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🔗 United States 🔗 Film 🔗 Film/American cinema 🔗 Science Fiction 🔗 United States/Texas

Primer is a 2004 American science fiction film about the accidental discovery of time travel. The film was written, directed, produced, edited and scored by Shane Carruth, who also stars with David Sullivan.

Primer is of note for its extremely low budget, experimental plot structure, philosophical implications, and complex technical dialogue, which Carruth, a college graduate with a degree in mathematics and a former engineer, chose not to simplify for the sake of the audience. The film collected the Grand Jury Prize at the 2004 Sundance Film Festival, before securing a limited release in the United States, and has since gained a cult following.

🔗 Human rights 🔗 Internet 🔗 Religion 🔗 Comedy 🔗 Freedom of speech 🔗 Islam 🔗 Journalism 🔗 Animation 🔗 Comics 🔗 South Park

Everybody Draw Mohammed Day (or Draw Mohammed Day) was a 2010 event in support of artists threatened with violence for drawing representations of the Islamic prophet Muhammad. It stemmed from a protest against censorship of the American television show South Park episode "201", led by the show's distributor Comedy Central, in response to death threats that had been made against some of those responsible for two segments broadcast in April 2010. A drawing representing Mohammed was posted on the Internet on April 20, 2010, with a message suggesting that "everybody" create a drawing depicting Mohammad on May 20 in support of free speech.

U.S. cartoonist Molly Norris of Seattle, Washington created the artwork in reaction to Internet death threats that had been made against animators Trey Parker and Matt Stone for depicting Muhammad in an episode of South Park. Postings on RevolutionMuslim.com (under the pen name Abu Talha al-Amrikee; later identified as Zachary Adam Chesser) had said that Parker and Stone could wind up like Theo van Gogh, a Dutch filmmaker who was stabbed and shot to death.

Norris claimed that, if people draw pictures of Muhammad, radical Islamist terrorists would not be able to murder them all, and threats to do so would become unrealistic. Within a week, Norris' idea became popular on Facebook, was supported by numerous bloggers, and generated coverage on the blog websites of major U.S. newspapers. As the publicity mounted, Norris and the man who created the first Facebook page promoting the May 20 event disassociated themselves from it. Nonetheless, planning for the protest continued with others "taking up the cause". Facebook had an "Everybody Draw Mohammed Day" page, which grew to over 100,000 participants (101,870 members by May 20). A protest page on Facebook against the initiative named "Against ‘Everybody Draw Mohammed Day'" attracted slightly more supporters (106,000 by May 20). Subsequently, Facebook was temporarily blocked by Pakistan; the ban was lifted after Facebook agreed to block the page for users in India and Pakistan.

In the media, Everybody Draw Mohammed Day attracted support from commentators who felt that the campaign represented important issues of freedom of speech, and the need to stand up for this freedom.

🔗 Mathematics

Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator D

${\displaystyle Df(x)={\frac {d}{dx}}f(x)\,,}$

and of the integration operator J

${\displaystyle Jf(x)=\int _{0}^{x}f(s)\,ds\,,}$

and developing a calculus for such operators generalizing the classical one.

In this context, the term powers refers to iterative application of a linear operator D to a function f, that is, repeatedly composing D with itself, as in ${\displaystyle D^{2}(f)=(D\circ D)(f)=D(D(f))}$.

For example, one may ask for a meaningful interpretation of:

${\displaystyle {\sqrt {D}}=D^{\frac {1}{2}}}$

as an analogue of the functional square root for the differentiation operator, that is, an expression for some linear operator that when applied twice to any function will have the same effect as differentiation. More generally, one can look at the question of defining a linear functional

${\displaystyle D^{a}}$

for every real-number a in such a way that, when a takes an integer value n ∈ ℤ, it coincides with the usual n-fold differentiation D if n > 0, and with the −nth power of J when n < 0.

One of the motivations behind the introduction and study of these sorts of extensions of the differentiation operator D is that the sets of operator powers { D^a |a ∈ ℝ } defined in this way are continuous semigroups with parameter a, of which the original discrete semigroup of { Dⁿ | n ∈ ℤ } for integer n is a denumerable subgroup: since continuous semigroups have a well developed mathematical theory, they can be applied to other branches of mathematics.

Fractional differential equations, also known as extraordinary differential equations, are a generalization of differential equations through the application of fractional calculus.

🔗 Biography 🔗 Military history 🔗 Architecture 🔗 Greece 🔗 Military history/Military biography 🔗 Biography/military biography 🔗 Military history/World War II 🔗 Military history/Cold War 🔗 Dance 🔗 Composers 🔗 Dance/Ballet 🔗 Classical music 🔗 Military history/Balkan military history 🔗 Biography/Musicians 🔗 Military history/European military history

Iannis Xenakis (also spelt as Yannis Xenakis) (Greek: Γιάννης (Ιάννης) Ξενάκης [ˈʝanis kseˈnacis]; 29 May 1922 – 4 February 2001) was a Greek-French composer, music theorist, architect, performance director and engineer. After 1947, he fled Greece, becoming a naturalized citizen of France. He is considered an important post-World War II composer whose works helped revolutionize 20th-century classical music.

Xenakis pioneered the use of mathematical models in music such as applications of set theory, stochastic processes and game theory and was also an important influence on the development of electronic and computer music. He integrated music with architecture, designing music for pre-existing spaces, and designing spaces to be integrated with specific music compositions and performances.

Among his most important works are Metastaseis (1953–54) for orchestra, which introduced independent parts for every musician of the orchestra; percussion works such as Psappha (1975) and Pléïades (1979); compositions that introduced spatialization by dispersing musicians among the audience, such as Terretektorh (1966); electronic works created using Xenakis's UPIC system; and the massive multimedia performances Xenakis called polytopes, that were a summa of his interests and skills. Among the numerous theoretical writings he authored, the book Formalized Music: Thought and Mathematics in Composition (French edition 1963, English translation 1971) is regarded as one of his most important. As an architect, Xenakis is primarily known for his early work under Le Corbusier: the Sainte Marie de La Tourette, on which the two architects collaborated, and the Philips Pavilion at Expo 58, which Xenakis designed by himself.

🔗 Psychology 🔗 Animal rights

The Pit of despair was a name used by American comparative psychologist Harry Harlow for a device he designed, technically called a vertical chamber apparatus, that he used in experiments on rhesus macaque monkeys at the University of Wisconsin–Madison in the 1970s. The aim of the research was to produce an animal model of clinical depression. Researcher Stephen Suomi described the device as "little more than a stainless-steel trough with sides that sloped to a rounded bottom":

A ​³⁄₈ in. wire mesh floor 1 in. above the bottom of the chamber allowed waste material to drop through the drain and out of holes drilled in the stainless-steel. The chamber was equipped with a food box and a water-bottle holder, and was covered with a pyramid top [removed in the accompanying photograph], designed to discourage incarcerated subjects from hanging from the upper part of the chamber.

Harlow had already placed newly born monkeys in isolation chambers for up to one year. With the "Pit of despair", he placed monkeys between three months and three years old in the chamber alone, after they had bonded with their mothers, for up to ten weeks. Within a few days, they had stopped moving about and remained huddled in a corner.

🔗 Philosophy 🔗 Philosophy/Philosophy of mind

The hard problem of consciousness is the problem of explaining why and how sentient organisms have qualia or phenomenal experiences—how and why it is that some internal states are subjective, felt states, such as heat or pain, rather than merely nonsubjective, unfelt states, as in a thermostat or a toaster. The philosopher David Chalmers, who introduced the term "hard problem" of consciousness, contrasts this with the "easy problems" of explaining the ability to discriminate, integrate information, report mental states, focus attention, and so forth. Easy problems are (relatively) easy because all that is required for their solution is to specify a mechanism that can perform the function. That is, regardless of how complex or poorly understood the phenomena of the easy problems may be, they can eventually be understood by relying entirely on standard scientific methodologies. Chalmers claims that the problem of experience is distinct from this set and will "persist even when the performance of all the relevant functions is explained".

The existence of a "hard problem" is controversial. It has been accepted by philosophers of mind such as Joseph Levine, Colin McGinn, and Ned Block and cognitive neuroscientists such as Francisco Varela, Giulio Tononi, and Christof Koch. However, its existence is disputed by philosophers of mind such as Daniel Dennett, Massimo Pigliucci, and Keith Frankish and cognitive neuroscientists such as Stanislas Dehaene and Bernard Baars.

🔗 Mathematics

In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. It is the next hyperoperation after exponentiation, but before pentation. The word was coined by Reuben Louis Goodstein from tetra- (four) and iteration.

Under the definition as repeated exponentiation, the notation ${\displaystyle {^{n}a}}$ means ${\displaystyle {a^{a^{\cdot ^{\cdot ^{a}}}}}}$, where n copies of a are iterated via exponentiation, right-to-left, I.e. the application of exponentiation ${\displaystyle n-1}$ times. n is called the "height" of the function, while a is called the "base," analogous to exponentiation. It would be read as "the nth tetration of a".

Tetration is also defined recursively as

${\displaystyle {^{n}a}:={\begin{cases}1&{\text{if }}n=0\\a^{\left(^{(n-1)}a\right)}&{\text{if }}n>0\end{cases}}}$,

allowing for attempts to extend tetration to non-natural numbers such as real and complex numbers.

The two inverses of tetration are called the super-root and the super-logarithm, analogous to the nth root and the logarithmic functions. None of the three functions are elementary.

Tetration is used for the notation of very large numbers.

🔗 Mathematics

In mathematics, Euler's identity (also known as Euler's equation) is the equality

${\displaystyle e^{i\pi }+1=0}$

where

e is Euler's number, the base of natural logarithms,

i is the imaginary unit, which by definition satisfies i² = −1, and

π is pi, the ratio of the circumference of a circle to its diameter.

Euler's identity is named after the Swiss mathematician Leonhard Euler. It is considered to be an exemplar of mathematical beauty as it shows a profound connection between the most fundamental numbers in mathematics.

🔗 Business 🔗 Psychology 🔗 Alternative Views 🔗 Education

In the field of psychology, the Dunning–Kruger effect is a cognitive bias in which people assess their cognitive ability as greater than it is. It is related to the cognitive bias of illusory superiority and comes from the inability of people to recognize their lack of ability. Without the self-awareness of metacognition, people cannot objectively evaluate their competence or incompetence.

As described by social psychologists David Dunning and Justin Kruger, the cognitive bias of illusory superiority results from an internal illusion in people of low ability and from an external misperception in people of high ability; that is, "the miscalibration of the incompetent stems from an error about the self, whereas the miscalibration of the highly competent stems from an error about others."

🔗 United States

The mean center of the United States population is determined by the United States Census Bureau from the results of each national census. The Bureau defines it as follows:

The concept of the center of population as used by the U.S. Census Bureau is that of a balance point. The center of population is the point at which an imaginary, weightless, rigid, and flat (no elevation effects) surface representation of the 50 states (or 48 conterminous states for calculations made prior to 1960) and the District of Columbia would balance if weights of identical size were placed on it so that each weight represented the location on one person. More specifically, this calculation is called the mean center of population.

After moving roughly 600 mi (966 km) west by south during the 19th century, the shift in the mean center of population during the 20th century was less pronounced, moving 324 mi (521 km) west and 101 mi (163 km) south. Nearly 79% of the overall southerly movement happened between 1950 and 2000. Given the strong pull of Texas, Florida, and the Western US, the population center would be heading towards and one day entering Oklahoma.