1.
Humor
–
Humour is the tendency of particular cognitive experiences to provoke laughter and provide amusement. The term derives from the medicine of the ancient Greeks. People of all ages and cultures respond to humour, most people are able to experience humour—be amused, smile or laugh at something funny—and thus are considered to have a sense of humour. The hypothetical person lacking a sense of humour would likely find the behaviour inducing it to be inexplicable, strange, for example, young children may favour slapstick such as Punch and Judy puppet shows or the Tom and Jerry cartoons, whose physical nature makes it accessible to them. By contrast, more sophisticated forms of such as satire require an understanding of its social meaning and context. Many theories exist about what humour is and what social function it serves, the benign-violation theory, endorsed by Peter McGraw, attempts to explain humours existence. The theory says humour only occurs when something seems wrong, unsettling, or threatening, Humour can be used as a method to easily engage in social interaction by taking away that awkward, uncomfortable, or uneasy feeling of social interactions. Others believe that the use of humour can facilitate social interactions. Some claim that humour cannot or should not be explained, white once said, Humor can be dissected as a frog can, but the thing dies in the process and the innards are discouraging to any but the pure scientific mind. Counter to this argument, protests against offensive cartoons invite the dissection of humour or its lack by aggrieved individuals and this process of dissecting humour does not necessarily banish a sense of humour but begs attention towards its politics and assumed universality. Arthur Schopenhauer lamented the misuse of humour to mean any type of comedy, however, both humour and comic are often used when theorising about the subject. The connotations of humour as opposed to comic are said to be that of response versus stimulus, additionally, humour was thought to include a combination of ridiculousness and wit in an individual, the paradigmatic case being Shakespeares Sir John Falstaff. The French were slow to adopt the term humour, in French, non-satirical humour can be specifically termed droll humour or recreational drollery. As with any art form, the acceptance of a style or incidence of humour depends on sociological factors. Throughout history, comedy has been used as a form of entertainment all over the world, both a social etiquette and a certain intelligence can be displayed through forms of wit and sarcasm. Eighteenth-century German author Georg Lichtenberg said that the more you know humour, later, in Greek philosophy, Aristotle, in the Poetics, suggested that an ugliness that does not disgust is fundamental to humour. Each rasa was associated with a specific bhavas portrayed on stage, due to cultural differences, they disassociated comedy from Greek dramatic representation, and instead identified it with Arabic poetic themes and forms, such as hija. They viewed comedy as simply the art of reprehension and made no reference to light and cheerful events or troublesome beginnings, after the Latin translations of the 12th century, the term comedy thus gained a new semantic meaning in Medieval literature
2.
Mathematics
–
Mathematics is the study of topics such as quantity, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof, when mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry, rigorous arguments first appeared in Greek mathematics, most notably in Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. Benjamin Peirce called mathematics the science that draws necessary conclusions, David Hilbert said of mathematics, We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times
3.
Stereotype
–
In social psychology, a stereotype is a thought that can be adopted about specific types of individuals or certain ways of doing things. These thoughts or beliefs may or may not accurately reflect reality, however, this is only a fundamental psychological definition of a stereotype. Within psychology and spanning across other disciplines, there are different conceptualizations, some of these definitions share commonalities, though each one may also harbor unique aspects that may contradict the others. The term stereotype derives from the Greek words στερεός, firm, solid and τύπος, impression, the term comes from the printing trade and was first adopted in 1798 by Firmin Didot to describe a printing plate that duplicated any typography. The duplicate printing plate, or the stereotype, is used for printing instead of the original, outside of printing, the first reference to stereotype was in 1850, as a noun that meant image perpetuated without change. However, it was not until 1922 that stereotype was first used in the psychological sense by American journalist Walter Lippmann in his work Public Opinion. Stereotypes, prejudice, and discrimination are understood as related but different concepts, although related, the three concepts can exist independently of each other. Studies of stereotype content examine what people think of others, rather than the reasons, early theories of stereotype content proposed by social psychologists such as Gordon Allport assumed that stereotypes of outgroups reflected uniform antipathy. For instance, Katz and Braly argued in their classic 1933 study that ethnic stereotypes were uniformly negative, by contrast, a newer model of stereotype content theorizes that stereotypes are frequently ambivalent and vary along two dimensions, warmth and competence. Warmth and competence are respectively predicted by lack of competition and status, groups that do not compete with the in-group for the same resources are perceived as warm, whereas high-status groups are considered competent. The groups within each of the four combinations of high and low levels of warmth, the model explains the phenomenon that some out-groups are admired but disliked, whereas others are liked but disrespected. This model was tested on a variety of national and international samples and was found to reliably predict stereotype content. Early studies suggested that stereotypes were only used by rigid, repressed, stereotyping can serve cognitive functions on an interpersonal level, and social functions on an intergroup level. For stereotyping to function on a level, an individual must see themselves as part of a group. Craig McGarty, Russell Spears, and Vincent Y, Yzerbyt argued that the cognitive functions of stereotyping are best understood in relation to its social functions, and vice versa. Stereotypes can help make sense of the world and they are a form of categorization that helps to simplify and systematize information. Thus, information is easily identified, recalled, predicted. Stereotypes are categories of objects or people, between stereotypes, objects or people are as different from each other as possible
4.
Mathematician
–
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, quantity, structure, space, models, one of the earliest known mathematicians was Thales of Miletus, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, the number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was All is number. It was the Pythagoreans who coined the term mathematics, and with whom the study of mathematics for its own sake begins, the first woman mathematician recorded by history was Hypatia of Alexandria. She succeeded her father as Librarian at the Great Library and wrote works on applied mathematics. Because of a dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked. Science and mathematics in the Islamic world during the Middle Ages followed various models and it was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences, an example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics, maths and astronomy of Ibn al-Haytham, the Renaissance brought an increased emphasis on mathematics and science to Europe. As time passed, many gravitated towards universities. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking. ”Thus, seminars, overall, science became the focus of universities in the 19th and 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. ”Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and then proceed to specialize in topics of their own choice at the graduate level. In some universities, a qualifying exam serves to test both the breadth and depth of an understanding of mathematics, the students, who pass, are permitted to work on a doctoral dissertation. Mathematicians involved with solving problems with applications in life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their knowledge and professional methodology. With professional focus on a variety of problems, theoretical systems
5.
Pun
–
The pun, also called paronomasia, is a form of word play that exploits multiple meanings of a term, or of similar-sounding words, for an intended humorous or rhetorical effect. These ambiguities can arise from the use of homophonic, homographic, metonymic. A pun differs from a malapropism in that a malapropism is a variation on a correct expression. Puns may be regarded as in-jokes or idiomatic constructions, as their usage and meaning are specific to a particular language, Puns have a long history in human writing. Sumerian cuneiform and Egyptian hieroglyphs were originally based on punning systems, punning has been credited as the fundamental concept behind alphabets, writing, and even human civilization. Puns can be classified in various ways, including, The homophonic pun, walter Redfern exemplified this type with his statement, To pun is to treat homonyms as synonyms. For example, in George Carlins phrase Atheism is a non-prophet institution, similarly, the joke Question, Why do we still have troops in Germany. A homographic pun exploits words which are spelled the same but possess different meanings, because of their nature, they rely on sight more than hearing, contrary to homophonic puns. They are also known as heteronymic puns, an example that combines homophonic and homographic punning is Douglas Adamss line You can tune a guitar, but you cant tuna fish. Unless of course, you play bass, the phrase uses the homophonic qualities of tune a and tuna, as well as the homographic pun on bass, in which ambiguity is reached through the identical spellings of /ˈbeɪs/, and /ˈbæs/. Homonymic puns, another type, arise from the exploitation of words which are both homographs and homophones. An adaptation of a joke repeated by Isaac Asimov gives us Did you hear about the little moron who strained himself while running into the screen door, playing on strained as to give much effort and to filter. A homonymic pun may also be polysemic, in which the words must be homonymic and also possess related meanings, however, lexicographers define polysemes as listed under a single dictionary lemma while homonyms are treated in separate lemmata. A compound pun is a statement that two or more puns. For example, a statement by Richard Whately includes four puns. Because he can eat the sand which is there, but what brought the sandwiches there. Why, Noah sent Ham, and his descendants mustered and bred and this pun uses sand which is there/sandwiches there, Ham/ham, mustered/mustard, and bred/bread. Similarly, the piano is not my forte links two meanings of the words forte and piano, one for the dynamic markings in music
6.
John Allen Paulos
–
John Allen Paulos is an American professor of mathematics at Temple University in Philadelphia, Pennsylvania. He has gained fame as a writer and speaker on mathematics, Paulos writes about many subjects, especially of the dangers of mathematical innumeracy, that is, the laypersons misconceptions about numbers, probability, and logic. Paulos was born in Denver Colorado and grew up in Chicago, Illinois and Milwaukee, in an interview he described himself as lifelong skeptic. He went to school in Milwaukee, Wisconsin. After his Bachelor of Mathematics at University of Wisconsin and his Master of Science at University of Washington he received his Ph. D. in mathematics from the University of Wisconsin–Madison and he was also part of the Peace Corps in the seventies. His academic work is mainly in logic and probability theory. His book Innumeracy, Mathematical Illiteracy and its Consequences was a bestseller, in his books Paulos discusses innumeracy with quirky anecdotes, scenarios and facts, encouraging readers in the end to look at their world in a more quantitative way. biography in A Numerate Life. Paulos also wrote a column for the UK newspaper The Guardian and is a Committee for Skeptical Inquiry fellow. In 2001 Paulos taught a course on quantitative literacy for journalists at the Columbia University School of Journalism, the course stimulated further programs at Columbia and elsewhere in precision and data-driven journalism. His long-running ABCNews. com monthly column Whos Counting deals with aspects of stories in the news. All the columns over a 10- year period are archived here and he is married and the father of two. Paulos tweets frequently at @JohnAllenPaulos Paulos received the 2013 JPBM Award for Communicating Mathematics on a Sustained Basis to Large Audiences, Paulos received the 2003 AAAS Award for Promoting the Public Understanding of Science and Technology. I Think Therefore I Laugh, The Flip Side of Philosophy, Innumeracy, Mathematical Illiteracy and its Consequences. Beyond Numeracy, Ruminations of a Numbers Man, once Upon a Number, The Hidden Mathematical Logic of Stories. A Mathematician Plays the Stock Market, irreligion, A Mathematician Explains Why the Arguments for God Just Dont Add Up. A Numerate Life - A Mathematician Explores the Vagaries of Life, His Own, statistics, NYT Opinionator piece How Much Oil Is Spilling
7.
New Cuyama, California
–
New Cuyama is a census-designated place in the Cuyama Valley, in Santa Barbara County, California, in the United States. It was named after the Chumash Indian word for clams, most likely due to the millions of petrified prehistoric clamshell fossils that are found in the surrounding areas, the town is home to the majority of the utility infrastructure for its residents, including nearby neighbor Cuyama, California. New Cuyama is located close to the intersection points for Santa Barbara, San Luis Obispo, Ventura. The town is served by Highway 166 and the public-use New Cuyama Airport, the population was 517 at the 2010 census. The area was considered territory of the Yokuts people, but Chumash Indians from the Pacific Coast are also known to have frequented the area, the imprint of an old Indian trail can still be seen leading over the hills of present-day Ventura County to the headwaters of Piru Creek. The name Cuyama comes from an Indian village named for the Chumash word kuyam, the areas recorded history dates to 1822 when Mexico won independence from Spain and took over the Spanish colony of Alta California. Much of the infrastructure from ARCOs settling of the still exists today and is used by town residents. The original ARCO-built gas processing plant is still in use and easily seen due south of New Cuyama, the town of New Cuyama, when founded, was considered the pearl of eastern Santa Barbara County, due to the flow of oil that was coming out of the region. During this time Richfield Oil Company built the town funded schools, now that oil and gas production have declined, the principal industry is once again agriculture. New Cuyama is located at 34°56′53″N 119°41′21″W and it is situated in the Cuyama Valley. According to the United States Census Bureau, the CDP covers an area of 0.7 square miles and this region experiences warm and dry summers, with no average monthly temperatures above 71.6 °F. According to the Köppen Climate Classification system, New Cuyama has a warm-summer Mediterranean climate, the 2010 United States Census reported that New Cuyama had a population of 517. The population density was 732.7 people per square mile, the racial makeup of New Cuyama was 418 White,3 African American,14 Native American,3 Asian,0 Pacific Islander,53 from other races, and 26 from two or more races. Hispanic or Latino of any race were 234 persons, the Census reported that 517 people lived in households,0 lived in non-institutionalized group quarters, and 0 were institutionalized. There were 15 unmarried opposite-sex partnerships, and 1 same-sex married couples or partnerships,45 households were made up of individuals and 20 had someone living alone who was 65 years of age or older. The average household size was 2.92, there were 122 families, the average family size was 3.54. The median age was 35.1 years, for every 100 females there were 105.2 males. For every 100 females age 18 and over, there were 97.2 males, there were 215 housing units at an average density of 304.7 per square mile, of which 119 were owner-occupied, and 58 were occupied by renters
8.
Abelian group
–
That is, these are the groups that obey the axiom of commutativity. Abelian groups generalize the arithmetic of addition of integers and they are named after Niels Henrik Abel. The concept of a group is one of the first concepts encountered in undergraduate abstract algebra, from which many other basic concepts, such as modules. The theory of groups is generally simpler than that of their non-abelian counterparts. On the other hand, the theory of abelian groups is an area of current research. An abelian group is a set, A, together with an operation • that combines any two elements a and b to form another element denoted a • b, the symbol • is a general placeholder for a concretely given operation. Identity element There exists an element e in A, such that for all elements a in A, the equation e • a = a • e = a holds. Inverse element For each a in A, there exists an element b in A such that a • b = b • a = e, commutativity For all a, b in A, a • b = b • a. A group in which the operation is not commutative is called a non-abelian group or non-commutative group. There are two main conventions for abelian groups – additive and multiplicative. Generally, the notation is the usual notation for groups, while the additive notation is the usual notation for modules. To verify that a group is abelian, a table – known as a Cayley table – can be constructed in a similar fashion to a multiplication table. If the group is G = under the operation ⋅, the th entry of this contains the product gi ⋅ gj. The group is abelian if and only if this table is symmetric about the main diagonal and this is true since if the group is abelian, then gi ⋅ gj = gj ⋅ gi. This implies that the th entry of the table equals the th entry, every cyclic group G is abelian, because if x, y are in G, then xy = aman = am + n = an + m = anam = yx. Thus the integers, Z, form a group under addition, as do the integers modulo n. Every ring is a group with respect to its addition operation. In a commutative ring the invertible elements, or units, form an abelian multiplicative group, in particular, the real numbers are an abelian group under addition, and the nonzero real numbers are an abelian group under multiplication
9.
Axiom of choice
–
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty. It states that for every indexed family i ∈ I of nonempty sets there exists an indexed family i ∈ I of elements such that x i ∈ S i for every i ∈ I. The axiom of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the well-ordering theorem. Informally put, the axiom of choice says that any collection of bins, each containing at least one object. One motivation for use is that a number of generally accepted mathematical results, such as Tychonoffs theorem. Contemporary set theorists also study axioms that are not compatible with the axiom of choice, the axiom of choice is avoided in some varieties of constructive mathematics, although there are varieties of constructive mathematics in which the axiom of choice is embraced. A choice function is a function f, defined on a collection X of nonempty sets, each choice function on a collection X of nonempty sets is an element of the Cartesian product of the sets in X. The axiom of choice asserts the existence of elements, it is therefore equivalent to, Given any family of nonempty sets. In this article and other discussions of the Axiom of Choice the following abbreviations are common, ZF – Zermelo–Fraenkel set theory omitting the Axiom of Choice. ZFC – Zermelo–Fraenkel set theory, extended to include the Axiom of Choice, There are many other equivalent statements of the axiom of choice. These are equivalent in the sense that, in the presence of basic axioms of set theory. One variation avoids the use of functions by, in effect. Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains one element in common with each of the sets in X. This guarantees for any partition of a set X the existence of a subset C of X containing exactly one element from each part of the partition. Another equivalent axiom only considers collections X that are essentially powersets of other sets, For any set A, authors who use this formulation often speak of the choice function on A, but be advised that this is a slightly different notion of choice function. With this alternate notion of function, the axiom of choice can be compactly stated as Every set has a choice function. Which is equivalent to For any set A there is a function f such that for any non-empty subset B of A, f lies in B. The negation of the axiom can thus be expressed as, There is a set A such that for all functions f, however, that particular case is a theorem of Zermelo–Fraenkel set theory without the axiom of choice, it is easily proved by mathematical induction
10.
Zorn's lemma
–
Zorns lemma can be stated as, Zorns lemma can be used to show that every nontrivial ring R with unity contains a maximal ideal. In the terminology above, the set P consists of all ideals in R except R itself and this set is partially ordered by set inclusion. Finding a maximal ideal is the same as finding an element in P. The ideal R was excluded because maximal ideals by definition are not equal to R, to apply Zorns lemma, take a chain T in P. If T is the empty set, then the ideal is an upper bound for T in P. Assume then that T is non-empty and it is necessary to show that T has an upper bound, that is, there exists an ideal I ⊆ R which is bigger than all members of T but still smaller than R. Take I to be the union of all the ideals in T and we wish to show that I is an upper bound for T in P. We will first show that I is an ideal of R, since every element of T is contained in I, this will show that I is an upper bound for T in P, as required. Because T contains at least one element, and that element contains at least 0, the union I contains at least 0 and is not empty. To prove that I is an ideal, note if a and b are elements of I. Since T is totally ordered, we know that J ⊆ K or K ⊆ J. In the first case, both a and b are members of the ideal K, therefore their sum a + b is a member of K, in the second case, both a and b are members of the ideal J, and thus a + b ∈ I. Furthermore, if r ∈ R, then ar and ra are elements of J, thus, I is an ideal in R. Now, an ideal is equal to R if and only if it contains 1. So, if I were equal to R, then it would contain 1, the hypothesis of Zorns lemma has been checked, and thus there is a maximal element in P, in other words a maximal ideal in R. Note that the proof depends on the fact that our ring R has a multiplicative unit 1, without this, the proof wouldnt work and indeed the statement would be false. For example, the ring with Q as additive group and trivial multiplication has no maximal ideal, a sketch of the proof of Zorns lemma follows, assuming the axiom of choice. Then there exists a partially ordered set, or poset, P such that every totally ordered subset has an upper bound, and every element has a bigger one. For every totally ordered subset T we may define a bigger element b, because T has an upper bound