measurement - 5 In computing - 6 The teaching of subtraction in schools - 7 Subtraction by hand - 8 See also - 9 References - 10 Bibliography - 11 External links Notation and terminology - (verbally, "two minus one equals one") - (verbally, "four minus two equals two") - (verbally, "six minus three equals three") - (verbally, "four minus six equals negative two") There are also situations where subtraction is "understood" even though no symbol appears: - A column of two numbers, with the lower number in red, usually indicates that the lower number in the column is to be subtracted, with the difference written below, under a line. This is most common in accounting. Formally, the number being subtracted is known as the subtrahend, while the number it is subtracted from is the minuend. The result is the difference. All of this terminology derives from Latin. "Subtraction" is an English word derived from the Latin verb subtrahere, which is in turn a compound of sub "from under" and trahere "to pull"; thus to subtract is to draw from below, take away. Using the gerundive suffix -nd results in "subtrahend", "thing to be subtracted". Likewise from minuere "to reduce or diminish", one gets "minuend", "thing to be diminished". Of integers and real numbers Imagine a line segment of length b with the left end labeled a and the right end labeled c. Starting from a, it takes b steps to the right to reach c. This movement to the right is modeled mathematically by addition: - a + b = c. From c, it takes b steps to the left to get back to a. This movement to the left is modeled by subtraction: - c − b = a. Now, a line segment labeled with the numbers 1, 2, and 3. From position 3, it takes no steps to the left to stay at 3, so 3 − 0 = 3. It takes 2 steps to the left to get to position 1, so 3 − 2 = 1. This picture is inadequate to describe what would happen after going 3 steps to the left of position 3. To represent such an operation, the line must be extended. To subtract arbitrary natural numbers, one begins with a line containing every natural number (0, 1, 2, 3, 4, 5, 6, ...). From 3, it takes 3 steps to the left to get to 0, so 3 − 3 = 0. But 3 − 4 is still invalid since it again leaves the line. The natural numbers are not a useful context for subtraction. - 3 − 4 = −1. Subtraction of natural numbers is not closed. The difference is not a natural number unless the minuend is greater than or equal to the subtrahend. For example 26 cannot be subtracted from 11 to give a natural number. Such a case uses one of two approaches: - Say that 26 cannot be subtracted from 11; subtraction becomes a partial function. - Give the answer as an integer representing a negative number, so the result of subtracting 26 from 11 is Subtraction of real numbers is defined as addition of signed numbers. Specifically, a number is subtracted by adding its additive inverse. Then we have 3 − π = 3 + (−π). This helps to keep the ring of real numbers "simple" by avoiding the introduction of "new" operators such as subtraction. Ordinarily a ring only has two operations defined on it; in the case of the integers, these are addition and multiplication. A ring already has the concept of additive inverses, but it does not have any notion of a separate subtraction operation, so the use of signed addition as subtraction allows us to apply the ring axioms to subtraction without needing to prove anything. Subtraction is anti-commutative, meaning that if one reverses the terms in a difference left-to-right, the result is the negative of the original result. Symbolically, if a and b are any two numbers, then - a − b = −(b − a). Subtraction is non-associative, which comes up when one tries to define repeated subtraction. Should the expression - "a − b − c" be defined to mean (a − b) − c or a − (b − c)? These two possibilities give different answers. To resolve this issue, one must establish an order of operations, with different orders giving different results. In the context of integers, subtraction of one also plays a special role: for any integer a, the integer (a − 1) is the largest integer less than a, also known as the predecessor of a. Units of measurement When subtracting two numbers with units of measurement such as kilograms or pounds, they must have the same unit. In most cases the difference will have the same unit as the original numbers. Changes in percentages can be reported in at least two forms, percentage change and percentage point change. Percentage change represents the relative change between the two quantities as a percentage, while percentage point change is simply the number obtained by subtracting the two percentages. As an example, suppose that 30% of widgets made in a factory are defective. Six months later, 20% of widgets are defective. The percentage change is -33 1/3%, while the percentage point change is -10 percentage points. The method of complements is a technique used to subtract one number from another using only addition of positive numbers. This method was commonly used in mechanical calculators and is still used in modern computers. To subtract a binary number y (the subtrahend) from another number x (the minuend), the ones' complement of y is added to x and one is added to the sum. The leading digit '1' of the result is then discarded. The method of complements is especially useful in binary (radix 2) since the ones' complement is very easily obtained by inverting each bit (changing '0' to '1' and vice versa). And adding 1 to get the two's complement can be done by simulating a carry into the least significant bit. For example: 01100100 (x, equals decimal 100) - 00010110 (y, equals decimal 22) becomes the sum: 01100100 (x) + 11101001 (ones' complement of y) + 1 (to get the two's complement) ========== 101001110 Dropping the initial "1" gives the answer: 01001110 (equals decimal 78) The teaching of subtraction in schools Methods used to teach subtraction to elementary school vary from country to country, and within a country, different methods are in fashion at different times. In what is, in the U.S., called traditional mathematics, a specific process is taught to students at the end of the 1st year or during the 2nd year for use with multi-digit whole numbers, and is extended in either the fourth or fifth grade to include decimal representations of fractional numbers. Almost all American schools currently teach a method of subtraction using borrowing or regrouping (the decomposition algorithm) and a system of markings called crutches. Although a method of borrowing had been known and published in textbooks previously, the use of crutches in American schools spread after William A. Brownell published a study claiming that crutches were beneficial to students using this method. This system caught on rapidly, displacing the other methods of subtraction in use in America at that time. Some European schools employ a method of subtraction called the Austrian method, also known as the additions method. There is no borrowing in this method. There are also crutches (markings to aid memory), which vary by country. Comparing the two main methods Both these methods break up the subtraction as a process of one digit subtractions by place value. Starting with a least significant digit, a subtraction of subtrahend: - sj sj−1 ... s1 - mk mk−1 ... m1, where each si and mi is a digit, proceeds by writing down m1 − s1, m2 − s2, and so forth, as long as si does not exceed mi. Otherwise, mi is increased by 10 and some other digit is modified to correct for this increase. The American method corrects by attempting to decrease the minuend digit mi+1 by one (or continuing the borrow leftwards until there is a non-zero digit from which to borrow). The European method corrects by increasing the subtrahend digit si+1 by one. Example: 704 − 512. The minuend is 704, the subtrahend is 512. The minuend digits are m3 = 7, m2 = 0 and m1 = 4. The subtrahend digits are s3 = 5, s2 = 1 and s1 = 2. Beginning at the one's place, 4 is not less than 2 so the difference 2 is written down in the result's one place. In the ten's place, 0 is less than 1, so the 0 is increased by 10, and the difference with 1, which is 9, is written down in the ten's place. The American method corrects for the increase of ten by reducing the digit in the minuend's hundreds place by one. That is, the 7 is struck through and replaced by a 6. The subtraction then proceeds in the hundreds place, where 6 is not less than 5, so the difference is written down in the result's hundred's place. We are now done, the result is 192. The Austrian method does not reduce the 7 to 6. Rather it increases the subtrahend hundred's digit by one. A small mark is made near or below this digit (depending on the school). Then the subtraction proceeds by asking what number when increased by 1, and 5 is added to it, makes 7. The answer is 1, and is written down in the result's hundred's place. There is an additional subtlety in that the student always employs a mental subtraction table in the American method. The Austrian method often encourages the student to mentally use the addition table in reverse. In the example above, rather than adding 1 to 5, getting 6, and subtracting that from 7, the student is asked to consider what number, when increased by 1, and 5 is added to it, makes 7. Subtraction by hand Subtraction from left to right In this method, each digit of the subtrahend is subtracted from the digit above it starting from right to left. If the top number is too small to subtract the bottom number from it, we add 10 to it; this 10 is 'borrowed' from the top digit to the left, which we subtract 1 from. Then we move on to subtracting the next digit and borrowing as needed, until every digit has been subtracted. Example: A variant of the American method where all borrowing is done before all subtraction. The partial differences method is different from other vertical subtraction methods because no borrowing or carrying takes place. In their place, one places plus or minus signs depending on whether the minuend is greater or smaller than the subtrahend. The sum of the partial differences is the total difference. Instead of finding the difference digit by digit, one can count up the numbers between the subtrahend and the minuend. 1234 − 567 = can be found by the following steps: - 567 + 3 = 570 - 570 + 30 = 600 - 600 + 400 = 1000 - 1000 + 234 = 1234 Add up the value from each step to get the total difference: 3 + 30 + 400 + 234 = 667. Breaking up the subtraction Another method that is useful for mental arithmetic is to split up the subtraction into small steps. 1234 − 567 = can be solved in the following way: - 1234 − 500 = 734 - 734 − 60 = 674 - 674 − 7 = 667 The same change method uses the fact that adding or subtracting the same number from the minuend and subtrahend does not change the answer. One adds the amount needed to get zeros in the subtrahend. "1234 − 567 =" can be solved as follows: - 1234 − 567 = 1237 − 570 = 1267 − 600 = 667 - "Subtraction". Oxford English Dictionary (3rd ed.). Oxford University Press. September 2005. (Subscription or UK public library membership required.) - "Subtrahend" is not a Latin word; in Latin it must be further conjugated, as in numerus subtrahendus "the number to be subtracted". - Paul E. Peterson, Michael Henderson, Martin R. West (2014) Teachers Versus the Public: What Americans Think about Schools and How to Fix Them Brookings Institution Press, p.163 - Janet Kolodzy (2006) Convergence Journalism: Writing and Reporting across the News Media Rowman & Littlefield Publishers, p.180 - David Gillborn (2008) Racism and Education: Coincidence Or Conspiracy? Routledge p.46 - Paul Klapper (1916). The Teaching of Arithmetic: A Manual for Teachers. pp. 80–. - Susan Ross and Mary Pratt-Cotter. 2000. "Subtraction in the United States: An Historical Perspective," The Mathematics Educator 8(1):4-11. P. 8: "This new version of the decomposition algorithm [i.e., using Brownell's crutch] has so completely dominated the field that it is rare to see any other algorithm used to teach subtraction today [in America]." - Ross, Susan C.; Pratt-Cotter, Mary (1999). "Subtraction From a Historical Perspective". School Science and Mathematics 99 (7): 389–393. - Klapper 1916, p. 177-. - David Eugene Smith (1913). The Teaching of Arithmetic. Ginn. pp. 77–. - The Many Ways of Arithmetic in UCSMP Everyday Mathematics Subtraction: Trade First - Partial-Differences Subtraction; The Many Ways of Arithmetic in UCSMP Everyday Mathematics Subtraction: Partial Differences - The Many Ways of Arithmetic in UCSMP Everyday Mathematics Subtraction: Counting Up - The Many Ways of Arithmetic in UCSMP Everyday Mathematics Subtraction: Left to Right Subtraction - The Many Ways of Arithmetic in UCSMP Everyday Mathematics Subtraction: Same Change Rule - Brownell, W. A. (1939). Learning as reorganization: An experimental study in third-grade arithmetic, Duke University Press. - Subtraction in the United States: An Historical Perspective, Susan Ross, Mary Pratt-Cotter, The Mathematics Educator, Vol. 8, No. 1 (original publication) and Vol. 10, No. 1 (reprint.) PDF \|Look up subtraction in Wiktionary, the free dictionary.\| \|Wikimedia Commons has media related to Subtraction.\| - Hazewinkel, Michiel, ed. (2001), "Subtraction", Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4 - Printable Worksheets: Subtraction Worksheets, One Digit Subtraction, Two Digit Subtraction, and Four Digit Subtraction - Subtraction Game at cut-the-knot - Subtraction on a Japanese abacus selected from Abacus: Mystery of the Bead
Every well-written paragraph needs three parts: context, content, and conclusion. These three parts are known collectively as the 3 Cs. When you use the 3 Cs, you present information logically, you help the reader understand your message, and you demonstrate the relevance of your idea. Context. The first sentence (or two) of a paragraph establishes the context. The context has two purposes: 1. Reveal the single idea that will be discussed, and 2. Demonstrate how the idea relates to the previously discussed idea. To establish context, first determine the single idea you will discuss next. The first sentence (or two) presents that idea. Second, think about the logical connections between the idea and the previous idea. The first sentence (or two) provides the transition from one idea to the next by demonstrating those connections. Example B1 illustrates how context is established. [final sentence of a paragraph about nurses’ responsibilities] When nurses fully understand these duties, they can interact as a team to improve patient well-being. [first sentence, i.e., context, of the next paragraph] A patient may have many needs that a single nurse, or other healthcare provider, cannot address alone. In example B.1, the first sentence of paragraph two establishes the context for the paragraph that follows. First, it reveals the main idea: patients have multiple needs. Second, it shows the relevance of the main idea to the previous idea. It does this by echoing words or concepts found in the final sentence of the previous paragraph. Here, the first sentence of paragraph two contains the words patient, needs, and single nurse. These words relate to patient, well-being, and team (of nurses) in the final sentence of paragraph one. As a result, the reader will know what to expect from the paragraph, will be able to make sense of the information to follow, and will understand its relevance within the logical flow of ideas. If you do not establish the context, the reader will have greater difficulty understanding your ideas. The reader may ask, rightly, “Hey, what am I reading about, and why?” The reader may be confused by the information, and you, as the writer, will seem to be presenting unconnected, irrelevant information that can be overlooked or forgotten. In short, you increase reader confusion and reduce the level of communication. Your job, therefore, is to ensure that each paragraph begins by establishing the context. Content. Once you have introduced the idea and its relevance, you provide the content. The content is the information about idea, i.e., the body of the paragraph. Each sentence within the body supports the main idea, explains it, and helps the reader understand it. When the body of the paragraph is complete, the reader should have all the necessary information to understand the idea. Example B.2 begins with the context (from example B.1, in italics) and provides information about the idea. A patient may have many needs that a single nurse, or other healthcare provider, cannot address alone. For example, the patient may have diverse medical needs, such as examinations and treatments for a host of medical conditions. The patient may also have cultural needs based on the social norms, values, and perspectives of his or her community. Finally, a patient may have emotional needs resulting from the interaction of fear of death and hope for recovery. Whereas the context in example B.2 introduced the idea that patients have multiple types of needs, the content described those needs. In this sample, the body of the paragraph listed three broad types of needs. Later paragraphs may discuss those needs in greater detail, which would make this entire paragraph the context for the document section. Three details is not a “magic number.” Provide as much, or as little, information as necessary to discuss the idea fully. Broader ideas require more information. Discrete ideas need less. The idea, therefore, determines the content—and the length of the body. If every sentence in the body helps the reader understand the idea, the body will be the right length. Your job, therefore, is to provide the information necessary for understanding the idea of the paragraph. Conclusion. The conclusion is the final sentence (or two) of the paragraph, and it is the most difficult to write. Similar to the context, the conclusion has two purposes: 1. Provide the conclusion, meaning, or purpose of the content, and 2. Create a transition to the following paragraph. Now that the reader has read the content, what do you want the reader to understand? What should the reader think about or do with the information? What action do you want the reader to perform? In short, what conclusion should the reader reach from the content you have provided? If you have done well with providing the context and content, the reader will be ready to accept your conclusion. The second function of the conclusion is to create the transition to the next paragraph, which is exactly the same process as creating a transition with the context, though in reverse. Example B.3 will conclude the paragraph example we’re using to understand the 3 Cs. A patient may have many needs that a single nurse, or other healthcare provider, cannot address alone. For example, the patient may have diverse medical needs, such as examinations and treatments for a host of medical conditions. The patient may also have cultural needs based on the social norms, values, and perspectives of his or her community. Finally, a patient may have emotional needs resulting from the interaction of fear of death and hope for recovery. To address this diversity of needs, a patient also needs a diverse team of caring, competent healthcare providers who work together to ensure the most positive outcome possible. The final sentence in Example B.3 concludes the information about types of patient needs. It gives the meaning and value of the content to the reader and makes the argument that patients need multiple caregivers. The reader, having just read about the types of patient needs, will be ready to accept this conclusion. Your job, therefore, is to help the reader reach a conclusion and make sense of the content. For every type of genre, but especially for academic and technical writing, the 3 Cs structure not only works but also is necessary if your purpose is to present information clearly, logically, and persuasively.
Programming is the process that makes it possible to create computer software, applications and websites. Currently, computers are unable to think for themselves, therefore they require users to give them sets of ordered instructions to know what to do. This is referred to as 'code'. Most of the resources you use on the computer and internet are made with code. Programming is a core element of the Digital Technologies curriculum because it helps students develop essential skills such as problem-solving, logic and critical thinking. General-purpose programming, also known as text-based programming, is one of the coding languages prescribed in the Australian Curriculum: Digital Technologies for secondary schools. This type of language is used to create programs by typing letters, numbers and symbols and requires programmers to use formal syntax. Object-oriented programming is the second coding language prescribed in the Australian Curriculum: Digital Technologies. In this type of language, users define not only the data type within a data structure, but also the types of operations that can be applied to the data structure. A programming language that supports the object-oriented programming paradigm. In object-oriented programming, objects represent a combination of data (the attributes of an object) and actions that can be performed on or with those data (the methods of the object). An example might be a declaration of a 'car', which has attributes that describe its physical nature (such as the number of doors, its colour, the size of the engine) and the actions it can perform (such as accelerating, braking and turning). The valid attributes and methods of an object are defined by its class, and these attributes and methods can be inherited from the definition of another class. Examples of OOP languages include C++, Eiffel, Java, Python and Scala. Learn more about it This is an online resource for teaching computer science to students. This chapter focuses on programming languages. This chapter focuses on complexity and tractability. This article is devoted to demystifying code. It explains what coding is, including programming and programming languages. It provides relevant examples. Explore a wide range of resources, including videos, interactives, learning guides and lesson plans for secondary computing courses in the UK. Quickstart is a continuing professional development (CPD) resource that provides the essential tools to develop a course. It helps secondary teachers figure out how to teach a creative and innovative computing curriculum underpinned by computational thinking. This book viewable online using the 'look inside' feature or purchased in hard copy provides a comprehensive guide to programming for all levels. How to teach it This lesson sequence offers approaches to teaching object-oriented principles using text-based programming. It attempts to address the problem that many programming languages are too complex and their environments too confusing for many students. This lesson sequence intentionally uses a visual-based programming tool to introduce designing and validating algorithms. Those students who complete this task can move to code the result in any text-based language with which they are familiar. This sequence provides a gentle introduction to the skill of decomposition by having students develop discrete modules that together serve a single need: a maths teacher asks for a program that can be used to demonstrate aspects of maths. This sequence can be used in conjunction with 'Comparing and selecting appropriate algorithms'. In this assignment, students design a program that asks the user to guess ten numbers that were generated pseudo-randomly. For the classroom Python is a free programming language. This webpage includes resources for learning to program with Python. This website provides tools and materials for teaching and learning computational thinking, problem-solving, and computer programming across secondary year levels. Code Monkey is a fun and educational game environment where students learn to code in a real programming language, no previous experience needed. Greenfoot uses a simple interface to teach object orientation using Java. Students create 'actors' that live in 'worlds' to build games, simulations, and other graphical programs. Learn coding languages. A free account allows access to 13 courses. There are more available if you subscribe. Explore Python, Java, C++, iOS and more. (Purchase required to access all courses.) What other schools are doing Programming interactive music Teacher Tony Hill explains how he implemented programming interactive music in his Year 8 class Khan Academy: Meet the professionals Short case studies of professionals in computing science who explain how they use their computer science and programming skills in their work. Students share and extend learning Design algorithms represented diagrammatically and in English, and trace algorithms to predict output for a given input and to identify errors (ACTDIP029) Implement and modify programs with user interfaces involving branching, iteration and functions in a general-purpose programming language (ACTDIP030) Design algorithms represented diagrammatically and in structured English and validate algorithms and programs through tracing and test cases (ACTDIP040) Implement modular programs, applying selected algorithms and data structures including using an object-oriented programming language (ACTDIP041)
The Reader's Journey, Volume 1 Lesson 2: The Literary Canon These books that engender such strong reactions are the subject of this lesson. Why do you think certain books are routinely assigned in classrooms across the country? Some books are considered classics or must-reads, readings that all educated persons should know. Others are selected because they illustrate a theme or type of writing students should master. When works of literature are commonly accepted as classics, they become part of our literary canon. The term literary canon refers to a group of literary works considered by a culture to be the most important and representative of a particular time period, group of authors, or place. For example, there can be a literary canon A literary canon creates a collection of these high quality works. But what do we mean by high quality? You will also explore this concept within this lesson. You will also begin reading a canonical work, the Adventures of Huckleberry Finn (also referred to as Huck Finn). You will not only master reading strategies for comprehending and enjoying this complex work, but you will also learn more about why this book has been a target for banning. We will consider many of the factors that influence those who choose these works, such as quality, importance, and representation, as well as age-appropriateness, topic, and language. Wondering what goals you will pursue during this lesson? Check out Lesson 2 Goals. Head to the next page to take your pretest. The questions listed below are vital to this lesson, because once you and your mentor determine what your prior knowledge, skills, and understandings are, then together you can tailor this study to your needs. In addition, these questions will help you decide which, if any, of the optional assignments to explore within this course. What are Note-Taking Principles? What are Theories of What Makes a Good Literary Canon? What Questions Should You Write While Annotating? Who Determines the Canon? What is a TCQC Short Answer Response? What Right or Rights Does the First Amendment Guarantee? What Language and Style Techniques Can Authors Use? What is Reading Step Two? What is Satire? What is Connotation? Your next step is to review note-taking strategies. Did you know that good note taking integrates several methods? Check out the next page. Lesson 1 offered some challenging readings to provide you with historical context, a sense of zeitgeist, and a grounding in key concepts. How well did you do at taking notes on these readings and ideas? The Adventures of Huckleberry Finn will test your ability in many skill areas, such as the ability to crack the code of dialect, understand satire, note significant details from a story, and thoughtfully examine some controversial issues of race relations in 19th century America. To be prepared properly for all the twists, turns, and hills of this reading journey, you will need the skill of note taking. In later lessons you will do more in-depth study of different aspects of note taking. For now, get a quick peek at some basic strategies. View the Note Taking Slide Show. Did you take notes on how to take notes? Whether you did or not, be prepared to use these strategies on the following pages. Note Charles B. Fairbanks' thoughts about reading in the sidebar, and discuss with your mentor. Are you ready to increase the savings in your word bank? Or do you need to dive into creating your own canon? Decide with your mentor which step to take next. This lesson and your readings offer interesting words that might be new to you. Continue your vocabulary mastery. Review the definitions of words you don't already know that appear on this page, in this lesson, and throughout the readings. Use multiple reference sources, if you aren't satisfied with initial definitions provided, to help you decipher meaning. (see definition #2 under "intransitive verb") Complete the practice activity for words you need to master. Time to explore the criteria for a canon and to create your own literary canon. Head to the next page. The Adventures of Huckleberry Finn resides in the American literary canon, but the canon is an ever-evolving group of works. Many famous authors, literary experts, educators, and philosophers wrestle over what justifies a work's placement in the canon. The overarching question is, "Does this book represent the quality and impact to be required reading of many people?" Start thinking about what choices you might make for a literary canon that all gifted sixth through eighth graders should read. According to Mortimer Adler and Charles Van Doren, experts on literature and culture, a book should meet the following criteria to be included in the canon: Charles Eliot's Harvard Classics and Adler's Great Books offer extensive lists of classic works. Some universities offer courses and even entire curricula strictly devoted to the study of these books. Check out these lists, and see how many names (authors or titles) you recognize or have already read. Now that you have some background information on making a literary canon, you're ready to create your own canon of works. Ready to play the role of professor? The first step in considering how you might update, revise, or even overhaul the canon is to consider which books you think are important, influential, inexhaustible, and relevant. The Newsweek column, "Life in Books," asks famous authors, filmmakers, politicians, and others holding influential positions to explain five books that are most important to them, one book they hope parents will read to their children, and one they've recently revisited and been disappointed with. Visit the Newsweek Web site and enter this phrase in the search bar: "a life in books." Select authors of interest to you, see what their favorite books are, and consider reading the books these authors list: If Newsweek called you and asked you to provide your own answers for that column, what would you say? This is your chance to influence what students and adults will be reading for a long time to come, so choose carefully. Create your own canon in your Reader's Journal by answering the questions in the Create Your Own Canon hand out. The last question on the sheet asks you to create your own canon for students your age. You will also want to: Update your canon as you proceed through the readings in this course and any other readings you choose independently. Your canon will remain a work in progress. Need some help? See what TIP Testers accomplished. View the work of students to get a sense of how others approach the challenge of developing a canon. View the Create Your Own Canon response of Emily, TIP Tester. View the Create Your Own Canon response of Kanan, TIP Tester. Read this definition of the literary canon with your mentor. It attempts to give a more expansive and complex definition of canon, ending with the question quoted below. Try to answer the question along with your mentor, and record your response in your Reader's Journal. As the term is ordinarily used, "literary canon" is defined by definition #7 above: "an authoritative list, as of the works of an author." Yet the sense of definition #3 ("standard, criterion") is also strongly implied as the means by which individual works find their way into the literary canon. How do the other definitions of canon resonate with the concept of an authoritative list of authors who are taught in literature courses? In what sense have authors been canonized saints or priests in Western culture, or to what extent may we think of the literary canon in the sense of #8, "a composition . . . in which the same melody is repeated by one or more voices, overlapping in time in the same or a related key"? —Kathryn B. Stockton It's time to analyze why the canon at times comes under scrutiny, if not attack. A number of works you've seen listed are often pulled from libraries, schools, and other institutions. Head to the next page to explore the book banning debate. No doubt as you built your literary canon you left out some books, perhaps because you forgot a few or perhaps because you thought some works were inappropriate for the canon. Did you feel so strongly about some of the books you chose not to include that you would advise the books never be read by children of certain ages? Some people believe certain books should be banned. When and why do some books get banned? Why would a school or library decide not to teach or stock certain literature? Take careful notes as you learn more about the issues surrounding removal of books from libraries and school syllabi. Many advocates of book banning feel that some books are not appropriate for certain audiences. They feel that some topics are too difficult or too adult for children or younger readers. They might consider violence, language, or mature content to be inappropriate. Consider the rating system used in the movie industry. Movies rated R, NC-17, or PG-13 are considered verboten to viewers of a young age. Take some time to look at the following Web sites containing more information about censorship, and take good quality notes. Many opponents of censorship cite the First Amendment to the U.S. Constitution as the primary argument against censorship. Several books are targeted for banning quite often. The Illinois Library Association and the American Library Association Web sites offer a lot of information about why books are sometimes banned, who initiates the requests, and other details. Head to the next page to crystallize your thoughts on this debate. Now consider your thoughts on this debate. First discuss these questions with your mentor, then determine your answers. Create your own list of criteria in your Reader's Journal. Share that list with your mentor, and seek feedback from friends, teachers, and family you trust. If you're really enjoying yourself, take a crack at the Disciplinary Hat activity on the Banned Book Debate. Otherwise, head to the sections on controversial language and diction in Huck Finn. Disciplinary Hat activities ask you to take on the role of a person who works in a particular field or discipline. In this exercise you will walk in the shoes of a professional who must decide to ban or preserve a book in the literary canon or who must develop a list for the canon. Select one of the following activities in order to consider the development of a canon or the issue of banned books from a perspective other than your own. Select the topic that most interests you, and explore it from the viewpoint of someone else who would also have an interest in this matter. To truly put yourself into his or her shoes, you will need to know what interests are most important to a person in this discipline or situation? Consider the banned book debate from someone else's point of view. First choose one of the following groups. Select a group that is accessible to you—meaning, a member of the group that you can interview locally or by e-mail. Address the debate through their eyes by doing the following: Bonus Challenge: Using local news sources and the public library, investigate whether the group you chose has challenged or banned a book in your local schools in the last 100 years. Work with your mentor to develop a list of reputable and legitimate online resources to consult, and, if needed, conduct some interviews. Write a letter to the local school board responding to the issue, representing your opinions. (Again, don't actually send the letter.) For a slightly different angle on this activity, consider another source for your interview: Talk to your mentor about how you could learn more about these constituencies and how they influence literary canons. Now let's take an in-depth look at one of the factors that can lead to book banning: the author's use of language. Head to the next page. You've probably already encountered one reason certain books are challenged or even banned: language. Even the smallest phrase or shortest word can make all the difference in a book's appropriateness for certain audiences. Every word has power. Soon you will begin reading the Adventures of Huckleberry Finn, a novel by Mark Twain (Samuel L. Clemens), considered by many to be part of the canon. It is also a book that has been banned from some schools and libraries. Before you begin reading it, let's explore how language can be the source of banning. These next few pages are crucial background to the challenge a contentious book presents. Let's explore the power of diction in the Huck Finn. If the reason a book is sometimes banned is due to its difficult language, why would an author choose to use a contentious word? Why would the writer not consider using a euphemism instead? Consider your own choice of words, your diction, when writing or even speaking. Head to the next page to explore specificity and connotation. Let's start with a basic level of diction where things aren't so controversial. Starting here will show you how writers make incremental choices in all their words that contribute to overall main ideas, themes, and tone. Before a writer even realizes it, he or she has set a mood, inspired emotions, and created reactions. Every word has its own connotations. Some reasons a writer might select one word instead of another are impact and meaning. General verbs are vague. They can be used by anyone for a variety of situations, but these verbs don't truly pin down the action for a reader. Active verbs create an immediate, cinematic, and memorable image. Think about the differences in diction between the following pairs of sentences. Discuss with your mentor, then hover your mouse over the analysis (below and to the right). Think about the differences in diction among the following four sentences. Discuss with your mentor, then hover your mouse over the analysis (below and to the right). How would you distinguish the different types of information each sentence gives? Head to the next page for an exploration of biased diction and strong language. Now let's step into the more challenging territory that words create. Look at two different ways a news organization might report an event. See your mentor for the analysis, available at Lesson 2 of the Mentor Guidelines Web site. Have your parents or guardians ever cautioned you against "strong language"? What words are off limits, and why? Love and hate are often cited as examples of strong language. To say you have fallen in love with someone is quite a declaration, as is a declaration of hatred. Yet do you hear people say every day: Then, they turn around and declare newfound love or hatred for something or someone else. What other synonyms might a speaker or writer use instead? Discuss with your mentor why such words fit that description. Experiment with general versus specific diction, biased versus more neutral diction, or stronger versus tamer language. Head to the next page to see how Huck Finn is full of contentious language from another era that raises some readers' hackles. Note also that there are many readers who believe such language is crucial to the book's status as a classic. Sometimes when we read literary works from another era, we may find the language to be archaic, biased, or strong. We may even be offended by the diction and the attitudes it represents because the language reminds us of horrible injustices and past crimes. Such language may cause problems for modern readers who don't comprehend the setting of another era or who would rather not explore the prejudices and problems of that time. In other words, reading a work from such an era can be contentious. For example, the Adventures of Huckleberry Finn, written in the late 1800s by Mark Twain, takes place in the Southern United States. Some of its language is considered racially inappropriate and offensive today. While we would never consider using such terms today, Americans from certain regions of the country once did, and that language is key to the setting Twain establishes in his story. Be prepared for some racially offensive language that challenges us as modern readers, as you read the angry rant of Huck's father, Pap. "Oh, yes, this is a wonderful govment, wonderful. Why, looky here. There was a free nigger there from Ohio—a mulatter, most as white as a white man. He had the whitest shirt on you ever see, too, and the shiniest hat; and there ain't a man in that town that's got as fine clothes as what he had; and he had a gold watch and chain, and a silver-headed cane—the awfulest old gray-headed nabob in the state. And what do you think? They said he was a p'fessor in a college, and could talk all kinds of languages, and knowed everything. And that ain't the wust. The said he could vote when he was at home. Well, that let me out. Thinks I, what is the country a-coming to?" (35) As you explore Step Two: Gathering the Tools, you will explore more fully how background knowledge, such as what we've covered these last several pages, is helpful to understanding a book such as Huck Finn. In Step One, you decided on a method to assess a particular reading's level of difficulty for you. In Step Two, you will gather the tools you need to help you meet any particular challenges you might encounter with that reading. In Lesson 1, you previewed the novel Huck Finn. Review the notes you made about this text in Lesson 1. Do you already know anything about the author, publication, genre, and relevant historical events? Let's explore a few Web sites and see what we can learn about the novel's background, before we begin our reading. This will help us place the novel historically, learn about the author, know how the book is received by others, and perhaps gain a few tips to help us with our reading. Ready to take notes? Any time you see many Web sites to visit, that's your cue to get out your note-taking tools! The Adventures of Huckleberry Finn was written by Mark Twain in 1884, and the novel itself is set roughly in the pre-Civil War era, about 1835-1845. You can find additional information about Mark Twain at the Official Mark Twain Web site, including some interesting fast facts. You may have noticed this novel on some lists of banned books. Before you decide to read Huck Finn, you might be curious to know why it is so often banned. Here are some interesting facts listed on the Banned Books Online page. Arming yourself with knowledge about the language in this book, about the time when it was written, and about the author's place in history may help you to read on a deeper level. This step will allow you to judge for yourself whether you think For more information about Step Two, go to the next page. In addition to background knowledge, you may also wish to gather some physical items to help you read. Wherever you read and however you read, you might also need some annotation tools to help you succeed. Gathering the appropriate tools before you begin your climb will help you read deeper, understand more, and ensure your success. Now you're ready to read and annotate Huck Finn. As you read chapter 1, jot down your initial reactions in your journal. Head to the next page to learn more about the dialect in this novel. Head to the following page if you seek a challenge while analyzing this novel. Some readers often struggle to decipher what the characters say as they begin reading Huck Finn. This text is a prime example of an author's use of diction and dialect. One strategy to help you make sense of the language is that of "translating" a few sentences or phrases from their dialect into yours. Translate a few samples of dialect from Huck Finn by reading the flash cards below. Analyze the following with your mentor: Select one of Huck's passages of first-person narration (50-100 words) and translate it in two ways: Another strategy you might try is to use the context in which each phrase is spoken. Think about the events that are occurring, and use cues about the characters' personalities and the setting to decipher what the characters are feeling and stating. If you are eager for a challenge as you investigate the literary devices of this novel, check out the next page. If you are ready to conduct an in-depth analysis through writing, skip to dialectical journaling. Consider completing this optional activity if you need additional challenge. As you follow Huck Finn on his adventures, he'll get tangled in all kinds of shenanigans that on the surface may seem simply to be a teen boy getting into trouble. But many critics think Mark Twain tried to challenge all kinds of social norms through the seemingly innocent antics of a young, impoverished boy. Satire challenges social norms. Satire, for our purposes, is a literary work that mocks and critiques human error, vice, or the faulty institutions, systems, and rituals people create. Satire uses the tools of exaggeration, incongruity, slapstick, and irony, among others, to highlight the wrongs that need correcting. View these Flash Cards to get a sense of how satire in Huck Finn uses these four tools. Head to the next page to complete your own analysis of the book's satire of religion and racism. If you are ready to conduct an in-depth analysis through writing, skip to dialectical journaling. If you are ready to conduct an in-depth analysis through writing, skip to dialectical journaling. A dialectical journal is a conversation between you, the reader, and the text. Each side of the page will represent one side of the conversation. Think about a cartoon image in which each character has his own speech bubble as he converses. Select at least three meaningful passages from your Huck Finn readings. Review the Dialectical Journal Rubric. What are you being challenged to do? Ask your mentor for any explanation and tips, if you need them. Review the following journal entries from other students: example 1 of The Bean Trees; example 2 by Nicole, TIP Tester; and example 3 by Chris, TIP Tester. These examples analyze excerpts from the novel The Bean Trees and the essay "A Fable for Tomorrow" from Rachel Carson's Silent Spring—readings that have not been assigned for this course. However, by looking at these, you can still get a good idea of how a reader can interact with the text and create a thoughtful dialectical journal. What strategies do you see these students employing? Choose one passage, and write a dialectical journal of at least 250 words in response to the passage. Remember all the strategies above, and keep the rubric close at hand. Need help focusing your journal? Pay close attention to these topics that Twain may be satirizing: If you continue to need challenge, you may be able to tackle the Disciplinary Hat: You, Literary Scholar. Otherwise, continue to work on your Timeline. Imagine you have been invited to speak to The Mark Twain House and Museum, due to your extensive knowledge and research of the text on the Adventures of Huckleberry Finn. You have been asked to speak on a controversial topic, the proposition: "The Adventures of Huckleberry Finn should be rewritten so as to remove any offensive language." To prepare for this speech, you must research the book carefully, trying to imagine whether edits will seriously improve or compromise the integrity of the work. Now it's time to get back to your Timeline. Add the year 1884, the year the Adventures of Huckleberry Finn was published, to your timeline. Also add the time span between 1835–1845, since Twain set the story forty to fifty years before 1884. Visit the sample updated timeline. As you make this addition, consider how the events in the book might have been influenced by events in that period of history. For example, Jim is attempting to escape slavery, and Huck seems concerned about whether or not to help him. Note the publication date in relation to the historical documents and other readings you completed in Lesson 1. Take new notes as necessary, and update your timeline if needed. There are two final steps to wrap up this lesson: a reflection on Reading Step Two, and a vocabulary quiz. In your Reader's Journal, reflect on your personal experience with Reading Step Two. Head to the next page to take your vocabulary quiz. The more diction you master, the easier your reading becomes. Build up your word bank by proving you know words that have been defined throughout these pages and throughout the first ten chapters of the Huck Finn. Keep in mind: if you haven't been learning new words as you read this lesson or the novel, you'll discover through this quiz where you've been taking shortcuts. You can return later to redo these activities and test your knowledge of other words. You might also consider returning to the pretest on page two to see what you know now that you didn't before. Go to Lesson 3 Return to page 23
Astronomical seeing refers to the blurring and twinkling of astronomical objects such as stars caused by turbulent mixing in the Earth's atmosphere varying the optical refractive index. The astronomical seeing conditions on a given night at a given location describe how much the Earth's atmosphere perturbs the images of stars as seen through a telescope. The most common seeing measurement is the diameter (or more correctly the full width at half maximum or FWHM) of the optical intensity across the seeing disc (the point spread function for imaging through the atmosphere). The FWHM of the point spread function (loosely called seeing disc diameter or "seeing") is a reference to the best possible angular resolution which can be achieved by an optical telescope in a long photographic exposure, and corresponds to the FWHM of the fuzzy blob seen when observing a point-like source (such as a star) through the atmosphere. The size of the seeing disc is determined by the astronomical seeing conditions at the time of the observation. The best conditions give a seeing disk diameter of ~0.4 arcseconds and are found at high-altitude observatories on small islands such as Mauna Kea or La Palma. Seeing is one of the biggest problems for Earth-based astronomy: while the big telescopes have theoretically milli-arcsecond resolution, the real image will never be better than the average seeing disc during the observation. This can easily mean a factor of 100 between the potential and practical resolution. Starting in the 1990s, new adaptive optics have been introduced that can help correct for these effects, dramatically improving the resolution of ground based telescopes. - 1 The effects of astronomical seeing - 2 Measures - 3 Overcoming atmospheric seeing - 4 See also - 5 References - 6 External links Typical short-exposure negative image of a binary star (Zeta Boötis in this case) as seen through atmospheric seeing. Each star should appear as a single Airy pattern, but the atmosphere causes the images of the two stars to break up into two patterns of speckles (one pattern above left, the other below right). The speckles are a little difficult to make out in this image due to the coarse pixel size on the camera used (see the simulated images below for a clearer example). The speckles move around rapidly, so that each star appears as a single fuzzy blob in long exposure images (called a seeing disc). The telescope used had a diameter of about 7r0 (see definition of r0 below, and example simulated image through a 7r0 telescope). Astronomical seeing has several effects: - It causes the images of point sources (such as stars), which in the absence of atmospheric turbulence would be steady Airy patterns produced by diffraction, to break up into speckle patterns, which change very rapidly with time (the resulting speckled images can be processed using speckle imaging) - Long exposure images of these changing speckle patterns result in a blurred image of the point source, called a seeing disc - The brightness of stars appears to fluctuate in a process known as scintillation or twinkling - Atmospheric seeing causes the fringes in an astronomical interferometer to move rapidly - The distribution of atmospheric seeing through the atmosphere (the CN2 profile described below) causes the image quality in adaptive optics systems to degrade the further you look from the location of reference star The effects of atmospheric seeing were indirectly responsible for the belief that there were canals on Mars.citation needed In viewing a bright object such as Mars, occasionally a still patch of air will come in front of the planet, resulting in a brief moment of clarity. Before the use of charge-coupled devices, there was no way of recording the image of the planet in the brief moment other than having the observer remember the image and draw it later. This had the effect of having the image of the planet be dependent on the observer's memory and preconceptions which led the belief that Mars had linear features. The effects of atmospheric seeing are qualitatively similar throughout the visible and near infra-red wavebands. At large telescopes the long exposure image resolution is generally slightly higher at longer wavelengths, and the timescale (t0 - see below) for the changes in the dancing speckle patterns is substantially lower. There are three common descriptions of the astronomical seeing conditions at an observatory: - The full width at half maximum (FWHM) of the seeing disc - r0 (the size of a typical "lump" of uniform air within the turbulent atmosphere1) and t0 (the time-scale over which the changes in the turbulence become significant) - The CN2 profile These are described in the sub-sections below: Without an atmosphere, a small star would have an apparent size, an "Airy disk", in a telescope image determined by diffraction and would be inversely proportional to the diameter of the telescope. However when light enters the Earth's atmosphere, the different temperature layers and different wind speeds distort the light waves, leading to distortions in the image of a star. The effects of the atmosphere can be modeled as rotating cells of air moving turbulently. At most observatories, the turbulence is only significant on scales larger than r0 (see below—the seeing parameter r0 is 10–20 cm at visible wavelengths under the best conditions) and this limits the resolution of telescopes to be about the same as given by a space-based 10–20 cm telescope. The distortion changes at a high rate, typically more frequently than 100 times a second. In a typical astronomical image of a star with an exposure time of seconds or even minutes, the different distortions average out as a filled disc called the point spread function or "seeing disc". The diameter of the seeing disk, most often defined as the full width at half maximum (FWHM), is a measure of the astronomical seeing conditions. It follows from this definition that seeing is always a variable quantity, different from place to place, from night to night, and even variable on a scale of minutes. Astronomers often talk about "good" nights with a low average seeing disc diameter, and "bad" nights where the seeing diameter was so high that all observations were worthless. Slow motion movie of what you see through a telescope when you look at a star at high magnification (negative images). The telescope used had a diameter of about 7r0 (see definition of r0 below, and example simulated image through a 7r0 telescope). Notice how the star breaks up into multiple blobs (speckles) -- entirely an atmospheric effect. Some telescope vibration is also noticeable. The FWHM of the seeing disc (or just seeing) is usually measured in arcseconds, abbreviated with the symbol (″). A 1.0″ seeing is a good one for average astronomical sites. The seeing of an urban environment is usually much worse. Good seeing nights tend to be clear, cold nights without wind gusts. Warm air rises (convection), degrading the seeing, as do wind and clouds. At the best high-altitude mountaintop observatories, the wind brings in stable air which has not previously been in contact with the ground, sometimes providing seeing as good as 0.4". The astronomical seeing conditions at an observatory can be well described by the parameters r0 and t0. For telescopes with diameters smaller than r0, the resolution of long-exposure images is determined primarily by diffraction and the size of the Airy pattern and thus is inversely proportional to the telescope diameter. For telescopes with diameters larger than r0, the image resolution is determined primarily by the atmosphere and is independent of telescope diameter, remaining constant at the value given by a telescope of diameter equal to r0. r0 also corresponds to the length-scale over which the turbulence becomes significant (10–20 cm at visible wavelengths at good observatories), and t0 corresponds to the time-scale over which the changes in the turbulence become significant. r0 determines the spacing of the actuators needed in an adaptive optics system, and t0 determines the correction speed required to compensate for the effects of the atmosphere. r0 and t0 vary with the wavelength used for the astronomical imaging, allowing slightly higher resolution imaging at longer wavelengths using large telescopes. Mathematical models can give an accurate model of the effects of astronomical seeing on images taken through ground-based telescopes. Three simulated short-exposure images are shown at the right through three different telescope diameters (as negative images to highlight the fainter features more clearly—a common astronomical convention). The telescope diameters are quoted in terms of the Fried parameter (defined below). is a commonly used measurement of the astronomical seeing at observatories. At visible wavelengths, varies from 20 cm at the best locations to 5 cm at typical sea-level sites. In reality, the pattern of blobs (speckles) in the images changes very rapidly, so that long-exposure photographs would just show a single large blurred blob in the centre for each telescope diameter. The diameter (FWHM) of the large blurred blob in long-exposure images is called the seeing disc diameter, and is independent of the telescope diameter used (as long as adaptive optics correction is not applied). It is first useful to give a brief overview of the basic theory of optical propagation through the atmosphere. In the standard classical theory, light is treated as an oscillation in a field . For monochromatic plane waves arriving from a distant point source with wave-vector : where is the complex field at position and time , with real and imaginary parts corresponding to the electric and magnetic field components, represents a phase offset, is the frequency of the light determined by , and is the amplitude of the light. The photon flux in this case is proportional to the square of the amplitude , and the optical phase corresponds to the complex argument of . As wavefronts pass through the Earth's atmosphere they may be perturbed by refractive index variations in the atmosphere. The diagram at the top-right of this page shows schematically a turbulent layer in the Earth's atmosphere perturbing planar wavefronts before they enter a telescope. The perturbed wavefront may be related at any given instant to the original planar wavefront in the following way: where represents the fractional change in wavefront amplitude and is the change in wavefront phase introduced by the atmosphere. It is important to emphasise that and describe the effect of the Earth's atmosphere, and the timescales for any changes in these functions will be set by the speed of refractive index fluctuations in the atmosphere. A description of the nature of the wavefront perturbations introduced by the atmosphere is provided by the Kolmogorov model developed by Tatarski,2 based partly on the studies of turbulence by the Russian mathematician Andreï Kolmogorov.34 This model is supported by a variety of experimental measurements5 and is widely used in simulations of astronomical imaging. The model assumes that the wavefront perturbations are brought about by variations in the refractive index of the atmosphere. These refractive index variations lead directly to phase fluctuations described by , but any amplitude fluctuations are only brought about as a second-order effect while the perturbed wavefronts propagate from the perturbing atmospheric layer to the telescope. For all reasonable models of the Earth's atmosphere at optical and infra-red wavelengths the instantaneous imaging performance is dominated by the phase fluctuations . The amplitude fluctuations described by have negligible effect on the structure of the images seen in the focus of a large telescope. For simplicity, the phase fluctuations in Tatarski's model are often assumed to have a Gaussian random distribution with the following second-order structure function: where is the atmospherically induced variance between the phase at two parts of the wavefront separated by a distance in the aperture plane, and represents the ensemble average. For the Gaussian random approximation, the structure function of Tatarski (1961) can be described in terms of a single parameter : indicates the strength of the phase fluctuations as it corresponds to the diameter of a circular telescope aperture at which atmospheric phase perturbations begin to seriously limit the image resolution. Typical values for I band (900 nm wavelength) observations at good sites are 20–40 cm. It should be noted6 that also corresponds to the aperture diameter for which the variance of the wavefront phase averaged over the aperture comes approximately to unity: This equation represents a commonly used definition for , a parameter frequently used to describe the atmospheric conditions at astronomical observatories. can be determined from a measured CN2 profile (described below) as follows: If turbulent evolution is assumed to occur on slow timescales, then the timescale t0 is simply proportional to r0 divided by the mean wind speed. The refractive index fluctuations caused by Gaussian random turbulence can be simulated using the following algorithm:7 where is the optical phase error introduced by atmospheric turbulence, R (k) is a two-dimensional square array of independent random complex numbers which have a Gaussian distribution about zero and white noise spectrum, K (k) is the (real) Fourier amplitude expected from the Kolmogorov (or Von Karman) spectrum, Re represents taking the real part, and FT represents a discrete Fourier transform of the resulting two-dimensional square array (typically an FFT). The assumption that the phase fluctuations in Tatarski's model have a Gaussian random distribution is usually unrealistic. In reality, turbulence exhibits intermittency.8 These fluctuations in the turbulence strength can be straightforwardly simulated as follows:9 where I (k) is a two-dimensional array which represents the spectrum of intermittency, with the same dimensions as R (k), and where represents convolution. The intermittency is described in terms of fluctuations in the turbulence strength . It can be seen that the equation for the Gaussian random case above is just the special case from this equation with: where is the Dirac delta function. A more thorough description of the astronomical seeing at an observatory is given by producing a profile of the turbulence strength as a function of altitude, called a profile. profiles are generally performed when deciding on the type of adaptive optics system which will be needed at a particular telescope, or in deciding whether or not a particular location would be a good site for setting up a new astronomical observatory. Typically, several methods are used simultaneously for measuring the profile and then compared. Some of the most common methods include: - SCIDAR (imaging the shadow patterns in the scintillation of starlight) - LOLAS (a small-aperture variant of SCIDAR designed for low-altitude profiling) - MooSci (11-channel lunar scintillometer for ground level profiling)10 - RADAR mapping of turbulence - Balloon-borne thermometers to measure how quickly the air temperature is fluctuating with time due to turbulence There are also mathematical functions describing the profile. Some are empirical fits from measured data and others attempt to incorporate elements of theory. One common model for continental land masses is known as Hufnagel-Valley after two workers in this subject. The first answer to this problem was speckle imaging, which allowed bright objects to be observed with very high resolution. Later came NASA's Hubble Space Telescope, working outside the atmosphere and thus not having any seeing problems and allowing observations of faint targets for the first time (although with poorer resolution than speckle observations of bright sources from ground-based telescopes because of Hubble's smaller telescope diameter). The highest resolution visible and infrared images currently come from imaging optical interferometers such as the Navy Prototype Optical Interferometer or Cambridge Optical Aperture Synthesis Telescope. Starting in the 1990s, many telescopes have begun to develop adaptive optics systems that partially solve the seeing problem, but none of the systems so far built or designed completely removes the atmosphere effect, and observations are usually limited to a small region of the sky surrounding relatively bright stars. Another cheaper technique, lucky imaging, has had very good results. This idea dates back to pre-war naked-eye observations of moments of good seeing, which were followed by observations of the planets on cine film after World War II. The technique relies on the fact that every so often the effects of the atmosphere will be negligible, and hence by recording large numbers of images in real-time, a 'lucky' excellent image can be picked out. This technique can outperform adaptive optics in many cases and is even accessible to amateurs. It does, however, require very much longer observation times than adaptive optics for imaging faint targets, and is limited in its maximum resolution. - Atmosphere and Telescope Simulator - Atmospheric turbulence simulator. - Clear Sky Chart - includes a weather forecast of astronomical seeing. - Transient lunar phenomenon Much of the above text is taken (with permission) from Lucky Exposures: Diffraction limited astronomical imaging through the atmosphere, by Robert Nigel Tubbs - Chromey, Frederick R. (2010). To measure the sky : an introduction to observational astronomy (1. publ. ed.). Cambridge: Cambridge University Press. p. 140. ISBN 9780521763868. - Tatarskiĭ, V. I. (1961). R.A. Silverman, ed. Wave Propagation in a Turbulent Medium. University of Michigan: McGraw-Hill Books. p. 285. Bibcode:1961wptm.book.....T. - Kolmogorov, A. N. (1941). "Dissipation of energy in the locally isotropic turbulence". Comptes rendus (Doklady) de l'Académie des Sciences de l'U.R.S.S. 32: 16–18. Bibcode:1941DoSSR..32...16K. - Kolmogorov, A. N. (1941). "The local structure of turbulence in incompressible viscous fluid for very large Reynold's numbers". Comptes rendus (Doklady) de l'Académie des Sciences de l'U.R.S.S. 30: 301–305. Bibcode:1941DoSSR..30..301K. - BUSCHER, D. F.; ARMSTRONG, J. T.; HUMMEL, C. A.; QUIRRENBACH, A.; MOZURKEWICH, D.; JOHNSTON, K. J.; DENISON, C. S.; COLAVITA, M. M.; SHAO, M. (February 1995). "Interferometric seeing measurements on Mt. Wilson: power spectra and outer scales". Applied Optics 34 (6): 1081–1096. Bibcode:1995ApOpt..34.1081B. doi:10.1364/AO.34.001081. PMID 21037637. - NIGHTINGALE, N. S.; BUSCHER, D. F. (July 1991). "Interferometric seeing measurements at the La Palma Observatory". Monthly Notices of the Royal Astronomical Society 251: 155–166. Bibcode:1991MNRAS.251..155N. doi:10.1093/mnras/251.1.155. - O'BYRNE, J. W. (Sep 1988). "Seeing measurements using a shearing interferometer". Publications of the Astronomical Society of the Pacific 100: 1169–1177. Bibcode:1988PASP..100.1169O. doi:10.1086/132285. - COLAVITA, M. M.; SHAO, M.; STAELIN, D. H. (October 1987). "Atmospheric phase measurements with the Mark III stellar interferometer". Applied Optics 26 (19): 4106–4112. Bibcode:1987ApOpt..26.4106C. doi:10.1364/AO.26.004106. PMID 20490196. - FRIED, D. L. (1965). "Statistics of a Geometric Representation of Wavefront Distortion". Journal of the Optical Society of America 55 (11): 1427–1435. Bibcode:1965OSAJ...55.1427F. doi:10.1364/JOSA.55.001427.*NOLL, R. J. (March 1976). "Zernike polynomials and atmospheric turbulence". Journal of the Optical Society of America 66 (3): 207–211. Bibcode:1976JOSA...66..207N. doi:10.1364/JOSA.66.000207. - The effect of temporal fluctuations in r0 on high-resolution observations, Robert N. Tubbs Proc SPIE 6272 pp 93T, 2006 - BATCHELOR, G. K., & TOWNSEND, A. A. 1949 (May). - Baldwin, J. E.; Warner, P. J.; Mackay, C. D., The point spread function in Lucky Imaging and variations in seeing on short timescales, Astronomy and Astrophysics V. 480 pp 589B. - The effect of temporal fluctuations in r0 on high-resolution observations, Robert N. Tubbs Proc SPIE 6272 pp 93T, 2006 - Villanueva, Steven, Jr.; Depoy, D. L.; Marshall, J.; Berdja, A.; Rheault, J. P.; Prieto, G.; Allen, R.; Carona, D. (July 2010). "MooSci: a lunar scintillometer" (PDF). Ground-based and Airborne Instrumentation for Astronomy III. Edited by McLean, Ian S.; Ramsay, Suzanne K.; Takami, Hideki. Proceedings of the SPIE, Volume 7735, article id. 773547, 9 pp. (2010). doi:10.1117/12.857413. - "A Mix of Colours and Wonder". Retrieved 15 June 2015. - Free 72-hour seeing prediction for every location on earth (Click on 'Charts&Tools' and then 'Astronomy Seeing') - The Royal Astronomical Society of Canada Calgary Centre - Atmospheric "Seeing". Includes animated illustrations of effects of seeing. - Seeing forecasts for North America - Seeing forecasts for Mauna Kea, Hawaii
The lunar phase or phase of the Moon is the shape of the directly sunlit portion of the Moon as viewed from Earth. The lunar phases gradually and cyclically change over the period of a synodic month (about 29.53 days), as the orbital positions of the Moon around Earth and of Earth around the Sun shift. The Moon's rotation is tidally locked by Earth's gravity; therefore, most of the same lunar side always faces Earth. This near side is variously sunlit, depending on the position of the Moon in its orbit. Thus, the sunlit portion of this face can vary from 0% (at new moon) to 100% (at full moon). The lunar terminator is the boundary between the illuminated and darkened hemispheres. Each of the four "intermediate" lunar phases (see below) is around 7.4 days, but this varies slightly due to the elliptical shape of the Moon's orbit. Aside from some craters near the lunar poles, such as Shoemaker, all parts of the Moon see around 14.77 days of daylight, followed by 14.77 days of "night". (The side of the Moon facing away from Earth is sometimes called the "dark side of the Moon", although that is a misnomer.) Phases of the MoonEdit In western culture, the four principal phases of the Moon are new moon, first quarter, full moon, and third quarter (also known as last quarter). These are the instances when the Moon's ecliptic longitude and the Sun's ecliptic longitude differ by 0°, 90°, 180°, and 270°, respectively.[a] Each of these phases occur at slightly different times when viewed from different points on Earth. During the intervals between principal phases, the Moon's apparent shape is either crescent or gibbous. These shapes, and the periods when the Moon shows them, are called the intermediate phases and last one-quarter of a synodic month, or 7.38 days, on average. However, their durations vary slightly because the Moon's orbit is rather elliptical, so the satellite's orbital speed is not constant. The descriptor waxing is used for an intermediate phase when the Moon's apparent shape is thickening, from new to full moon, and waning when the shape is thinning. The eight principal and intermediate phases are given the following names, in sequential order: \|Moon Phase\|\|Northern Hemisphere\|\|Southern Hemisphere\|\|Visibility\|\|Mid-phase \|Northern Hemisphere\|\|Southern Hemisphere\|\|Photograph\| \|New Moon\|\|Disc completely in Sun's shadow (lit by earthshine only) \|Invisible (too close to Sun)\|\|Noon\|\|6 am\|\|6 pm\| \|Waxing crescent\|\|Right side, 0.1%–49.9% lit disc\|\|Left side, 0.1–49.9% lit disc\|\|Late morning to post-dusk\|\|3 pm\|\|9 am\|\|9 pm\| \|First Quarter\|\|Right side, 50% lit disc\|\|Left side, 50% lit disc\|\|Afternoon and early evening\|\|6 pm\|\|Noon\|\|Midnight\| \|Waxing gibbous\|\|Right side, 50.1%–99.9% lit disc\|\|Left side, 50.1%–99.9% lit disc\|\|Late afternoon and most of night\|\|9 pm\|\|3 pm\|\|3 am\| \|Full Moon\|\|100% illuminated disc\|\|Sunset to sunrise (all night)\|\|Midnight\|\|6 pm\|\|6 am\| \|Waning gibbous\|\|Left side, 99.9%–50.1% lit disc\|\|Right side, 99.9%–50.1% lit disc\|\|Most of night and early morning\|\|3 am\|\|9 pm\|\|9 am\| \|Last Quarter\|\|Left side, 50% lit disc\|\|Right side, 50% lit disc\|\|Late night and morning\|\|6 am\|\|Midnight\|\|Noon\| \|Waning crescent\|\|Left side, 49.9%–0.1% lit disc\|\|Right side, 49.9%–0.1% lit disc\|\|Pre-dawn to early afternoon\|\|9 am\|\|3 am\|\|3 pm\| Waxing and waningEdit When the Sun and Moon are aligned on the same side of the Earth, the Moon is "new", and the side of the Moon facing Earth is not illuminated by the Sun. As the Moon waxes (the amount of illuminated surface as seen from Earth is increasing), the lunar phases progress through new moon, crescent moon, first-quarter moon, gibbous moon, and full moon. The Moon is then said to wane as it passes through the gibbous moon, third-quarter moon, crescent moon, and back to new moon. The terms old moon and new moon are not interchangeable. The "old moon" is a waning sliver (which eventually becomes undetectable to the naked eye) until the moment it aligns with the Sun and begins to wax, at which point it becomes new again. Half moon is often used to mean the first- and third-quarter moons, while the term quarter refers to the extent of the Moon's cycle around the Earth, not its shape. When an illuminated hemisphere is viewed from a certain angle, the portion of the illuminated area that is visible will have a two-dimensional shape as defined by the intersection of an ellipse and circle (in which the ellipse's major axis coincides with the circle's diameter). If the half-ellipse is convex with respect to the half-circle, then the shape will be gibbous (bulging outwards), whereas if the half-ellipse is concave with respect to the half-circle, then the shape will be a crescent. When a crescent moon occurs, the phenomenon of earthshine may be apparent, where the night side of the Moon dimly reflects indirect sunlight reflected from Earth. Orientation by latitudeEdit In the Northern Hemisphere, if the left (east) side of the Moon is dark, then the bright part is thickening, and the Moon is described as waxing (shifting toward full moon). If the right (west) side of the Moon is dark, then the bright part is thinning, and the Moon is described as waning (past full and shifting toward new moon). Assuming that the viewer is in the Northern Hemisphere, the right side of the Moon is the part that is always waxing. (That is, if the right side is dark, the Moon is becoming darker; if the right side is lit, the Moon is getting brighter.) In the Southern Hemisphere, the Moon is observed from a perspective inverted, or rotated 180°, to that of the Northern and to all of the images in this article, so that the opposite sides appear to wax or wane. Closer to the Equator, the lunar terminator will appear horizontal during the morning and evening. Since the above descriptions of the lunar phases only apply at middle or high latitudes, observers moving towards the tropics from northern or southern latitudes will see the Moon rotated anti-clockwise or clockwise with respect to the images in this article. The lunar crescent can open upward or downward, with the "horns" of the crescent pointing up or down, respectively. When the Sun appears above the Moon in the sky, the crescent opens downward; when the Moon is above the Sun, the crescent opens upward. The crescent Moon is most clearly and brightly visible when the Sun is below the horizon, which implies that the Moon must be above the Sun, and the crescent must open upward. This is therefore the orientation in which the crescent Moon is most often seen from the tropics. The waxing and waning crescents look very similar. The waxing crescent appears in the western sky in the evening, and the waning crescent in the eastern sky in the morning. When the Moon as seen from Earth is a narrow crescent, Earth as viewed from the Moon is almost fully lit by the Sun. Often, the dark side of the Moon is dimly illuminated by indirect sunlight reflected from Earth, but is bright enough to be easily visible from Earth. This phenomenon is called earthshine and sometimes picturesquely described as "the old moon in the new moon's arms" or "the new moon in the old moon's arms". The Gregorian calendar month, which is 1⁄12 of a tropical year, is about 30.44 days, while the cycle of lunar phases (the Moon's synodic period) repeats every 29.53 days on average. Therefore, the timing of the lunar phases shifts by an average of almost one day for each successive month. (A lunar year lasts about 354 days.) Photographing the Moon's phase every day for a month (starting in the evening after sunset, and repeating roughly 24 hours and 50 minutes later, and ending in the morning before sunrise) and arranging the series of photos on a calendar would create a composite image like the example calendar (May 8 – June 6, 2005) shown on the left. May 20 is blank because a picture would be taken before midnight on May 19 and the next after midnight on May 21. Similarly, on a calendar listing moonrise or moonset times, some days will appear to be skipped. When moonrise precedes midnight one night, the next moonrise will follow midnight on the next night (so too with moonset). The "skipped day" is just a feature of the Moon's eastward movement in relation to the Sun, which at most latitudes, causes the Moon to rise later each day. The Moon follows a predictable orbit every month. The approximate age of the moon, and hence the approximate phase, can be calculated for any date by calculating the number of days since a known new moon (such as January 1, 1900 or August 11, 1999) and reducing this modulo 29.530588853 (the length of a synodic month). The difference between two dates can be calculated by subtracting the Julian Day Number of one from that of the other, or there are simpler formulae giving (for instance) the number of days since December 31, 1899. However, this calculation assumes a perfectly circular orbit and makes no allowance for the time of day at which the new moon happened, therefore may be incorrect by several hours (it also becomes less accurate the larger the difference between the required date and the reference date); it is accurate enough to use in a novelty clock application showing moon phase, but specialist usage taking account of lunar apogee and perigee requires a more elaborate calculation. The Earth subtends an angle of about two degrees, when seen from the Moon. This means that an observer on Earth who sees the Moon when it is close to the eastern horizon sees it from an angle that is about 2 degrees different from the line of sight of an observer who sees the Moon on the western horizon. The Moon moves about 12 degrees around its orbit per day, so, if these observers were stationary, they would see the phases of the Moon at times that differ by about one-sixth of a day, or 4 hours. But in reality the observers are on the surface of the rotating Earth, so someone who sees the Moon on the eastern horizon at one moment sees it on the western horizon about 12 hours later. This adds an oscillation to the apparent progression of the lunar phases. They appear to occur more slowly when the Moon is high in the sky than when it is below the horizon. The Moon appears to move jerkily, and the phases do the same. The amplitude of this oscillation is never more than about four hours, which is a small fraction of a month. It does not have any obvious effect on the appearance of the Moon. However, it does affect accurate calculations of the times of lunar phases. It might be expected that once every month, when the Moon passes between Earth and the Sun during a new moon, its shadow would fall on Earth causing a solar eclipse, but this does not happen every month. Nor is it true that during every full moon, the Earth's shadow falls on the Moon, causing a lunar eclipse. Solar and lunar eclipses are not observed every month because the plane of the Moon's orbit around the Earth is tilted by about 5° with respect to the plane of Earth's orbit around the Sun (the plane of the ecliptic). Thus, when new and full moons occur, the Moon usually lies to the north or south of a direct line through the Earth and Sun. Although an eclipse can only occur when the Moon is either new (solar) or full (lunar), it must also be positioned very near the intersection of Earth's orbital plane about the Sun and the Moon's orbital plane about the Earth (that is, at one of its nodes). This happens about twice per year, and so there are between four and seven eclipses in a calendar year. Most of these eclipses are partial; total eclipses of the Moon or Sun are less frequent. - Strictly, the quarter phases happen when the observer–Moon–Sun angle is 90°, also known as quadrature. This is not exactly the same as having the Sun–observer–Moon angle a right-angle, but the difference is very slight. - "Hawaiian Moon Names". Imiloa, Hilo Attractions. - "Free Astronomy Lesson 7 - The Phases of the Moon". Synapses.co.uk. Retrieved 2015-12-28. - Origin: 1350–1400; Middle English < Latin gibbōsus humped, equivalent to gibb "(a) hump" + -ōsus "-ous"; "Gibbous". Dictionary.com. - CNN, Leah Asmelash and David Allan. "A black moon is coming on July 31. Here's what that means". CNN. - "Phases of the Moon and Percent of the Moon Illuminated". aa.usno.navy.mil. Retrieved 2018-02-12. - Buick, Tony; Pugh, Philip (2011). How to Photograph the Moon and Planets with Your Digital Camera. Springer. ISBN 978-1-4419-5828-0. - Kelley, David H.; Milone, Eugene F. (2011). Exploring Ancient Skies: A Survey of Ancient and Cultural Astronomy (2nd ed.). Springer. ISBN 978-1-4419-7624-6. - Kutner, Marc L. (2003). Astronomy: A Physical Perspective. Cambridge University Press. ISBN 978-0-521-52927-3. - Lynch, Mike. Texas Starwatch. Voyageur Press. ISBN 978-1-61060-511-3. - Naylor, John (2002). Out of the Blue: A 24-Hour Skywatcher's Guide. Cambridge University Press. ISBN 978-0-521-80925-2. - Ruggles, Clive L. N. (2005). Ancient Astronomy: An Encyclopedia of Cosmologies and Myth. ABC-CLIO. ISBN 978-1-85109-477-6. This article's use of external links may not follow Wikipedia's policies or guidelines. (April 2015) (Learn how and when to remove this template message) \|Wikimedia Commons has media related to Lunar phases.\| - Six Millennium Catalog of Phases of the Moon - U.S. Naval Service on Moon Phase / What the Moon Looks Like Today (United States Naval Observatory) - Full Moon Names - Current Moon Phase - The Length of the Lunar Cycle (numerical integration analysis) - Open Source Physics Lunar Phase Model - Lunar phase simulator (animation) - Starchild: Moonlight Madness Lunar Phases Game - Names and Images of the 8 moon phases - Astrophysics Science Project Integrating Research & Education: Lunar Phases Quiz - Lunar Phase Image Sets In High-Resolution (1200x1200 pixels) at 1-Degree Intervals - Views of the Moon From 4 Sides at Any Relative Phase - Front/Back/East/West Lunar Phase Explorers - Mnemonic devices for the Lunar phases - Moon activity idea from Jet Propulsion Laboratory
Learn something new every day More Info... by email Linguistic analysis refers to the scientific analysis of a language sample. It involves at least one of the five main branches of linguistics, which are phonology, morphology, syntax, semantics, and pragmatics. Linguistic analysis can be used to describe the unconscious rules and processes that speakers of a language use to create spoken or written language, and this can be useful to those who want to learn a language or translate from one language to another. Some argue that it can also provide insight into the minds of the speakers of a given language, although this idea is controversial. The discipline of linguistics is defined as the scientific study of language. People who have an education in linguistics and practice linguistic analysis are called linguists. The drive behind linguistic analysis is to understand and describe the knowledge that underlies the ability to speak a given language, and to understand how the human mind processes and creates language. The five main branches of linguistics are phonology, morphology, syntax, semantics, and pragmatics. An extended language analysis may cover all five of the branches, or it may focus on only one aspect of the language being analyzed. Each of the five branches focuses on a single area of language. Phonology refers to the study of the sounds of a language. Every language has its own inventory of sounds and logical rules for combining those sounds to create words. The phonology of a language essentially refers to its sound system and the processes used to combine sounds in spoken language. Morphology refers to the study of the internal structure of the words of a language. In any given language, there are many words to which a speaker can add a suffix, prefix, or infix to create a new word. In some languages, these processes are more productive than others. The morphology of a language refers to the word-building rules speakers use to create new words or alter the meaning of existing words in their language. Syntax is the study of sentence structure. Every language has its own rules for combining words to create sentences. Syntactic analysis attempts to define and describe the rules that speakers use to put words together to create meaningful phrases and sentences. Semantics is the study of meaning in language. Linguists attempt to identify not only how speakers of a language discern the meanings of words in their language, but also how the logical rules speakers apply to determine the meaning of phrases, sentences, and entire paragraphs. The meaning of a given word can depend on the context in which it is used, and the definition of a word may vary slightly from speaker to speaker. Pragmatics is the study of the social use of language. All speakers of a language use different registers, or different conversational styles, depending on the company in which they find themselves. A linguistic analysis that focuses on pragmatics may describe the social aspects of the language sample being analyzed, such as how the status of the individuals involved in the speech act could affect the meaning of a given utterance. Linguistic analysis has been used to determine historical relationships between languages and people from different regions of the world. Some governmental agencies have used linguistic analysis to confirm or deny individuals' claims of citizenship. This use of linguistic analysis remains controversial, because language use can vary greatly across geographical regions and social class, which makes it difficult to accurately define and describe the language spoken by the citizens of a particular country.
Airplane aerodynamics: fundamentals and flight principles. Fundamentals of aerodynamics Air, like any other fluid, is able to flow and change its shape when subjected to even minute pressures because of the lack of strong molecular cohesion. For example, gas will completely fill any container into which it is placed, expanding or contracting to adjust its shape to the limits of the container. Because air has mass and weight, it is a body, and as a body, it reacts to the scientific laws of bodies in the same manner as other gaseous bodies. This body of air resting upon the surface of the earth has weight and at sea level develops an average pressure of 14.7 pounds on each square inch of surface, or 29.92 inches of mercury—but as its thickness is limited, the higher the altitude, the less air there is above. For this reason, the weight of the atmosphere at 18,000 feet is only one-half what it is at sea level. Though there are various kinds of pressure, this discussion is mainly concerned with atmospheric pressure. It is one of the basic factors in weather changes, helps to lift the airplane, and actuates some of the important flight instruments in the airplane. These instruments are the altimeter, the airspeed indicator, the rate-of-climb indicator, and the manifold pressure gauge. Though air is very light, it has mass and is affected by the attraction of gravity. Therefore, like any other substance, it has weight, and because of its weight, it has force. Since it is a fluid substance, this force is exerted equally in all directions, and its effect on bodies within the air is called pressure. Under standard conditions at sea level, the average pressure exerted on the human body by the weight of the atmosphere around it is approximately 14.7 lb./sqin. The density of air has significant effects on the airplane’s capability. As air becomes less dense, it reduces (1) power because the engine takes in less air, (2) thrust because the propeller is less efficient in thin air, and (3) lift because the thin air exerts less force on the airfoils. Effects of pressure on density Since air is a gas, it can be compressed or expanded. When air is compressed, a greater amount of air can occupy a given volume. Conversely, when pressure on a given volume of air is decreased, the air expands and occupies a greater space. That is, the original column of air at a lower pressure contains a smaller mass of air. In other words, the density is decreased. In fact, density is directly proportional to pressure. If the pressure is doubled, the density is doubled, and if the pressure is lowered, so is the density. This statement is true, only at a constant temperature. Effects of temperature on density The effect of increasing the temperature of a substance is to decrease its density. Conversely, decreasing the temperature has the effect of increasing the density. Thus, the density of air varies inversely as the absolute temperature varies. This statement is true, only at a constant pressure. In the atmosphere, both temperature and pressure decrease with altitude, and have conflicting effects upon density. However, the fairly rapid drop in pressure as altitude is increased usually has the dominating effect. Hence, density can be expected to decrease with altitude. Effects of humidity on density The preceding paragraphs have assumed that the air was perfectly dry. In reality, it is never completely dry. The small amount of water vapor suspended in the atmosphere may be almost negligible under certain conditions, but in other conditions humidity may become an important factor in the performance of an airplane. Water vapor is lighter than air; consequently, moist air is lighter than dry air. It is lightest or least dense when, in a given set of conditions, it contains the maximum amount of water vapor. The higher the temperature, the greater amount of water vapor the air can hold. When comparing two separate air masses, the first warm and moist (both qualities tending to lighten the air) and the second cold and dry (both qualities making it heavier), the first necessarily must be less dense than the second. Pressure, temperature, and humidity have a great influence on airplane performance, because of their effect upon density. Bernoulli's principle of pressure Three centuries ago, Mr. Daniel Bernoulli, a Swiss mathematician, explained how the pressure of a moving fluid (liquid or gas) varies with its speed of motion. Specifically, he stated that an increase in the speed of movement or flow would cause a decrease in the fluid’s pressure. This is exactly what happens to air passing over the curved top of the airplane wing. A practical application of Bernoulli’s theorem is the venturi tube. The venturi tube has an air inlet which narrows to a throat (constricted point) and an outlet section which increases in diameter toward the rear. The diameter of the outlet is the same as that of the inlet. At the throat, the airflow speeds up and the pressure decreases; at the outlet, the airflow slows and the pressure increases. Figure 1: Air pressure decreases in a venturi. Air has viscosity, and will encounter resistance to flow over a surface. The viscous nature of airflow reduces the local velocities on a surface and is responsible for skin friction drag. As the air passes over the wing’s surface, the air particles nearest the surface come to rest. The next layer of particles is slowed down but not stopped. Some small but measurable distance from the surface, the air particles are moving at free stream velocity. The layer of air over the wing’s surface, which is slowed down or stopped by viscosity, is termed the “boundary layer.” Typical boundary layer thicknesses on an airplane range from small fractions of an inch near the leading edge of a wing to the order of 12 inches at the aft end of a large airplane such as a Boeing 747. There are two different types of boundary layer flow: laminar and turbulent. The laminar boundary layer is a very smooth flow, while the turbulent boundary layer contains swirls or “eddies.” The laminar flow creates less skin friction drag than the turbulent flow, but is less stable. Boundary layer flow over a wing surface begins as a smooth laminar flow. As the flow continues back from the leading edge, the laminar boundary layer increases in thickness. At some distance back from the leading edge, the smooth laminar flow breaks down and transitions to a turbulent flow. From a drag standpoint, it is advisable to have the transition from laminar to turbulent flow as far aft on the wing as possible, or have a large amount of the wing surface within the laminar portion of the boundary layer. The low energy laminar flow, however, tends to break down more suddenly than the turbulent layer. Figure 2: Boundary layer. Another phenomenon associated with viscous flow is separation. Separation occurs when the airflow breaks away from an airfoil. The natural progression is from laminar boundary layer to turbulent boundary layer and then to airflow separation. Airflow separation produces high drag and ultimately destroys lift. The boundary layer separation point moves forward on the wing as the angle of attack is increased. The explanation of lift can best be explained by looking at a cylinder rotating in an airstream. The local velocity near the cylinder is composed of the airstream velocity and the cylinder’s rotational velocity, which decreases with distance from the cylinder. On a cylinder, which is rotating in such a way that the top surface area is rotating in the same direction as the airflow, the local velocity at the surface is high on top and low on the bottom. As shown in figure 3, at point “A,” a stagnation point exists where the airstream line that impinges on the surface splits; some air goes over and some under. Another stagnation point exists at “B,” where the two airstreams rejoin and resume at identical velocities. We now have upwash ahead of the rotating cylinder and downwash at the rear. The difference in surface velocity accounts for a difference in pressure, with the pressure being lower on the top than the bottom. This low pressure area produces an upward force known as the “Magnus Effect.” This mechanically induced circulation illustrates the relationship between circulation and lift. An airfoil with a positive angle of attack develops air circulation as its sharp trailing edge forces the rear stagnation point to be aft of the trailing edge, while the front stagnation point is below the leading edge. Figure 3: The Magnus effect is a lifting effect produced, when a rotating cylinder produces a pressure differential. If air is recognized as a body and it is accepted that it must follow the above laws, one can begin to see how and why an airplane wing develops lift as it moves through the air. It has already been discussed in general terms the question of how an airplane wing can sustain flight when the airplane is heavier than air. Perhaps the explanation can best be reduced to its most elementary concept by stating that lift (flight) is simply the result of fluid flow (air) about an airfoil—or in everyday language, the result of moving an airfoil (wing), by whatever means, through the air. Since it is the airfoil which harnesses the force developed by its movement through the air, a discussion and explanation of this structure will be presented. An airfoil is a structure designed to obtain reaction upon its surface from the air through which it moves or that moves past such a structure. Air acts in various ways when submitted to different pressures and velocities; but this discussion will be confined to the parts of an airplane that a pilot is most concerned with in flight—namely, the airfoils designed to produce lift. By looking at a typical airfoil profile, such as the cross section of a wing, one can see several obvious characteristics of design. Figure 4: Typical airfoil section. Notice that there is a difference in the curvatures of the upper and lower surfaces of the airfoil (the curvature is called camber). The camber of the upper surface is more pronounced than that of the lower surface, which is somewhat flat in most instances. In figure 4, note that the two extremities of the airfoil profile also differ in appearance. The end which faces forward in flight is called the leading edge, and is rounded; while the other end, the trailing edge, is quite narrow and tapered. A reference line often used in discussing the airfoil is the chord line, a straight line drawn through the profile connecting the extremities of the leading and trailing edges. The distance from this chord line to the upper and lower surfaces of the wing denotes the magnitude of the upper and lower camber at any point. Another reference line, drawn from the leading edge to the trailing edge, is the “mean camber line.” This mean line is equidistant at all points from the upper and lower contours. The construction of the wing, so as to provide actions greater than its weight, is done by shaping the wing so that advantage can be taken of the air’s response to certain physical laws, and thus develop two actions from the air mass; a positive pressure lifting action from the air mass below the wing, and a negative pressure lifting action from lowered pressure above the wing. The fact that most lift is the result of the airflow’s downwash from above the wing, must be thoroughly understood in order to continue further in the study of flight. It is neither accurate nor does it serve a useful purpose, however, to assign specific values to the percentage of lift generated by the upper surface of an airfoil versus that generated by the lower surface. These are not constant values and will vary, not only with flight conditions, but with different wing designs. It should be understood that different airfoils have different flight characteristics. Many thousands of airfoils have been tested in wind tunnels and in actual flight, but no one airfoil has been found that satisfies every flight requirement. The weight, speed, and purpose of each airplane dictate the shape of its airfoil. It was learned many years ago that the most efficient airfoil for producing the greatest lift was one that had a concave, or “scooped out” lower surface. Later it was also learned that as a fixed design, this type of airfoil sacrificed too much speed while producing lift and, therefore, was not suitable for high-speed flight. It is interesting to note, however, that through advanced progress in engineering, today’s high-speed jets can again take advantage of the concave airfoil’s high lift characteristics. Leading edge (Kreuger) flaps and trailing edge (Fowler) flaps, when extended from the basic wing structure, literally change the airfoil shape into the classic concave form, thereby generating much greater lift during slow flight conditions. On the other hand, an airfoil that is perfectly streamlined and offers little wind resistance sometimes does not have enough lifting power to take the airplane off the ground. Thus, modern airplanes have airfoils which strike a medium between extremes in design, the shape varying according to the needs of the airplane for which it is designed. Figure 5 shows some of the more common airfoil sections. Figure 5: Airfoil designs. Momentum effects of airflow In a wind tunnel or in flight, an airfoil is simply a streamlined object inserted into a moving stream of air. If the airfoil profile were in the shape of a teardrop, the speed and the pressure changes of the air passing over the top and bottom would be the same on both sides. But if the teardrop shaped airfoil were cut in half lengthwise, a form resembling the basic airfoil (wing) section would result. If the airfoil were then inclined so the airflow strikes it at an angle (angle of attack), the air molecules moving over the upper surface would be forced to move faster than would the molecules moving along the bottom of the airfoil, since the upper molecules must travel a greater distance due to the curvature of the upper surface. This increased velocity reduces the pressure above the airfoil. Bernoulli’s principle of pressure by itself does not explain the distribution of pressure over the upper surface of the airfoil. A discussion of the influence of momentum of the air as it flows in various curved paths near the airfoil will be presented. Figure 6: Momentum influences airflow over an airfoil. Momentum is the resistance a moving body offers to having its direction or amount of motion changed. When a body is forced to move in a circular path, it offers resistance in the direction away from the center of the curved path. This is “centrifugal force.” While the particles of air move in the curved path AB, centrifugal force tends to throw them in the direction of the arrows between A and B and hence, causes the air to exert more than normal pressure on the leading edge of the airfoil. But after the air particles pass B (the point of reversal of the curvature of the path) the centrifugal force tends to throw them in the direction of the arrows between B and C (causing reduced pressure on the airfoil). This effect is held until the particles reach C, the second point of reversal of curvature of the airflow. Again the centrifugal force is reversed and the particles may even tend to give slightly more than normal pressure on the trailing edge of the airfoil, as indicated by the short arrows between C and D. Therefore, the air pressure on the upper surface of the airfoil is distributed so that the pressure is much greater on the leading edge than the surrounding atmospheric pressure, causing strong resistance to forward motion; but the air pressure is less than surrounding atmospheric pressure over a large portion of the top surface (B to C). Fluid flow or airflow then, is the basis for flight in airplanes, and is a product of the velocity of the airplane. The velocity of the airplane is very important to the pilot since it affects the lift and drag forces of the airplane. The pilot uses the velocity (airspeed) to fly at a minimum glide angle, at maximum endurance, and for a number of other flight maneuvers. Airspeed is the velocity of the airplane relative to the air mass through which it is flying. From experiments conducted on wind tunnel models and on full size airplanes, it has been determined that as air flows along the surface of a wing at different angles of attack, there are regions along the surface where the pressure is negative, or less than atmospheric, and regions where the pressure is positive, or greater than atmospheric. This negative pressure on the upper surface creates a relatively larger force on the wing than is caused by the positive pressure resulting from the air striking the lower wing surface. Figure 7 shows the pressure distribution along an airfoil at three different angles of attack. In general, at high angles of attack the center of pressure moves forward, while at low angles of attack the center of pressure moves aft. In the design of wing structures, this center of pressure travel is very important, since it affects the position of the airloads imposed on the wing structure in low angle-of-attack conditions and high angle-of-attack conditions. The airplane’s aerodynamic balance and controllability are governed by changes in the center of pressure. Figure 7: Pressure distribution on an airfoil. The center of pressure is determined through calculation and wind tunnel tests by varying the airfoil’s angle of attack through normal operating extremes. As the angle of attack is changed, so are the various pressure distribution characteristics. Figure 8: Force vectors on an airfoil. Positive (+) and negative (–) pressure forces are totaled for each angle of attack and the resultant force is obtained. The total resultant pressure is represented by the resultant force vector shown in figure 8. The point of application of this force vector is termed the “center of pressure” (CP). For any given angle of attack, the center of pressure is the point where the resultant force crosses the chord line. This point is expressed as a percentage of the chord of the airfoil. A center of pressure at 30 percent of a 60-inch chord would be 18 inches aft of the wing’s leading edge. It would appear then that if the designer would place the wing so that its center of pressure was at the airplane’s center of gravity, the airplane would always balance. The difficulty arises, however, that the location of the center of pressure changes with change in the airfoil’s angle of attack. Figure 9: CP changes with an angle of attack. In the airplane’s normal range of flight attitudes, if the angle of attack is increased, the center of pressure moves forward; and if decreased, it moves rearward. Since the center of gravity is fixed at one point, it is evident that as the angle of attack increases, the center of lift (CL) moves ahead of the center of gravity, creating a force which tends to raise the nose of the airplane or tends to increase the angle of attack still more. On the other hand, if the angle of attack is decreased, the center of lift (CL) moves aft and tends to decrease the angle a greater amount. It is seen then, that the ordinary airfoil is inherently unstable, and that an auxiliary device, such as the horizontal tail surface, must be added to make the airplane balance longitudinally. The balance of an airplane in flight depends, therefore, on the relative position of the center of gravity (CG) and the center of pressure (CP) of the airfoil. Experience has shown that an airplane with the center of gravity in the vicinity of 20 percent of the wing chord can be made to balance and fly satisfactorily. Airplane loading and weight distribution also affect center of gravity and cause additional forces, which in turn affect airplane balance. This concludes the Airplane Aerodynamics Page. You can now test how much you remember from this page at the Airplane Aerodynamics question bank or read on at the Flight Controls Page.
Hover over each Learning Benefit below for a detailed explanation. Fine Motor Skills A great many children are endlessly fascinated by these little plastic blocks. And while free play with them fosters creativity, you can use LEGO® bricks in a more structured way to enhance learning and development across a number of areas. Solving math problems!: Have your child use LEGO® bricks to build an answer to a math problem. - Multiplication and Division are easier when you can not only manipulate the pieces, but use them to build and solve the equation. - Area and Perimeter: Each dot on the top is a standard unit. Use graph paper and lay out a piece. Demonstrate how to count around the piece (perimeter) or determine the dots on the inside (area). - Fractions: Stack short, single color towers you can break apart to demonstrate fractions. Build your child’s fraction skills by giving her a bag of LEGO® pieces. Have her sort by color and find out what fraction of the bag each color represents. Build something with the results! - Addition/Subtraction: Make problems easier by using the number of bumps on the blocks to support your child as she can literally “see” how to add them together, or break them apart. For visual consistency, use LEGO® bricks of the same color. - Counting and Regrouping: If your child struggles with math, try this fun game: Set two piles of LEGO® pieces in front of her. Have her count out each pile’s blocks strategically (by 5’s, 10’s, tally marks, multiplication groupings, etc., depending on what area of math he needs to work on). Draw a front-end loader with a “<” as it’s scoop (or modify a photo). Make another loader with a “>” as its scoop. Tell your child that the loader wants to pick up the bigger pile and to place the appropriate card between the two piles. If she is correct, she gets to build with the larger pile. - Spatial thinking and Language: Create two identical piles of bricks. Place a visual barrier between you and your child. Take turns having each of you build a creation and describe in words as you do so, having the other try and duplicate the project without any visual cues. Wonderful tool to enhance memory, executive function skills, reasoning abilities, specificity of reference, and so on. Curious how far you can go mathematically with LEGO® pieces? Check out this article about a LEGO® Death Star made to scale. - Hopscotch: Make the equivalent of a hopscotch board, bullseye, or number grid that you can have your child throw LEGO® pieces onto (from a set distance). Depending on your child’s ability level, you can have him or her do double digit addition, multiplication, or even square roots and percentages to get their score. - Estimation: Build something and see if your child can estimate how many bricks it took. Check by skip counting, tally counting, etc. Graph the results. Do this several times, leaving each item in tact. Have your child order the items from least number of bricks to most by visually comparing. - Weight and Measurement: How many of X brick does it take to balance out the weight of a selected object? What about a different sized brick? Can your child come up with a ratio equation to demonstrate? Your child can also use different length LEGO® bricks to measure various objects. What about measuring her own building? Give her a set time (1 minute?) and see how tall a LEGO® tower she can build. Then measure it! Do the race several more times. Graph the results. What is her average size tower? Another idea is to use LEGO® pieces as a unit and measure things using fastened together LEGO® pieces. How many bricks long is her shoe? The table? - Money: Set up a store and price out coveted LEGO® pieces. Give your child a set amount of money and have her buy or trade for LEGO® pieces. Be sure you have her count out the needed change! - Games: Play War or Go Fish with longer and shorter LEGO® bricks instead of cards. Count up the total number of dots at the end and build something with your winnings! Think about using bricks also for comparing, contrasting, finding equivalences, etc. - STEM: Don’t forget LEGO® robotics for STEM (science, technology, engineering and math) learning! - Visual Spatial: Make a LEGO® creation yourself. See if your child can match your design. These activities will foster visual discrimination, hand-eye coordination, and 3D engineering. Want an extra challenge? See if they can make the mirror image! - Spot the Mistake: Make a complex pattern from LEGO® bricks, with at least one mistake. Can your child find and correct it? Storytelling: Most children adore animating their LEGO® creations. Support the internalization of story structure and creative thinking and problem solving by having your child create stop-motion animation movies of her creations. http://www.abcya.com/animate.htm (for drawings) or http://www.clayanimator.com/english/stop_motion_animator.html. - Want to do comics instead? Check this out. - Or invite your child to make LEGO® avatars and create story lines or write character descriptions with them. You can also upload the screen grabs to http://www.toondoo.com/, http://www.reasonablyclever.com/mini-mizers/classic-kid-safe-mini-mizer/ or http://www.reasonablyclever.com/mm2/mini2.swf. - Use the screen grabs of the avatars and make a wanted poster at http://www.tuxpi.com/photo-effects/wanted-poster or http://www.glassgiant.com/wanted/. - Storytelling Pieces: Use industrial strength glue to affix magnets to the back of LEGO® characters or LEGO® “extras” (e.g., animals, trees, bikes, etc.). The pieces need to be (mostly) flat. For example, you can affix a person flat against a flat building base. Encourage your child to create story lines or act out adventures in a new “space,” a magnetized cookie sheet or refrigerator door. - If you build it…:Give your child a set number of LEGO® bricks and a time limit (say, 15 minutes). Use a fun online timer. Then, have your child use the same set and build a completely different creation. You can give more or less time than before, depending on how easily your child can switch gears in her thinking. You can also set parameters along which the project must change (e.g., can’t be the same type of structure, or X% of the creation must be different, etc.). Check out this online option. - Social Studies, Science, or Reading: Invite your child to extend what they are doing in Social Studies or science with LEGO® bricks! They can make a model of a slave cabin, a rain forest, a house for their favorite character, a vehicle for the villain in their tale, etc. - What Am I?: Build something. Your child can ask up to 20 questions to figure out what you made! - LEGO® Smile: App that lets you take a photo and turn it into an image that looks like its made of LEGO® bricks. Fun! Online Options: There are a number of online sites that will provide various challenges, creativity, or virtual playing options. Preview the choices below to make sure they are a good match for your family values and your child. - LEGO® Universe Creation Lab - LEGO® online games by category (action, strategy, creative, adventure, preschool) - Online challenges - Minecraft is a game that lets your child build an imaginary LEGO®-type world. It is open-ended and allows for great imagination. Players scavenge for resources in order to build things before dark, when the imaginary monsters arrive. Check it out before you have your child play; the classic version is free. - Make a LEGO® maze! Create a maze (or invite your motivated child to!) and see if she can roll a marble successfully out! - Kids can create their own LEGO® web page to display creations or to strategically grow virtual items by using challenging blueprints. According to LEGO®, it is a safe, moderated online environment for kids. - LEGO® Bricks in Space: Team up with the crew on board the International Space Station (ISS) to explore the effects of micro gravity on simple machines made with LEGO® bricks. - Monthly LEGO® Builds: “Blueprints” for a new item to build each month. Recommended Products for Your Child Ages 8-10
If you could measure the average distance from the Earth to the Sun over the course of an entire year, you'd discover something unsettling. With each passing year that you made that measurement, you'd find the Earth was a little bit farther away from the Sun — about 1.5 centimeters (0.6 inches) more distant — than the year prior. For billions of years, Earth has been migrating outward in its orbit, a trend that should continue for billions of years to come. But this is only a temporary situation. Eventually, the Earth will lose its orbital energy and spiral into the Sun, even in the event that the Sun doesn't engulf the Earth in its red giant phase. A whole lot of factors will come into play in the Solar System's far future, but in the end, Einstein himself will have the last say. Here's how the Earth's orbit will evolve, right up until the bitter end. For most people, the idea that Earth would change its orbit over time is a bizarre and confusing one. After all, planetary motion has been very well understood since the time of Kepler, more than 400 years ago. His first law of planetary motion — that planets move in elliptical orbits with the Sun at one focus — is exactly true in Newtonian gravity. This is even more impressive when you consider that Newton's law of gravitation itself wasn't even derived until more than 60 years after Kepler laid out his laws. And yet, both Kepler's and Newton's laws are only approximately true in reality, with six separate effects all potentially playing the "spoiler" role to what would otherwise be an exact, perfectly stable solution. Here's a rundown of each one, along with the effects they induce. 1.) Nuclear fusion in the Sun. With every second that goes by, a significant amount of the light atomic nuclei inside the Sun are transformed into heavier elements and isotopes through the process of nuclear fusion. When you fuse light elements into heavier ones, the heavier nuclei wind up more tightly bound, which requires the emission of energy. The end product of the Sun's fusion, helium-4, is actually 0.7% lighter than the four protons that came together through a chain reaction to produce it. All told, the Sun loses a total of 4 million tons of mass via Einstein's E = mc² with each new second that passes. This mass loss, however small it is, adds up over time. With each year that goes by, the loss of this mass due to nuclear fusion causes the Earth's orbit to outspiral by 1.5 cm (0.6 inches) per year. Over its lifetime so far, the Sun has lost the equivalent of the mass of Saturn due to nuclear fusion. 2.) The Earth smashes into particles as it orbits the Sun. This was an enormous effect in the early days of the Solar System: back when we still had a protoplanetary disk of material surrounding our Sun. It will be an enormous effect once again when the Sun enters the red giant phase of its life, as copious amounts of matter — about 33% of the Sun's total mass — will be ejected some 7.6 billion years from now. In both cases, as this material collides with Earth, our orbit will change, with the exact changes dependent on the speed of the material relative to Earth: an inward migration when the Solar System forms and an outward migration at the Sun's end-of-life. But right now, we're mostly struck only by solar wind particles: at the paltry clip of about 18,000 tons per year. This is completely negligible right now, changing Earth's orbit by only about a proton's width every million years or so. 3.) The gravitational effects of the other massive objects in our Solar System. This one might matter, and it also might not. In our Solar System, we have many objects that orbit the Sun or other bodies. They all have finite, non-negligible sizes and masses, and they mutually exert gravitational forces on one another. Whenever this occurs, there the chance that these orbits will become chaotic and evolve with time. According to the latest research, there's approximately a 1% chance that one or more of the four inner planets in our Solar System today — Mercury, Venus, Earth and Mars — will become orbitally unstable over the next few billion years. If that occurs, Earth's orbit could change significantly, possibly even hurling our planet into the Sun or ejecting it from the Solar System entirely. This is the most unpredictable component of our planetary orbit. 4.) The Sun swells into a red giant star. We know this is coming, and we also know roughly what it's going to look like. The inner core will contract and heat up; the outer layers will puff outwards and grow tremendously; helium fusion will ignite in the star's core; a large fraction of the overall mass will wind up ejected. But most importantly, especially for our purposes, the inner planets will be consumed by the now-expanded red giant star that our Sun evolves into. Mercury will be gone. Venus will be swallowed as well. And Earth, unless it can spiral outwards to more than 15% its current radius — something only questionably likely to happen, possibly requiring an orbital instability between now and then — will be gone as well. Assuming Earth survives, however, and it may, surviving the red giant phase implies that the outspiraling phase will now end. 5.) Other objects in the galaxy. Every so often, a large mass such as a star, brown dwarf, or rogue planet will pass close to our Solar System. Although it's exceedingly unlikely that such an object will pass closely enough to perturb the Earth's orbit before the Sun becomes a red giant, there's a lot of time ahead of us once that phase passes. By the time the Universe is about 100,000 times its current age, a close gravitational encounter becomes likely. With Mercury and Venus gone, Earth will be the innermost planet to our Sun. When that inevitable encounter occurs, one of two things is likely to happen. Either the interloping mass will severely perturb the Earth, causing its orbit to become unstable, or the Sun-Earth system (with possibly Mars, Jupiter, and potentially other planets remaining as well) will be ejected from our host galaxy entirely. This is a chaotic and unpredictable process, and literally anything can occur if we wait long enough. 6.) Gravitational radiation. But if the Earth remains bound to the Sun — something very likely to occur if the remnant of our Solar System is ejected from the galaxy — gravitational radiation will cause the Earth to slowly spiral into the Sun. Whenever two masses orbit one another in Einstein's theory of gravity, General Relativity, gravitational waves are emitted. Given the current masses and positions of the Sun and Earth, this only amounts to an orbital change of 1.5 attometers per year, meaning that it takes about a millennium for Earth to inspiral by the width of a single proton. But if there are no other remaining effects at play, this will become the only one that will matter on cosmic timescales. If nothing else interferes with this, the Earth will spiral into the Sun after a whopping 1026 years pass: 10 quadrillion times the present age of the Universe. All six of these effects are very real, and they all contribute to the Earth's changing orbit. Each one of them, individually, has the opportunity to be the most important at different epochs. - In the earliest stages of the Solar System, when the planets and moons are still forming, collisions from early planets and planetesimals dominate how Earth's/proto-Earth's orbit changes. - Today, mass loss due to nuclear fusion dominates the Earth's present outspiraling. - If gravitational instabilities occur, the influence of the other planets could alter or even ruin the Earth's orbit before we become a red giant. - During the Sun's transformation into a red giant, everything depends on whether the Earth is swallowed or not; if it is, that's the end-of-the-line for our planet. - After the Sun becomes a white dwarf, a cosmic game of gravitational pinball will ensue; either Earth will come unbound from the Sun or the entire remaining Solar System, with Earth intact, will be ejected. - But if Earth survives for this long, it will continue to gravitationally inspiral until, at last, it's finally consumed by the black dwarf our star eventually becomes. Right now, the Earth is slowly drifting away from the Sun, driven by the relentless effect of nuclear fusion on the Sun. As time goes on, the Sun burns through more and more of its fuel, losing mass in the process and loosening its gravitational grip on the Earth. Assuming this continues until the red giant phase arrives, either our planet will be consumed by the Sun at this time, or it will survive to see the Sun become a white dwarf. At that point, gravitational radiation will cause our planet's orbit to slowly decay, whereupon it will begin to inspiral into the Sun. Unless a rogue object passes through our Solar System and ejects the Earth, this inspiral will continue, eventually leading the Earth to fall into our Sun's stellar corpse when the Universe is some ten quadrillion times its current age. The Earth may be drifting away from the Sun for now, but if we remain bound to our parent star, gravitational infall remains our inevitable long-term fate.
A black hole is a region of spacetime exhibiting gravitational acceleration so strong that nothing—no particles or even electromagnetic radiation such as light—can escape from it. The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. The boundary of the region from which no escape is possible is called the event horizon. Although the event horizon has an enormous effect on the fate and circumstances of an object crossing it, no locally detectable features appear to be observed. In many ways, a black hole acts like an ideal black body, as it reflects no light. Moreover, quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is on the order of billionths of a kelvin for black holes of stellar mass, making it essentially impossible to observe. Objects whose gravitational fields are too strong for light to escape were first considered in the 18th century by John Michell and Pierre-Simon Laplace. The first modern solution of general relativity that would characterize a black hole was found by Karl Schwarzschild in 1916, although its interpretation as a region of space from which nothing can escape was first published by David Finkelstein in 1958. Black holes were long considered a mathematical curiosity; it was during the 1960s that theoretical work showed they were a generic prediction of general relativity. The discovery of neutron stars by Jocelyn Bell Burnell in 1967 sparked interest in gravitationally collapsed compact objects as a possible astrophysical reality. Black holes of stellar mass are expected to form when very massive stars collapse at the end of their life cycle. After a black hole has formed, it can continue to grow by absorbing mass from its surroundings. By absorbing other stars and merging with other black holes, supermassive black holes of millions of solar masses (M☉) may form. There is consensus that supermassive black holes exist in the centers of most galaxies. The presence of a black hole can be inferred through its interaction with other matter and with electromagnetic radiation such as visible light. Matter that falls onto a black hole can form an external accretion disk heated by friction, forming some of the brightest objects in the universe. If there are other stars orbiting a black hole, their orbits can be used to determine the black hole's mass and location. Such observations can be used to exclude possible alternatives such as neutron stars. In this way, astronomers have identified numerous stellar black hole candidates in binary systems, and established that the radio source known as Sagittarius A, at the core of the Milky Way galaxy, contains a supermassive black hole of about 4.3 million solar masses. On 11 February 2016, the LIGO collaboration announced the first direct detection of gravitational waves, which also represented the first observation of a black hole merger. As of December 2018[update], eleven gravitational wave events have been observed that originated from ten merging black holes (along with one binary neutron star merger). On 10 April 2019, the first ever direct image of a black hole and its vicinity was published, following observations made by the Event Horizon Telescope in 2017 of the supermassive black hole in Messier 87's galactic centre. - 1 History - 2 Properties and structure - 3 Formation and evolution - 4 Observational evidence - 4.1 Detection of gravitational waves from merging black holes - 4.2 Proper motions of stars orbiting Sagittarius A - 4.3 Accretion of matter - 4.4 Microlensing (proposed) - 4.5 Alternatives - 5 Open questions - 6 See also - 7 Notes - 8 References - 9 Further reading - 10 External links The idea of a body so massive that even light could not escape was briefly proposed by astronomical pioneer and English clergyman John Michell in a letter published in November 1784. Michell's simplistic calculations assumed such a body might have the same density as the Sun, and concluded that such a body would form when a star's diameter exceeds the Sun's by a factor of 500, and the surface escape velocity exceeds the usual speed of light. Michell correctly noted that such supermassive but non-radiating bodies might be detectable through their gravitational effects on nearby visible bodies. Scholars of the time were initially excited by the proposal that giant but invisible stars might be hiding in plain view, but enthusiasm dampened when the wavelike nature of light became apparent in the early nineteenth century. If light were a wave rather than a "corpuscle", it is unclear what, if any, influence gravity would have on escaping light waves. Modern physics discredits Michell's notion of a light ray shooting directly from the surface of a supermassive star, being slowed down by the star's gravity, stopping, and then free-falling back to the star's surface. In 1915, Albert Einstein developed his theory of general relativity, having earlier shown that gravity does influence light's motion. Only a few months later, Karl Schwarzschild found a solution to the Einstein field equations, which describes the gravitational field of a point mass and a spherical mass. A few months after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz, independently gave the same solution for the point mass and wrote more extensively about its properties. This solution had a peculiar behaviour at what is now called the Schwarzschild radius, where it became singular, meaning that some of the terms in the Einstein equations became infinite. The nature of this surface was not quite understood at the time. In 1924, Arthur Eddington showed that the singularity disappeared after a change of coordinates (see Eddington–Finkelstein coordinates), although it took until 1933 for Georges Lemaître to realize that this meant the singularity at the Schwarzschild radius was a non-physical coordinate singularity. Arthur Eddington did however comment on the possibility of a star with mass compressed to the Schwarzschild radius in a 1926 book, noting that Einstein's theory allows us to rule out overly large densities for visible stars like Betelgeuse because "a star of 250 million km radius could not possibly have so high a density as the sun. Firstly, the force of gravitation would be so great that light would be unable to escape from it, the rays falling back to the star like a stone to the earth. Secondly, the red shift of the spectral lines would be so great that the spectrum would be shifted out of existence. Thirdly, the mass would produce so much curvature of the space-time metric that space would close up around the star, leaving us outside (i.e., nowhere)." In 1931, Subrahmanyan Chandrasekhar calculated, using special relativity, that a non-rotating body of electron-degenerate matter above a certain limiting mass (now called the Chandrasekhar limit at 1.4 M☉) has no stable solutions. His arguments were opposed by many of his contemporaries like Eddington and Lev Landau, who argued that some yet unknown mechanism would stop the collapse. They were partly correct: a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star, which is itself stable. But in 1939, Robert Oppenheimer and others predicted that neutron stars above another limit (the Tolman–Oppenheimer–Volkoff limit) would collapse further for the reasons presented by Chandrasekhar, and concluded that no law of physics was likely to intervene and stop at least some stars from collapsing to black holes. Their original calculations, based on the Pauli exclusion principle, gave it as 0.7 M☉; subsequent consideration of strong force-mediated neutron-neutron repulsion raised the estimate to approximately 1.5 M☉ to 3.0 M☉. Observations of the neutron star merger GW170817, which is thought to have generated a black hole shortly afterward, have refined the TOV limit estimate to ~2.17 M☉. Oppenheimer and his co-authors interpreted the singularity at the boundary of the Schwarzschild radius as indicating that this was the boundary of a bubble in which time stopped. This is a valid point of view for external observers, but not for infalling observers. Because of this property, the collapsed stars were called "frozen stars", because an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it to the Schwarzschild radius. In 1958, David Finkelstein identified the Schwarzschild surface as an event horizon, "a perfect unidirectional membrane: causal influences can cross it in only one direction". This did not strictly contradict Oppenheimer's results, but extended them to include the point of view of infalling observers. Finkelstein's solution extended the Schwarzschild solution for the future of observers falling into a black hole. A complete extension had already been found by Martin Kruskal, who was urged to publish it. These results came at the beginning of the golden age of general relativity, which was marked by general relativity and black holes becoming mainstream subjects of research. This process was helped by the discovery of pulsars by Jocelyn Bell Burnell in 1967, which, by 1969, were shown to be rapidly rotating neutron stars. Until that time, neutron stars, like black holes, were regarded as just theoretical curiosities; but the discovery of pulsars showed their physical relevance and spurred a further interest in all types of compact objects that might be formed by gravitational collapse. In this period more general black hole solutions were found. In 1963, Roy Kerr found the exact solution for a rotating black hole. Two years later, Ezra Newman found the axisymmetric solution for a black hole that is both rotating and electrically charged. Through the work of Werner Israel, Brandon Carter, and David Robinson the no-hair theorem emerged, stating that a stationary black hole solution is completely described by the three parameters of the Kerr–Newman metric: mass, angular momentum, and electric charge. At first, it was suspected that the strange features of the black hole solutions were pathological artifacts from the symmetry conditions imposed, and that the singularities would not appear in generic situations. This view was held in particular by Vladimir Belinsky, Isaak Khalatnikov, and Evgeny Lifshitz, who tried to prove that no singularities appear in generic solutions. However, in the late 1960s Roger Penrose and Stephen Hawking used global techniques to prove that singularities appear generically. Work by James Bardeen, Jacob Bekenstein, Carter, and Hawking in the early 1970s led to the formulation of black hole thermodynamics. These laws describe the behaviour of a black hole in close analogy to the laws of thermodynamics by relating mass to energy, area to entropy, and surface gravity to temperature. The analogy was completed when Hawking, in 1974, showed that quantum field theory implies that black holes should radiate like a black body with a temperature proportional to the surface gravity of the black hole, predicting the effect now known as Hawking radiation. John Michell used the term "dark star", and in the early 20th century, physicists used the term "gravitationally collapsed object". Science writer Marcia Bartusiak traces the term "black hole" to physicist Robert H. Dicke, who in the early 1960s reportedly compared the phenomenon to the Black Hole of Calcutta, notorious as a prison where people entered but never left alive. The term "black hole" was used in print by Life and Science News magazines in 1963, and by science journalist Ann Ewing in her article "'Black Holes' in Space", dated 18 January 1964, which was a report on a meeting of the American Association for the Advancement of Science held in Cleveland, Ohio. In December 1967, a student reportedly suggested the phrase "black hole" at a lecture by John Wheeler; Wheeler adopted the term for its brevity and "advertising value", and it quickly caught on, leading some to credit Wheeler with coining the phrase. Properties and structure The no-hair conjecture postulates that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: mass, charge, and angular momentum; the black hole is otherwise featureless. If the conjecture is true, any two black holes that share the same values for these properties, or parameters, are indistinguishable from one another. The degree to which the conjecture is true for real black holes under the laws of modern physics, is currently an unsolved problem. These properties are special because they are visible from outside a black hole. For example, a charged black hole repels other like charges just like any other charged object. Similarly, the total mass inside a sphere containing a black hole can be found by using the gravitational analog of Gauss's law, the ADM mass, far away from the black hole.[clarification needed] Likewise, the angular momentum can be measured from far away using frame dragging by the gravitomagnetic field.[clarification needed] When an object falls into a black hole, any information about the shape of the object or distribution of charge on it is evenly distributed along the horizon of the black hole, and is lost to outside observers. The behavior of the horizon in this situation is a dissipative system that is closely analogous to that of a conductive stretchy membrane with friction and electrical resistance—the membrane paradigm. This is different from other field theories such as electromagnetism, which do not have any friction or resistivity at the microscopic level, because they are time-reversible. Because a black hole eventually achieves a stable state with only three parameters, there is no way to avoid losing information about the initial conditions: the gravitational and electric fields of a black hole give very little information about what went in. The information that is lost includes every quantity that cannot be measured far away from the black hole horizon, including approximately conserved quantum numbers such as the total baryon number and lepton number. This behavior is so puzzling that it has been called the black hole information loss paradox. The simplest static black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after Karl Schwarzschild who discovered this solution in 1916. According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric. This means there is no observable difference at a distance between the gravitational field of such a black hole and that of any other spherical object of the same mass. The popular notion of a black hole "sucking in everything" in its surroundings is therefore correct only near a black hole's horizon; far away, the external gravitational field is identical to that of any other body of the same mass. Solutions describing more general black holes also exist. Non-rotating charged black holes are described by the Reissner–Nordström metric, while the Kerr metric describes a non-charged rotating black hole. The most general stationary black hole solution known is the Kerr–Newman metric, which describes a black hole with both charge and angular momentum. While the mass of a black hole can take any positive value, the charge and angular momentum are constrained by the mass. In Planck units, the total electric charge Q and the total angular momentum J are expected to satisfy for a black hole of mass M. Black holes with the minimum possible mass satisfying this inequality are called extremal. Solutions of Einstein's equations that violate this inequality exist, but they do not possess an event horizon. These solutions have so-called naked singularities that can be observed from the outside, and hence are deemed unphysical. The cosmic censorship hypothesis rules out the formation of such singularities, when they are created through the gravitational collapse of realistic matter. This is supported by numerical simulations. Due to the relatively large strength of the electromagnetic force, black holes forming from the collapse of stars are expected to retain the nearly neutral charge of the star. Rotation, however, is expected to be a universal feature of compact astrophysical objects. The black-hole candidate binary X-ray source GRS 1915+105 appears to have an angular momentum near the maximum allowed value. That uncharged limit is \|Supermassive black hole\|\|105–1010 MSun\|\|0.001–400 AU\| \|Intermediate-mass black hole\|\|103 MSun\|\|103 km ≈ REarth\| \|Stellar black hole\|\|10 MSun\|\|30 km\| \|Micro black hole\|\|up to MMoon\|\|up to 0.1 mm\| Black holes are commonly classified according to their mass, independent of angular momentum, J. The size of a black hole, as determined by the radius of the event horizon, or Schwarzschild radius, is proportional to the mass, M, through where rs is the Schwarzschild radius and MSun is the mass of the Sun. For a black hole with nonzero spin and/or electric charge, the radius is smaller,[Note 2] until an extremal black hole could have an event horizon close to The defining feature of a black hole is the appearance of an event horizon—a boundary in spacetime through which matter and light can pass only inward towards the mass of the black hole. Nothing, not even light, can escape from inside the event horizon. The event horizon is referred to as such because if an event occurs within the boundary, information from that event cannot reach an outside observer, making it impossible to determine whether such an event occurred. As predicted by general relativity, the presence of a mass deforms spacetime in such a way that the paths taken by particles bend towards the mass. At the event horizon of a black hole, this deformation becomes so strong that there are no paths that lead away from the black hole. To a distant observer, clocks near a black hole would appear to tick more slowly than those further away from the black hole. Due to this effect, known as gravitational time dilation, an object falling into a black hole appears to slow as it approaches the event horizon, taking an infinite time to reach it. At the same time, all processes on this object slow down, from the view point of a fixed outside observer, causing any light emitted by the object to appear redder and dimmer, an effect known as gravitational redshift. Eventually, the falling object fades away until it can no longer be seen. Typically this process happens very rapidly with an object disappearing from view within less than a second. On the other hand, indestructible observers falling into a black hole do not notice any of these effects as they cross the event horizon. According to their own clocks, which appear to them to tick normally, they cross the event horizon after a finite time without noting any singular behaviour; in classical general relativity, it is impossible to determine the location of the event horizon from local observations, due to Einstein's equivalence principle. The topology of the event horizon of a black hole at equilibrium is always spherical.[Note 4] For non-rotating (static) black holes the geometry of the event horizon is precisely spherical, while for rotating black holes the event horizon is oblate. At the center of a black hole, as described by general relativity, may lie a gravitational singularity, a region where the spacetime curvature becomes infinite. For a non-rotating black hole, this region takes the shape of a single point and for a rotating black hole, it is smeared out to form a ring singularity that lies in the plane of rotation. In both cases, the singular region has zero volume. It can also be shown that the singular region contains all the mass of the black hole solution. The singular region can thus be thought of as having infinite density. Observers falling into a Schwarzschild black hole (i.e., non-rotating and not charged) cannot avoid being carried into the singularity, once they cross the event horizon. They can prolong the experience by accelerating away to slow their descent, but only up to a limit. When they reach the singularity, they are crushed to infinite density and their mass is added to the total of the black hole. Before that happens, they will have been torn apart by the growing tidal forces in a process sometimes referred to as spaghettification or the "noodle effect". In the case of a charged (Reissner–Nordström) or rotating (Kerr) black hole, it is possible to avoid the singularity. Extending these solutions as far as possible reveals the hypothetical possibility of exiting the black hole into a different spacetime with the black hole acting as a wormhole. The possibility of traveling to another universe is, however, only theoretical since any perturbation would destroy this possibility. It also appears to be possible to follow closed timelike curves (returning to one's own past) around the Kerr singularity, which leads to problems with causality like the grandfather paradox. It is expected that none of these peculiar effects would survive in a proper quantum treatment of rotating and charged black holes. The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory. This breakdown, however, is expected; it occurs in a situation where quantum effects should describe these actions, due to the extremely high density and therefore particle interactions. To date, it has not been possible to combine quantum and gravitational effects into a single theory, although there exist attempts to formulate such a theory of quantum gravity. It is generally expected that such a theory will not feature any singularities. The photon sphere is a spherical boundary of zero thickness in which photons that move on tangents to that sphere would be trapped in a circular orbit about the black hole. For non-rotating black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius. Their orbits would be dynamically unstable, hence any small perturbation, such as a particle of infalling matter, would cause an instability that would grow over time, either setting the photon on an outward trajectory causing it to escape the black hole, or on an inward spiral where it would eventually cross the event horizon. While light can still escape from the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole. Hence any light that reaches an outside observer from the photon sphere must have been emitted by objects between the photon sphere and the event horizon. Rotating black holes are surrounded by a region of spacetime in which it is impossible to stand still, called the ergosphere. This is the result of a process known as frame-dragging; general relativity predicts that any rotating mass will tend to slightly "drag" along the spacetime immediately surrounding it. Any object near the rotating mass will tend to start moving in the direction of rotation. For a rotating black hole, this effect is so strong near the event horizon that an object would have to move faster than the speed of light in the opposite direction to just stand still. The ergosphere of a black hole is a volume whose inner boundary is the black hole's oblate spheroid event horizon and a pumpkin-shaped outer boundary, which coincides with the event horizon at the poles but noticeably wider around the equator. The outer boundary is sometimes called the ergosurface. Objects and radiation can escape normally from the ergosphere. Through the Penrose process, objects can emerge from the ergosphere with more energy than they entered. This energy is taken from the rotational energy of the black hole causing the latter to slow. A variation of the Penrose process in the presence of strong magnetic fields, the Blandford–Znajek process is considered a likely mechanism for the enormous luminosity and relativistic jets of quasars and other active galactic nuclei. Innermost stable circular orbit (ISCO) In Newtonian gravity, test particles can stably orbit at arbitrary distances from a central object. In general relativity, however, there exists an innermost stable circular orbit (often called the ISCO), inside of which, any infinitesimal perturbations to a circular orbit will lead to inspiral into the black hole. The location of the ISCO depends on the spin of the black hole, in the case of a Schwarzschild black hole (spin zero) is: and decreases with increasing black hole spin for particles orbiting in the same direction as the spin. Formation and evolution Given the bizarre character of black holes, it was long questioned whether such objects could actually exist in nature or whether they were merely pathological solutions to Einstein's equations. Einstein himself wrongly thought black holes would not form, because he held that the angular momentum of collapsing particles would stabilize their motion at some radius. This led the general relativity community to dismiss all results to the contrary for many years. However, a minority of relativists continued to contend that black holes were physical objects, and by the end of the 1960s, they had persuaded the majority of researchers in the field that there is no obstacle to the formation of an event horizon. Penrose demonstrated that once an event horizon forms, general relativity without quantum mechanics requires that a singularity will form within. Shortly afterwards, Hawking showed that many cosmological solutions that describe the Big Bang have singularities without scalar fields or other exotic matter (see "Penrose–Hawking singularity theorems").[clarification needed] The Kerr solution, the no-hair theorem, and the laws of black hole thermodynamics showed that the physical properties of black holes were simple and comprehensible, making them respectable subjects for research. Conventional black holes are formed by gravitational collapse of heavy objects such as stars, but they can also in theory be formed by other processes. Gravitational collapse occurs when an object's internal pressure is insufficient to resist the object's own gravity. For stars this usually occurs either because a star has too little "fuel" left to maintain its temperature through stellar nucleosynthesis, or because a star that would have been stable receives extra matter in a way that does not raise its core temperature. In either case the star's temperature is no longer high enough to prevent it from collapsing under its own weight. The collapse may be stopped by the degeneracy pressure of the star's constituents, allowing the condensation of matter into an exotic denser state. The result is one of the various types of compact star. Which type forms depends on the mass of the remnant of the original star left after the outer layers have been blown away. Such explosions and pulsations lead to planetary nebula. This mass can be substantially less than the original star. Remnants exceeding 5 M☉ are produced by stars that were over 20 M☉ before the collapse. If the mass of the remnant exceeds about 3–4 M☉ (the Tolman–Oppenheimer–Volkoff limit), either because the original star was very heavy or because the remnant collected additional mass through accretion of matter, even the degeneracy pressure of neutrons is insufficient to stop the collapse. No known mechanism (except possibly quark degeneracy pressure, see quark star) is powerful enough to stop the implosion and the object will inevitably collapse to form a black hole. The gravitational collapse of heavy stars is assumed to be responsible for the formation of stellar mass black holes. Star formation in the early universe may have resulted in very massive stars, which upon their collapse would have produced black holes of up to 103 M☉. These black holes could be the seeds of the supermassive black holes found in the centers of most galaxies. It has further been suggested that supermassive black holes with typical masses of ~105 M☉ could have formed from the direct collapse of gas clouds in the young universe. Some candidates for such objects have been found in observations of the young universe. While most of the energy released during gravitational collapse is emitted very quickly, an outside observer does not actually see the end of this process. Even though the collapse takes a finite amount of time from the reference frame of infalling matter, a distant observer would see the infalling material slow and halt just above the event horizon, due to gravitational time dilation. Light from the collapsing material takes longer and longer to reach the observer, with the light emitted just before the event horizon forms delayed an infinite amount of time. Thus the external observer never sees the formation of the event horizon; instead, the collapsing material seems to become dimmer and increasingly red-shifted, eventually fading away. Primordial black holes and the Big Bang Gravitational collapse requires great density. In the current epoch of the universe these high densities are found only in stars, but in the early universe shortly after the Big Bang densities were much greater, possibly allowing for the creation of black holes. High density alone is not enough to allow black hole formation since a uniform mass distribution will not allow the mass to bunch up. In order for primordial black holes to have formed in such a dense medium, there must have been initial density perturbations that could then grow under their own gravity. Different models for the early universe vary widely in their predictions of the scale of these fluctuations. Various models predict the creation of primordial black holes ranging in size from a Planck mass to hundreds of thousands of solar masses. Despite the early universe being extremely dense—far denser than is usually required to form a black hole—it did not re-collapse into a black hole during the Big Bang. Models for gravitational collapse of objects of relatively constant size, such as stars, do not necessarily apply in the same way to rapidly expanding space such as the Big Bang. Gravitational collapse is not the only process that could create black holes. In principle, black holes could be formed in high-energy collisions that achieve sufficient density. As of 2002, no such events have been detected, either directly or indirectly as a deficiency of the mass balance in particle accelerator experiments. This suggests that there must be a lower limit for the mass of black holes. Theoretically, this boundary is expected to lie around the Planck mass (mP=√ ≈ 1.2×1019 GeV/c2 ≈ 2.2×10−8 kg), where quantum effects are expected to invalidate the predictions of general relativity. This would put the creation of black holes firmly out of reach of any high-energy process occurring on or near the Earth. However, certain developments in quantum gravity suggest that the Planck mass could be much lower: some braneworld scenarios for example put the boundary as low as 1 TeV/c2. This would make it conceivable for micro black holes to be created in the high-energy collisions that occur when cosmic rays hit the Earth's atmosphere, or possibly in the Large Hadron Collider at CERN. These theories are very speculative, and the creation of black holes in these processes is deemed unlikely by many specialists. Even if micro black holes could be formed, it is expected that they would evaporate in about 10−25 seconds, posing no threat to the Earth. Once a black hole has formed, it can continue to grow by absorbing additional matter. Any black hole will continually absorb gas and interstellar dust from its surroundings. This is the primary process through which supermassive black holes seem to have grown. A similar process has been suggested for the formation of intermediate-mass black holes found in globular clusters. Black holes can also merge with other objects such as stars or even other black holes. This is thought to have been important, especially in the early growth of supermassive black holes, which could have formed from the aggregation of many smaller objects. The process has also been proposed as the origin of some intermediate-mass black holes. In 1974, Hawking predicted that black holes are not entirely black but emit small amounts of thermal radiation at a temperature ℏ c3/(8 π G M kB); this effect has become known as Hawking radiation. By applying quantum field theory to a static black hole background, he determined that a black hole should emit particles that display a perfect black body spectrum. Since Hawking's publication, many others have verified the result through various approaches. If Hawking's theory of black hole radiation is correct, then black holes are expected to shrink and evaporate over time as they lose mass by the emission of photons and other particles. The temperature of this thermal spectrum (Hawking temperature) is proportional to the surface gravity of the black hole, which, for a Schwarzschild black hole, is inversely proportional to the mass. Hence, large black holes emit less radiation than small black holes. A stellar black hole of 1 M☉ has a Hawking temperature of 62 nanokelvins. This is far less than the 2.7 K temperature of the cosmic microwave background radiation. Stellar-mass or larger black holes receive more mass from the cosmic microwave background than they emit through Hawking radiation and thus will grow instead of shrinking. To have a Hawking temperature larger than 2.7 K (and be able to evaporate), a black hole would need a mass less than the Moon. Such a black hole would have a diameter of less than a tenth of a millimeter. If a black hole is very small, the radiation effects are expected to become very strong. A black hole with the mass of a car would have a diameter of about 10−24 m and take a nanosecond to evaporate, during which time it would briefly have a luminosity of more than 200 times that of the Sun. Lower-mass black holes are expected to evaporate even faster; for example, a black hole of mass 1 TeV/c2 would take less than 10−88 seconds to evaporate completely. For such a small black hole, quantum gravitation effects are expected to play an important role and could hypothetically make such a small black hole stable, although current developments in quantum gravity do not indicate this is the case. The Hawking radiation for an astrophysical black hole is predicted to be very weak and would thus be exceedingly difficult to detect from Earth. A possible exception, however, is the burst of gamma rays emitted in the last stage of the evaporation of primordial black holes. Searches for such flashes have proven unsuccessful and provide stringent limits on the possibility of existence of low mass primordial black holes. NASA's Fermi Gamma-ray Space Telescope launched in 2008 will continue the search for these flashes. If black holes evaporate via Hawking radiation, a solar mass black hole will evaporate (beginning once the temperature of the cosmic microwave background drops below that of the black hole) over a period of 1064 years. A supermassive black hole with a mass of 1011 (100 billion) M☉ will evaporate in around 2×10100 years. Some monster black holes in the universe are predicted to continue to grow up to perhaps 1014 M☉ during the collapse of superclusters of galaxies. Even these would evaporate over a timescale of up to 10106 years. By nature, black holes do not themselves emit any electromagnetic radiation other than the hypothetical Hawking radiation, so astrophysicists searching for black holes must generally rely on indirect observations. For example, a black hole's existence can sometimes be inferred by observing its gravitational influence upon its surroundings. On 10 April 2019 an image was released of a black hole, which is seen in magnified fashion because the light paths near the event horizon are highly bent. The dark shadow in the middle results from light paths absorbed by the black hole. The image is in false color, as the detected light halo in this image is not in the visible spectrum, but radio waves. The Event Horizon Telescope (EHT), run by MIT's Haystack Observatory, is an active program that directly observes the immediate environment of the event horizon of black holes, such as the black hole at the centre of the Milky Way. In April 2017, EHT began observation of the black hole in the center of Messier 87. "In all, eight radio observatories on six mountains and four continents observed the galaxy in Virgo on and off for 10 days in April 2017" to provide the data yielding the image two years later in April 2019. After two years of data processing, EHT released the first direct image of a black hole, specifically the supermassive black hole that lies in the center of the aforementioned galaxy. What is visible is not the black hole, which shows as black because of the loss of all light within this dark region, rather it is the gases at the edge of the event horizon, which are displayed as orange or red, that define the black hole. The brightening of this material in the 'bottom' half of the processed EHT image is thought to be caused by Doppler beaming, whereby material approaching the viewer at relativistic speeds is perceived as brighter than material moving away. In the case of a black hole this phenomenon implies that the visible material is rotating at relativistic speeds (>1,000 km/s), the only speeds at which it is possible to centrifugally balance the immense gravitational attraction of the singularity, and thereby remain in orbit above the event horizon. This configuration of bright material implies that the EHT observed M87* from a perspective catching the black hole's accretion disc nearly edge-on, as the whole system rotated clockwise. However, the extreme gravitational lensing associated with black holes produces the illusion of a perspective that sees the accretion disc from above. In reality, most of the ring in the EHT image was created when the light emitted by the far side of the accretion disc bent around the black hole's gravity well and escaped such that most of the possible perspectives on M87* can see the entire disc, even that directly behind the "shadow". Prior to this, in 2015, the EHT detected magnetic fields just outside the event horizon of Sagittarius A, and even discerned some of their properties. The field lines that pass through the accretion disc were found to be a complex mixture of ordered and tangled. The existence of magnetic fields had been predicted by theoretical studies of black holes. Detection of gravitational waves from merging black holes On 14 September 2015 the LIGO gravitational wave observatory made the first-ever successful direct observation of gravitational waves. The signal was consistent with theoretical predictions for the gravitational waves produced by the merger of two black holes: one with about 36 solar masses, and the other around 29 solar masses. This observation provides the most concrete evidence for the existence of black holes to date. For instance, the gravitational wave signal suggests that the separation of the two objects prior to the merger was just 350 km (or roughly four times the Schwarzschild radius corresponding to the inferred masses). The objects must therefore have been extremely compact, leaving black holes as the most plausible interpretation. More importantly, the signal observed by LIGO also included the start of the post-merger ringdown, the signal produced as the newly formed compact object settles down to a stationary state. Arguably, the ringdown is the most direct way of observing a black hole. From the LIGO signal it is possible to extract the frequency and damping time of the dominant mode of the ringdown. From these it is possible to infer the mass and angular momentum of the final object, which match independent predictions from numerical simulations of the merger. The frequency and decay time of the dominant mode are determined by the geometry of the photon sphere. Hence, observation of this mode confirms the presence of a photon sphere, however it cannot exclude possible exotic alternatives to black holes that are compact enough to have a photon sphere. The observation also provides the first observational evidence for the existence of stellar-mass black hole binaries. Furthermore, it is the first observational evidence of stellar-mass black holes weighing 25 solar masses or more. Proper motions of stars orbiting Sagittarius A The proper motions of stars near the center of our own Milky Way provide strong observational evidence that these stars are orbiting a supermassive black hole. Since 1995, astronomers have tracked the motions of 90 stars orbiting an invisible object coincident with the radio source Sagittarius A. By fitting their motions to Keplerian orbits, the astronomers were able to infer, in 1998, that a 2.6 million M☉ object must be contained in a volume with a radius of 0.02 light-years to cause the motions of those stars. Since then, one of the stars—called S2—has completed a full orbit. From the orbital data, astronomers were able to refine the calculations of the mass to 4.3 million M☉ and a radius of less than 0.002 light years for the object causing the orbital motion of those stars. The upper limit on the object's size is still too large to test whether it is smaller than its Schwarzschild radius; nevertheless, these observations strongly suggest that the central object is a supermassive black hole as there are no other plausible scenarios for confining so much invisible mass into such a small volume. Additionally, there is some observational evidence that this object might possess an event horizon, a feature unique to black holes. Accretion of matter Due to conservation of angular momentum, gas falling into the gravitational well created by a massive object will typically form a disk-like structure around the object. Artists' impressions such as the accompanying representation of a black hole with corona commonly depict the black hole as if it were a flat-space body hiding the part of the disk just behind it, but in reality gravitational lensing would greatly distort the image of the accretion disk. Within such a disk, friction would cause angular momentum to be transported outward, allowing matter to fall further inward, thus releasing potential energy and increasing the temperature of the gas. When the accreting object is a neutron star or a black hole, the gas in the inner accretion disk orbits at very high speeds because of its proximity to the compact object. The resulting friction is so significant that it heats the inner disk to temperatures at which it emits vast amounts of electromagnetic radiation (mainly X-rays). These bright X-ray sources may be detected by telescopes. This process of accretion is one of the most efficient energy-producing processes known; up to 40% of the rest mass of the accreted material can be emitted as radiation. (In nuclear fusion only about 0.7% of the rest mass will be emitted as energy.) In many cases, accretion disks are accompanied by relativistic jets that are emitted along the poles, which carry away much of the energy. The mechanism for the creation of these jets is currently not well understood, in part due to insufficient data. As such, many of the universe's more energetic phenomena have been attributed to the accretion of matter on black holes. In particular, active galactic nuclei and quasars are believed to be the accretion disks of supermassive black holes. Similarly, X-ray binaries are generally accepted to be binary star systems in which one of the two stars is a compact object accreting matter from its companion. It has also been suggested that some ultraluminous X-ray sources may be the accretion disks of intermediate-mass black holes. X-ray binaries are binary star systems that emit a majority of their radiation in the X-ray part of the spectrum. These X-ray emissions are generally thought to result when one of the stars (compact object) accretes matter from another (regular) star. The presence of an ordinary star in such a system provides an opportunity for studying the central object and to determine if it might be a black hole. If such a system emits signals that can be directly traced back to the compact object, it cannot be a black hole. The absence of such a signal does, however, not exclude the possibility that the compact object is a neutron star. By studying the companion star it is often possible to obtain the orbital parameters of the system and to obtain an estimate for the mass of the compact object. If this is much larger than the Tolman–Oppenheimer–Volkoff limit (the maximum mass a star can have without collapsing) then the object cannot be a neutron star and is generally expected to be a black hole. The first strong candidate for a black hole, Cygnus X-1, was discovered in this way by Charles Thomas Bolton, Louise Webster and Paul Murdin in 1972. Some doubt, however, remained due to the uncertainties that result from the companion star being much heavier than the candidate black hole. Currently, better candidates for black holes are found in a class of X-ray binaries called soft X-ray transients. In this class of system, the companion star is of relatively low mass allowing for more accurate estimates of the black hole mass. Moreover, these systems actively emit X-rays for only several months once every 10–50 years. During the period of low X-ray emission (called quiescence), the accretion disk is extremely faint allowing detailed observation of the companion star during this period. One of the best such candidates is V404 Cygni. Quiescence and advection-dominated accretion flow The faintness of the accretion disk of an X-ray binary during quiescence is suspected to be caused by the flow of mass entering a mode called an advection-dominated accretion flow (ADAF). In this mode, almost all the energy generated by friction in the disk is swept along with the flow instead of radiated away. If this model is correct, then it forms strong qualitative evidence for the presence of an event horizon, since if the object at the center of the disk had a solid surface, it would emit large amounts of radiation as the highly energetic gas hits the surface,[clarification needed] an effect that is observed for neutron stars in a similar state. The X-ray emissions from accretion disks sometimes flicker at certain frequencies. These signals are called quasi-periodic oscillations and are thought to be caused by material moving along the inner edge of the accretion disk (the innermost stable circular orbit). As such their frequency is linked to the mass of the compact object. They can thus be used as an alternative way to determine the mass of candidate black holes. Astronomers use the term "active galaxy" to describe galaxies with unusual characteristics, such as unusual spectral line emission and very strong radio emission. Theoretical and observational studies have shown that the activity in these active galactic nuclei (AGN) may be explained by the presence of supermassive black holes, which can be millions of times more massive than stellar ones. The models of these AGN consist of a central black hole that may be millions or billions of times more massive than the Sun; a disk of gas and dust called an accretion disk; and two jets perpendicular to the accretion disk. Although supermassive black holes are expected to be found in most AGN, only some galaxies' nuclei have been more carefully studied in attempts to both identify and measure the actual masses of the central supermassive black hole candidates. Some of the most notable galaxies with supermassive black hole candidates include the Andromeda Galaxy, M32, M87, NGC 3115, NGC 3377, NGC 4258, NGC 4889, NGC 1277, OJ 287, APM 08279+5255 and the Sombrero Galaxy. It is now widely accepted that the center of nearly every galaxy, not just active ones, contains a supermassive black hole. The close observational correlation between the mass of this hole and the velocity dispersion of the host galaxy's bulge, known as the M-sigma relation, strongly suggests a connection between the formation of the black hole and the galaxy itself. Another way the black hole nature of an object may be tested in the future is through observation of effects caused by a strong gravitational field in their vicinity. One such effect is gravitational lensing: The deformation of spacetime around a massive object causes light rays to be deflected much as light passing through an optic lens. Observations have been made of weak gravitational lensing, in which light rays are deflected by only a few arcseconds. However, it has never been directly observed for a black hole. One possibility for observing gravitational lensing by a black hole would be to observe stars in orbit around the black hole. There are several candidates for such an observation in orbit around Sagittarius A. The evidence for stellar black holes strongly relies on the existence of an upper limit for the mass of a neutron star. The size of this limit heavily depends on the assumptions made about the properties of dense matter. New exotic phases of matter could push up this bound. A phase of free quarks at high density might allow the existence of dense quark stars, and some supersymmetric models predict the existence of Q stars. Some extensions of the standard model posit the existence of preons as fundamental building blocks of quarks and leptons, which could hypothetically form preon stars. These hypothetical models could potentially explain a number of observations of stellar black hole candidates. However, it can be shown from arguments in general relativity that any such object will have a maximum mass. Since the average density of a black hole inside its Schwarzschild radius is inversely proportional to the square of its mass, supermassive black holes are much less dense than stellar black holes (the average density of a 108 M☉ black hole is comparable to that of water). Consequently, the physics of matter forming a supermassive black hole is much better understood and the possible alternative explanations for supermassive black hole observations are much more mundane. For example, a supermassive black hole could be modelled by a large cluster of very dark objects. However, such alternatives are typically not stable enough to explain the supermassive black hole candidates. The evidence for the existence of stellar and supermassive black holes implies that in order for black holes to not form, general relativity must fail as a theory of gravity, perhaps due to the onset of quantum mechanical corrections. A much anticipated feature of a theory of quantum gravity is that it will not feature singularities or event horizons and thus black holes would not be real artifacts. For example, in the fuzzball model based on string theory, the individual states of a black hole solution do not generally have an event horizon or singularity, but for a classical/semi-classical observer the statistical average of such states appears just as an ordinary black hole as deduced from general relativity. A few theoretical objects have been conjectured to match observations of astronomical black hole candidates identically or near-identically, but which function via a different mechanism. These include the gravastar, the black star, and the dark-energy star. Entropy and thermodynamics In 1971, Hawking showed under general conditions[Note 5] that the total area of the event horizons of any collection of classical black holes can never decrease, even if they collide and merge. This result, now known as the second law of black hole mechanics, is remarkably similar to the second law of thermodynamics, which states that the total entropy of an isolated system can never decrease. As with classical objects at absolute zero temperature, it was assumed that black holes had zero entropy. If this were the case, the second law of thermodynamics would be violated by entropy-laden matter entering a black hole, resulting in a decrease of the total entropy of the universe. Therefore, Bekenstein proposed that a black hole should have an entropy, and that it should be proportional to its horizon area. The link with the laws of thermodynamics was further strengthened by Hawking's discovery that quantum field theory predicts that a black hole radiates blackbody radiation at a constant temperature. This seemingly causes a violation of the second law of black hole mechanics, since the radiation will carry away energy from the black hole causing it to shrink. The radiation, however also carries away entropy, and it can be proven under general assumptions that the sum of the entropy of the matter surrounding a black hole and one quarter of the area of the horizon as measured in Planck units is in fact always increasing. This allows the formulation of the first law of black hole mechanics as an analogue of the first law of thermodynamics, with the mass acting as energy, the surface gravity as temperature and the area as entropy. One puzzling feature is that the entropy of a black hole scales with its area rather than with its volume, since entropy is normally an extensive quantity that scales linearly with the volume of the system. This odd property led Gerard 't Hooft and Leonard Susskind to propose the holographic principle, which suggests that anything that happens in a volume of spacetime can be described by data on the boundary of that volume. Although general relativity can be used to perform a semi-classical calculation of black hole entropy, this situation is theoretically unsatisfying. In statistical mechanics, entropy is understood as counting the number of microscopic configurations of a system that have the same macroscopic qualities (such as mass, charge, pressure, etc.). Without a satisfactory theory of quantum gravity, one cannot perform such a computation for black holes. Some progress has been made in various approaches to quantum gravity. In 1995, Andrew Strominger and Cumrun Vafa showed that counting the microstates of a specific supersymmetric black hole in string theory reproduced the Bekenstein–Hawking entropy. Since then, similar results have been reported for different black holes both in string theory and in other approaches to quantum gravity like loop quantum gravity. Information loss paradox \|Unsolved problem in physics:\| Is physical information lost in black holes?(more unsolved problems in physics) Because a black hole has only a few internal parameters, most of the information about the matter that went into forming the black hole is lost. Regardless of the type of matter which goes into a black hole, it appears that only information concerning the total mass, charge, and angular momentum are conserved. As long as black holes were thought to persist forever this information loss is not that problematic, as the information can be thought of as existing inside the black hole, inaccessible from the outside, but represented on the event horizon in accordance with the holographic principle. However, black holes slowly evaporate by emitting Hawking radiation. This radiation does not appear to carry any additional information about the matter that formed the black hole, meaning that this information appears to be gone forever. The question whether information is truly lost in black holes (the black hole information paradox) has divided the theoretical physics community (see Thorne–Hawking–Preskill bet). In quantum mechanics, loss of information corresponds to the violation of vital property called unitarity, which has to do with the conservation of probability. It has been argued that loss of unitarity would also imply violation of conservation of energy. Over recent years evidence has been building that indeed information and unitarity are preserved in a full quantum gravitational treatment of the problem. According to quantum field theory in curved spacetime, a single emission of Hawking radiation involves two mutually entangled particles. The outgoing particle escapes and is emitted as a quantum of Hawking radiation; the infalling particle is swallowed by the black hole. Assume a black hole formed a finite time in the past and will fully evaporate away in some finite time in the future. Then, it will emit only a finite amount of information encoded within its Hawking radiation. Assume that at time , more than half of the information had already been emitted. According to widely accepted research by physicists like Don Page and Leonard Susskind, an outgoing particle emitted at time must be entangled with all the Hawking radiation the black hole has previously emitted. This creates a paradox: a principle called "monogamy of entanglement" requires that, like any quantum system, the outgoing particle cannot be fully entangled with two independent systems at the same time; yet here the outgoing particle appears to be entangled both with the infalling particle and, independently, with past Hawking radiation. In order to resolve the paradox, physicists may eventually be forced to give up one of three time-tested theories: Einstein's equivalence principle, unitarity, or existing quantum field theory. One possible solution, which violates the equivalence principle, is that a "firewall" destroys incoming particles at the event horizon. A 2016 analysis of LIGO data shows tentative signs of echoes caused by a fuzzy event horizon; such echoes may be possible in firewall or fuzzball theories but should not occur in classical general relativity. Over the next two years, additional LIGO data should establish whether the echoes were just random noise, or whether they are instead evidence of a violation of classical general relativity. - Binary black hole - Black brane - Black hole complementarity - Black Hole Initiative - Black holes in fiction - Black hole starship - Black string - BTZ black hole - General relativity - Kugelblitz (astrophysics) - List of black holes - List of nearest black holes - Outline of black holes - Sonic black hole, also Dumb hole - Stellar black hole - Supermassive black holes - Susskind-Hawking battle - Timeline of black hole physics - White hole - The value of cJ/GM2 can exceed 1 for objects other than black holes. 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Year 2: Multiplication and Division Pupils should use a variety of language to describe multiplication and division. They are taught multiplication and division with larger numbers through equal grouping and sharing out quantities, relating multiplication tables to arrays and repeated addition and finding more complex fractions of objects, numbers and quantities. Pupils should be introduced to the multiplication tables. They should practise to become fluent in the 2, 5 and 10 multiplication tables and connect them to each other. They connect the 10 multiplication table to place value, and the 5 multiplication table to the divisions on the clock face. They begin to use other multiplication tables and recall multiplication facts, including using related division facts to perform written and mental calculations. Pupils should work with a range of materials and contexts in which multiplication and division relate to grouping and sharing discrete and continuous quantities, relating these to fractions and measures (e.g. 40 ÷ 2 = 20, 20 is a half of 40). They use commutativity and inverse relations to develop multiplicative reasoning (e.g. 4 × 5 = 20 and 20 ÷ 5 = 4).
Numeration systems are methods for representing quantities. As a simple example, suppose you have a basket of oranges. You might want to keep track of the number of oranges in the basket. Or you might want to sell the oranges to someone else. Or you might simply want to give the basket a numerical code that could be used to tell when and where the oranges came from. In order to perform any of these simple mathematical operations, you would have to begin with some kind of numeration system. Why numeration systems exist This example illustrates the three primary reasons that numeration systems exist. First, it is often necessary to tell the number of items contained in a collection or set of those items. To do that, you have to have some method for counting the items. The total number of items is represented by a number known as a cardinal number. If the basket mentioned above contained 30 oranges, then 30 would be a cardinal number since it tells how many of an item there are. Numbers can also be used to express the rank or sequence or order of items. For example, the individual oranges in the basket could be numbered according to the sequence in which they were picked. Orange #1 would be the first orange picked; orange #2, the second picked; orange #3, the third picked; and so on. Numbers used in this way are known as ordinal numbers. Finally, numbers can be used for purposes of identification. Some method must be devised to keep checking and savings accounts, credit card accounts, drivers' licenses, and other kinds of records for different people separated from each other. Conceivably, one could give a name to such records (John T. Jones's checking account at Old Kent Bank), but the number of options using words is insufficient to make such a system work. The use of numbers (account #338-4498-1949) makes it possible to create an unlimited number of separate and individualized records. No one knows exactly when the first numeration system was invented. A notched baboon bone dating back 35,000 years was found in Africa and was apparently used for counting. In the 1930s, a wolf bone was found in Czechoslovakia with 57 notches in several patterns of regular intervals. The bone was dated as being 30,000 years old and is assumed to be a hunter's record of his kills. The earliest recorded numbering systems go back at least to 3000 b.c., when Sumerians in Mesopotamia were using a numbering system for recording business transactions. People in Egypt and India were using numbering systems at about the same time. The decimal or base-10 numbering system goes back to around 1800 b.c., and decimal systems were common in European and Indian cultures from at least 1000 b.c. One of the most important inventions in western culture was the development of the Hindu-Arabic notation system (1, 2, 3, … 9). That system eventually became the international standard for numeration. The Hindu-Arabic system had been around for at least 2,000 years before the Europeans heard about it, and it included many important innovations. One of these was the placeholding concept of zero. Although the concept of zero as a placeholder had appeared in many cultures in different forms, the first actual written zero as we know it today appeared in India in a.d. 876. The Hindu-Arabic system was brought into Europe in the tenth century with Gerbert of Aurillac (c. 945–1003), a French scholar who studied at Muslim schools in Spain before being named pope (Sylvester II). The system slowly and steadily replaced the numeration system based on Roman numerals (I, II, III, IV, etc.) in Europe, especially in business transactions and mathematics. By the sixteenth century, Europe had largely adopted the far simpler and more economical Hindu-Arabic system of notation, although Roman numerals were still used at times and are even used today. Numeration systems continue to be invented to this day, especially when companies develop systems of serial numbers to identify new products. The binary (base-2), octal (base-8), and hexadecimal (base-16) numbering systems used in computers were developed in the late 1950s for processing electronic signals in computers. The bases of numeration systems Every numeration system is founded on some number as its base. The base of a system can be thought of as the highest number to which one can count without repeating any previous number. In the decimal system used in most parts of the world today, the base is 10. Counting in the decimal system involves the use of ten different digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. To count beyond 9, one uses the same digits over again—but in different combinations: a 1 with a 0, a 1 with a 1, a 1 with a 2, and so on. The base chosen for a numeration system often reflects actual methods of counting used by humans. For example, the decimal system may have developed because most humans have ten fingers. An easy way to create numbers, then, is to count off one's ten fingers, one at a time. Most numeration systems make use of a concept known as place value. That term means that the numerical value of a digit depends on its location in a number. For example, the number one hundred eleven consists of three 1s: 111. Yet each of the 1s in the number has a different meaning because of its location in the number. The first 1, 1 11, means 100 because it stands in the third position from the right in the number, the hundreds place. (Note that position placement from the right is based on the decimal as a starting point.) The second 1, 11 1, means ten because it stands in the second position from the right, the tens place. The third 1, 111, means one because it stands in the first position from the right, the units place. One way to think of the place value of a digit is as an exponent (or power) of the base. Starting from the right of the number, each digit has a value one exponent larger. The digit farthest to the right, then, has its value multiplied by 100 (or 1). The digit next to it on the left has its value multiplied by 101 (or 10). The digit next on the left has its value multiplied by 102 (or 100). And so forth. The Roman numeration system is an example of a system without place value. The number III in the Roman system stands for three. Each of the Is has exactly the same value (one), no matter where it occurs in the number. One disadvantage of the Roman system is the much greater difficulty of performing mathematical operations, such as addition, subtraction, multiplication, and division. Examples of nondecimal numeration systems Throughout history, numeration systems with many bases have been used. Besides the base 10-system with which we are most familiar, the two most common are those with base 2 and base 60. Base 2. The base 2- (or binary) numeration system makes use of only two digits: 0 and 1. Counting in this system proceeds as follows: 0; 1; 10; 11; 100; 101; 110; etc. In order to understand the decimal value of these numbers, think of the base 2-system in terms of exponents of base 2. The value of any number in the binary system depends on its place, as shown below: The value of a number in the binary system can be determined in the same way as in the decimal system. Anyone who has been brought up with the decimal system might wonder what the point of using the binary system is. At first glance, it seems extremely complicated. One major application of the binary system is in electrical and electronic systems in which a switch can be turned on or off. When you press a button on a handheld calculator, for example, you send an electric current through chips in the calculator. The current turns some switches on and some switches off. If an on position is represented by the number 1 and an off position by the number 0, calculations can be performed in the binary system. Base 60. How the base-60 numeration system was developed is unknown. But we do know that the system has been widely used throughout human history. It first appeared in the Sumerian civilization in Mesopotamia in about 3000 b.c. Remnants of the system remain today. For example, we use it in telling time. Each hour is divided into 60 minutes and, in turn, each minute into 60 seconds. In counting time, we do not count from 1 to 10 and start over again, but from 1 to 60 before starting over. Navigational systems also use a base-60 system. Each degree of arc on Earth's surface (longitude and latitude) is divided into 60 minutes of arc. Each minute, in turn, is divided into 60 seconds of arc. "Numeration Systems." UXL Encyclopedia of Science. 2002. Encyclopedia.com. (August 30, 2016). http://www.encyclopedia.com/doc/1G2-3438100463.html "Numeration Systems." UXL Encyclopedia of Science. 2002. Retrieved August 30, 2016 from Encyclopedia.com: http://www.encyclopedia.com/doc/1G2-3438100463.html Numerals are symbols or groups of symbols that represents a number. For example, the symbols 12, twelve, and XII are different numerals that all represent the same number. Numeration systems are structured methods or procedures for counting in order to determine the total units in a collection. Numeration systems consist of counting bases (base 2, base 5, base 10, base 20, etc.) and some form of representation. This representation might be as primitive as the hand signals used in aborigine cultures and in the trading pits of stock exchanges, or it could be written on paper or inscribed magnetically in an electronic medium like a computer hard-drive. Numeration systems exist for three reasons: to identify, to order, and to tally. Numeration systems are used to identify people and property, because they preserve confidentiality, increase security, and minimize errors caused when there are many people with the same name or many identical objects in the same production run in a factory assembly Base ten numerals tens = 10 hundred = 100 thousands = 1,000 ten thousands = 10,000 hundred thousands =100,000 millions = 1,000,000 ten millions = 10,000,000 hundred millions 100,0000,0000 billions = 1,000,000,000 line. There are thousands of people named John Jones, and even if John Jones uses his middle initial, he can still be confused with another John Jones with the same initial. Thus, numeration systems are developed for credit cards, social security cards, bank accounts, serial numbers for products, and other reasons. These identification numbers might be very long to defeat a criminal who is randomly guessing at numbers in order to steal from someone’s bank account or credit card account. Numeration systems also define a person or unit’s order in a series, for example, to determine who crosses a finish line in a race in first, second, or third place. Numbers that define order are known as the ordinal numbers (first, second, etc.) and contrast with the cardinal numbers (one, two, three, etc.) which express a tally or total of units. Finally, numeration systems are used to tally or total; to find out how many items or units are involved in a calculation involving addition, subtraction, multiplication, or division. No one knows exactly when ordered numeration systems began, but counting has been around for tens of thousands of years. A notched baboon bone dating back 35,000 years was found in Africa and was apparently used for counting. In the 1930s, a wolf bone was found in Czechoslovakia with 57 notches in several patterns of regular intervals. The bone was dated as 30,000 years old and is assumed to be a hunter’s record of his kills. The earliest recorded numbering systems go back at least 3000 BC, when Sumerians in Mesopotamia were using a numbering system for recording business transactions, and Egyptians and people in ancient India were also using numbering systems around the same time. The decimal, or base 10, numbering system goes back to at least 1800 BC, and decimal systems were common in European and Indian cultures from at least 1000 BC. One of the most important innovations in western culture was the development of the Hindu-Arabic notation system (1, 2, 3, . . . 9), which is the international standard today. The Hindu-Arabic system had been around for at least 2,000 years before the Europeans heard about it, and it has many important innovations. One of these was the place-holding concept of zero. Although the concept of zero as a null place holder had appeared in many cultures in different forms, the first actual written zero as is known today appeared in India in 876 AD. The Hindu-Arabic system was brought into Europe in the tenth century with Gerbert of Aurillac (945–1003), and it slowly and steadily began to replace Roman numerals (I, II, III, IV, . . .) in Europe, especially in business transactions and mathematics. By the sixteenth century, Europe was well versed in the far simpler and more economical Hindu-Arabic system of notation, though Roman Numerals were still used, and are even used today. Numeration systems continue to be invented to this day, especially when companies develop systems of serial numbers to identify new products. The binary (base 2), octal (base 8), and hexadecimal (or base 16) numbering systems used in computers were extensively developed in the late 1950s for processing electronic signals in computers. The base of a numeration system is its frame of reference or the starting point on which it grounds its counting method. Although any numeration system must be abstract, the basic concept of number makes more sense to people if it has some obvious, immediate reference point in human experience. For that reason, many bases of numeration systems are founded upon the most obvious and immediate things in a person’s visual field: a person’s arms, hands, fingers, and toes. Common bases of numeration systems are the two arms of a person (base 2 system), the fingers of one hand (base 5 system), the fingers of both hands (base 10 system), or the total of all a person’s fingers and toes (base 20 system). There are many other bases for numeration systems (base 4, base 7, base 8, base 16, etc.), but only a few will be discussed here. Although most base 2 numeration systems have now been replaced by decimal (or base 10) systems, the base 2 system was one of the most common numeration systems in ancient times. In a base 2 system, to indicate a number like three or four, the person says “two-and-one” or “two-and-two.” The number 10 is indicated with “two-and-two-and-two-and-two-and-two.” However, as a person counts to higher and higher numbers in a base 2 system, it becomes harder and harder to remember one’s place in the long string of twos. Thus, as cultures grew more complex and needed to count to higher numbers, base 2 systems became obsolete. The base 10 or decimal system has now spread throughout the world and is the most commonly used numeration system today. The digits to the left and right of the decimal point are named according to their distance from the decimal. The first ten numbers, in their order of distance from the left of the decimal point are: These numbers continue indefinitely. To the right of the decimal point the numbers are one tenth, one hundredth, one thousandth, one ten-thousandth, one hundred-thousandth, one millionth, and so on. The base 60 system seems very strange to Western readers. From long habit, Westerners are accustomed to the decimal system, and it is easy to understand numbering systems based on two (arms), five (fingers), ten (fingers on both hands), and so on. However, the base 60 system survives in the time-measuring system of 60 seconds to a minute and 60 minutes to an hour. It also survives in angle measurement and in navigational systems that measure longitude and latitude: 60 seconds equal one minute of arc, 60 minutes equal one degree of arc, and 360 degrees of arc equal an entire circle. The base 60 system began with the Sumerians in Mesopotamia around 3000 BC. No one knows how it got started, though scholars speculate that it had something to do with the 60 to 1 ratio between the weights of the Sumerian measurement system. Others speculate that it was the result of the combining of a base 6 and base 10 numbering system. A rational explanation for using 60 as a base is that 60 can be divided evenly by 2, 3, 4, 5, and 6, which simplifies many computations. A place-value system assigns a certain value to the spatial location of a number in a series. For example, in the decimal system, a number’s position relative to others in a series defines its category as being in the tens, hundreds, thousands, ten-thousands, and so on. In the number 1,234, the “4” occupies the slot representing zero through 9, the “3” occupies the slot representing 10 through 99, the “2” occupies the slot representing 100 through 999, and the “1” occupies the slot representing 1000 through 9999. Place value systems are important because they make common arithmetic functions much more efficient. If people are to manipulate spatial symbols readily, they need a method that is simple, consistent, and symmetrical so that numbers can be lined up visually, and can be quickly grouped at a glance according to their value. Without the place values of the decimal system, simple arithmetic functions of addition, subtraction, multiplication, and division are enormously difficult because they are intimidating, time-consuming, overly complicated, and prone to error. The Roman numeral system (I, II, III, IV, . . .) lacks an efficient way to represent place, and it makes simple arithmetic functions very difficult to perform for most people. Compare below the simple process of adding 17, 38, and 3 in Roman numerals and Hindu-Arabic numerals. Most people who are familiar with Hindu-Arabic numbers find that adding the Roman numerals on the left is baffling. Although place-value systems make it easier for people to do arithmetic, they also help computers perform electronic computations at very fast speeds. A common place-value system used in computers is the binary number system, which is a base 2 system. The binary system has two values: “0” and “1.” These values correspond with the signals “high” and “low” in the electronic circuits of computers. Because these numbers are so simple, computers can process them electronically up to a trillion times per second, depending on the speed of the computer. In the binary system, each place from right to left is valued at 2 times the place to its right. Thus, the first place can be zero or one, the second place to the left is valued at two, the third place to the left is valued at four, the fourth place to the left is valued at eight, and so on. The following list indicates the binary values of the first ten numbers of a decimal system: Arc —The continuous path described by a curved line. Base —The foundation or reference point upon which a counting system is built. Hindu-Arabic numbers —Although commonly called Arabic numerals, the numbering system represented as 1, 2, 3, 4, . . ., 9 represents a combination of innovations from Arabic and Hindu (or Indian) cultures. Latitude —The lines that run east and west on a map that are used to measure the distance north and south of the equator. Longitude —The lines on a map that run perpendicular to the equator, which are used to measure distances east and west. Mesopotamia —The area in the ancient Middle East between the Tigris and Euphrates rivers, which is now in Iraq. Place-value —The location of a number relative to others in a sequence. In the decimal system the number 3 in the series 2,300 occupies the hundreds place. Roman numerals —The numbering system developed during the Roman Empire: I, II, III, IV, V, and so on. For example, the decimal number 3 above has two 1s in its binary format. The 1 on the right in the binary format is equal to 1, because its place value can only be 1 or 0. However, the 1 on the left in the binary format (for the decimal number 3) occupies the place that is valued at 2 in the binary system. Consider another example: look at the decimal number 10 as it is formatted in the binary system: 1010. The fourth number (1) from the right occupies the place valued at 8; the 0 in the third place means it is valued at zero; the 1 in the second place from the right means it is valued at 2; and the 0 in the right-most place means zero. Thus, in the binary place-value system, 8 + 0 + 2 + 0 = 10. Although this system seems cumbersome to people who are used to the decimal notation system, it is perfectly suited for the ways that computers manipulate electric currents to process large quantities of data at very fast rates. Ball, W.W. Rouse. A Short Account of the History of Mathematics. London: Sterling Publications, 2002. Burton, David M. Elementary Number Theory. Boston, MA: McGraw-Hill Higher Education, 2007. Clawson, Calvin C. The Mathematical Traveler: Exploring the Grand History of Numbers Cambridge, MA: Perseus Publishing, 2003. Reid, Constance. From Zero to Infinity: What Makes Numbers Interesting. Wellesley, MA: A.K. Peters, 2006. Schroeder, Manfred Robert. Number Theory in Science and Communications: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-similarity. Berlin, Germany, and New York: Springer, 2006. Vinogradov, Ivan Matveevich. Elements of Number Theory. Dover Publications, 2003. Weisstein, Eric W. The CRC Concise Encyclopedia of Mathematics. Boca Raton, FL: Chapman & Hall/CRC Press, 2003. "Numeration Systems." The Gale Encyclopedia of Science. 2008. Encyclopedia.com. (August 30, 2016). http://www.encyclopedia.com/article-1G2-2830101625/numeration-systems.html "Numeration Systems." The Gale Encyclopedia of Science. 2008. Retrieved August 30, 2016 from Encyclopedia.com: http://www.encyclopedia.com/article-1G2-2830101625/numeration-systems.html
A great power is a sovereign state that is recognized as having the ability to exert its influence on a global scale. Great powers characteristically possess military and economic strength, as well as diplomatic and soft power influence, which may cause small powers to consider the great powers' opinions before taking actions of their own. International relations theorists have posited that great power status can be characterized into power capabilities, spatial aspects, and status dimensions. Sometimes the status of great powers is formally recognized in conferences such as the Congress of Vienna or an international structure such as the United Nations Security Council. The term "great power" was first used to represent the most important powers in Europe during the post-Napoleonic era. The "Great Powers" - then the Austrian Empire, France, Prussia, Russia, and the British Empire - constituted the "Concert of Europe" and claimed the right to joint enforcement of the postwar treaties. The formalization of the division between small powers and great powers came about with the signing of the Treaty of Chaumont in 1814. Since then, the international balance of power has shifted numerous times, most dramatically during World War I and World War II. While some nations are widely considered to be great powers, there is no definitive list of them. In literature, alternative terms for great power are often world power or major power, but these terms can also be interchangeable with superpower. - 1 Characteristics - 2 History - 3 Hierarchy of great powers - 4 List of great powers by date - 5 See also - 6 Notes - 7 References - 8 Further reading There are no set or defined characteristics of a great power. These characteristics have often been treated as empirical, self-evident to the assessor. However, this approach has the disadvantage of subjectivity. As a result, there have been attempts to derive some common criteria and to treat these as essential elements of great power status. Early writings on the subject tended to judge states by the realist criterion, as expressed by the historian A. J. P. Taylor when he noted that "The test of a great power is the test of strength for war." Later writers have expanded this test, attempting to define power in terms of overall military, economic, and political capacity. Kenneth Waltz, the founder of the neorealist theory of international relations, uses a set of five criteria to determine great power: population and territory; resource endowment; economic capability; political stability and competence; and military strength. These expanded criteria can be divided into three heads: power capabilities, spatial aspects, and status. As noted above, for many, power capabilities were the sole criterion. However, even under the more expansive tests, power retains a vital place. This aspect has received mixed treatment, with some confusion as to the degree of power required. Writers have approached the concept of great power with differing conceptualizations of the world situation, from multi-polarity to overwhelming hegemony. In his essay, 'French Diplomacy in the Postwar Period', the French historian Jean-Baptiste Duroselle spoke of the concept of multi-polarity: "A Great power is one which is capable of preserving its own independence against any other single power." This differed from earlier writers, notably from Leopold von Ranke, who clearly had a different idea of the world situation. In his essay 'The Great Powers', written in 1833, von Ranke wrote: "If one could establish as a definition of a Great power that it must be able to maintain itself against all others, even when they are united, then Frederick has raised Prussia to that position." These positions have been the subject of criticism. All states have a geographic scope of interests, actions, or projected power. This is a crucial factor in distinguishing a great power from a regional power; by definition the scope of a regional power is restricted to its region. It has been suggested that a great power should be possessed of actual influence throughout the scope of the prevailing international system. Arnold J. Toynbee, for example, observes that "Great power may be defined as a political force exerting an effect co-extensive with the widest range of the society in which it operates. The Great powers of 1914 were 'world-powers' because Western society had recently become 'world-wide'." Other suggestions have been made that a great power should have the capacity to engage in extra-regional affairs and that a great power ought to be possessed of extra-regional interests, two propositions which are often closely connected. Formal or informal acknowledgment of a nation's great-power status has also been a criterion for being a great power. As political scientist George Modelski notes, "The status of Great power is sometimes confused with the condition of being powerful, The office, as it is known, did in fact evolve from the role played by the great military states in earlier periods ... But the Great power system institutionalizes the position of the powerful state in a web of rights and obligations." This approach restricts analysis to the post-Congress of Vienna epoch; it being there that great powers were first formally recognized. In the absence of such a formal act of recognition it has been suggested that great power status can arise by implication, by judging the nature of a state's relations with other great powers. A further option is to examine a state's willingness to act as a great power. As a nation will seldom declare that it is acting as such, this usually entails a retrospective examination of state conduct. As a result this is of limited use in establishing the nature of contemporary powers, at least not without the exercise of subjective observation. Other important criteria throughout history are that great powers should have enough influence to be included in discussions of political and diplomatic questions of the day, and have influence on the final outcome and resolution. Historically, when major political questions were addressed, several great powers met to discuss them. Before the era of groups like the United Nations, participants of such meetings were not officially named, but were decided based on their great power status. These were conferences which settled important questions based on major historical events. This might mean deciding the political resolution of various geographical and nationalist claims following a major conflict, or other contexts. There are several historical conferences and treaties which display this pattern, such as the Congress of Vienna, the Congress of Berlin, the discussions of the Treaty of Versailles which redrew the map of Europe, and the Treaty of Westphalia. Different sets of great, or significant, powers have existed throughout history; however, the term "great power" has only been used in scholarly or diplomatic discourse since the Congress of Vienna in 1815. The Congress established the Concert of Europe as an attempt to preserve peace after the years of Napoleonic Wars. Lord Castlereagh, the British Foreign Secretary, first used the term in its diplomatic context, in a letter sent on February 13, 1814: "It affords me great satisfaction to acquaint you that there is every prospect of the Congress terminating with a general accord and Guarantee between the Great powers of Europe, with a determination to support the arrangement agreed upon, and to turn the general influence and if necessary the general arms against the Power that shall first attempt to disturb the Continental peace." The Congress of Vienna consisted of five main powers: the Austrian Empire, France, Prussia, Russia, and the United Kingdom. These five primary participants constituted the original great powers as we know the term today. Other powers, such as Spain, Portugal, and Sweden were consulted on certain specific issues, but they were not full participants. Kingdom of Hanover, Bavaria, and Württemberg were also consulted on issues relating to Germany. Of the five original great powers recognised at the Congress of Vienna, only France and the United Kingdom have maintained that status continuously to the present day, although France was defeated in the Franco-Prussian War and occupied during World War II. After the Congress of Vienna, the British Empire emerged as the pre-eminent power, due to its navy and the extent of its territories, which signalled the beginning of the Pax Britannica and of The Great Game between Britain and Russia. The balance of power between the Great Powers became a major influence in European politics, prompting Otto von Bismarck to say "All politics reduces itself to this formula: try to be one of three, as long as the world is governed by the unstable equilibrium of five great powers." Over time, the relative power of these five nations fluctuated, which by the dawn of the 20th century had served to create an entirely different balance of power. Some, such as the United Kingdom and Prussia (as part of the newly formed German state), experienced continued economic growth and political power. Others, such as Russia and Austria-Hungary, stagnated. At the same time, other states were emerging and expanding in power, largely through the process of industrialization. The foremost of these emerging powers were Japan after the Meiji Restoration and the United States after its civil war, both of which had been minor powers in 1815. By the dawn of the 20th century the balance of world power had changed substantially since the Congress of Vienna. The Eight-Nation Alliance was a belligerent alliance of eight nations against the Boxer Rebellion in China. It formed in 1900 and consisted of the five Congress powers plus Italy, Japan, and the United States, representing the great powers at the beginning of 20th century. Great powers at war Shifts of international power have most notably occurred through major conflicts. The conclusion of the Great War and the resulting treaties of Versailles, St-Germain, and Trianon witnessed the United Kingdom, France, Italy, Japan and the United States as the chief arbiters of the new world order. In the aftermath of World War I the German Empire was defeated, the Austria-Hungarian empire was divided into new, less powerful states and the Russian Empire fell to a revolution. During the Treaty of Versailles the "Big Three"—France, United Kingdom and the United States—held noticeably more power and influence on the proceedings and outcome of the treaty than Italy or Japan. The victorious great powers also gained an acknowledgement of their status through permanent seats at the League of Nations Council, where they acted as a type of executive body directing the Assembly of the League. However, the Council began with only four permanent members—Great Britain, France, Italy, and Japan—because the United States, meant to be the fifth permanent member, left because the US Senate voted on 19 March 1920 against the ratification of the Treaty of Versailles, thus preventing American participation in the League. When World War II started in 1939, it divided the world into two alliances—the Allies (the United Kingdom and France at first in Europe, China in Asia since 1937, followed in 1941 by the Soviet Union, the United States); and the Axis powers consisting of Germany, Italy and Japan.[nb 1] The end of World War II saw the United States, United Kingdom, and Soviet Union emerge as the primary victors. The importance of the Republic of China and France was acknowledged by their inclusion, along with the other three, in the group of countries allotted permanent seats in the United Nations Security Council. Since the end of the World Wars, the term "great power" has been joined by a number of other power classifications. Foremost among these is the concept of the superpower, used to describe those nations with overwhelming power and influence in the rest of the world. It was first coined in 1944 by William T.R. Fox and according to him, there were three superpowers: the British Empire, the United States, and the Soviet Union. But by the mid-1950s the British Empire lost its superpower status, leaving the United States and the Soviet Union as the world's superpowers.[nb 2] The term middle power has emerged for those nations which exercise a degree of global influence, but are insufficient to be decisive on international affairs. Regional powers are those whose influence is generally confined to their region of the world. During the Cold War, the Asian power of Japan and the European powers of the United Kingdom, France, and West Germany rebuilt their economies. France and the United Kingdom maintained technologically advanced armed forces with power projection capabilities and maintain large defence budgets to this day. Yet, as the Cold War continued, authorities began to question if France and the United Kingdom could retain their long-held statuses as great powers. China, with the world's largest population, has slowly risen to great power status, with large growth in economic and military power in the post-war period. After 1949, the Republic of China began to lose its recognition as the sole legitimate government of China by the other great powers, in favour of the People's Republic of China. Subsequently, in 1971, it lost its permanent seat at the UN Security Council to the People's Republic of China. Great powers at peace According to Joshua Baron -a "researcher, lecturer, and consultant on international conflict"- since the early 1960s direct military conflicts and major confrontations have "receded into the background" with regards to relations among the great powers. Baron argues several reasons why this is the case, citing the unprecedented rise of the United States and its predominant position as the key reason. Baron highlights that since World War Two no other great power has been able to achieve parity or near parity with the United States, with the exception of the Soviet Union for a brief time. This position is unique among the great powers since the start of the modern era (the 16th century), where there has traditionally always been "tremendous parity among the great powers". This unique period of American Primacy has been an important factor in maintaining a condition of peace between the great powers. Another important factor is the apparent consensus among Western great powers that military force is no longer an effective tool of resolving disputes among their peers. This "subset" of great powers -France, Germany, Japan, the United Kingdom and the United States- consider maintaining a "state of peace" as desirable. As evidence, Baron outlines that since the Cuban missile crisis (1962) during the Cold War, these influential Western nations have resolved all disputes among the great powers peacefully at the United Nations and other forums of international discussion. Referring to great power relations pre-1960, Joshua Baron highlights that starting from around the 16th century and the rise of several European great powers, military conflicts and confrontations was the defining characteristic of diplomacy and relations between such powers. "Between 1500 and 1953, there were 64 wars in which at least one great power was opposed to another, and they averaged little more than five years in length. In approximately a 450-year time frame, on average at least two great powers were fighting one another in each and every year." Even during the period of Pax Britannica (or "the British Peace") between 1815 and 1914, war and military confrontations among the great powers was still a frequent occurrence. In fact, Joshua Baron points out that in terms of militarized conflicts or confrontations Britain lead the way in this period with nineteen such instances against; Russia (8), France (5), Germany/Prussia (5) and Italy (1). In his 2014 publication Great Power Peace and American Primacy, Joshua Baron considers China, France, Russia, Germany, Japan, the United Kingdom and the United States as the current great powers. Aftermath of the Cold War China, France, Russia, the United Kingdom and the United States are often referred to as great powers by academics due to "their political and economic dominance of the global arena". These five nations are the only states to have permanent seats with veto power on the UN Security Council. They are also the only recognized "Nuclear Weapons States" under the Nuclear Non-Proliferation Treaty, and maintain military expenditures which are among the largest in the world. However, there is no unanimous agreement among authorities as to the current status of these powers or what precisely defines a great power. For example, sources have at times referred to China, France, Russia and the United Kingdom as middle powers. Following the dissolution of the Soviet Union, its UN Security Council permanent seat was transferred to the Russian Federation in 1991, as its successor state. The newly formed Russian Federation emerged on the level of a great power, leaving the United States as the only remaining global superpower[nb 3] (although some support a multipolar world view). Many academics also consider Germany and Japan to be great powers too, but due to their large advanced economies (having the third and fourth largest economies respectively) as opposed to their strategic and hard power capabilities (I.e the lack of permanent seats and veto power on the UN Security Council or strategic military reach). Like China, France, Russia and the United Kingdom; Germany and Japan have also been referred to as middle powers. In addition to those contemporary great powers mentioned above, Malik Mohan considers India to be a great power too. Although unlike the contemporary great powers who have long been considered so, India's recognition among authorities as a great power is comparatively recent. However there is no collective agreement among observers as to the status of India, for example, a number of academics believe that India is still emerging as a great power, while some believe that India is a middle power. With continuing European integration, the European Union is increasingly being seen as a great power in its own right, with representation at the WTO and at G8 and G-20 summits. This is most notable in areas where the European Union has exclusive competence (i.e. economic affairs). It also reflects a non-traditional conception of Europe's world role as a global "civilian power", exercising collective influence in the functional spheres of trade and diplomacy, as an alternative to military dominance. The European Union is a supranational union and not a sovereign state, and has limited scope in the areas of foreign affairs and defense policy. These remain largely with the member states of the European Union, which include the three great powers of France, Germany and the United Kingdom (referred to as the "EU three"). Brazil and India are widely regarded as emerging powers with the potential to be great powers. Political scientist Stephen P. Cohen asserts that India is an emerging power, but highlights that some strategists consider India to be already a great power. Some academics such as Zbigniew Brzezinski and Dr David A. Robinson already regard India as a major or great power. Permanent membership of the UN Security Council is widely regarded as being a central tenet of great power status in the modern world; Brazil, Germany, India and Japan form the G4 nations which support one another (and have varying degrees of support from the existing permanent members) in becoming permanent members. There are however few signs that reform of the Security Council will happen in the near future. Hierarchy of great powers Acclaimed political scientist, geo-strategist, and former United States National Security Advisor Zbigniew Brzezinski, appraised the current standing of the great powers in his 2012 publication Strategic Vision: America and the Crisis of Global Power. In relation to great powers, he makes the following points: "The United States is still preeminent but the legitimacy, effectiveness, and durability of its leadership is increasingly questioned worldwide because of the complexity of its internal and external challenges. ... The European Union could compete to be the world's number two power, but this would require a more robust political union, with a common foreign policy and a shared defense capability. ... In contrast, China's remarkable economic momentum, its capacity for decisive political decisions motivated by clearheaded and self centered national interest, its relative freedom from debilitating external commitments, and its steadily increasing military potential coupled with the worldwide expectation that soon it will challenge America's premier global status justify ranking China just below the United States in the current international hierarchy. ... A sequential ranking of other major powers beyond the top two would be imprecise at best. Any list, however, has to include Russia, Japan, and India, as well as the EU's informal leaders: Great Britain, Germany, and France." List of great powers by date - Even though the book The Economics of World War II lists seven great powers at the start of 1939 (the British Empire, the Empire of Japan, France, the Kingdom of Italy, Nazi Germany, the Soviet Union and the United States), it focuses only on six of them, because France surrendered shortly after the war began. - The 1956 Suez Crisis suggested that the United Kingdom, financially weakened by two world wars, could not then pursue its foreign policy objectives on an equal footing with the new superpowers without sacrificing convertibility of its reserve currency as a central goal of policy. – from superpower cited by Klug, Adam; Smith, Gregor W. (1999). "Suez and Sterling, 1956". Explorations in Economic History 36 (3): 181–203. doi:10.1006/exeh.1999.0720. - The fall of the Berlin Wall and the breakup of the Soviet Union left the United States as the only remaining superpower in the 1990s. - After the Statute of Westminster came into effect in 1931, the United Kingdom no longer represented the British Empire in world affairs. - "the prime minister of Canada (during the Treaty of Versailles) said that there were 'only three major powers left in the world the United States, Britain and Japan' ... (but) The Great Powers could not be consistent. At the instance of Britain, Japan's ally, they gave Japan five delegates to the Peace Conference, just like themselves, but in the Supreme Council the Japanese were generally ignored or treated as something of a joke." from MacMillan, Margaret (2003). Paris 1919. United States of America: Random House Trade. p. 306. ISBN 0-375-76052-0. - Peter Howard, B.A., B.S., M.A., Ph.D. Assistant Professor, School of International Service, American University. (2008). "Great Powers". Encarta. MSN. Archived from the original on 2009-10-31. Retrieved 2008-12-20. - Louden, Robert (2007). The world we want. United States of America: Oxford University Press US. p. 187. ISBN 0195321375. - Kelsen, Hans (2000). The Law of the United Nations: A Critical Analysis of Its Fundamental Problems. United States of America: The Lawbook Exchange, Ltd. pp. 272–281, 911. ISBN 1-58477-077-5. - Fueter, Eduard (1922). World history, 1815–1930. United States of America: Harcourt, Brace and Company. pp. 25–28, 36–44. ISBN 1-58477-077-5. - Danilovic, Vesna. "When the Stakes Are High—Deterrence and Conflict among Major Powers", University of Michigan Press (2002), pp 27, 225–228 (PDF chapter downloads) (PDF copy).[dead link] - T. V. Paul, James J. Wirtz, Michel Fortmann (2005). Balance of Power. United States of America: State University of New York Press, 2005. pp. 59, 282. ISBN 0791464016. Accordingly, the great powers after the Cold War are Britain, China, France, Germany, Japan, Russia, and the United States p.59 - Charles Webster, (ed), British Diplomacy, 1813–1815: Selected Documents Dealing with the Reconciliation of Europe, (1931), p307. - Toje, A. (2010). The European Union as a Small Power: After the post-Cold War. New York: Palgrave Macmillan. - Dictionary - World power - Dictionary - Major power - Thesaurus - World Power - Waltz, Kenneth N (1979). Theory of International Politics. McGraw-Hill. p. 131. ISBN 0-201-08349-3. - Taylor, Alan JP (1954). The Struggle for Mastery in Europe 1848–1918. Oxford: Clarendon. p. xxiv. ISBN 0-19-881270-1. - Organski, AFK – World Politics, Knopf (1958) - contained on page 204 in: Kertesz and Fitsomons (eds) – Diplomacy in a Changing World, University of Notre Dame Press (1960) - Iggers and von Moltke "In the Theory and Practice of History", Bobbs-Merril (1973) - Toynbee, Arnold J (1926). The World After the Peace Conference. Humphrey Milford and Oxford University Press. p. 4. - Stoll, Richard J – State Power, World Views, and the Major Powers, Contained in: Stoll and Ward (eds) – Power in World Politics, Lynne Rienner (1989) - Modelski, George (1972). Principles of World Politics. Free Press. p. 141. ISBN 978-0-02-921440-4. - Domke, William K – Power, Political Capacity, and Security in the Global System, Contained in: Stoll and Ward (eds) – Power in World Politics, Lynn Rienner (1989) - Bartlett, C. J. (1996-10-15). Peace, War and the European Powers, 1814–1914. Palgrave Macmillan. p. 106. ISBN 9780312161385. Retrieved 26 December 2013. - Cassels, Alan (1996). Ideology and International Relations in the Modern World. Psychology Press. p. 86. ISBN 9780415119269. Retrieved 26 December 2013. - "The Transformation of European Politics, 1763–1848". Retrieved 2011-06-12. - Britain And Germany: from Ally to Enemy[dead link] - "Multi-polarity vs Bipolarity, Subsidiary hypotheses, Balance of Power" (PPT). University of Rochester. Retrieved 2008-12-20.[dead link] - Tonge, Stephen; head of history at Catholic University School in Dublin. "European History Austria-Hungary 1870–1914". Retrieved 2008-12-20. - Dallin, David (2006-11-30). The Rise of Russia in Asia. Read Books. ISBN 978-1-4067-2919-1. - Power Transitions as the cause of war. - Globalization and Autonomy by Julie Sunday, McMaster University. - MacMillan, Margaret (2003). Paris 1919. United States of America: Random House Trade. pp. 36, 306, 431. ISBN 0-375-76052-0. - Boemeke, Manfred; Gerald D. Feldman; Elisabeth Glaser-Schmidt (1998). The Treaty of Versailles: 75 Years After. United States of America: Cambridge University Press. ISBN 0-521-62132-1. - Paris 1919 by Margaret MacMillan has the Council of Five (Britain, France, Italy, Japan and the United States) as the main victors and remaining Great Powers. - Harrison, M (2000) The Economics of World War II: Six Great Powers in International Comparison, Cambridge University Press. - The Superpowers: The United States, Britain and the Soviet Union – Their Responsibility for Peace (1944), written by William T.R. Fox - Holmes, John. "Middle Power". The Canadian Encyclopedia. Retrieved 2008-12-20. - Baron, Joshua (22 January 2014). Great Power Peace and American Primacy: The Origins and Future of a New International Order. United States: Palgrave Macmillan. ISBN 1137299487. - Yasmi Adriansyah, 'Questioning Indonesia's place in the world', Asia Times (20 September 2011): 'Though there are still debates on which countries belong to which category, there is a common understanding that the GP [great power] countries are the United States, China, United Kingdom, France and Russia. Besides their political and economic dominance of the global arena, these countries have special status in the United Nations Security Council with their permanent seats and veto rights.' - "The 15 countries with the highest military expenditure in 2012 (table)" (PDF). Stockholm International Peace Research Institute. Retrieved 15 April 2013. - Gerald Segal, Does China Matter?, Foreign Affairs (September/October 1999). - according to P. Shearman, M. Sussex, European Security After 9/11, Ashgate, 2004, both UK and France were global powers now reduced to middle-power status. - Neumann, Iver B. (2008). "Russia as a great power, 1815–2007". Journal of International Relations and Development 11: 128–151 [p. 128]. doi:10.1057/jird.2008.7. "As long as Russia's rationality of government deviates from present-day hegemonic neo-liberal models by favouring direct state rule rather than indirect governance, the West will not recognize Russia as a fully fledged great power." - Garnett, Sherman (6 November 1995). "Russia ponders its nuclear options". Washington Times. p. 2. "Russia must deal with the rise of other middle powers in Eurasia at a time when it is more of a middle power itself." - Kitney, Geoff (25 March 2000). "Putin It To The People". Sydney Morning Herald. p. 41. "The Council for Foreign and Defence Policy, which includes senior figures believed to be close to Putin, will soon publish a report saying Russia's superpower days are finished and that the country should settle for being a middle power with a matching defence structure." - T.V. Paul; James Wirtz; Michel Fortmann (8 September 2004). Balance of Power: Theory and Practice in the 21st Century. Stanford University Press. pp. 59–. ISBN 978-0-8047-5017-2. Retrieved 14 October 2012. - Great Powers - Asia’s Overlooked Great Power, APR 18, 2007 - Worldcrunch.com (2011-11-28). "Europe's Superpower: Germany Is The New Indispensable (And Resented) Nation - All News Is Global". Worldcrunch.com. Retrieved 2013-11-17. - Winder, Simon (2011-11-19). "Germany: The reluctant superpower". The Daily Telegraph. - Sperling, James (2001). "Neither Hegemony nor Dominance: Reconsidering German Power in Post Cold-War Europe". British Journal of Political Science 31 (2). doi:10.1017/S0007123401000151. - Max Otte, Jürgen Greve (2000). A Rising Middle Power?: German Foreign Policy in Transformation, 1989–1999. Germany. p. 324. ISBN 0-312-22653-5. - Er LP (2006) Japan's Human Security Rolein Southeast Asia - "Merkel as a world star - Germany's place in the world", The Economist (November 18, 2006), p. 27: "Germany, says Volker Perthes, director of the German Institute for International and Security Affairs, is now pretty much where it belongs: squarely at the centre. Whether it wants to be or not, the country is a Mittelmacht, or middle power." - Susanna Vogt, "Germany and the G20", in Wilhelm Hofmeister, Susanna Vogt, G20: Perceptions and Perspectives for Global Governance (Singapore: Oct. 19, 2011), p. 76, citing Thomas Fues and Julia Leininger (2008): "Germany and the Heiligendamm Process", in Andrew Cooper and Agata Antkiewicz (eds.): Emerging Powers in Global Governance: Lessons from the Heiligendamm Process, Waterloo: Wilfrid Laurier University Press, p. 246: "Germany’s motivation for the initiative had been '... driven by a combination of leadership qualities and national interests of a middle power with civilian characteristics'." - "Change of Great Powers", in Global Encyclopaedia of Political Geography, by M.A. Chaudhary and Guatam Chaudhary (New Delhi, 2009.), p. 101: "Germany is considered by experts to be an economic power. It is considered as a middle power in Europe by Chancellor Angela Merkel, former President Johannes Rau and leading media of the country." - Susanne Gratius, Is Germany still a EU-ropean power?, FRIDE Policy Brief, No. 115 (February 2012), pp. 1, 2: "Being the world's fourth largest economic power and the second largest in terms of exports has not led to any greater effort to correct Germany's low profile in foreign policy ... For historic reasons and because of its size, Germany has played a middle-power role in Europe for over 50 years." - Malik, Mohan (2011). China and India: Great Power Rivals. United States: FirstForumPress. ISBN 1935049410. - Brewster, David (2012). India as an Asia Pacific Power. United States: Routledge. ISBN 1136620087. - Charalampos Efstathopoulosa, 'Reinterpreting India's Rise through the Middle Power Prism', Asian Journal of Political Science, Vol. 19, Issue 1 (2011), p. 75: 'India's role in the contemporary world order can be optimally asserted by the middle power concept. The concept allows for distinguishing both strengths and weakness of India's globalist agency, shifting the analytical focus beyond material-statistical calculations to theorise behavioural, normative and ideational parameters.' - Buzan, Barry (2004). The United States and the Great Powers. Cambridge, United Kingdom: Polity Press. p. 70. ISBN 0-7456-3375-7. - Veit Bachmann and James D Sidaway, "Zivilmacht Europa: A Critical Geopolitics of the European Union as a Global Power", Transactions of the Institute of British Geographers, New Series, Vol. 34, No. 1 (Jan., 2009), pp. 94–109. - Strategic Vision: America & the Crisis of Global Power by Dr. Zbigniew Brzezinski, pp 43–45. Published 2012. - "India: Emerging Power", by Stephen P. Cohen, p. 60 - "India’s Rise as a Great Power, Part One: Regional and Global Implications". Futuredirections.org.au. 7 July 2011. Retrieved 2013-11-17. - McCarthy, Justin (1880). A History of Our Own Times, from 1880 to the Diamond Jubilee. New York, United States of America: Harper & Brothers, Publishers. pp. 475–476. - McCourt, David (28 May 2014). Britain and World Power Since 1945: Constructing a Nation's Role in International Politics. United States of America: University of Michigan Press. ISBN 0472072218. - UW Press: Korea's Future and the Great Powers - Yong Deng and Thomas G. Moore (2004) "China Views Globalization: Toward a New Great-Power Politics?" The Washington Quarterly[dead link] - Friedman, George (2008-06-15). "The Geopolitics of China". Stratfor. Archived from the original on June 12, 2009. Retrieved 2008-07-10. - Kennedy, Paul (1987). The Rise and Fall of the Great Powers. United States of America: Random House. p. 204. ISBN 0-394-54674-1. - Best, Antony; Hanhimäki, Jussi; Maiolo, Joseph; Schulze, Kirsten (2008). International History of the Twentieth Century and Beyond. United States of America: Routledge. p. 9. ISBN 0415438969. - Wight, Martin (2002). Power Politics. United Kingdom: Continuum International Publishing Group. p. 46. ISBN 0826461743. - Waltz, Kenneth (1979). Theory of International Politics. United States of America: McGraw-Hill. p. 162. ISBN 0-07-554852-6. - Richard N. Haass, "Asia’s overlooked Great Power", Project Syndicate April 20, 2007. - "Analyzing American Power in the Post-Cold War Era". Retrieved 2007-02-28. - Mearsheimer, John J. (2001). The Tragedy of Great Power Politics. New York: Norton. ISBN 0393020258. - Waltz, Kenneth N. (1979). Theory of International Politics. Reading: Addison-Wesley. ISBN 0201083493. - Witkopf, Eugene R. (1981). World Politics: Trend and Transformation. New York: St. Martin's Press. ISBN 0312892462. - Duroselle, Jean-Baptiste. France and the Nazi Threat: The Collapse of French Diplomacy 1932–1939. Enigma Books. ISBN 1-929631-15-4.
Constitution of Denmark \|This article is part of a series on the\| politics and government of \|Kingdom of Denmark portal\| The Constitutional Act of the Kingdom of Denmark (Danish: Danmarks Riges Grundlov), or simply the Constitution (Danish: Grundloven), is the constitution of the Kingdom of Denmark, applying equally in Denmark proper, Greenland and the Faroe Islands. In its present form, the Constitutional Act is from 1953, but the principal features of the Act go back to 1849, making it one of the oldest constitutions. As defined in the Constitution, Denmark is a constitutional monarchy, governed under a parliamentary system. The constitution lays down the framework for governance and establishes the structure, procedures, powers and duties of the Folketing (the Danish parliament) and the government, as well as other institutions. Later sections set out fundamental rights and the duties of citizens, such as freedom of speech, freedom of religion and compulsory military service. Its adoption in 1849 ended an absolute monarchy and introduced democracy. Denmark celebrates the adoption of the Constitution on 5 June—the date in which the first Constitution was ratified—every year as Constitution Day. The Danish Parliament (Folketinget) cannot make any laws which may be repugnant or contrary to the Constitutional Act. While Denmark has no constitutional court, laws can be declared unconstitutional and rendered void by the Supreme Court of Denmark. - 1 Principles and structure - 2 History - 3 Structure and content - 3.1 Chapter I: Fundamental principles (§§ 1-4) - 3.2 Chapter II: The Royal House (§§ 5-11) - 3.3 Chapter III: The government (§§ 12-27) - 3.4 Chapter IV: General elections to the Folketing (§§ 28-34) - 3.5 Chapter V: Procedures in the Folketing (§§ 35-58) - 3.6 Chapter VI: The courts (§§ 59-65) - 3.7 Chapter VII: Religions (§§ 66-70) - 3.8 Chapter VIII: Civil rights (§§ 71-85) - 3.9 Chapter IX: Miscellaneous (§§ 86-87) - 3.10 Chapter X: Changes to the Constitution (§ 88) - 3.11 Chapter XI: Entry info force (§ 89) - 4 Constitutional institutions - 5 Themes - 6 Other constitutional laws of the Kingdom of Denmark - 7 See also - 8 Notes - 9 References - 10 External links Principles and structure The Danish Constitution differs from all other Danish laws by virtue of its superseding status. As such, these laws are not permitted to contravene the provisions of the Constitution Act. The main principle of the Constitutional Act was to limit the King's power (section 2). It creates a comparatively weak constitutional monarch who is dependent on Ministers for advice and Parliament to draft and pass legislation. The Constitution of 1849 established a bicameral parliament, the Rigsdag, consisting of the Landsting and the Folketing. The most significant change in the Constitution of 1953 was the abolishment of the Landsting, leaving the unicameral Folketing. It also enshrined fundamental civil rights, which remain in the current constitution: such as habeas corpus (section 71), private property rights (section 72) and freedom of speech (section 77). The Constitutional Act has been changed (replaced) very few times, but always with the consent of Danish citizens. The wording in the Act is so general that it can still be applied today, despite major changes in society and political life in the intervening years. However, since Denmark lacks a Constitutional Court, scrutiny of legislation for compatibility with the Constitution is a matter for ordinary courts, ultimately the Supreme Court. Significantly this means that the actual testing of compatibility can only be instigated by a citizen or company who is affected by the question. This section needs additional citations for verification. (April 2016) (Learn how and when to remove this template message) During the late middle ages and the renaissance, the power of the king was tempered by a håndfæstning, a coronation charter each king had to sign before being accepted as king by the nobility. This tradition was abandoned in 1665 when King Frederick III of Denmark managed to establish a hereditary absolute monarchy by Lex Regia (The Law of The King, Danish: Kongeloven). This was Europe's only formal absolutist constitution. Under Lex Regia, absolute power was inherited for almost 200 years. In the beginning of the 19th century, there were a growing democratic movement in Denmark and King Frederick VI only made some small concessions, such as creation of Consultative Estate Assemblies (Danish: Rådgivende Stænderforsamlinger) in 1834. But these only served to help the political movements, of which the National Liberals and the Friends of Peasants were the forerunners. When Christian VIII became king in 1839, he continued the political line of only making small democratic concessions, while upholding the absolute monarchy. Denmark was in a personal union between kingdom of Denmark and the duchies of Schleswig, Holstein, and Lauenburg called The Unitary State (Danish: Helstaten). Under the slogan Denmark to the Eider, the National Liberals campaigned for Schleswig to become an integral part of Denmark, while separating Holstein and Lauenburg from Denmark. Holstein and Lauenburg were then part of the German Confederation, while Schleswig was not. On the other side, German nationalists in Schleswig were keen to keep Schleswig and Holstein together, and wanted Schleswig to join the German Confederation. Christian VIII had reached the conclusion that, should the Unitary State survive, a constitution covering both Denmark, Schleswig and Holstein was necessary. Before his death in 1848, he adviced his heir Frederick VII to create such a constitution. Drafting and signing the 1849 Constitution Ditlev Gothard Monrad, who became Secretary in 1848, drafted the first copy of the Constitution, based on a collection of the constitutions of the time, sketching out 80 paragraphs, whose basic principles and structure resembles the current constitution. The language of the draft was later revised by Secretary Orla Lehmann among others, and treated in the Constitutional Assembly of 1848 (Danish: Grundlovsudvalget af 1848). Sources of inspiration for the Danish Constitution include the Constitution of Norway of 1814 and the Constitution of Belgium, both of which establish constitutional monarchies. The government's draft was laid before the Constitutional Assembly of the Realm (Den Grundlovgivende Rigsforsamling), part of which had been elected on 5 October 1848, the remainder having been appointed by the King. The 152 members were mostly interested in the political aspects, the laws governing elections and the composition of the two chambers of Parliament. The Constitution was adopted during a period of strong national unity, namely the First Schleswig War, which lasted from 1848–1851. The first modern constitution of Denmark was signed on 5 June 1849 by King Frederick VII. The event marked the country's transition to constitutional monarchy, replacing the old constitution like Lex Regia from 1665 which had introduced absolute monarchy in Denmark. The Constitution has been rewritten four times since 1849, largely building upon the original text. 5 June 1849, has since been a Danish national holiday. Parallel constitution for helstaten (1855-1866) The question of the status of Schleswig was still up for debate, and after First Schleswig War it was clear that the there was a need for a new constitution that should cover the entire Danish realm, and not just Denmark. In 1855 the rigsdag accepted Helstatsforfatning (Constitution for The Entire State), which was a parallel constitution that also covered affairs common to Denmark, Schleswig and Holstein. In 1863 this constitution was changed, the new one was called Novemberforfatningen. This was shortly before Second Schleswig war, where Denmark lost control of Schleswig and Holstein, rendering the parallel constitution void. The Revised Constitution (1866) In 1866, the defeat in the Second Schleswig War, and the loss of Schleswig-Holstein led to tightened election rules for the Upper Chamber, which paralyzed legislative work, leading to provisional laws. The conservative Højre had pressed for a new constitution, giving the upper chamber of parliament more power, making it more exclusive and switching power to the conservatives from the original long standing dominance of the National liberals, who lost influence and was later disbanded. This long period of dominance of the Højre party under the leadership of Jacob Brønnum Scavenius Estrup with the backing of the king Christian IX of Denmark was named the provisorietid (provisional period) because the government was based on provisional laws instead of parliamentary decisions. This also gave rise to a conflict with the Liberals (farm owners) at that time and now known as Venstre (Left). This constitutional battle concluded in 1901 with the so-called systemskifte (change of system) with the liberals as victors. At this point the king and Højre finally accepted parliamentarism as the ruling principle of Danish political life. This principle was not codified until the 1953 constitution. Universal suffrage (1915) In 1915, the tightening from 1866 was reversed, and women were given the right to vote. Also, a new requirement for changing the constitution was introduced. Not only must the new constitution be passed by two consecutive parliaments, it must also pass a referendum, where 45% of the electorate must vote yes. This meant that Prime Minister Thorvald Stauning's attempt to change the Constitution in 1939 failed. Reunion with Schleswig (1920) In 1920, a new referendum was held to change the Constitution again, allowing for the reunification of Denmark following the defeat of Germany in World War I. This followed a referendum held in the former Danish territories of Schleswig-Holstein regarding how the new border should be placed. This resulted in upper Schleswig becoming Danish, today known as Southern Jutland, and the rest remained German. Current Constitution (1953) In 1953, the fourth constitution abolished the Upper Chamber (the Landsting), giving Denmark a unicameral parliament. It also enabled females to inherit the throne (see Succession), but the change still favored boys over girls (this was changed by a referendum in 2009 so the first-born inherits the throne regardless of sex). Finally, the required number of votes in favor of a change of the Constitution was decreased to the current value of 40% of the electorate. Structure and content Chapter I: Fundamental principles (§§ 1-4) § 2 Defines Denmark as a constitutional monarchy, where the status as monarch is inherited according to Act of Succession. Since this act is specified in the Constitution, it is considered a part of the constitution, and has to be changed by the same procedure as the constitution. This was most recently done in 2009. §4 Establishes the Church of Denmark as the official church of Denmark Chapter II: The Royal House (§§ 5-11) While this section references the king, it is generally understood to be the monarch, which can also be a queen. This is also true for the rest of the Constitution. § 5 States that the monarch needs the approval of the Folketing in order to become regent in other countries § 6 Requires that the danish monarch belongs to the evangelical Lutheran faith, though not necessarily as member of the Church of Denmark § 7 States that the age of majority for the monarch is 18 years. § 8 Requires that a new monarch to swear to uphold the Constitution. § 9 Allows the Folketing to make a law defining who is to govern if the monarch is incapable (for example due to being minor), or simply being out travelling. Also states what will happen if there is no heir to the throne. Then the Folketing shall elect a new monarch. §§ 10-11 Sets the guidelines for the payment of expenses to the royal house. These are decided by the Folketing. Chapter III: The government (§§ 12-27) §12-14 States that while the "king" (which can be a queen) formally holds the executive power, it is always exercised through the ministers, and that they are responsible. The monarch cannot act on their own; the status as monarch is purely ceremonial. Throughout the Constitution the king nearly always means the government. § 15 Established Danish politics as a Parliamentary system: No minister can remain in their post if there is a majority against them § 16 Makes it possible for ministers to be prosecuted at the special court rigsret (see §§ 59-60) for the way they run the government § 17-18 Describes the Council of the State and the Council of the Ministers, two formal bodies which hold no power anymore, since the monarch is politically independent § 19 States that it is the Folketing who defines the foreign policy, not the government. § 20 Makes it possible for Denmark to hand over sovereignty to intergovernmental organizations, which is often a requirement for joining them. However, this is only possible with a 5/6 supermajority in the Folketing. If there is only a simple majority, there can be held a referendum on the question. This paragraph was used in 1972 when Denmark, after a referendum, joined the EEC (now EU). More recently, in 2015 an (unsuccessful) referendum was held on one of its EU-opt-outs. § 21 Allows ministers to propose laws which are then considered in the Folketing. This is a right normally only reserved for members of the Folketing, but ministers need not be a part of the Folketing. § 22 Requires the monarch to sign all laws, and requires the government to ensure they are fulfilled § 23 Allows the government to make temporary laws. This is only allowed under exceptionally urgent circumstances, where the Folketing is not able to be called together. All laws must as fast as possible be considered by the Folketing. § 24 Allows the government to pardon criminals. § 25 A transitional provision, which allows laws and exceptions from before the first Constitution of 1849 to remain in force. § 26 Allows the state to mint coins. § 27 Rules that gives privileges a group of central civil servants (such as police and military personnel) called tjenestemænd. § 29 To vote you need to be a Danish citizens, live in Denmark, and be over 18 years old. The age limit is not set by the Constitution; it only requires that if it is to change, there has to be held a referendum about it. § 30 Allows all voters to run for a membership of the Folketing. The only exception is if they have been convicted of a crime that makes them "unworthy". This is first decided after the election by the Folketing (see § 33) § 31 The general election is direct and secret, and makes use of a voting system that ensures proportional representation. The details are to be defined by law. § 33 The Folketing decides whether its members are "worthy" as per § 30. § 34 It is high treason to threaten or undermine the security or freedom of the Folketing. Chapter V: Procedures in the Folketing (§§ 35-58) § 35 The newly elected Folketing meets within 12 working days of the elections. First they decide if their members are "worthy" (see § 33), then they elect a chairman and vice chairmen for the current business year. § 36 Each business year start the first Tuesday in October, and last until the first Tuesday in October next year. At the first day, they meet and elects a chairman and vice chairmen for the new business year. § 37 The Folketing meets the same place the government is located (Christiansborg palace), but in exceptional situations meet elsewhere. § 38 A business year always start with a speech from the prime minister, which are then discussed. § 39 The chairman calls a meeting, and are obliged to do so if the prime minister or 2/5 of the Folketing requires this in writing. Every meeting (or request for a meeting) is followed by a agenda. § 40 Ministers have the right to be and speak in the Folketing, but cannot vote (unless they are also members of the Folketing). § 41 Every member of the Folketing can suggest laws or decisions. All laws needs to be brought up in 3 times, before they can be approved. 2/5 of the Folketing can required that there is at least 12 working days between second and third session. Exceptions are laws about budgets, loans, taxes, expropriation, citizenship, and laws that are urgent to get passed. At the end of a business year, all pending laws or decisions is dropped. § 42 This paragraph concerns referendums, and is the longest in the constitution. 1/3 of the Folketing can (written and within 3 days from it was passed) require a referendum about the law. They Folketing can then decide to redact the law or keep it, but if they keep it, the prime minister will decide a date for a referendum, which will be held 12-18 days later. The law is defeated if there is en majority against it, and that majority consists of at least 30 % of the voter base. Certain laws cannot be subject to referendums, those mentioned in § 41, laws required by treaties, laws concerning the Royal house, and laws concerning foreign policy. § 43 All taxes, all state loans, and the size of the military are needed to have a basis in a law § 44 No foreigner can be given citizenship unless by law. Foreigners can only buy land or buildings, if are law allows them to. § 45 The financial budget for the following fiscal year (which start 1. January), have to be submitted at least 4 months before the ending of the current fiscal year (and then resubmit in the next business year because of § 41). If the Folketing does not manage to approve a new budget in time, a temporary budget has to be made. § 46 A budget (or temporary budget) are required to charge taxes. Money can only be spend, if they are approved by the budget or the law. (However, there is a precedent that the financial committee of the Folketing can pre-approve a spending, before it is made to law.) § 47 The public accounts shall be submitted to the Folketing within 6 month of the start of the next financial year. It is accessed by the state accountants, who are chosen by the Folketing. It is their job to check if it follows the financial laws. Once they have made their statement, the Folketing vote for its approval. § 48 The Folketing make their own rules of procedure. § 49 The meetings are open to the public, however can be closed for the public. This has not been done since 1924. § 50 The quorum for the Folketing is 90 members (out of 179) § 51 The Folketing can establish commissions to investigate important cases. The consists of members of the Folketing, and can demand information from citizens and public agencies. § 52 Appointment of member to committees have to be done to ensure proportional representation. § 53 All members of the parliament can demand answers from the ministers § 54 Non-members always have to go through a member, if they wish to bring something up for the Folketing (with exceptions of ministers, who also have this right, see § 21 and § 40). § 55 The Folketing chooses one or two ombudsmen. § 56 Members of the Parliament are free to vote and speak as they wish. They can not make any binding agreement to vote in a certain way, neither with their party or with the electorate. However, there is often party discipline, because it can be politically consequences to go against your own party. However, happens relatively often. § 57 Members of the Folketing are immune to be prosecuted or put in jail, unless they are caught red-handed, and they have absolute freedom of speech in the Folketing. However, the Folketing can take this immunity away from the members. § 58 The members salary are decided by law. Chapter VI: The courts (§§ 59-65) §§ 59-60 The rigsret, which is the court who hear cases against ministers for the way they run the government, consists of the 15 most senior Supreme Court judges, and an equal number appointed by the Folketing (the members of the Folketing can not themselves be judges). The politically appointed judges are chosen for 6 years, but once they are on a case, they cannot be replaced. § 61 The rules that governs the courts are decided by law. However, there can never be constructed special courts to handle specific cases, they must all go through the same system. § 62 The courts must be independent of the government. Related to § 3, this paragraph is a strengthening of that independence. § 63 It is possible to sue the government and other who exercise power (e.g. municipalities), and the court system will handle them. However, no such case will have a suspensive effect on the decision that is being disputed. It is possible to create special courts to handle these cases, but their verdicts shall be possible to get tested in the Supreme Court. § 64 Judges shall follow the law, but not take orders in any other form. They cannot be fired or moved to another position against their will, unless this is as a general restructuring of the court system. There are two exceptions here. First, a judge who is over 65 years can be fired, but will still get full pay until they were forced to retire due to age. And second, a judge can be removed from their position by verdict from another judge. § 65 Proceedings in the court room should, as much as possible, be transparent. And during criminal proceedings, lay judges must be used. How exactly is defined by law. Chapter VII: Religions (§§ 66-70) § 66 The Folketing decides by law a Constitution for the Church of Denmark. However, even though this provision is from the original Constitution of 1849, there have never been adopted such law. § 67 Guarantees freedom of religion, by allowing all to create and join religious communities as they seem fit. The only requirements is that these communities may not be a thread to "good morals or the public order". § 68 Frees people from paying taxes to other than their own religion. Denmark have a church tax, but it is only paid by members of the Church of Denmark. § 69 Rules for religious communities other than the Church of Denmark is decided by law. § 70 Guarantees that civil and political rights cannot be removed from people because of their religion or their race. However, they cannot use them to be exempted from civil duties. Chapter VIII: Civil rights (§§ 71-85) § 71 The personal freedom is inviolable, and no citizen can be put in jail because of their race, religion or political views. Detention is only possible if permitted by law. If people are put under arrest, they have to be put before a judge within 24 hours. This judge decides if the subject should be freed, or put under provisional detention. I Greenland, it is possible by law to exempt from the 24-hour deadline. The judges decision can be appealed to a higher court. Detention is only possible if the person is charged for a crime that can be punished by jail. If detention happens outside the criminal system or the immigration law (e.g. at a psychiatric hospital), the detained can always require the legality to be considered by a court.Furthermore, the care of these people are under supervision of an oversight committee set down by the Folketing. § 73 The right to property in inviolable. Expropriation is only possible by law, and when full compensation is given. Whenever a law concerning expropriation is passed, it is possible by 1/3 of the Folketing to require the law to be confirmed after a general election. It is possible to appeal all cases of expropriation to the court system. § 74 All limitations to free and equal trade, except those necessary for the public good, are to be abolished. § 75 The political system shall work towards that all who is able to work, is able to get a job. People who are not able to get a job, have the right for support from the public system. However, they must accept the requirements that follows. § 78 All citizens have the right to create or join associations. Associations that work through violence or other illegal means, can be dissolved by a judge. The government can ban an association, and then immediately have to take the case to the courts. Dissolution of political association can always be brought before the Supreme Court. § 79 Denmark have freedom of assembly, as long as people are unarmed. However, the police can dissolve an assembly, if it is a threat to the public order. § 80 The police can only use force to dissolve an assembly, after it three times "in the name of the king and the law" have asked the assembly to dissolve itself. § 81 Every man has a duty to participate in the military draft. The law las our more details for this. § 82 Municipality have the right to govern themselves, under the laws that the Folketing decides. § 83 There is no privileges attached to nobility. § 85 For soldiers, the freedoms in § 71 (freedom from detention), § 78 (freedom of association) and § 79 (freedom of assembly) can be restricted by military law. Chapter IX: Miscellaneous (§§ 86-87) § 86 The age requirement for voting in municipially elections and are the same as for general elections. In Greenland and the Faroe Islands, however, it is decided by law. § 87 Transitional provision, that ensured the rights of Icelandic citizens. When Iceland 1918 became independent from Denmark and instead, by the Danish–Icelandic Act of Union, entered into a personal union with Denmark, Icelandic citizens were given the same rights in Denmark as Danish citizens. When Iceland in 1944 became a republic, this rules was limited to icelandic citizens who, as of 1946, was living or had recently lived in Denmark. This provision fastened this right in the Constitution. Chapter X: Changes to the Constitution (§ 88) To change the Constitution, there is required a majority in two consecutive Folketing: before and after a general election. In addition, the Constitution must pass a referendum, with the additional demand that at least 40% of voting age population must vote in favour. Chapter XI: Entry info force (§ 89) The Constitution entered into force on 5 june 1953, the day it was signed by King Frederik IX. However, the sitting Rigsdag, who, according to the old constitution, consisted of two chambers (Folketinget and Landstinget) remained in place until next general election, which was held in september 1953. The Constitution establishes Denmark as a constitutional monarcy, where the monarch serves as a ceremonial Head of state. The title of monarch is hereditary and passed on to the firstborn child, with equal rights for sons and daughters. The political system of Denmark can be described as a democracy with a parliamentary system of governance. The powers of the state is separated into 3 different branches. The legislative branch held by the Folketing, the executive branch held by the Danish government, and the judicial branch held by the Courts of Denmark. The Monarchy of Denmark The Danish monarch,[a] as the head of state, holds great de jure power, but de facto only serves as a figurehead who is not interfering in politics. The monarch formally holds executive power and, co-jointly with the Folketing, legislative power, since each new law requires royal assent. By article 12, 13 and 14, the powers vested in the monarch can only be exercised through the ministers, who are responsible for all acts, thus removing any political or legal liability from the monarch.[b] The monarch appoints the ministers after advice from the Prime Minister. The Prime Minister is itself appointed after advice from the leaders of the political parties of the Folketing, a process known as a Queen's meeting (Danish: dronningerunde). The monarch and the Cabinet attend regular meetings in the Council of State, where royal assent is given, and the monarch is regularly briefed on the political situation by the Prime Minister and Foreign minister. The Government of Denmark The Government holds executive power, and is responsible for carrying out the acts of the Folketing. The Government does not have to pass a vote of confidence before taking the seat, but any minister can be subject to a motion of no confidence. If a vote of no confidence is successfully passed against the Prime Minister, the government must resign or call a snap election. The Folketing is the legislative branch of Denmark, and is located at Christiansborg. It consists of 179 members,[c] of which 2 members are elected in Greenland, and 2 in the Faroe Islands. General elections is nominally held every 4 years, but the Prime Minister can at any point call a snap election. All Danish citizens over the age of 18 years who are living permanently within Denmark is eligible to vote, except those placed under legal guardianship. The same group of people is able to run for office. The electoral system is characterized as a party-list proportional representation system, with an election threshold on 2 %. As a result, Denmark has a multi-party parliamentary system, where no single party has an absolute majority. The session starts anew each year on the first Tuesday in October, and when interrupted by a general election; all previously unfinished business is cancelled. The Folketing then elects a speaker, who is responsible for convening meetings. The Folketing lay down their own rules of procedure, subject to the requirements in the Constitution. Among those, the required quorum of 90 members of the Folketing, and the rule that every proposed law requires three readings in the Folketing, before it can be passed into law. The Folketing also have the responsibility of holding the government accountable for the governance. The members of the Folketing does this by submitting questing to the ministers and convene them to explanatory hearings. In addition, the Folketing elect a number of State Auditors (Danish: Statsrevisorer), who has the responsibility to look through the public accounts, and check that everything is okay, and that the government only spend money approved by the Folketing. Furthermore, the Folketing also appoints an ombudsman, who investigates wrongdoings by the public administrative authorities on behalf of the public. The Courts of Denmark The court system are independent of the other two branches. The Constitution does not stipulate how the courts are organised; instead this is laid down by statue. In the normal system there is Distric Courts, High Courts and the Supreme Court, and in addition to these, there is some special courts. There are certain rights in the Constitution with respect to the juridiciary system. There exist a speciel Court of Impeachment, which can procecute ministers for how they act in the office. The Church of Denmark The Evangelical-Lutheran Church of Denmark is the state church established by the Constitution. Civil rights and freedoms The Constitution of Denmark outlines fundamental rights in sections 71–80. Several of these are of only limited scope and thus serve as a sort of lower bar. The European Convention on Human Rights was introduced in Denmark by law on 29 April 1992 and supplements the mentioned paragraphs. Freedom of speech and freedom of the press in Denmark are ensured by section 77 of the Constitution. Section 4 establishes that the Evangelical Lutheran Church is "the people's church" (folkekirken), and as such is supported by the state. Freedom of religion is granted in section 67, and official discrimination based on faith is forbidden in section 70. Section 20 of the current constitution establishes that specified parts of national sovereignty can be delegated to international authorities if the Parliament or the electorate votes for it. This section has been debated heavily in connection with Denmark's membership of the European Union (EU), as critics hold that changing governments have violated the Constitution by surrendering too much power. In 1996, Prime Minister Poul Nyrup Rasmussen was sued by twelve Eurosceptics for violating this section. The Supreme Court acquitted Rasmussen (and thereby earlier governments dating back to 1972) but reaffirmed that there are limits to how much sovereignty can be surrendered. In 2011, Prime Ministers Lars Løkke Rasmussen faced a similar challenge when he was sued by twenty-eight citizens for having adopted the European Lisbon Treaty without a referendum. The group of professors, actors, writers and Eurosceptic politicians argued that the Lisbon Treaty hands over parts of national sovereignty to the EU and therefore a referendum should have taken place. The case was later dismissed. Greenland and the Faroe Islands Section 32 states "special rules may be provided by Statute for the commencement and determination of Faroe Islands and Greenland representation in the Parliament." This section refers to home rule in both territories. The specific arrangements for the transfer of powers and monetary competency to Greenland and the Faroe Islands are contained in separate statues, with equal constitutional status (see below). Changes to the constitution According to section 88 of the 1953 Constitution, changes require a majority in two consecutive Parliaments: before and after a general election. In addition, the Constitution must pass a popular vote, with the additional demand that at least 40% of voting age population must vote in favour. The Constitution sets out only the basic principles, with more detailed regulation left over to the Danish Parliament. Symbolic status of the king When reading the Danish Constitution, it is important to bear in mind that the King is meant to be read as the government because of the monarch's symbolic status. This is a consequence of sections 12 and 13, by which the King executes his power through his ministers, who are responsible for governing. An implication of these sections is that the monarch cannot act alone in disregard of the ministers, so the Danish monarch does not interfere in politics. Separation of powers As in many other democracies, the Danish Constitutional Act divides power into three independent branches—the legislative, the executive and the judicial branches—in order to encourage checks and balances and prevent abuse of power. The Danish Parliament is the legislative power, enacting the laws of the country. The Cabinet (Government) is the executive power, formally acting out the role of the Monarch, by ensuring that laws are implemented. The Supreme Court and lower courts of law are the judicial power, pronouncing judgements in disputes between citizens and between the authorities and citizens. The Constitution is heavily influenced by the French philosopher Montesquieu, whose separation of powers was aimed at achieving mutual monitoring of each of the branches of government. However, the division between legislative and executive power in Denmark is not as sharp as in the United States. In several sections the Constitutional Act sets out the powers and duties of the Danish Parliament. Section 15 in the Act, which deals with the parliamentary principle, lays down that "a Minister shall not remain in office after the Parliament has passed a vote of no confidence in him". This suggests that Ministers are accountable to Parliament and even subservient to it. The Cabinet exerts executive power through its Ministers, but cannot remain in office if the majority of the Folketing goes against it. Another important feature of the Danish parliamentary system is that the Constitutional Act lays down that "the Members of the Folketing shall be elected for a period of four years", but still, "the King may at any time issue writs for a new election". Other constitutional laws of the Kingdom of Denmark The Danish constitution contains these additional parts: - The parts of cc, the former absolute monarchist constitution from 1665, that were not superseded. - The Act of Succession to the Danish Throne of 27 March 1953 also has status as a constitutional law, as it is directly referred to in Article 2 of the Constitutional Act. Therefore, amendments to the Act of Succession require adherence to the constitutional amendment procedure as provided for in Article 88 of the Danish Constitution Act. An amendment to abolish male preference to the throne (bill no. 1, Folketing session of 2005–06) was passed by a referendum in 2009. - To an extent the laws granting self government to the Faroe Islands and Greenland can be considered constitutional. - Certain particular customs, not explicitly referred to in the Constitutional Act itself, have been recognised as carrying constitutional legal weight (such as the right of the Finance Committee to authorise public expenditure outside of the national budget), also form part of Danish Constitutional law. - Codified constitution - Constitutional law - Constitutional economics - Politics of Denmark - Index of Denmark-related articles - While the Constitution consistently refer to the monarch as the "king", this can also be a queen regnant. In fact, the current monarch of Denmark is Queen Margrethe II. - For this reason, when reading the Constitution, the word king, in the context of exercising acts of state, is to be read as the Government (consisting of the Prime Minister and other ministers) - While the Constitution says that "not more than" 179 members are elected, the law concerning general elections states that exactly 179 members are elected. - "CIA World Factbook: Denmark: Government". Retrieved 8 July 2009. - "The Constitutional Act of Denmark". thedanishparliament.dk. The Danish Parliament (Folketinget). Archived from the original on 20 November 2012. Retrieved 14 April 2016. - Tschentscher, Axel. "The Constitution of Denmark – Section 88". Servat.unibe.ch. Retrieved 2016-02-12. - The Constitution of Denmark Accessed on 14 April 2016. - Werlauff, Erik (2010). Civil Procedure in Denmark. Kluwer Law International. p. 11. - firstname.lastname@example.org (2018-04-13). "Vis". danmarkshistorien.dk (in Danish). Retrieved 2018-06-10. - Folketinget Archived 7 May 2009 at the Wayback Machine. - email@example.com (2018-04-13). "Vis". danmarkshistorien.dk (in Danish). Retrieved 2018-06-10. - firstname.lastname@example.org (2018-04-13). "Vis". danmarkshistorien.dk (in Danish). Retrieved 2018-06-10. - email@example.com (2018-04-13). "Vis". danmarkshistorien.dk (in Danish). Retrieved 2018-06-10. - firstname.lastname@example.org (2018-05-18). "Kritik af enevælden og debat om Slesvig". danmarkshistorien.dk (in Danish). Retrieved 2018-06-11. - email@example.com (2018-05-18). "Marts 1848". danmarkshistorien.dk (in Danish). Retrieved 2018-06-11. - Grundloven 1849 by Erik Strange Petersen Aarhus University in danish - Søren Mørch: 24 statsministre. ISBN 87-02-00361-9. - "Folkekirkens fælt forvirrede forfatning". Information (in Danish). 2011-06-03. Retrieved 2018-06-10. Since 1849 the Constitution have prescribed: »The constitution of the Church of Denmark is decided by law.« However, such a constitution for the Church of Denmark has never successfully been completed. - "Kirkeskat". Folkekirken.dk (in Danish). Retrieved 2018-06-10. The church tax is a membership fee you pay when you are a member of the Church of Denmark. - "Dansk-Islandsk Forbundslov - Wikisource". da.wikisource.org (in Danish). Retrieved 2018-06-10. § 6: Danish citizens enjoy on Iceland in every case equally rights with those Icelandic citizens born on Iceland, and vice versa - Lov om ophævelse af Dansk-islandsk Forbundslov m.m. (LOV nr 205), 1950-05-16, retrieved 2018-06-10. "§2, pt. 1: Icelandic citizens, who as of 6. march 1946 was living in Denmark, keep the in the Danish-Icelandic Act of Union of 30. november 1918 contained acces to seek residence in Denmark and to, when they have such residence, in every case enjoy equal rights as Danish citizens. The same applies to Icelandic citizens who have had residence in Denmark at any time within the last 10 years before 6. march 1918" - "HM The Queen". The Danish Monarchy - Front Page. 2016-04-07. Retrieved 2018-06-20. HM The Queen takes no part in politics and does not express any political opinions. - Grundloven, Mikael Witte 1997 ISBN 87-7724-672-1 - "The Division of Powers". The Danish Parliament. Retrieved 2018-06-20. The political party leaders will then advise the Queen on whom to invite to lead the negotiations to form a new Government. The person who has the support of a majority of party leaders is chosen as the chief negotiator and usually also becomes Prime Minister. In principle, the Constitutional Act gives the Queen the authority to appoint and dismiss Ministers, but she has no real political influence. In practice, it is the Prime Minister who selects Ministers, and subsequently the Queen formally appoints the Ministers recommended by the Prime Minister. - "HM The Queen". The Danish Monarchy - Front Page. 2016-04-07. Retrieved 2018-06-20. Additionally, The Queen is the formal Head of the Government and therefore presides over the State Council, where the Acts that have been passed by the Folketing are signed into law. The Prime Minister and the Minister of Foreign Affairs report regularly to The Queen to inform her of the latest political developments. - "My Constitutional Act with explanations". [the Queen] must belong to the Evangelical-Lutheran Church. However, she need not necessarily be a member of the Evangelical- Lutheran Church of Denmark (Folkekirken). - Bekendtgørelse af lov om valg til Folketinget (LBK nr 1426), 2017-12-08, retrieved 2018-06-20, § 7. To the Folketing, a total of 179 people are chosen. - Pop, Valentina (11 January 2011). "Danish PM sued over Lisbon Treaty". Brussels: EUobserver. Retrieved 14 April 2016. \|Wikisource has original text related to this article:\|
It can be very helpful to know how to calculate the area of triangles in 3D space. You can use it to calculate the surface area of an object, which in turn you can use to calculate/set mass or density of objects. Primarily, I use area to create distribution attributes for particle emission, such that polygons of varying size emit a spatially consistent amount of particles. For example, in Houdini, if area is assigned as a primitive attribute (you have measured the area of each polygon and stored it) you simply multiply area by emission rate and will get a fairly even distribution of particles emitted from a surface. Of course, Houdini has a built in operator to calculate area, but if you don’t have such an operator in your 3D program, or you are writing your own code, here’s how to do it. The main tools needed to calculate an area of a triangle in 3D space are covered in my post about distance. The basic formula using vectors goes something like this: Given three vector points in space, A, B, and C, the area of the triangle formed by those points is 1/2 the magnitude (see distance) of the cross product (see cross product) of vector AB and AC. It can be written in mathematical notation like this: 1/2 * \|AB x AC\| It can also be explained diagrammatically like so: So, given three points, A, B, and C, pick one point arbitrarily and calculate two distance vectors between that point and the other two points (distance vectors AB and AC) by doing vector subtraction. Find the cross product between those vectors. The cross product outputs a vector. Now, calculate the magnitude of this vector, and finally divide by 2 (or multiply by 0.5).
For some time, scientists have known that Mars was once a much warmer and wetter environment than it is today. However, between 4.2 and 3.7 billion years ago, its atmosphere was slowly stripped away, which turned the surface into the cold and desiccated place we know today. Even after multiple missions have confirmed the presence of ancient lake beds and rivers, there are still unanswered questions about how much water Mars once had. One of the most important unanswered questions is whether or not large seas or an ocean ever existed in the northern lowlands. According to a new study by an international team of scientists, the Hypanis Valles ancient river system is actually the remains of a river delta. The presence of this geological feature is an indication that this river system once emptied into an ancient Martian sea in Mars’ northern hemisphere. Mars modern landscape is something of a paradox. It’s many surface features are very similar to those on Earth that are caused by water-borne erosion. But for the life of them, scientists cannot imagine how water could have flown on Mars’ cold and desiccated surface for most of Mars’ history. Whereas Mars was once a warmer, wetter place, it has had a very thin atmosphere for billions of years now, which makes water flow and erosion highly unlikely. In fact, while the surface of Mars periodically becomes warm enough to allow for ice to thaw, liquid water would boil once exposed to the thin atmosphere. However, in a new study led by an international team of researchers from the UK, France and Switzerland, it has been determined that a different kind of transport process involving the sublimation of water ice could have led to the Martian landscape becoming what it is today. The study, which was led Dr. Jan Raack – a Marie Sklodowska-Curie Research Fellow at The Open University – was recently published in the scientific journal Nature Communications. Titled “Water Induced Sediment Levitation Enhances Downslope Transport on Mars”, this research study consisted of experiments that tested how processes on Mars’ surface could allow water transport without it being in liquid form. To conduct their experiments, the team used the Mars Simulation Chamber, an instrument at The Open University that is capable of simulating the atmospheric conditions on Mars. This involved lowering the atmospheric pressure inside the chamber to what is normal for Mars – about 7 mbar, compared to 1000 mbar (1 bar or 100 kilopascals) here on Earth – while also adjusting temperatures. On Mars, temperatures range from a low of -143 °C (-255 °F) during winter at the poles to a high of 35 °C (95 °F) at the equator during midday in the summer. Having recreated these conditions, the team found that when water ice exposed to the simulated Martian atmosphere, it would not simply melt. Instead, it would become unstable and begin violently boiling off. However, the team also found that this process would be capable of moving large amounts of sand and sediment, which would effectively “levitate” on the boiling water. This means that, compared to Earth, relatively small amounts of liquid water are capable of moving sediment across the surface of Mars. These levitating pockets of sand and debris would be capable of forming tje large dunes, gullies, recurring slope lineae, and other features observed on Mars. In the past, scientists have indicated how these features were the result of sediment transportation down slopes, but were unclear as to the mechanisms behind them. As Dr. Jan Raack explained in a OUNews press release: “Our research has discovered that this levitation effect caused by boiling water under low pressure enables the rapid transport of sand and sediment across the surface. This is a new geological phenomenon, which doesn’t happen on Earth, and could be vital to understanding similar processes on other planetary surfaces.” Through these experiments, Dr. Raack and his colleagues were able to shed light on how conditions on Mars could allow for features that we tend to associate with flowing water here on Earth. In addition to helping to resolve a somewhat contentious debate concerning Mars’ geological history and evolution, this study is also significant when it comes to future exploration missions. Dr. Raack acknowledges the need for more research to confirm their study’s conclusions, and indicated that the ESA’s ExoMars 2020 Rover will be well-situated to conduct it once it is deployed : “This is a controlled laboratory experiment, however, the research shows that the effects of relatively small amounts of water on Mars in forming features on the surface may have been widely underestimated. We need to carry out more research into how water levitates on Mars, and missions such as the ESA ExoMars 2020 Rover will provide vital insight to help us better understand our closest neighbour.” Over the past few decades, our ongoing studies of Mars have revealed some very fascinating things about the planet. In the 1960s and early 70s, the Mariner probes revealed that Mars was a dry, frigid planet that was most likely devoid of life. But as our understanding of the planet has deepened, it has come to be known that Mars once had a warmer, wetter environment that could have supported life. This in turn has inspired multiple missions whose purpose it has been to find evidence of this past life. The key questions in this search, however, are where to look and what to look for? In a new study led by researchers from the University of Kansas, a team of international scientists recommended that future missions should look for vanadium. This rare element, they claim, could point the way towards fossilized evidence of life. To be clear, finding signs of life on a planet like Mars is no easy task. As Craig Marshall indicated in a University of Kansas press release: “You’ve got your work cut out if you’re looking at ancient sedimentary rock for microfossils here on Earth – and even more so on Mars. On Earth, the rocks have been here for 3.5 billion years, and tectonic collisions and realignments have put a lot of stress and pressure on rocks. Also, these rocks can get buried, and temperature increases with depth.” In their paper, Marshall and his colleagues recommend that missions like NASA’s Mars 2020 rover, the ESA’s ExoMars 2020 rover, and other proposed surface missions could combine Raman spectroscopy with the search for vanadium to find evidence of fossilized life. On Earth, this element has been found in crude oils, asphalts, and black shales that have been formed by the slow decay of biological organic material. In addition, paleontologists and astrobiologists have used Raman spectroscopy – a technique that reveals the cellular compositions of samples – on Mars for some time to search for signs of life. In this respect, the addition of vanadium would provide material that would act as a biosignature to confirm the existence of organic life in samples under study. As Marshall explained: “People say, ‘If it looks like life and has a Raman signal of carbon, then we have life. But, of course, we know there can be carbonaceous materials made in other processes — like in hydrothermal vents — consistent with looking like microfossils that also have some carbon signal. People also make wonderful carbon structures artificially that look like microfossils — exactly the same. So, we’re at a juncture now where it’s really hard to tell if there’s life only based on morphology and Raman spectroscopy.” This is not the first time that Marshall and his co-authors have advocated using vanadium to search for signs of life. Such was the subject of a presentation they made at the Astrobiology Science Conference in 2015. What’s more, Marshall and his team emphasize that it would be possible to perform this technique using instruments that are already part of NASA’s Mars 2020 mission. Their proposed method also involves new technique known as X-ray fluorescence microscopy, which looks at elemental composition. To test this technique, the team examined thermally altered organic-walled microfossils which were once organic materials )called acritarchs). From their data, they confirmed that traces of vanadium are present within microfossils that were indisputably organic in origin. “We tested acritarchs to do a proof-of-concept on a microfossil where there’s no shadow of a doubt that we’re looking at preserved ancient biology,” Marshall said. “The age of this microfossil we think is Devonian. These guys are aquatic microorganisms — they’re thought to be microalgae, a eukaryotic cell, more advanced than bacterial. We found the vanadium content you’d expect in cyanobacterial material.” These microfossilized bit of life, they argue, are probably not very distinct from the kinds of life that could have existed on Mars billions of years ago. Other scientific research has also indicated that vanadium is the result of organic compounds (like chlorophyll) from living organisms undergoing a transformation process caused by heat and pressure (i.e. diagenetic alteration). In other words, after living creatures die and become buried in sediment, vanadium forms in their remains as a result of being buried under more and more layers of rock – i.e. fossilization. Or, as Marshall explained it: “Vanadium gets complexed in the chlorophyll molecule. Chlorophylls typically have magnesium at the center — under burial, vanadium replaces the magnesium. The chlorophyll molecule gets entangled within the carbonaceous material, thus preserving the vanadium. It’s like if you have a rope stored in your garage and before you put it away you wrap it so you can unravel it the next time you need it. But over time on the garage floor it becomes tangled, things get caught in it. Even when you shake that rope hard, things don’t come out. It’s a tangled mess. Similarly, if you look at carbonaceous material there’s a tangled mess of sheets of carbon and you’ve got the vanadium mixed in.” At present, their research appears to have attracted the interesting of the European Space Agency. Howell Edwards, who also conducts research using Raman spectroscopy (and who’s work has been supported by an ARC grant), is part of the ESA’s Mars Explorer team, where he is responsible for instrumentation on the ExoMars 2020 rover. But, as Marshall indicated, the team also hopes that NASA will consider their study: “Hopefully someone at NASA reads the paper. Interestingly enough, the scientist who is lead primary investigator for the X-ray spectrometer for the space probe, they call it the PIXL, was his first graduate student from Macquarie University, before his KU times. I think I’ll email her the paper and say, ‘This might be of interest.’” The next decade is expected to be a very auspicious time for exploration missions to Mars. Multiple rovers will be exploring the surface, hoping to find the elusive evidence of life. These missions will also help pave the way for NASA’s crewed mission to Mars by the 2030s, which will see astronauts landing on the surface of the Red Planet for the first time in history. If, in fact, these missions find evidence of life, it will have a profound effect on all future mission to Mars. It will also have an immeasurable impact on humanity’s perception of itself, knowing at long last that billions of years ago, life did not emerge on Earth alone! For years now, scientists have understood that Mars was once a warmer, wetter place. Between terrain features that indicate the presence of rivers and lakes to mineral deposits that appeared to have dissolved in water, there is no shortage of evidence attesting to this “watery” past. However, just how warm and wet the climate was billions of years ago (and since) has been a subject of much debate. According to a new study from an international team of scientists from the University of Nevada, Las Vegas (UNLV), it seems that Mars may have been a lot wetter than previous estimates gave it credit for. With the help of Berkeley Laboratory, they conducted simulations on a mineral that has been found in Martian meteorites. From this, they determined that Mars may have had a lot more water on its surface than previously thought. When it comes to studying the Solar System, meteorites are sometimes the only physical evidence available to researchers. This includes Mars, where meteorites recovered from Earth’s surface have helped to shed light on the planet’s geological past and what kinds of processes have shaped its crust. For geoscientists, they are the best means of determining what Mars looked like eons ago. Unfortunately for geoscientists, these meteorites have underdone changes as a result of the cataclysmic force that expelled them from Mars. As Dr. Christopher Adcock, an Assistant Research Professor at with the Dept. of Geoscience at UNLV and the lead author of the study, told Universe Today via email: “Martian meteorites are pieces of Mars, basically they are our only samples of Mars on Earth until there is a sample return mission. Many of the discoveries we have made about Mars came from studying martian meteorites and wouldn’t be possible without them. Unfortunately, these meteorites have all experienced shock from being ejected of the Martian surface during impacts.” Of the over 100 Martian meteorites that have been retrieved here on Earth, and range in age from between 4 billion years to 165 million years. They are also believed to have come from only a few regions on Mars, and were likely ejecta created from impact events. And in the course of examining them, scientists have noticed the presence of a calcium phosphate mineral known as merrillite. As a member of the whitlockite group that is commonly found in Lunar and Martian meteorities, this mineral is known for being anhydrous (i.e. containing no water). As such, researchers have drawn the conclusion that the presence of this minerals indicates that Mars had an arid environment when these rocks were ejected. This is certainly consistent with what Mars looks like today – cold, icy and dry as a bone. This consisted of placing the synthetic whitlockite sample inside a projectile, then using a helium gas gun to accelerate it up to speeds of 700 meters per second (2520 km/h or 1500 mph) into a metal plate – thus subjecting it to intense heat and pressure. The sample was then examined using the Berkeley Lab’s Advanced Light Source (ALS) and the Argonne National Laboratory’s Advanced Photon Source (APS) instruments. “When we analyzed what came out of the capsule, we found a significant amount of the whitlockite had dehydrated to the mineral merrillite,” said Adcock. “Merrillite is found in many meteorites (including Martian). The means it is possible the rocks meteorites are made from originally started life with whitlockite in them in an environment with more water than previously thought. If true, it would indicate more water in the Martian past and the early Solar System.” Not only does this find raise the “water budget” for Mars in the past, it also raises new questions about Mars’ habitability. In addition to being soluble in water, whitlockite also contains phosphorous – a crucial element for life here on Earth. Combined with recent evidence that shows that liquid water still exists on Mars’ surface – albeit intermittently – this raises new questions about whether or not Mars had life in the past (or even today). But as Adcock explained, further experiments and evidence will be needed to determine if these results are indicative of a more watery past: “As far as life goes, our results are very favorable for the possibility – but we need more data. Really we need a sample return mission or we need to go there in person – a human mission. Science is closing in on the answers to a number of big questions about our solar system, life elsewhere, and Mars. But it is difficult work when it all has to be done from far away.” And sample returns are certainly on the horizon. NASA hopes to conduct the first step in this process with their Mars 2020 Rover, which will collect samples and leave them in a cache for future retrieval. The ESA’s ExoMars rover is expected to make the journey to Mars in the same year, and will also obtain samples as part of a sample-return mission to Earth. These missions are scheduled to launch the summer of 2020, when the planets will be at their closest again. And with crewed missions to the surface planned for the following decade, we might see the first non-meteorite samples of Mars brought back to Earth for analysis. Watch how Schiaparelli will land on Mars. Touchdown will occur at 10:48 a.m. EDT (14:48 GMT) Wednesday Oct. 19. Cross your fingers for good weather on the Red Planet on October 19. That’s the day the European Space Agency’s Schiaparelli lander pops open its parachute, fires nine, liquid-fueled thrusters and descends to the surface of Mars. Assuming fair weather, the lander should settle down safely on the wide-open plains of Meridiani Planum near the Martian equator northwest of NASA’s Opportunity rover. The region is rich in hematite, an iron-rich mineral associated with hot springs here on Earth. The 8-foot-wide probe will be released three days earlier from the Trace Gas Orbiter (TGO) and coast toward Mars before entering its atmosphere at 13,000 mph (21,000 km/hr). During the 6-minute-long descent, Schiaparelli will decelerate gradually using the atmosphere to brake its speed, a technique called aerobraking. Not only is Meridiani Planum flat, it’s low, which means the atmosphere is thick enough to allow Schiaparelli’s heat shield to reduce its speed sufficiently so the chute can be safely deployed. The final firing of its thrusters will ensure a soft and controlled landing. The lander is one-half of the ExoMars 2016 mission, a joint venture between the European Space Agency and Russia’s Roscosmos. The Trace Gas Orbiter (TGO) will fire its thrusters to place itself in orbit about the Red Planet the same day Schiparelli lands. Its job is to inventory the atmosphere in search of organic molecules, methane in particular. Plumes of methane, which may be biological or geological (or both) in origin, have recently been detected at several locations on Mars including Syrtis Major, the planet’s most prominent dark marking. The orbiter will hopefully pinpoint the source(s) as well as study seasonal changes in locations and concentrations. Methane (CH4) has long been associated with life here on Earth. More than 90% of the colorless, odorless gas is produced by living organisms, primarily bacteria. Sunlight breaks methane down into other gases over a span of about 300 years. Because the gas relatively short-lived, seeing it on Mars implies an active, current source. There may be several: Long-extinct bacteria that released methane that became trapped in ice or minerals in the upper crust. Changing temperature and pressure could stress the ice and release that ancient gas into today’s atmosphere. Bacteria that are actively producing methane to this day. Abiological sources. Iron can combine with oxygen in terrestrial hot springs and volcanoes to create methane. This gas can also become trapped in solid forms of water or ‘cages’ called clathrate hydrates that can preserve it for a long time. Olivine, a common mineral on Earth and Mars, can react with water under the right conditions to form another mineral called serpentine. When altered by heat, water and pressure, such in environments such as hydrothermal springs, serpentine can produce methane. Will it turn out to be burping bacteria or mineral processes? Let’s hope TGO can point the way. The Trace Gas Orbiter will also use the Martian atmosphere to slow its speed and trim its orbital loop into a 248-mile-high (400 km) circle suitable for science observations. But don’t expect much in the way of scientific results right away; aerobraking maneuvers will take about a year, so TGO’s job of teasing out atmospheric ingredients won’t begin until December 2017. The study runs for 5 years. The orbiter will also examine Martian water vapor, nitrogen oxides and other organics with far greater accuracy than any previous probe as well as monitor seasonal changes in the atmosphere’s composition and temperature. And get this — its instruments can map subsurface hydrogen, a key ingredient in both water and methane, down to a depth of a meter (39.4 inches) with greater resolution compared to previous studies. Who knows? We may discover hidden ice deposits or methane sinks that could influence where future rovers will land. Additional missions to Mars are already on the docket, including ExoMars 2020. More about that in a minute. While TGO’s mission will require years, the lander is expected to survive for only four Martian days (called ‘sols’) by using the excess energy capacity of its batteries. A set of scientific sensors will measure wind speed and direction, humidity, pressure and electric fields on the surface. A descent camera will take pictures of the landing site on the way down; we’ll should see those photos the very next day. Data and imagery from the lander will be transmitted to ESA’s Mars Express and a NASA Relay Orbiter, then relayed to Earth. This animation shows the paths of the Trace Gas Orbiter and Schiaparelli lander on Oct. 19 when they arrive at Mars. If you’re wondering why the lander’s mission is so brief, it’s because Schiaparelli is essentially a test vehicle. Its primary purpose is to test technologies for landing on Mars including the special materials used for protection against the heat of entry, a parachute system, a Doppler radar device for measuring altitude and liquid-fueled braking thrusters. Martian dust storms can be cause for concern during any landing attempt. Since it’s now autumn in the planet’s northern hemisphere, a time when storms are common, there’s been some finger-nail biting of late. The good news is that storms of recent weeks have calmed and Mars has entered a welcome quiet spell. To watch events unfold in real time, check out ESA’s live stream channel,Facebook pageand Twitter updates. The announcement of the separation of the lander from the orbiter will be made around 11 a.m. Eastern Time (15:00 GMT) Sunday October 16. Live coverage of the Trace Gas Orbiter arrival and Schiaparelli landing on Mars runs from 9-11:15 a.m. Eastern (13:00-15:15 GMT) on Wednesday October 19.Photos taken by Schiaparelli’s descent camera will be available starting at 4 a.m. Eastern (8:00 GMT) on October 20. More details here.We’ll also keep you updated on Universe Today. Everything we learn during the current mission will be applied to planning and executing the next — ExoMars 2020, slated to launch in 2020. That venture will send a rover to the surface to search and chemically test for signs of life, present or past. It will collect samples with a drill at various depths and analyze the fines for bio-molecules. Getting down deep is important because the planet’s thin atmosphere lets through harsh UV light from the sun, sterilizing the surface. Are you ready for adventure? See you on Mars (vicariously)! Liftoff of the ExoMars 2018 rover mission currently under development jointly by Europe and Russia has just been postponed for two years to 2020, according to an announcement today, May 2, from the European Space Agency (ESA) and the Russian space agency Roscosmos. The delay was forced by a variety of technical and funding issues that ate up the schedule margin to enable a successful outcome for what will be Europe’s first Mars rover. The goal is to search for signs of life. “Taking into account the delays in European and Russian industrial activities and deliveries of the scientific payload, a launch in 2020 would be the best solution,” ESA explained in a statement today. The ambitious ExoMars rover is the second of two joint Euro-Russian missions to explore the Red Planet. It is equipped with an ESA deep driller and a NASA instrument to search for preserved organic molecules. The renamed ExoMars 2020 mission involves a European-led rover and a Russian-led surface platform and is also slated to blastoff on an Russian Proton rocket. Roscosmos and ESA jointly decided to move the launch to the next available Mars launch window in July 2020. The costs associated with the delay are not known. The delay means that the Euro-Russian rover mission will launch the same year as NASA’s 2020 rover. The rover is being built by prime contractor Airbus Defense and Space in Stevenage, England. The descent module and surface science package are provided by Roscosmos with some contributions by ESA. Recognizing the potential for a delay, ESA and Roscosmos set up a tiger team in late 2015 to assess the best options. “Russian and European experts made their best efforts to meet the 2018 launch schedule for the mission, and in late 2015, a dedicated ESA-Roscosmos Tiger Team, also including Russian and European industries, initiated an analysis of all possible solutions to recover schedule delays and accommodate schedule contingencies,” said ESA in the statement. The tiger team reported their results to ESA Director General Johann-Dietrich Woerner and Roscosmos Director General Igor Komarov. Woerner and Komarov then “jointly decided to move the launch to the next available Mars launch window in July 2020, and tasked their project teams to develop, in cooperation with the industrial contactors, a new baseline schedule aiming towards a 2020 launch. Additional measures will also be taken to maintain close control over the activities on both sides up to launch.” The ExoMars 2016 interplanetary mission is comprised of the Trace Gas Orbiter (TGO) and the Schiaparelli lander. The spacecraft are due to arrive at Mars in October 2016. The goal of TGO is to search for possible signatures of life in the form of trace amounts of atmospheric methane on the Red Planet. The main purpose of Schiaparelli is to demonstrate key entry, descent, and landing technologies for the follow on 2nd ExoMars mission that will land the first European rover on the Red Planet. The now planned 2020 ExoMars mission will deliver an advanced rover to the Red Planet’s surface. It is equipped with the first ever deep driller that can collect samples to depths of 2 meters (seven feet) where the environment is shielded from the harsh conditions on the surface – namely the constant bombardment of cosmic radiation and the presence of strong oxidants like perchlorates that can destroy organic molecules. ExoMars was originally a joint NASA/ESA project. But thanks to hefty cuts to NASA’s budget by Washington DC politicians, NASA was forced to terminate the agencies involvement after several years of extremely detailed work and withdraw from participation as a full partner in the exciting ExoMars missions. NASA is still providing the critical MOMA science instrument that will search for organic molecules. Thereafter Russia agreed to take NASA’s place and provide the much needed funding and rockets for the pair of launches in March 2016 and May 2018. TGO will also help search for safe landing sites for the ExoMars 2020 lander and serve as the all important data communication relay station sending signals and science from the rover and surface science platform back to Earth. ExoMars 2016 is Europe’s most advanced mission to Mars and joins Europe’s still operating Mars Express Orbiter (MEX), which arrived back in 2004, as well as a fleet of NASA and Indian probes. The Trace Gas Orbiter (TGO) and Schiaparelli lander arrive at Mars on October 19, 2016. Stay tuned here for Ken’s continuing Earth and planetary science and human spaceflight news.
The first burst error correcting code was the Fire Code, which was once widely used on hard disk drives. Here we look at how it works and how it was used. Data recording and transmission need different types of error correction because the channels act in different ways. For example a deep-space probe returning signals to Earth has limited power and the received signals will be very noisy and will contain many random errors. On the other hand storage media tend to suffer from burst errors due to defects in the medium or from particles of contaminant between the head and the medium. Here we look at the correction of burst errors. Using the Hamming code described in an earlier piece, single bit errors could be corrected. Clearly using bit interleaving, a large number of Hamming codes could be created across a data block such that a burst error would cause a single bit error in many different codes, but the amount of redundancy needed would be very great. An error-correcting code incorporating interleaving principles could correct a burst error with a single code, which could be more efficient. Fig.1 - A burst error is defined as a series of bits where those at the ends must be in error (1) whereas those between (X) may or may not be. It is important to consider what a burst is in the context of error correction. If a pinhole in a magnetic coating on a hard drive intersects a data track, or if an arcing switch interferes with a transmission, the signal is impaired for a short time and for the rest of the time it is fine. The effect of impairment is interesting, because it does not always cause errors. For example a noise spike whose polarity opposes the polarity of a data bit may cancel it out and cause an error, but a noise spike having the same polarity as that of a data bit could reinforce it and no error occurs. As a result a burst error has a peculiar definition. The first and last bits of the burst are always in error, but the bits in between may or may not be in error. Fig.1 shows the idea. It is important because it defines what the error detector needs to look for. Fig.2a) shows a very simple parity generating circuit that could be designed to run at very high bit rate. Essentially the register forms a delay of nine bits, so as bit 0 appears on the output of the delay at one input to the XOR gate, bit 9 appears on the other input, so the XOR of bits 0 and 9 enters the delay. By the time that emerges from the delay, bit 18 will be on the input, and the gate calculates the XOR of bits 0,9 and 18 and so on. Fig.2b) shows that the effect of the circuit of Fig.2a) is that of a ring having a circumference of nine bits rolling along a line of bits. Every time the ring contacts a new bit its value is XORed with the value in the ring. A simple delay line and XOR gate at a) creates in this example nine check bits that form parity on bits 0,9,18,27….. 1,10,19,28…… 2,11,20,29…. And so on. The effect is analogous to a ring b) rolling down the serial data and making a new XOR at each bit. The hard-working XOR gate is calculating parity on every ninth bit in the message. In other words, one parity check is on bits 0,9,18,27…., the next is on bits 1,10,19,28… and leaves nine check bits in the register. As this parity checking is convolutional, there is no limit to the length of the data block that can be used. A possible burst error of three bits is shown in Fig.3a) and this reflects in the pattern of parity errors, in which the syndrome literally draws a map of the bits in error in the burst. Fig.3b) shows that a different configuration of errors could produce the same syndrome. This is serious, because if it is believed, a miscorrection will result and a mechanism has to be found that prevents such an occurrence. The syndrome of Fig.3b) could result from the ends of a long burst. It follows that prevention of miscorrection can be achieved by a system that can detect bursts that are longer than those that can be corrected. Fig.3 - A genuine single burst of three bits at a) is mapped in the ring on replay. A different failure shown in b) produces the same syndrome. Steps must be taken to detect that to prevent miscorrection. If the system is designed to correct a burst of length up to b bits, then in the worst case where only the first and last bits are in error, there will be a maximum of b-2 error free bits inside the burst. If the parity generator uses a delay of 2b - 1 bits, the ring of Fig.2b) will have a circumference of 2b – 1 bits. Outside any single correctable burst of b bits there must be b-1 bits that are not in error, whose parity bits will be zero. That is the principle of the Fire code that was devised by Philip Fire in 1959. It was used extensively in hard disk drives to overcome errors due to media defects and contamination. The nine-bit example of Fig.2 must have a maximum burst size b of 5 bits. On reading the data, the parity check of Fig.2a) is repeated to create a ring of parity bits. The decoder rotates the ring, looking for a run of zeros. If it can’t find a contiguous run of four (b – 1) zeros in the syndrome, the error is un-correctable. However, if it finds a run of b – 1 zeros or more, the end of the burst has been located with respect to the repeating sequence of nine bits. Obviously the same pattern of parity failures would be found if the that burst error had occurred 9, 18, 27….. bits away and an additional mechanism is needed to determine where the burst was, so the pattern in the ring can correct it. The Fire code combines the parity generator of Fig.2 with a cyclic code whose purpose is to find where the burst is so that the parity check can correct it. The polynomial also gives some protection against a random error occurring elsewhere in the block that would prevent a burst being corrected. Fig.4 shows a simple Fire code in which a polynomial generator having a sequence length of 31 is multiplied by one having a sequence length of 9 to create 279-bit code words. On writing data, the serial data are also clocked into the encoder. As the last data bit is written, the redundancy calculation has completed and the feedback is turned off so the check bits can be written immediately after the data, to form a code word. Fig.4 - A Fire code having a sequence length of 279 bits of which 14 are check bits. As 2b -1 is 9 here, then b must be 5, the biggest burst that can be corrected. If the data are subsequently read and shifted into the decoder, the in the case there is no error the syndrome will be all zeros and no action needs to be taken. However, if there is an error there will be a non-zero syndrome. In order to attempt correction, the input to the twisted ring counter is held at zero and the counter is clocked. Fig.5 - In a punctured Fire code, the search for the burst results in a count with respect to the start of the code, not the start of the data block. The ring counter begins to step through sequential powers of a Galois Field. If the problem is a single correctable burst, one of those powers is also the burst error. It is a characteristic of Galois Fields that sequential powers are highly non-sequential in pure binary. As the ring counter is stepped, if the burst error is within the allowable burst size, at some point a contiguous row of at least b -1 zeros will be found in the ring counter. This will only take place at one count. The idea is shown in Fig.5. In actual use, Fire codes designed to correct large burst errors will have long sequence lengths, much longer than the size of a typical data block. The codewords will be punctured, meaning that only the end of the codeword is occupied by data, followed by the check bits. The part of the codeword before the data is considered to be all zeros. In writing and reading this is not a problem because zeros can be fed into a twisted ring counter indefinitely and nothing happens. However, when an error is encountered, the number of clocks needed to locate b – 1 or more zeros is counted from the start of the codeword, so the number of leading zeros needs to be subtracted to locate the error with respect to the data. You might also like... The CRC (cyclic redundancy check) was primarily an error detector, but it did allow some early error correction systems to be implemented. There are many different CRCs but they all work in much the same way, which is that the… The mathematics of finite fields and sequences seems to be a long way from everyday life, but it happens in the background every time we use a computer and without it, an explanation of modern error correction cannot be given. Computer marketing departments typically do not promote all company products. Rather they focus on high margin products. Here we look at one of the first practical error-correcting codes to find wide usage. Richard Hamming worked with early computers and became frustrated when errors made them crash. The rest is history. Error correction is fascinating not least because it involves concepts that are not much used elsewhere, along with some idiomatic terminology that needs careful definition.
Radius Teacher Resources Find Radius educational ideas and activities Showing 141 - 160 of 2,423 resources In this length of the arc worksheet, students are given the measurements of the radius and central angle and they find the length of the arc. Students complete 6 problems. Sixth graders explore geometry by analyzing specific shapes in class. For this circle identification lesson, 6th graders utilize a computer and projector to view the different measurements of a circle. Students define the terms radius, diameter and circumference in order to find the area of any given circle. In this circles worksheet, students label parts of a circle that are given. They choose from center, radius, diameter or chord. Students then draw a circle and draw the given parts on their circle. The worksheet ends with a test prep section where they are given a multiple choice question and a story problem. Students work with circles, angles and estimating angles in the night sky. In this circles and angles lesson, students practice measuring a degree using the circumference of a circle and apply the degree to determine a way to use their hands take measurements. They determine the angular size of the moon, planet or a star using the given algorithm. In this math word problem worksheet, 6th graders complete problems about the length and radius of certain shapes. Students complete 15 problems. In this arcs and chords worksheet, 10th graders solve 7 different types of problems related to identifying arcs and chords in a circle. First, they find the measure of each arc to the nearest tenth, if O is the center point. Then, students find the length of a radius in a circle where the chord is 16 inches long and 6 inches from the center. They also find the distance from the center of the circle to the chord. In this solids activity, 10th graders solve and complete 10 different word problems that include determining the volume and surface area of various solids. First, they determine the surface area of a cube as described. Then, students determine the radius of an object given the diameter and length. In addition, they determine the amount of a substance held in a cylindrical glass, In this circles worksheet, 10th graders solve and complete 5 different problems related to measuring circles. First, they find the length of a given line when it is tangent to the circle with a given radius. Then, students write a two-column proof given the information. In addition, they determine the radius of each circle given the measure of each line segment. In this circumference of a circle worksheet, students complete 5 problems showing their understanding of circumference, diameter and radius. Students prove their understanding by showing their work and explaining their thinking. In this circumference worksheet, 6th graders read the steps to find the circumference of a circle using radius and diameter. They solve six problems. Learners study the properties of circles. In this circles lesson, students read a word problem about circles. Learners watch a video about the activity and then practice drawing the circle solution to the problem. Students watch another video segment and discuss the methods in the video. Learners identify circles around the classroom and find their centers and radii. Students finish with two assessments for the topic. As a sample exam, or exam itself, this might save you some time. However, you will need to review the questions to see if they are all topics covered in your chemistry class. Topics included are electron configuration, Pauli Exclusion Principle, atomic and ionic radii, ionization energy, electron affinity, and trends in the periodic table of elements. In this chain rule and directional derivatives instructional activity, students solve 4 different word problems related to determining points. First, they find the rate at which a trees volume grows per year when its radius is a particular number and its height is a certain number. Then, students find the directional derivative of a function at a point in the direction of the vector. In addition, they find the directions of the steepest slope and the magnitude of the slope in that direction. In this circles worksheet, 10th graders solve and complete 10 different problems that include various parts of a circle. First, they write the name of the designated coordinates in each. Then, students determine the diameter, chord, center, and radius in each using the given information. For this geometry worksheet, students focus on the parts of a circle. Students solve for 8 problems, and decide if what is shown depicts a radius, diameter or a chord. In this circumference of a circle worksheet, students discuss the definition of a radius and diameter of a circle. Students then complete 6 problems where they decided if the marked part of a circle is a radius, diameter or neither. High schoolers explore the concept of surface area. In this surface area lesson, students find the surface area of a cylinder. High schoolers use Cabri Jr. to make a chart of circle radius, rectangle height and length and then find the surface area of a cylinder. Sixth graders discover what circumference is. In this measurement instructional activity, 6th graders identify the radius and diameter of different circles. Students discover how to find the area of a circle using the radius and diameter. For this finding the area of a circle worksheet, 7th graders read the formula, then calculate the area for 5 circles, given the radius, with answers included. In this geometry worksheet, students calculate the circumference of a circle. They calculate the diameter and radius using the correct formula. There are 5 questions with an answer key.
Where did the moon come form, how did the moon form, how old is the moon, how did it get there? There is much speculation and mystery surrounding the subject of the moon and its origins. There are currently three main stream theories attempting to explain the origin of the moon. The fission theory suggests the moon was once part of the earth and somehow separated from our planet in its early history. The condensation theory suggests the moon and earth condensed together from the original nebula that formed the solar system. The capture theory states the Moon was formed not in the vicinity of the Earth, but in a different part of the solar system, and was later captured by the Earth. The impact theory states an object in space the size of mars crashed into Earth ejecting large volumes of matter into earths orbit which condensed to form the moon. Although there are facts that disprove every theory we are told by mainstream science, they are still put out there. According to mainstream scientists, the Earth and the moon are the same age; but according to the facts, this is not true. Some moon rocks are as old as 5.3 billion years old, and others are as old as 20 billion years. The Earth itself is said to be 4.6 billion years old. Elements such as Uranium 236 and neptunium 237 were discovered in lunar rocks and are not found naturally on earth; This fact, and the age of lunar rocks disprove the fission, impact, and condensation theory. Scientists also discovered that the moon contains heavier elements on the surface, the crust is composed primarily of illeminite, a mineral containing large amounts of titanium, uranium 236 and neptunium 237. The heavier elements of a naturally forming objects in space would have ended up in the center and the surface would contain the lighter elements; this means the moon is not a naturally forming object, this fact also disproves the condensation, and capture theory. On November 20, 1969, the Apollo 12 crew crashed a lunar modual onto the moon, this created a moon quake which caused the moon reverberated like a bell for over an hour, leading to the conclusion the moon has a light, or no core. According to Thomas J Glover, our moon has a diameter of 2,160 miles and a gravity of .17, that of earth. NASA’s more accurate moon gravity figure is 1.6, with a current orbital speed is 19,051 miles per hour. The moons density is 3.3 times an equal volume of water while earth’s average density is 5.5 times that of an equal volume of water. The fact that the Moon is only 60 percent as dense as Earth has led scientists to two theories that the Moon is without an iron core, and possibly, is partially hollow. Data and computations point to the conclusion that our Moon is internally hollow to a great extent. Since most scientists claim that there is no natural explanation for such a peculiar phenomenon, the inevitable conclusion indicated that the Moon is artificially hollow. Our Soviet theorists, agree. Isaac Asimov, a Russian professor of biochemistry and writer of popular science books, said by all cosmic laws, the Moon should not be orbiting Earth. He went on saying, “we cannot help but come to the conclusion that the Moon by rights ought not to be there. The fact that it is, is one of those strokes of luck almost too good to accept. Small planets, such as Earth, with weak gravitational fields, might well lack satellites. In general, then, when a planet does have satellites, those satellites are much smaller than the planet itself. Therefore, even if the Earth has a satellite, there would be every reason to suspect that at best it would be a tiny world, perhaps 30 miles in diameter. But that is not so. Earth not only has a satellite, but it is a giant satellite, 2,160 miles in diameter. Its too big to have been captured by the earth. The chances of such a capture having been effected and the moon they having taken up nearly circular orbit around our earth are too small to make such an eventually credible.” According to our scientists, the Moon is bigger than it should be, apparently older than it should be and much lighter in mass than it should be. It occupies an unlikely orbit and is so extraordinary that all existing explanations for its presence are fraught with difficulties and none of them could be considered remotely watertight. These are just some scientific findings which disprove all the theories suggested by mainstream science. There are some historical facts which indicate the moons presence in our sky is younger than the human species itself. Our ancestors on both sides of the globe tell of a time when there was no moon orbiting our land. Ancient, which include Greek philosophers, describes a time when there was no moon near Earth. Democritus and Anaxagoras taught that there was a time when the Earth was without the Moon. Aristotle wrote that Arcadia in Greece, before being inhabited by the Hellenes, had a population of Pelasgians, and that these aborigines occupied the land already before there was a moon in the sky above the Earth. Censorinus, a Roman grammarian and miscellaneous writer from the 3rd century A D, also refers to the time in the past when there was no moon in the sky. The memory of a world without a moon lives in oral tradition among the Native tribes in South America. The Natives of the Bogota highlands, in the eastern Cordilleras of Colombia, relate some of their tribal reminiscences to the time before there was a moon. “In the earliest times, when the moon was not yet in the heavens,” as described the tribesmen of Chibchas. People on both sides of the globe have oral and written records of a time when there was no moon in the sky. Another theory of the moons origins does not share the popularity of that of the mainstream theories. Theorists suggest the moon is a hollowed out planetoid, partially artificial, belonging to and still in use by the Annunaki. One thing to note about the moon is the chemical composition of moon dust is different than rocks, which means it is not a result of weathering. This means it must have originated elsewhere. Another thing to note about moon rocks is that despite having no magnetic field, moon rocks were magnetized, which shocked scientists. If you believe the earth does not have a solid, or molten interior, and is hollow, one thing you may wonder is “Where does the Earths magnetic field come from?”. If you understand the Reptilian Agenda you may understand my theory on the purpose of the moon and the magnetic field surrounding earth. I theorize the moon is not only a base, or home to another species, but also a machine belonging to the Blood Line Elite, which generates the magnetic field around our environment. As organic machinery, our bodies are containers for our souls, or consciousness. As soon as a conscious being, human or not, dies on Earth, he or she is trapped in this “prison planet”, with the magnetic field as a net, keeping us from escaping the Matrix controlled by the Reptilian Elite; we are forced to reincarnate here to be used as a cheap energy source and be their eternal slaves.
In the run-up to the first flight of a human aircraft to another planet, NASA has just started funding an unusual project that involves sending a "swarm" of small spacecraft to study the atmosphere of Venus. The project involves sending out a series of tiny flying sensors called LEAVES (Lofted Environmental and Atmospheric Venus Sensors), which will fly up like a swarm and report on what they find along the way, according to a press release from NASA. A space swarm It's a suggestive idea, but the (relatively) low-cost spacecraft could make it much more feasible to continue studying a planet that NASA previously described as hell. Leaves in the wind Scientists at the Ohio Aerospace Institute have designed the LEAVES to resemble and function as lightweight, high-tech kites. A swarm of kites that is released from an orbital spacecraft and descends through the clouds into the upper atmosphere of Venus. While there, the built-in sensors and electronics that pick up atmospheric chemicals will relay their findings to the spacecraft. Nine hours of flight and the swarm of falling LEAVES will have dropped too low to continue providing useful readings, or will be swallowed by the planet's acidic, sulfur-rich environment. Space swarm, the day will come The LEAVES mission is a beautiful evolution of NASA projects, and the fact that the agency has so far allocated only 500.000 to further develop the technology shouldn't be misleading. The "space swarm" project is far-reaching, it will take some time but it is very promising. LEAVES could someday provide scientists with crucial information about what is happening in Venus's atmosphere, an area that scientists previously speculated to be filled with clouds that teeming with fluctuating microbial life.
Astronomy is a majestic scientific field that delves into the study of celestial objects and phenomena in the universe. It is a branch of natural science that has captivated the human imagination for centuries and continues to provide profound insights into the mysteries of the cosmos. Through the use of advanced telescopes, satellites, and space probes, astronomers are constantly exploring and unraveling the secrets of the universe, making groundbreaking discoveries that expand our understanding of the cosmos. The study of astronomy begins with the observation and analysis of celestial bodies such as stars, planets, moons, comets, asteroids, and galaxies. Astronomers use powerful telescopes to observe these objects in different wavelengths of light, allowing them to study their composition, size, and behavior. They also utilize spectroscopy to analyze the light emitted by celestial bodies, which provides crucial information about their chemical composition, temperature, and motion. Furthermore, the launch of space telescopes and satellites has revolutionized the field of astronomy, allowing scientists to observe the universe from outside the Earth’s atmosphere. Instruments such as the Hubble Space Telescope, the Chandra X-ray Observatory, and the Kepler Space Telescope have provided breathtaking images and valuable data that have transformed our understanding of the cosmos. In addition to observing celestial objects, astronomers also utilize the principles of physics, chemistry, and mathematics to study the fundamental processes that govern the universe. By applying these principles, they can investigate phenomena such as the formation and evolution of stars, the dynamics of galaxies, and the behavior of exotic objects like black holes and neutron stars. One of the most intriguing areas of astronomy is the search for exoplanets, which are planets that orbit stars outside our solar system. Recent advancements in technology have led to the discovery of thousands of exoplanets, some of which may harbor the conditions necessary for life. This has ignited the search for extraterrestrial life and has raised profound questions about the potential for life beyond Earth. Astronomy also plays a vital role in our understanding of the origins and fate of the universe. By studying the cosmic microwave background radiation, astronomers can make significant inferences about the early universe and the processes that led to the formation of galaxies and stars. Additionally, the study of dark matter and dark energy, two mysterious components that make up most of the universe, has become a major focus of research in modern astronomy. Overall, astronomy is a dynamic and ever-evolving field that continues to push the boundaries of human knowledge and understanding. Through the exploration of the universe, scientists are gaining deeper insights into the nature of space, time, and the fundamental laws that govern the cosmos. With ongoing advancements in technology and theoretical modeling, the future of astronomy holds great promise for unlocking the profound mysteries of the universe and expanding our cosmic perspective.
Make sure you thoroughly understand the following essential ideas: - The difference between square and hexagonal packing in two dimensions. - The definition and significance of the unit cell. - Sketch the three Bravais lattices of the cubic system, and calculate the number of atoms contained in each of these unit cells. - Show how alternative ways of stacking three close-packed layers can lead to the hexagonal or cubic close packed structures. - Explain the origin and significance of octahedral and tetrahedral holes in stacked close-packed layers, and show how they can arise. Close-Packing of Identical Spheres Crystals are of course three-dimensional objects, but we will begin by exploring the properties of arrays in two-dimensional space. This will make it easier to develop some of the basic ideas without the added complication of getting you to visualize in 3-D — something that often requires a bit of practice. Suppose you have a dozen or so marbles. How can you arrange them in a single compact layer on a table top? Obviously, they must be in contact with each other in order to minimize the area they cover. It turns out that there are two efficient ways of achieving this: The essential difference here is that any marble within the interior of the square-packed array is in contact with four other marbles, while this number rises to six in the hexagonal-packed arrangement. It should also be apparent that the latter scheme covers a smaller area (contains less empty space) and is therefore a more efficient packing arrangement. If you are good at geometry, you can show that square packing covers 78 percent of the area, while hexagonal packing yields 91 percent coverage. If we go from the world of marbles to that of atoms, which kind of packing would the atoms of a given element prefer? If the atoms are identical and are bound together mainly by dispersion forces which are completely non-directional, they will favor a structure in which as many atoms can be in direct contact as possible. This will, of course, be the hexagonal arrangement. Directed chemical bonds between atoms have a major effect on the packing. The version of hexagonal packing shown at the right occurs in the form of carbon known as graphite which forms 2-dimensional sheets. Each carbon atom within a sheet is bonded to three other carbon atoms. The result is just the basic hexagonal structure with some atoms missing. The coordination number of 3 reflects the sp2-hybridization of carbon in graphite, resulting in plane-trigonal bonding and thus the sheet structure. Adjacent sheets are bound by weak dispersion forces, allowing the sheets to slip over one another and giving rise to the lubricating and flaking properties of graphite. The underlying order of a crystalline solid can be represented by an array of regularly spaced points that indicate the locations of the crystal's basic structural units. This array is called a crystal lattice. Crystal lattices can be thought of as being built up from repeating units containing just a few atoms. These repeating units act much as a rubber stamp: press it on the paper, move ("translate") it by an amount equal to the lattice spacing, and stamp the paper again. The gray circles represent a square array of lattice points. The orange square is the simplest unit cell that can be used to define the 2-dimensional lattice. Building out the lattice by moving ("translating") the unit cell in a series of steps, Although real crystals do not actually grow in this manner, this process is conceptually important because it allows us to classify a lattice type in terms of the simple repeating unit that is used to "build" it. We call this shape the unit cell. Any number of primitive shapes can be used to define the unit cell of a given crystal lattice. The one that is actually used is largely a matter of convenience, and it may contain a lattice point in its center, as you see in two of the unit cells shown here. In general, the best unit cell is the simplest one that is capable of building out the lattice. Shown above are unit cells for the close-packed square and hexagonal lattices we discussed near the start of this lesson. Although we could use a hexagon for the second of these lattices, the rhombus is preferred because it is simpler. Notice that in both of these lattices, the corners of the unit cells are centered on a lattice point. This means that an atom or molecule located on this point in a real crystal lattice is shared with its neighboring cells. As is shown more clearly here for a two-dimensional square-packed lattice, a single unit cell can claim "ownership" of only one-quarter of each molecule, and thus "contains" 4 × ¼ = 1 molecule. The unit cell of the graphite form of carbon is also a rhombus, in keeping with the hexagonal symmetry of this arrangement. Notice that to generate this structure from the unit cell, we need to shift the cell in both the x- and y- directions in order to leave empty spaces at the correct spots. We could alternatively use regular hexagons as the unit cells, but the x+y shifts would still be required, so the simpler rhombus is usually preferred. As you will see in the next section, the empty spaces within these unit cells play an important role when we move from two- to three-dimensional lattices. In order to keep this lesson within reasonable bounds, we are limiting it mostly to crystals belonging to the so-called cubic system. In doing so, we can develop the major concepts that are useful for understanding more complicated structures (as if there are not enough complications in cubics alone!) But in addition, it happens that cubic crystals are very commonly encountered; most metallic elements have cubic structures, and so does ordinary salt, sodium chloride. We usually think of a cubic shape in terms of the equality of its edge lengths and the 90° angles between its sides, but there is another way of classifying shapes that chemists find very useful. This is to look at what geometric transformations (such as rotations around an axis) we can perform that leave the appearance unchanged. For example, you can rotate a cube 90° around an axis perpendicular to any pair of its six faces without making any apparent change to it. We say that the cube possesses three mutually perpendicular four-fold rotational axes, abbreviated C4 axes. But if you think about it, a cube can also be rotated around the axes that extend between opposite corners; in this case, it takes three 120° rotations to go through a complete circle, so these axes (also four in number) are three-fold or C3 axes. Cubic crystals belong to one of the seven crystal systems whose lattice points can be extended indefinitely to fill three-dimensional space and which can be constructed by successive translations (movements) of a primitive unit cell in three dimensions. As we will see below, the cubic system, as well as some of the others, can have variants in which additional lattice points can be placed at the center of the unit or at the center of each face. The three types of cubic lattices The three Bravais lattices which form the cubic crystal system are shown here. Structural examples of all three are known, with body- and face-centered (BCC and FCC) being much more common; most metallic elements crystallize in one of these latter forms. But although the simple cubic structure is uncommon by itself, it turns out that many BCC and FCC structures composed of ions can be regarded as interpenetrating combinations of two simple cubic lattices, one made up of positive ions and the other of negative ions. Notice that only the FCC structure, which we will describe below, is a close-packed lattice within the cubic system. Close-packed lattices in three dimensions Close-packed lattices allow the maximum amount of interaction between atoms. If these interactions are mainly attractive, then close-packing usually leads to more energetically stable structures. These lattice geometries are widely seen in metallic, atomic, and simple ionic crystals. As we pointed out above, hexagonal packing of a single layer is more efficient than square-packing, so this is where we begin. Imagine that we start with the single layer of green atoms shown below. We will call this the A layer. If we place a second layer of atoms (orange) on top of the A-layer, we would expect the atoms of the new layer to nestle in the hollows in the first layer. But if all the atoms are identical, only some of these void spaces will be accessible. In the diagram on the left, notice that there are two classes of void spaces between the A atoms; one set (colored blue) has a vertex pointing up, while the other set (not colored) has down-pointing vertices. Each void space constitutes a depression in which atoms of a second layer (the B-layer) can nest. The two sets of void spaces are completely equivalent, but only one of these sets can be occupied by a second layer of atoms whose size is similar to those in the bottom layer. In the illustration on the right above we have arbitrarily placed the B-layer atoms in the blue voids, but could just as well have selected the white ones. Two choices for the third layer lead to two different close-packed lattice types Now consider what happens when we lay down a third layer of atoms. These will fit into the void spaces within the B-layer. As before, there are two sets of these positions, but unlike the case described above, they are not equivalent. The atoms in the third layer are represented by open blue circles in order to avoid obscuring the layers underneath. In the illustration on the left, this third layer is placed on the B-layer at locations that are directly above the atoms of the A-layer, so our third layer is just a another A layer. If we add still more layers, the vertical sequence A-B-A-B-A-B-A... repeats indefinitely. In the diagram on the right above, the blue atoms have been placed above the white (unoccupied) void spaces in layer A. Because this third layer is displaced horizontally (in our view) from layer A, we will call it layer C. As we add more layers of atoms, the sequence of layers is A-B-C-A-B-C-A-B-C..., so we call it ABC packing. These two diagrams that show exploded views of the vertical stacking further illustrate the rather small fundamental difference between these two arrangements— but, as you will see below, they have widely divergent structural consequences. Note the opposite orientations of the A and C layers The Hexagonal closed-packed structure The HCP stacking shown on the left just above takes us out of the cubic crystal system into the hexagonal system, so we will not say much more about it here except to point out each atom has 12 nearest neighbors: six in its own layer, and three in each layer above and below it. The cubic close-packed structure Below we reproduce the FCC structure that was shown above. You will notice that the B-layer atoms form a hexagon, but this is a cubic structure. How can this be? The answer is that the FCC stack is inclined with respect to the faces of the cube, and is in fact coincident with one of the three-fold axes that passes through opposite corners. It requires a bit of study to see the relationship, and we have provided two views to help you. The one on the left shows the cube in the normal isometric projection; the one on the right looks down upon the top of the cube at a slightly inclined angle. Both the CCP and HCP structures fill 74 percent of the available space when the atoms have the same size. You should see that the two shaded planes cutting along diagonals within the interior of the cube contain atoms of different colors, meaning that they belong to different layers of the CCP stack. Each plane contains three atoms from the B layer and three from the C layer, thus reducing the symmetry to C3, which a cubic lattice must have. The FCC unit cell The figure below shows the the face-centered cubic unit cell of a cubic-close packed lattice. How many atoms are contained in a unit cell? Each corner atom is shared with eight adjacent unit cells and so a single unit cell can claim only 1/8 of each of the eight corner atoms. Similarly, each of the six atoms centered on a face is only half-owned by the cell. The grand total is then (8 × 1/8) + (6 × ½) = 4 atoms per unit cell. Interstitial Void Spaces The atoms in each layer in these close-packing stacks sit in a depression in the layer below it. As we explained above, these void spaces are not completely filled. (It is geometrically impossible for more than two identical spheres to be in contact at a single point.) We will see later that these interstitial void spaces can sometimes accommodate additional (but generally smaller) atoms or ions. If we look down on top of two layers of close-packed spheres, we can pick out two classes of void spaces which we call tetrahedral and octahedral holes. If we direct our attention to a region in the above diagram where a single atom is in contact with the three atoms in the layers directly below it, the void space is known as a tetrahedral hole. A similar space will be be found between this single atom and the three atoms (not shown) that would lie on top of it in an extended lattice. Any interstitial atom that might occupy this site will interact with the four atoms surrounding it, so this is also called a four-coordinate interstitial space. Don't be misled by this name; the boundaries of the void space are spherical sections, not tetrahedra. The tetrahedron is just an imaginary construction whose four corners point to the centers of the four atoms that are in contact. Similarly, when two sets of three trigonally-oriented spheres are in close-packed contact, they will be oriented 60° apart and the centers of the spheres will define the six corners of an imaginary octahedron centered in the void space between the two layers, so we call these octahedral holes or six-coordinate interstitial sites. Octahedral sites are larger than tetrahedral sites. An octahedron has six corners and eight sides. We usually draw octahedra as a double square pyramid standing on one corner (left), but in order to visualize the octahedral shape in a close-packed lattice, it is better to think of the octahedron as lying on one of its faces (right). Each sphere in a close-packed lattice is associated with one octahedral site, whereas there are only half as many tetrahedral sites. This can be seen in this diagram that shows the central atom in the B layer in alignment with the hollows in the C and A layers above and below. The face-centered cubic unit cell contains a single octahedral hole within itself, but octahedral holes shared with adjacent cells exist at the centers of each edge. Each of these twelve edge-located sites is shared with four adjacent cells, and thus contributes (12 × ¼) = 3 atoms to the cell. Added to the single hole contained in the middle of the cell, this makes a total of 4 octahedral sites per unit cell. This is the same as the number we calculated above for the number of atoms in the cell. Common cubic close-packed structures It can be shown from elementary trigonometry that an atom will fit exactly into an octahedral site if its radius is 0.414 as great as that of the host atoms. The corresponding figure for the smaller tetrahedral holes is 0.225. Many pure metals and compounds form face-centered cubic (cubic close- packed) structures. The existence of tetrahedral and octahedral holes in these lattices presents an opportunity for "foreign" atoms to occupy some or all of these interstitial sites. In order to retain close-packing, the interstitial atoms must be small enough to fit into these holes without disrupting the host CCP lattice. When these atoms are too large, which is commonly the case in ionic compounds, the atoms in the interstitial sites will push the host atoms apart so that the face-centered cubic lattice is somewhat opened up and loses its close-packing character. The rock-salt structure Alkali halides that crystallize with the "rock-salt" structure exemplified by sodium chloride can be regarded either as a FCC structure of one kind of ion in which the octahedral holes are occupied by ions of opposite charge, or as two interpenetrating FCC lattices made up of the two kinds of ions. The two shaded octahedra illustrate the identical coordination of the two kinds of ions; each atom or ion of a given kind is surrounded by six of the opposite kind, resulting in a coordination expressed as (6:6). How many NaCl units are contained in the unit cell? If we ignore the atoms that were placed outside the cell in order to construct the octahedra, you should be able to count fourteen "orange" atoms and thirteen "blue" ones. But many of these are shared with adjacent unit cells. An atom at the corner of the cube is shared by eight adjacent cubes, and thus makes a 1/8 contribution to any one cell. Similarly, the center of an edge is common to four other cells, and an atom centered in a face is shared with two cells. Taking all this into consideration, you should be able to confirm the following tally showing that there are four AB units in a unit cell of this kind. \|8 at corners: 8 x 1/8 = 1 \|12 at edge centers: 12 x ¼ = 3 \|6 at face centers: 6 x ½ = 3 \|1 at body center = 1 If we take into consideration the actual sizes of the ions (Na+ = 116 pm, Cl– = 167 pm), it is apparent that neither ion will fit into the octahedral holes with a CCP lattice composed of the other ion, so the actual structure of NaCl is somewhat expanded beyond the close-packed model. The space-filling model on the right depicts a face-centered cubic unit cell of chloride ions (purple), with the sodium ions (green) occupying the octahedral sites. The zinc-blende structure: using some tetrahedral holes Since there are two tetrahedral sites for every atom in a close-packed lattice, we can have binary compounds of 1:1 or 1:2 stoichiometry depending on whether half or all of the tetrahedral holes are occupied. Zinc-blende is the mineralogical name for zinc sulfide, ZnS. An impure form known as sphalerite is the major ore from which zinc is obtained. This structure consists essentially of a FCC (CCP) lattice of sulfur atoms (orange) (equivalent to the lattice of chloride ions in NaCl) in which zinc ions (green) occupy half of the tetrahedral sites. As with any FCC lattice, there are four atoms of sulfur per unit cell, and the the four zinc atoms are totally contained in the unit cell. Each atom in this structure has four nearest neighbors, and is thus tetrahedrally coordinated. It is interesting to note that if all the atoms are replaced with carbon, this would correspond to the diamond structure. The fluorite structure: all tetrahedral sites occupied Fluorite, CaF2, having twice as many ions of fluoride as of calcium, makes use of all eight tetrahedral holes in the CPP lattice of calcium ions (orange) depicted here. To help you understand this structure, we have shown some of the octahedral sites in the next cell on the right; you can see that the calcium ion at A is surrounded by eight fluoride ions, and this is of course the case for all of the calcium sites. Since each fluoride ion has four nearest-neighbor calcium ions, the coordination in this structure is described as (8:4). Although the radii of the two ions (F–= 117 pm, Ca2+ = 126 pm does not allow true close packing, they are similar enough that one could just as well describe the structure as a FCC lattice of fluoride ions with calcium ions in the octahedral holes. Simple- and body-centered cubic structures In Section 4 we saw that the only cubic lattice that can allow close packing is the face-centered cubic structure. The simplest of the three cubic lattice types, the simple cubic lattice, lacks the hexagonally-arranged layers that are required for close packing. But as shown in this exploded view, the void space between the two square-packed layers of this cell constitutes an octahedral hole that can accommodate another atom, yielding a packing arrangement that in favorable cases can approximate true close-packing. Each second-layer B atom (blue) resides within the unit cell defined the A layers above and below it. The A and B atoms can be of the same kind or they can be different. If they are the same, we have a body-centered cubic lattice. If they are different, and especially if they are oppositely-charged ions (as in the CsCl structure), there are size restrictions: if the B atom is too large to fit into the interstitial space, or if it is so small that the A layers (which all carry the same electric charge) come into contact without sufficient A-B coulombic attractions, this structural arrangement may not be stable. The cesium chloride structure CsCl is the common model for the BCC structure. As with so many other structures involving two different atoms or ions, we can regard the same basic structure in different ways. Thus if we look beyond a single unit cell, we see that CsCl can be represented as two interpenetrating simple cubic lattices in which each atom occupies an octahedral hole within the cubes of the other lattice.
Have you ever thought about circles? What about types of numbers? Take a look at this dilemma. In the front of Kenneth Graham Middle School there is a flag with a circular garden beneath it. The students in Mr. Kennedy’s homeroom decided that this circular garden would be their community service project. The students elected Candice the leader of the project and she got right to work organizing the decorating. She asked for a group of students to plant flowers and rake the leaves left from last autumn. It was a perfect spring project. “We need more dirt,” Sam said soon after the clean-up had begun. “I think so too,” said Kyle. Candice went out to assess the situation. The rain and snow of the winter and early spring had left the ground sparse. There definitely was not enough dirt to plant in. Candice began to figure out the area of the circular garden. She knew that the formula for area is That is as far as Candice got. She couldn’t remember the next step. This is where you come in. Using irrational numbers is necessary to solve this problem. But first, you should understand what we mean when we say “irrational number”. There are many different ways to classify or name numbers. All numbers are considered real numbers. When you were in the lower grades, you worked with whole numbers. Whole numbers are counting numbers. We consider whole numbers as the set of numbers In middle school, you may also have learned about integers. The set of integers includes whole numbers, but also includes their opposites. Therefore, we can say that whole positive and negative numbers are part of the set of integers We can’t stop classifying numbers with whole numbers and integers because sometimes we can measure a part of a whole or a whole with parts. These numbers are called rational numbers. A rational number is any number that can be written as a fraction where the numerator or the denominator is not equal to zero. Let’s think about this. A whole number or an integer could also be a rational number because we can put it over 1. -4 could be written as There are two special types of decimals that are considered rational numbers and one kind of decimal that is NOT a rational number. A terminating decimal is a decimal that is considered to be a rational number. A terminating decimal is a decimal that looks like it goes on and on, but at some point has an end. It terminates or ends somewhere. This is a terminating decimal. It goes on for a while, but then ends. A repeating decimal is also considered a rational number. A repeating decimal has values that repeat forever. This is a repeating decimal. Ah ha! This is the last type of number that is a decimal, but is NOT a rational number. It is called an irrational number. An irrational number is a decimal that does not end and has no repetition. It goes on and on and on. Irrational numbers cannot be represented as fractions. The most famous irrational number is pi How can we determine if a fraction or a decimal is rational or irrational? If a number can be written in fraction form then it is rational. If a number cannot be written in fraction form then it is irrational. Besides Write each of these definitions and one example of each in your notebook. Now that you have had some practice identifying real numbers, you can compare them. You have used number lines to compare numbers before. They can be extremely helpful in comparing the values of different numbers, including irrational numbers. The best strategy is to convert each individual value to a decimal. In the case of irrational numbers, you will have to round them to a reasonable place value. Once the numbers are decimals, you can easily compare them on a number line. Remember when you find the solutions to these types of problems that after you order the values, you should convert them back into their original form. Place the following values on a number line: First find the decimal values of each number. The number -3.2 is already a decimal. Then you can place these values on a number line. This may seem tricky, but if you think about the approximate decimal value of each number then it becomes easier. Classify each real number. Solution: Irrational number Solution: Rational number Solution: Integer and rational number Now let's go back to the dilemma from the beginning of the Concept. First, let’s take the measurement for the diameter and figure out the measurement of the radius. The radius is one-half of the diameter. Now we can substitute this into the formula and solve. We can use 3.14 as an approximation for - Whole Numbers - the set of positive counting numbers. - the set of whole numbers and their opposites. - Rational Numbers - any number that can be written in fraction form including terminating and repeating decimals. - Irrational Numbers - any number that cannot be written in fraction form. These are numbers that do not have an end point or repetition when written in decimal form – the decimal values continue indefinitely. π, the ratio of the diameter to the circumference of a circle. We use 3.14 to approximate this irrational number. - Real Numbers - the set of rational and irrational numbers make up the set of real numbers. Here is one for you to try on your own. Because the number is written as a fraction, we know it is a rational number. Directions: Classify each of the following numbers as real, whole, integer, rational or irrational. Some numbers will have more than one classification. Directions: Answer each question as true or false. - An irrational number can also be a real number. - An irrational number is a real number and an integer. - A whole number is also an integer. - A decimal is considered a real number and a rational number. - A negative decimal can still be considered an integer. - An irrational number is a terminating decimal. - A radical is always an irrational number. - Negative whole numbers are integers and are also rational numbers. - Pi is an example of an irrational number. - A repeating decimal is also a rational number.
Exchange Rates - An Introduction - GCSE, AS, A-Level, IB - AQA, Edexcel, OCR, IB, Eduqas, WJEC Last updated 22 Nov 2021 An exchange rate is the price of one currency in terms of another – in other words, the purchasing power of one currency against another. The exchange rate is one of the most important prices in any economy An exchange rate is the price of one currency in terms of another – in other words, the purchasing power of one currency against another. Exchange rates are traded in the global currency market. Key concept – external purchasing power of one currency against another Over six trillion US$s worth of currencies are traded across global FX markets every day What is a currency depreciation? A currency depreciation happens inside a floating exchange rate system and means that one currency (the £) buys less of another currency (the US dollar or the Euro). As an example, the pound falls from £1 buys Euro 1.30 to £1 buys Euro 1.10. What is a currency appreciation? A currency appreciation happens within a floating exchange rate system. Currency appreciation is an increase in the external value of one currency in relation to another currency. What are foreign currency reserves? Foreign exchange reserves are cash and other reserve assets such as gold held by a central bank that are available to balance payments of the country, influence (managed) the foreign exchange rate of its currency, and to maintain confidence in financial markets. What are the main types of exchange rate (currency) systems? - Free floating currency - Managed floating exchange rate - Semi-fixed currency (crawling peg) - Fully-fixed exchange rate (hard peg) - Currency board system (hard peg) Make sure you have at least one example of a country for each currency system
\|Division of New France\| Acadia (French: Acadie) was a colony of New France in northeastern North America that included parts of eastern Quebec, the Maritime provinces, and modern-day Maine to the Kennebec River. During much of the 17th and early 18th centuries, Norridgewock on the Kennebec River and Castine at the end of the Penobscot River were the southern-most settlements of Acadia. The actual specification by the French government for the territory refers to lands bordering the Atlantic coast, roughly between the 40th and 46th parallels. Later, the territory was divided into the British colonies which became Canadian provinces and American states. The population of Acadia included members of the Wabanaki Confederacy and descendants of emigrants from France (i.e., Acadians). The two communities inter-married, which resulted in a significant portion of the population of Acadia being Métis. The first capital of Acadia, established in 1605, was Port-Royal. A British force from Virginia attacked and burned down the town in 1613 but it was later rebuilt nearby, where it remained the longest serving capital of French Acadia until the British conquest of Acadia in 1710. Over seventy-four years there were six colonial wars, in which English and later British interests tried to capture Acadia starting with King William's War in 1689. During these wars, along with some French troops from Quebec, some Acadians, the Wabanaki Confederacy, and French priests continuously raided New England settlements along the border in Maine. While Acadia was officially conquered in 1710 during Queen Anne's War, present-day New Brunswick and much of Maine remained contested territory. Present-day Prince Edward Island (Île Saint-Jean) and Cape Breton (Île Royale) as agreed under Article XIII of the Treaty of Utrecht remained under French control. By militarily defeating the Wabanaki Confederacy and the French priests, present-day Maine fell during Father Rale's War. During King George's War, France and New France made significant attempts to regain mainland Nova Scotia. After Father Le Loutre's War, present-day New Brunswick fell to the British. Finally, during the French and Indian War (the North American theatre of the Seven Years' War), both Île Royale and Île Saint-Jean fell to the British in 1758. Today, Acadia is used to refer to regions of North America that are historically associated with the lands, descendants, and/or culture of the former French region. It particularly refers to regions of The Maritimes with French roots, language, and culture, primarily in New Brunswick, Nova Scotia, the Magdalen Islands and Prince Edward Island, as well as in Maine. It can also be used to refer to the Acadian diaspora in southern Louisiana, a region also referred to as Acadiana. In the abstract, Acadia refers to the existence of a French culture in any of these regions. - 1 Etymology - 2 17th century - 3 18th century - 4 Notable military figures of Acadia - 5 Government - 6 Demographics - 7 Economy - 8 See also - 9 References - 10 Further reading - 11 External links The origin of the designation Acadia is credited to the explorer Giovanni da Verrazzano, who on his 16th century map applied the ancient Greek name "Arcadia" to the entire Atlantic coast north of Virginia (note the inclusion of the 'r' of the original Greek name). "Arcadia" derives from the Arcadia district in Greece which since Classical antiquity had the extended meanings of "refuge" or "idyllic place". The Dictionary of Canadian Biography says: "Arcadia, the name Verrazzano gave to Maryland or Virginia 'on account of the beauty of the trees,' made its first cartographical appearance in the 1548 Gastaldo map and is the only name on that map to survive in Canadian usage." In 1603 a British colony south of the St. Lawrence between the 40th and 46th parallels was agreed by Henry IV who recognised the territory as "La Cadie". Also in the 17th century Champlain fixed its present orthography with the 'r' omitted. William Francis Ganong, a cartographer, has shown its gradual progress northeastwards, in a succession of maps, to its resting place in the Atlantic Provinces of Canada. Another interesting note is the similarity in the pronunciation of Acadie and the Míkmawísimk suffix -akadie, which means "a place of abundance." The modern usage is still seen in place names such as Shunacadie (meaning: place of abundant cranberries) or Shubenacadie (meaning: place of abundant wild potatoes). It is thought that intercultural conversation between early French traders and Mi'kmaq hunters may have resulted in the name l'Arcadie being changed to l'Acadie. The history of Acadia was significantly influenced by the warfare that took place on its soil during the 17th and 18th century. Prior to that time period, the Mi’kmaq lived in Acadia for centuries. The French arrived in 1604, and Catholic Mi’kmaq and Acadians were the predominant populations in the colony for the next 150 years. Early European colonists, who would later become known as Acadians, were French subjects primarily from the Pleumartin to Poitiers in the Vienne département of west-central France. The first French settlement was established by Pierre Dugua Des Monts, Governor of Acadia, under the authority of King Henry IV, on Saint Croix Island in 1604. The following year, the settlement was moved across the Bay of Fundy to Port Royal after a difficult winter on the island and deaths from scurvy. In 1607 the colony received bad news: King Henry had revoked Sieur de Monts' royal fur monopoly, citing that the income was insufficient to justify supplying the colony further. Thus recalled, the last of the Acadians left Port Royal in August 1607. Their allies, the native Mi'kmaq nation, kept careful watch over their possessions, though. When the former Lieutenant Governor, Jean de Biencourt de Poutrincourt et de Saint-Just, returned in 1610, he found Port Royal just as it was left. Acadian Civil War A number of years later, Acadia was plunged into what some historians have described as a civil war between 1640 – 1645. The war was between Port Royal, where Governor of Acadia Charles de Menou d'Aulnay de Charnisay was stationed, and present-day Saint John, New Brunswick, where Governor of Acadia Charles de Saint-Étienne de la Tour was stationed. In the war, there were four major battles. D'Aulnay ultimately won the war against La Tour. During the first 80 years the French and Acadians were in Acadia, there were ten significant battles as the English, Scottish, Dutch and French fought for possession of the colony. These battles happened at Port Royal, Saint John, Cap de Sable (present-day Port La Tour, Nova Scotia), Jemseg, Castine and Baleine. During the next seventy four years, there were six colonial wars that took place in Nova Scotia and Acadia (see the French and Indian Wars as well as Father Rale's War and Father Le Loutre's War). These wars were fought between New England and New France and their respective native allies before the British defeated the French in North America (1763). After the British Conquest of Acadia in 1710, mainland Nova Scotia was under the control of British colonial government, but both present-day New Brunswick and virtually all of present-day Maine remained contested territory between New England and New France. The war was fought on two fronts: the southern border of Acadia, which New France defined as the Kennebec River in southern Maine. The other front was in Nova Scotia and involved preventing the British from taking the capital of Acadia, Port Royal (See Queen Anne's War), establishing themselves at Canso (See Father Rale's War) and founding Halifax (see Father Le Loutre's War). In response to King Philip's War in New England, the native peoples in Acadia joined the Wabanaki Confederacy to form a political and military alliance with New France. The Confederacy remained significant military allies to New France through six wars. Until the final war – the French and Indian War- the Wabanaki Confederacy remained the dominant military force in the region. There were tensions on the border between New England and Acadia, which New France defined as the Kennebec River in southern Maine. English settlers from Massachusetts (whose charter included the Maine area) had expanded their settlements into Acadia. To secure New France's claim to Acadia, it established Catholic missions (churches) among the four largest native villages in the region: one on the Kennebec River (Norridgewock); one further north on the Penobscot River (Penobscot), one on the St. John River (Medoctec). and one at Shubenacadie (Saint Anne's Mission). King William's War During King William's War, some Acadians, the Wabanaki Confederacy and the French Priests participated in defending Acadia at its border with New England, which New France defined as the Kennebec River in southern Maine. Toward this end, the members of the Wabanaki Confederacy on the Saint John River and other places, joined the New France expedition against present-day Bristol, Maine (the Siege of Pemaquid (1689)), Salmon Falls and present-day Portland, Maine. In response, the New Englanders retaliated by attacking Port Royal and present-day Guysborough. In 1694, the Wabanaki Confederacy participated in the Raid on Oyster River at present-day Durham, New Hampshire. Two years later, New France, led by Pierre Le Moyne d'Iberville, returned and fought a naval battle in the Bay of Fundy before moving on to raid Bristol, Maine again. At the end of the war England returned the territory to France in the Treaty of Ryswick and the borders of Acadia remained the same. Queen Anne's War During Queen Anne's War, some Acadians, the Wabanaki Confederacy and the French Priests participated again in defending Acadia at its border against New England. They made numerous raids on New England settlements along the border in the Northeast Coast Campaign and the famous Raid on Deerfield. In retaliation, Major Benjamin Church went on his fifth and final expedition to Acadia. He raided present-day Castine, Maine and then continued on by conducting raids against Grand Pre, Pisiquid and Chignecto. A few years later, defeated in the Siege of Pemaquid (1696), Captain March made an unsuccessful siege on the Capital of Acadia, Port Royal (1707). British forces were successful with the Siege of Port Royal (1710), while the Wabanaki Conferacy were successful in the nearby Battle of Bloody Creek in 1711 and continued raids along the Maine frontier. During Queen Anne's War, the Conquest of Acadia (1710) was confirmed by the Treaty of Utrecht of 1713. Acadia was defined as mainland-Nova Scotia by the French. Present-day New Brunswick and most of Maine remained contested territory, while the British conceded present-day Prince Edward Island and Cape Breton Island, which France quickly renamed Île St Jean and Île Royale respectively. On the latter island, the French established a fortress at Louisbourg to guard the sea approaches to Quebec. On June 23, 1713, the French residents of Nova Scotia were given one year to declare allegiance to Britain or leave the region. In the meantime, the French signalled their preparedness for future hostilities by beginning the construction of Fortress Louisbourg on Île Royale, now Cape Breton Island. The British grew increasingly alarmed by the prospect of disloyalty in wartime of the Acadians now under their rule. French missionaries worked to maintain the loyalty of Acadians, and to maintain a hold on the mainland part of Acadia. Despite the British conquest in 1710, Nova Scotia and Acadia remained primarily occupied by Catholic Acadians and Mi'kmaq. Father Rale's War During the escalation that preceded Father Rale's War (1722–1725), some Acadians, the Wabanaki Confederacy and the French priests participated again in defending Acadia at its border against New England. Present-day New Brunswick and most of Maine remained contested territory between New England and Acadia. Mi'kmaq raided the new fort at Canso, Nova Scotia (1720). The Confederacy made numerous raids on New England settlements along the border into New England. Towards the end of January 1722, Governor Samuel Shute chose to launch a punitive expedition against Sébastien Rale, a Jesuit missionary, at Norridgewock. This breach of the border of Acadia drew all of the tribes of the Wabanaki Confederacy into the conflict. Under potential siege by the Confederacy, in May 1722, Lieutenant Governor John Doucett took 22 Mi'kmaq hostage at Annapolis Royal to prevent the capital from being attacked. In July 1722 the Abenaki and Mi'kmaq created a blockade of Annapolis Royal, with the intent of starving the capital. The natives captured 18 fishing vessels and prisoners from present-day Yarmouth to Canso. They also seized prisoners and vessels from the Bay of Fundy. As a result of the escalating conflict, Massachusetts Governor Samuel Shute officially declared war on July 22, 1722. The first battle of Father Rale's War happened in the Nova Scotia theatre. In response to the blockade of Annapolis Royal, at the end of July 1722, New England launched a campaign to end the blockade and retrieve over 86 New England prisoners taken by the natives. One of these operations resulted in the Battle at Jeddore. The next was a raid on Canso in 1723. Then in July 1724 when a group of sixty Mikmaq and Maliseets raided Annapolis Royal. As a result of Father Rale's War, present-day central Maine fell to the New Englanders with the defeat of Sébastien Rale at Norridgewock and the subsequent retreat of the native population from the Kennebec and Penobscot rivers. King George's War King George's War began when the war declarations from Europe reached the French fortress at Louisbourg first, on May 3, 1744, and the forces there wasted little time in beginning hostilities. Concerned about their overland supply lines to Quebec, they first raided the British fishing port of Canso on May 23, and then organized an attack on Annapolis Royal, then the capital of Nova Scotia. However, French forces were delayed in departing Louisbourg, and their Mi'kmaq and Maliseet allies decided to attack on their own in early July. Annapolis had received news of the war declaration, and was somewhat prepared when the Indians began besieging Fort Anne. Lacking heavy weapons, the Indians withdrew after a few days. Then, in mid-August, a larger French force arrived before Fort Anne, but was also unable to mount an effective attack or siege against the garrison, which had received supplies and reinforcements from Massachusetts. In 1745, British colonial forces conducted the Siege of Port Toulouse (St. Peter's) and then captured Fortress Louisbourg after a siege of six weeks. France launched a major expedition to recover Acadia in 1746. Beset by storms, disease, and finally the death of its commander, the Duc d'Anville, it returned to France in tatters without reaching its objective. French officer Jean-Baptiste Nicolas Roch de Ramezay also arrived from Quebec and conducted the Battle at Port-la-Joye on Île Saint-Jean and the Battle of Grand Pré. Father Le Loutre's War (1749–1755) Despite the British conquest of Acadia in 1710, Nova Scotia remained primarily occupied by Catholic Acadians and Mi'kmaq. Present-day New Brunswick remained contested territory between New England and Acadia. To prevent the establishment of Protestant settlements in the region, Mi'kmaq raided the early British settlements of present-day Shelburne (1715) and Canso (1720). A generation later, Father Le Loutre's War began when Edward Cornwallis arrived to establish Halifax with 13 transports on June 21, 1749. By unilaterally establishing Halifax the British violated treaties of 1726 with the Mi'kmaq which they had signed after Father Rale's War ended in 1725. The British quickly began to build other settlements. To guard against Mi'kmaq, Acadian and French attacks on the new Protestant settlements, they erected fortifications in Halifax (Citadel Hill) (1749), Dartmouth (1750), Bedford (Fort Sackville) (1751), Lunenburg (1753) and Lawrencetown (1754). There were numerous Mi'kmaq and Acadian raids on these villages such as the Raid on Dartmouth (1751). Within 18 months of establishing Halifax, the British also took firm control of peninsular Nova Scotia by building fortifications in all the major Acadian communities: present-day Windsor (Fort Edward, 1750); Grand Pre (Fort Vieux Logis, 1749) and Chignecto (Fort Lawrence, 1750). (A British fort already existed at the other major Acadian centre of Annapolis Royal, Nova Scotia. Cobequid remained without a fort.) Numerous Mi'kmaq and Acadian raids took place against these fortifications, such as the Siege of Grand Pre (1749). Expulsion of the Acadians In the years after the British conquest, the Acadians refused to swear unconditional oaths of allegiance to the British crown. During this time period some Acadians participated in militia operations against the British and maintained vital supply lines to Fortress Louisbourg and Fort Beausejour. During the French and Indian War, the British sought to neutralize any military threat Acadians posed and to interrupt the vital supply lines Acadians provided to Louisbourg by deporting them. This process began in 1755, after the British captured Fort Beauséjour and began the expulsion of the Acadians with the Bay of Fundy Campaign. Between six and seven thousand Acadians were expelled from Nova Scotia to the lower British American colonies. Some Acadians eluded capture by fleeing deep into the wilderness or into French-controlled Canada. The Quebec town of L'Acadie (now a sector of Saint-Jean-sur-Richelieu) was founded by expelled Acadians. After the Siege of Louisbourg (1758), a second wave of the expulsion began with the St. John River Campaign, Petitcodiac River Campaign, Gulf of St. Lawrence Campaign and the Île Saint-Jean Campaign. Any pretense that France might maintain or regain control over the remnants of Acadia came to an end with the fall of Montreal in 1760 and the 1763 Treaty of Paris, which permanently ceded almost all of eastern New France to Britain. After 1764, many exiled Acadians finally settled in Louisiana, which had been transferred by France to Spain at the end of the French and Indian War. The name Acadian was corrupted to Cajun, which was first used as a pejorative term until its later mainstream acceptance. Britain eventually moderated its policies and allowed Acadians to return to Nova Scotia. Notable military figures of Acadia The following list includes those who were born in Acadia or those who became naturalized citizens prior to fall of the French in the region in 1763. Those who came for brief periods from other countries are not included (e.g. John Gorham, Edward Cornwallis, James Wolfe, Boishébert, etc.). Charles de Menou d'Aulnay – Civil War in Acadia Françoise-Marie Jacquelin – Civil War in Acadia Daniel d'Auger de Subercase, last governor of Acadia 1706–1710 - Charles de Saint-Étienne de la Tour – Civil War in Acadia - Chief Madockawando – King William's War - John Gyles – King William's War - Father Louis-Pierre Thury– King William's War - Pierre Maisonnat dit Baptiste – Queen Anne's War - Charles Morris (jurist) – King George's War - Pierre Maillard – Father Le Loutre's War - Joseph-Nicolas Gautier – Father Le Loutre's War - Pierre II Surette – French and Indian War Acadia was located in territory disputed between France and Great Britain. England controlled the area from 1621 to 1632 (see William Alexander, 1st Earl of Stirling) and again from 1654 until 1670 (see William Crowne and Thomas Temple), with control permanently regained by its successor state, the Kingdom of Great Britain, in 1710 (ceded under the Treaty of Utrecht in 1713). Although France controlled the territory in the remaining periods, French monarchs consistently neglected Acadia. Civil government under the French regime was held by a series of Governors (see List of governors of Acadia). The government of New France was located in Quebec, but it had only nominal authority over the Acadians. The Acadians implemented village self-rule. Even after Canada had given up its elected spokesmen, the Acadians continued to demand a say in their own government, as late as 1706 petitioning the monarchy to allow them to elect spokesmen each year by a plurality of voices. In a sign of his indifference to the colony, Louis XV agreed to their demand. This representative assembly was a direct offshoot of a government system that developed out of the seigneurial and church parish imported from the Old World. The seigneurial system was a "set of legal regimes and practices pertaining to local landholding, politics, economics, and jurisprudence." It should be noted that many of the French Governors of Acadia prior to Hector d'Andigné de Grandfontaine held seigneuries in Acadia. As Seigneur, in addition to the power held as Governor, they held the right to grant land, collect their seigneurial rents, and act in judgement over disputes within their domain. After Acadia came under direct Royal rule under Grandfontaine the Seigneurs continued to fulfill governance roles. The Acadian seignuerial system came to an end when the British Crown bought the seigneurial rights in the 1730s. The Catholic parish system along with the accompanying parish priest also aided in the development Acadian self-government. Priests, given their respected position, often assisted the community in representation with the civil government located at Port Royal/Annapolis Royal. Within each parish the Acadians used the elected “marguilliers” (wardens) of the “conseil de fabrique” to administer more than just the churches' affairs in the Parishes. The Acadians extended this system to see to the administrative needs of the community in general. The Acadians protected this structure from the priests and were “No mere subordinates to clerical authority, wardens were “always suspicious of any interference by the priests” in the life of the rural parish, an institution which was, ..., largely a creation of the inhabitants.” During the British regime many of the Deputies were drawn from this marguillier group. The Acadians occupied a borderland region of the British and French empires. As such the Acadian homeland was subjected to the ravages of war on numerous occasions. Through experience the Acadians learned to distrust imperial authorities (British and French). This is evidenced in a small way when Acadians were uncooperative with census takers. Administrators complained of constant in-fighting among the population, which filed many petty civil suits with colonial magistrates. Most of these were over boundary lines, as the Acadians were very quick to protect their new lands. Governance under the British after 1710 After 1710, the British military administration continued to utilize the deputy system the Acadians had developed under French colonial rule. Prior to 1732 the deputies were appointed by the governor from men in the districts of Acadian families "as ancientest and most considerable in Lands & possessions,". This appears to be in contravention of various British penal laws which made it nearly impossible for Roman Catholics and Protestant recusants to hold military and government positions. The need for effective administration and communication in many of the British colonies trumped the laws. In 1732 the governance institution was formalized. Under the formalized system the colony was divided into eight districts. Annually on October 11 free elections were to take place where each district, depending on its size, was to elect two, three, or four deputies. In observance of the Lord's Day, if October 11 fell on a Sunday the elections were to take place on the immediately following Monday. Notice of the annual election was to be given in all districts thirty days before the election date. Immediately following election, deputies, both outgoing and incoming, were to report to Annapolis Royal to receive the governor's approval and instructions. Prior to 1732 deputies had complained about the time and expense of holding office and carrying out their duties. Under the new elected deputy system each district was to provide for the expenses of their elected deputies. The duties of the deputies were broad and included reporting to the government in council the affairs of the districts, distribution of government proclamations, assistance in the settlement of various local disputes (primarily related to land), and ensuring that various weights and measures used in trade were "Conformable to the Standard". In addition to deputies, several other public positions existed. Each district had a clerk who worked closely with the deputies and under his duties recorded the records and orders of government, deeds and conveyances, and kept other public records. With the rapid expansion of the Acadian populace, there was also a growing number of cattle and sheep. The burgeoning herds and flocks, often free-ranging, necessitated the creation of the position of Overseer of Flocks. These individuals controlled where the flocks grazed, settled disputes and recorded the names of individuals slaughtering animals to ensure proper ownership. Skins and hides were inspected for brands. After the purchase by the British Crown of the seigniorial rights in Acadia, various rents and fees were due to the Crown. In the Minas, Piziquid and Cobequid Districts the seigniorial fees were collected by the "Collector & Receiver of All His Majesty's Quit Rents, Dues, or Revenues". The Collector was to keep a record of all rents and other fees collected, submit the rents to Annapolis Royal, and retain fifteen percent to cover his expenses. After a 1692 visit, Antoine Laumet de La Mothe, sieur de Cadillac, described the Acadian men as "'well-built, of good height, and they would be accepted without difficulty as soldiers in a guards' regiment. [They are] well-proportioned and their hair is usually blond. [They are] robust, and will endure great fatigue; [they] are fine subjects of the king, passionately loving the French of Europe'". It is interesting to note that Charles Morris describes the Acadians as being "...tall and well proportioned, they delight much in wearing long hair, they are of dark complexion, in general, and somewhat of the mixture of Indians; but there are some of a light complexion. They retain the language and customs of their neighbours the French, with a mixed affectation of the native Indians, and imitate them in their haunting and wild tones in their merriment; they are naturally full cheer and merry, subtle, speak and promise fair..." Most Acadians were illiterate, and many of the records, including notarial deeds, were destroyed or scattered during the Great Expulsion. For a time, Port Royal did have schools, but these were closed when the British excluded Roman Catholic religious orders from operating in Acadia. Despite their nominal faith, Acadians often worked on Sundays and religious holidays. Before 1654, trading companies and patent holders concerned with fishing recruited men in France to come to Acadia to work at the commercial outposts. The original Acadian population was a small number of indentured servants and soldiers brought by the fur-trading companies. Gradually, fishermen began settling in the area as well, rather than return to France with the seasonal fishing fleet. The majority of the recruiting took place at La Rochelle. Between 1653 and 1654, 104 men were recruited at La Rochelle. Of these, 31% were builders, 15% were soldiers and sailors, 8% were food preparers, 6.7% were farm workers, and an additional 6.7% worked in the clothing trades. Fifty-five percent of Acadia's first families came from western and west-central France, primarily from Poitou, Aunis, Angoumois, and Saintonge. Over 85% of these (47% of the total), were former residents of the La Chaussée area of Poitou. Many of the families who arrived in 1632 with Razilly shared some blood ties; those not related by blood shared cultural ties with the others. The number of original immigrants was very small, and only about 100 surnames existed within the Acadian community. Although the majority of Acadian settlers came from France there were also members of the populace from Ireland, Spain (both Spanish and Basque), Portugal, England, Scotland, Belgium (Flemish), Channel Islands, and Croatia. Some of the earliest settlers married women of the local Mi'kmaq tribe who had converted to Roman Catholicism. A Parisian lawyer, Marc Lescarbot, who spent just over a year in Acadia, arriving in May 1606, described the Micmac as having "courage, fidelity, generosity, and humanity, and their hospitality is so innate and praiseworthy that they receive among them every man who is not an enemy. They are not simpletons. ... So that if we commonly call them Savages, the word is abusive and unmerited." Most of the immigrants to Acadia were peasants in Europe, making them social equals in the New World. The colony had limited economic support or cultural contacts with France, leaving a "social vacuum" that allowed "individual talents and industry ... [to supplant] inherited social position as the measure of a man's worth." Acadians lived as social equals, with the elderly and priests considered slightly superior. Unlike the French colonists in Canada and the early English colonies in Plymouth and Jamestown, Acadians maintained an extended kinship system, and the large extended families assisted in building homes and barns, as well as cultivating and harvesting crops. They also relied on interfamily cooperation to accomplish community goals, such as building dikes to reclaim tidal marshes. Marriages were generally not love matches but were arranged for economic or social reasons. Parental consent was required for anyone under 25 who wished to marry, and both the mother's and father's consent was recorded in the marriage deed. Divorce was not permitted in New France, and annulments were almost impossible to get. Legal separation was offered as an option but was seldom used. The Acadians were suspicious of outsiders and on occasion did not readily cooperate with census takers. The first reliable population figures for the area came with the census of 1671, which noted fewer than 450 people. By 1714, the Acadian population had expanded to 2,528 individuals, mostly from natural increase rather than immigration. Most Acadian women in the 18th century gave birth to living children an average of eleven times. Although these numbers are identical to those in Canada, 75% of Acadian children reached adulthood, many more than in other parts of New France. The isolation of the Acadian communities meant the people were not exposed to many of the imported epidemics, allowing the children to remain healthier. In the 18th century, some Acadians migrated to nearby Île Saint-Jean (now Prince Edward Island) to take advantage of the fertile cropland. In 1732, the island had 347 settlers but within 25 years its population had expanded to 5000 Europeans. The bulk of this population explosion on Île Saint-Jean took place in the early 1750s and has as its source Acadians removing themselves during the rising tensions on peninsular Nova Scotia after the settlement of Halifax in 1749. Le Loutre played a role in these removals through acts of encouragement and threats. The exodus to Île Saint-Jean became a flood with refugees fleeing British held territory after the initial expulsions of 1755. In 1714, a few Acadian families emigrated to Île Royale. These families had little property. But for the majority of Acadians, they could not be enticed by the French government to abandon their heritage and the land of their forefathers for an area which was unknown and uncultivated. Most Acadian households were self-sufficient, with families engaged in subsistence farming only for a few years while they established their farms. Very rapidly the Acadians established productive farms that yielded surplus crops that allowed them to trade with both Boston and Louisbourg. Farms tended to remain small plots of land worked by individual families rather than slave labor. The highly productive dyked marshlands and cleared uplands produced an abundance of fodder that supported significant production of cows, sheep and pigs. Farmers grew various grains: wheat, oats, barley, hops and rye; vegetables: peas, cabbage, turnips, onions, carrots, chives, shallots, asparagus, parsnips and beets; fruit: apples, pears, cherries, plums, raspberry and white strawberry. In addition they grew crops of hemp and flax for the production of cloth, rope, etc. From the rivers, estuaries and seas they harvested shad, smelts, gaspereau, cod, salmon, bass, etc., utilizing fish traps in the rivers, weirs in the inter-tidal zone and from the sea with lines and nets from their boats. The fishery was pursued on a commercial basis as in 1715 at the Minas Basin settlements, when the Acadian population there numbered only in the hundreds, they had “between 30 - 40 sail of vessels, built by themselves, which they employ in fishing” reported Lieutenant-Governor Thomas Caulfield to the Board of Trade. Charles Morris observed the Acadians at Minas hunting beluga whales. The Acadians also varied their diets by hunting for moose, hare, ducks and geese, and pigeon. After 1630, the Acadians began to build dikes and drain the sea marsh above Port Royal. The high salinity of the reclaimed coastal marshland meant that the land would need to sit for three years after it was drained before it could be cultivated. The land reclamation techniques that were used closely resembled the enclosures near La Rochelle that helped make solar salt. As time progressed, the Acadian agriculture improved, and Acadians traded with the British colonies in New England to gain ironware, fine cloth, rum, and salt. During the French administration of Acadia, this trade was illegal, but it did not stop some English traders from establishing small stores in Port Royal. Under English rule, the Acadians traded with New England and often smuggled their excess food to Boston merchants waiting at Baie Verte for transshipment to the French at Louisbourg on Cape Breton Island. Many adult sons who did not inherit land from their parents settled on adjacent vacant lands to remain close to their families. As the Acadian population expanded and available land became limited around Port Royal, new settlements took root to the northeast, in the Upper Bay of Fundy, including Mines, Pisiquid, and Beaubassin. Many of the pioneers into that area persuaded some of their relatives to accompany them, and most of the frontier settlements contained only five to ten interrelated family units. - Acadian French - Former colonies and territories in Canada - List of Acadians - List of governors of Acadia - Military history of Nova Scotia - Military history of the Acadians - William Williamson. The history of the state of Maine. Vol. 2. 1832. p. 27; p. 266 (La Corne declares such to Lawrence in 1750); p. 293 - Griffiths, E. From Migrant to Acadian. McGill-Queen's University Press. 2005. p.61; John Ried. International Region of the Northeast. In Buckner, Campbell, and Frank (eds). The Acadiensis Reader: Volume One: Atlantic Canada Before Confederation. 1998. p. 40; Villebon, p. 121 - For the 144 years prior to the founding of Halifax (1749), Port Royal/ Annapolis Royal was the capital of Acadia 112 of those years (78% of the time). The other locations that served as the Capital of Acadia are: LaHave, Nova Scotia (1632–1636 ); present day Castine, Maine (1670–1674); Beaubassin (1678–1684); Jemseg, New Brunswick(1690–1691); present day Fredericton, New Brunswick (1691–1694), and present day Saint John, New Brunswick (1695–1699). (See Brenda Dunn. Port Royal/ Annapolis Royal. 2004. Nimbus Publishing) - Chalmers, George. A collection of treaties between Great Britain and other powers. 1985. http://www.heraldica.org/topics/france/utrecht1a.pdf - Beaujot 1998, p. 79 - Lescarbot, Marc (1928). Nova Francia, A Description of Arcadia, 1606. p. 1. - Faragher, John Mack (2006-02-17). A Great and Noble Scheme: The Tragic Story of the Expulsion of the French Acadians from their American Homeland (Kindle Edition Location 176-181). - Reid, John G. (1998), "An International Region of the Northeast: Rise and Decline, 1635–1762", in Buckner; Campbell; Frank, The Acadiensis Reader: Volume 1 (third ed.), p. 31 - Faragher, John Mack (2005). A Great and Noble Scheme. W.W. Norton & Co., New York. pp. 17–19. ISBN 0-393-05135-8 - M. A. MacDonald, Fortune & La Tour: The civil war in Acadia, Toronto: Methuen. 1983 - Until 1784, New Brunswick was considered part of Nova Scotia. - William Williamson 1832. p. 27 - "Wabanaki". Wabanaki. August 21, 2012. Retrieved 2012-09-10. - William Williamson. The history of the state of Maine. Vol. 2. 1832. p. 27; Griffiths, E. From Migrant to Acadian. McGill-Queen's University Press. 2005. p.61; Campbell, Gary. The Road to Canada: The Grand Communications Route from Saint John to Quebec. Goose Lane Editions and The New Brunswick Heritage Military Project. 2005. p. 21. - "Meductic Indian Village / Fort Meductic National Historic Site of Canada". Parks Canada. Retrieved December 20, 2011. - John Grenier, The Far Reaches of Empire. University of Oklahoma Press, 2008, p. 51, p. 54. - "Mission Sainte-Anne; Shubenacadie, Nova Scotia". Northeastarch.com. Retrieved 2012-09-15. - "Drake. The Border Wars of New England. pp. 264–266". Archive.org. Retrieved 2012-09-10. - "Rale, Sébastien". Dictionary of Canadian Biography Online. Biographi.ca. October 18, 2007. Retrieved 2012-09-10. - Grenier, p. 56 - Beamish Murdoch. History of Nova Scotia or Acadia, p. 399 - A history of Nova-Scotia, or Acadie, Volume 1, by Beamish Murdoch, p. 398 - The Nova Scotia theatre of the Dummer War is named the "Mi'kmaq-Maliseet War" by John Grenier. The Far Reaches of Empire: War in Nova Scotia 1710–1760. University of Oklahoma Press. 2008. - Beamish Murdoch. A history of Nova-Scotia, or Acadie, Volume 1, p. 399; Geoffery Plank, An Unsettled Conquest, p. 78 - Benjamin Church, p. 289; John Grenier, p. 62 - Faragher, John Mack, A Great and Noble Scheme New York; W. W. Norton & Company, 2005. pp. 164–165; Brenda Dunn, p. 123 - The framework Father Le Loutre's War is developed by John Grenier in his books The Far Reaches of Empire. War in Nova Scotia, 1710–1760. (University of Oklahoma Press, 2008) and The first way of war: American war making on the frontier, 1607–1814 (Cambridge University Press, 2005). He outlines his rational for naming these conflicts as Father Le Loutre's War; Thomas Beamish Akins. History of Halifax, Brookhouse Press. 1895. (2002 edition). p 7 - Wicken, p. 181; Griffith, p. 390; Also see http://www.northeastarch.com/vieux_logis.html - John Grenier. The Far Reaches of Empire: War in Nova Scotia, 1710–1760. Oklahoma University Press. - John Grenier, Far Reaches of Empire: War in Nova Scotia 1710–1760. Oklahoma University Press. 2008 - Stephen E. Patterson. "Indian-White Relations in Nova Scotia, 1749–61: A Study in Political Interaction." Buckner, P, Campbell, G. and Frank, D. (eds). The Acadiensis Reader Vol 1: Atlantic Canada Before Confederation. 1998. pp.105–106.; Also see Stephen Patterson, Colonial Wars and Aboriginal Peoples, p. 144. - Mouhot, Jean-Francois (2009) Les Réfugiés Acadiens en France (1758–1785): L'Impossible réintégration?, Editions du Septentrion, Québec, 456p. ISBN 2-89448-513-1 - Lacoursière, Jacques (1995). Histoire populaire du Québec, Tome 1, des origines à 1791. Éditions du Septentrion, Québec. p. 270. ISBN 2-89448-050-4; see also John Mack Faragher (2005). A Great and Noble Scheme: The Tragic Story of the Expulsion of the French Acadians from their American Homeland, New York: W.W. Norton, 562 pages ISBN 0-393-05135-8 (online excerpt). - Ville de Saint-Jean-sur-Richelieu history[dead link] - John Grenier. War in Nova Scotia. 2008. - Moogk 2000, p. 7 - Moogk 2000, p. 9 - Moogk 2000, p. 176 - Moogk 2000, p. 175 - Jonathan Fowler. The Neutral Frnech of Mi’kma’ki: An Archaeology of Acadian Identities Prior to 1755. University of Oxford, 2009. - Jonathan Fowler - Brasseaux (1987), p. 8. - MacMechan, Archibald, ed. Nova Scotia Archives II, A Calendar of Two Letter-Books and One Commission-Book in the Possession of the Government of Nova Scotia, 1713–1741. Herald Printing House, Halifax, NS. 1900. p. 59. - McMechan, NS Archives II, p. 190. - McMechan, NS Archives II, p. 248. - Morris, Charles. A Brief Survey of Nova Scotia. Retrieved from the National Archives of Canada. Lent by: The Royal Artillery Regimental Library, Woolwich, UK. - Moogk 2000, p. 174 - Charles Morris. A Brief Survey of Nova Scotia. Lent by: - The Royal Artillery Regimental Library, Woolwich. - Moogk 2000, p. 92 - Stephen White. Patronymes Acadiens/Acadian Family Names. Société du Monument Lefebvre, Moncton, 1992. - Moogk 2000, p. 18 - Blupete http://www.blupete.com/Hist/BiosNS/1600-00/Lescarbot.htm - Brasseaux 1987, p. 3 - Brasseaux 1987, p. 11 - Moogk 2000, p. 270 - Moogk 2000, p. 180 - Moogk 2000, p. 229 - Moogk 2000, p. 219 - Moogk 2000, p. 6 - Bona Arsenault, Histoire des Acadiens, Éditions Leméac, p 114 - Brasseaux 1987, p. 10 - Brasseaux 1987, p. 9 - Jonathan Fowler. The Neutral French of Mi'kma'ki: An Archaeology of Acadian Identities Prior to 1755. University of Oxford, 2009. Note: Dr Fowler's analysis of census records and other primary documents reveal that most farms by 1686 were producing in livestock alone, on a per capita basis, twice as much as was needed for their own consumption. This does not include food crops and the animals harvested from the natural environment. - Moogk 2000, p. 12 - John S. Erskine. The French Period in Nova Scotia. A.D. 1500-1758 And Present Remains a historical, archaeological, and botanical survey. Copyright John Erskine, Wolfville, 1975. - Andrew Hill Clark. Acadian - The Geography of Early Nova Scotia to 1760. The University of Wisconsin Press, 1968. - Jonathan Fowler. The Neutral French of Mi'kma'ki: An Archaeology of Acadian Identities Prior to 1755. University of Oxford, 2009. - N.E.S. Griffiths. From Migrant to Acadian. - A North American Border People 1604-1755. McGill-Queens University Press, 2005. - Archibald MacMechan, Archibald (Ed.) Nova Scotia Archives II, A Calendar of Two Letter-Books and One Commission-Book in the Possession of the Government of Nova Scotia, 1713-1741. Herald Printing House, Halifax, NS. 1900 - Charles Morris. A Brief Survey of Nova Scotia. Lent by – The Royal Artillery Library, Woolwich, UK. - Brasseaux 1987, p. 16 - Moogk 2000, p. 178 - Brasseaux 1987, p. 12 - Beaujot, Roderic (1998), "Demographic Considerations in Canadian Language Policy", in Ricento, Thomas; Burnaby, Barbara, Language and Politics in the United States and Canada: Myths and Realities, Mahwah, NJ: Lawrence Erlbaum Associates, ISBN 0-8058-2838-9 - Brasseaux, Carl A. (1987), The Founding of New Acadia: The Beginnings of Acadian Life in Louisiana, 1765–1803, Baton Rouge, LA: Louisiana State University Press, ISBN 0-8071-1296-8 - Moogk, Peter (2000), La Nouvelle France: The Making of French Canada—A Cultural History, East Lansing, MI: Michigan State University Press, ISBN 0-87013-528-7 - Clark, Andrew Hill (1968), Acadia: The Geography of Early Nova Scotia to 1760, University of Wisconsin Press, ISBN 0-299-05080-7 - Magord, André, The Quest for Autonomy in Acadia (Bruxelles etc., Peter Lang, 2008) (Études Canadiennes – Canadian Studies, 18). - Plank, (2001), An Unsettled Conquest: The British Campaign against the Peoples of Acadia, University of Pennsylvania Press ISBN 0-8122-1869-8 - Dean Jobb, ( 2005) The Acadians: A People's Story of Exile and Triumph. John Wiley & Sons, (published in the United States as The Cajuns: A People's Story of Exile and Triumph) - Philip Henry Smith (1884) Acadia: A lost chapter in American history Oxford University - Acadia : missing links of a lost chapter in American history. Vol 1 (1895) - Acadia : missing links of a lost chapter in American history. Vol 2 (1895) \|Wikisource has the text of the 1911 Encyclopædia Britannica article Acadie.\| \|Wikimedia Commons has media related to Acadia.\| - Acadian Heritage Portal (French) – Acadian history, genealogy and folklore - National Society of Acadia (French) - Acadian Ancestral Home by Lucie LeBlanc Consentino – a repository for Acadian history & genealogy

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