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Classical

Specialty Definition: 20th century classical music

(From Wikipedia, the free Encyclopedia)

20th century classical music was extremely diverse, ranging from the late Romantic style of Sergei Rachmaninov to the complete serialism of Pierre Boulez, and from the simple triadic harmonies of minimalist composers such as Philip Glass to the musique concrète pioneered by Pierre Schaeffer.

Romantic style

Particularly in the early part of the century, many composers wrote music which was an extension of 19th century Romantic music. Harmony, though sometimes complex, was tonal, and traditional instrumental groupings such as the orchestra and string quartet remained the most usual. Traditional forms such as the symphony and concerto remained in use.

Many prominent composers — among them Béla Bartók, Dmitri Shostakovich and Benjamin Britten — made significant advances in style and technique while still employing a melodic, harmonic, structural and textural language which was related to that of the 19th century and quite accessible to the average listener. Music along these lines was written throughout the 20th century, and continues to be written today, but many other 20th century composers took more experimental routes.

The Schoenberg "Trinity", atonality and serialism

Arnold Schoenberg is one of the most significant figures in 20th century music. His early works are in a late Romantic style, influenced by Richard Wagner and Gustav Mahler, but he later abandoned a tonal framework altogether, instead writing freely atonal music (he is often reckoned to have been the first composer to have done so). In time, he developed the twelve-tone technique of composition, intended to be a replacement for traditional tonal pitch organisation. His pupils Anton Webern and Alban Berg also developed and furthered the use of the twelve-tone system and were notable for their use of the technique in their own right. They together are known, colloquially, as the Schoenberg "trinity" or the Second Viennese School.

Schoenberg's music and that of his followers was very controversial in its day, and remains so to some degree now. Many listeners found (and still find) his music hard to follow, lacking a sense of definite melody. Nontheless, works such as Pierrot Lunaire are regarded as classics of the 20th century, and the style he pioneered was very influential. Many composers have since written music which does not rely on traditional tonality.

The twelve-tone technique itself was later adapted by other composers to control aspects of music other than the pitch of the notes (such as dynamics and methods of attack), creating completely serialised music. The "pointillistic" style of Webern — in which individual sounds are carefully placed within the piece such that each has importance — was very influential in the years following World War II among composers such as Pierre Boulez.

Cage and music in the everyday

John Cage is another prominent figure in 20th century music. Cage questioned the very definition of music in his pieces, and stressed that all sounds are essentially music. Cage in the "silent" 4'33" presents us with the idea that the unintentional sounds are just as musically valid as the sounds originating from an instrument. Cage also notably used aleatoric music, and found sounds in order to create an interesting and different type of music.

Cage, though, has been seen by some to be too avant-garde in his approach; for this reason, many find his music unappealing.

Minimalistic ideals

Many composers in the later 20th century began to explore what is now called minimalism. Minimalism in music may be summarized as music created from small melodic, harmonic or rhythmic ideas and using small or gradual variations to add interest to the music. Notable composers who used these minimalistic ideas were Terry Riley, Philip Glass, Steve Reich, and La Monte Young. Riley is seen by some as the "father" of minimalistic music with In C, a work comprised of melodic cells that each pefromer in an ensemble plays through at their own rate. Steve Reich in his early works wrote in a minimalistic fashion, but began to depart from strict minimalism and explored many other contemporary musical ideas.

Minimalistic music is often contentious amongst traditional listeners. Critics find minimalistic music to be overly repetitive and empty while proponents argue that the static elements that are often prevelant draw more interest to small changes.

Electronic music

Technological advances in the 20th century enabled composers to use electronic means of producing sound. This took several forms: some composers simply incorporated electronic instruments into relatively conventional pieces. Olivier Messiaen, for example, used the ondes martenot in a number of works.

Other composers abandoned conventional instruments and used magnetic tape to create music, recording sounds and then manipulating them in some way. Pierre Schaeffer was the pioneer of such music, termed musique concrete. Some figures, such as Karlheinz Stockhausen, used purely electronic means to create their work. In the United States of America, Milton Babbitt used the RCA Mark II Synthesizer to create music. Sometimes such electronic music was combined with more conventional instruments, Stockhausen's Hymnen and Edgar Varèse's Déserts offering two examples (although Déserts is sometimes performed today without the tape part).

A number of institutions sprung up in the 20th century specialising in electronic music, with IRCAM in Paris perhaps the best known.

See electronic music and electronic art music for more details on this subject.

See also

• List of 20th century classical composers

  Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "20th century classical music."

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Ancient philosophy

(From Wikipedia, the free Encyclopedia)

Ancient Philosophy -- Western.

Pre-Socratic Philosophers:

The history of Philosophy in the west begins with the Greeks, and particularly with a group of philosophers commonly called the pre-Socratics. This is not to say that there were not other pre-philosophical rumblings in Egyptian, Semitic, and Babylonian cultures. Certainly there were great thinkers and writers in each of these cultures, and there is evidence that some of the earliest Greek philosophers may have had contact with at least some of the products of Egyptian and Babylonian thought. However, the early Greek thinkers add at least one element which differentiates their thought from all those who came before them. For the first time in history, we discover in their writings something more than dogmatic assertions about the way the world is ordered -- we find reasoned arguments for various beliefs about the world.

As it turns out nearly all of the various cosmologies proposed by the early Greek philosophers are profoundly and demonstrably false, but this does not diminish their importance. For, even if later philosophers summarily rejected the answers they provided, they could not escape their questions.

Where does everything come from?

What is it really made out of?

How do we explain the plurality things found in nature?

And why are we able to describe them with a singular mathematics?

And just as important as the questions they asked was the method they followed in forming and transmitting their answers. The pre-Socratic philosophers rejected traditional mythological explanations for the phenomenon they saw around them in favor of more rational explanations. In other words they depended on reason and observation to illuminate the true nature of the would around them, and they used rational argument to advance their views to others. And though there has been a great deal of argument about the relative weights that reason and observation should have, philosophers for two and a half millennia are basically united in the use of the very method first used by the pre-Socratics.

Pre-Socratic philosophers are often very hard to pin down, and it is sometimes very difficult to determine the actual line of argument they used in supporting their particular views. This problem arises not from some defect in the men themselves or in their ideas, but is simply the result of their separation from us in history. While most of these men produced significant texts, we have no complete versions of any of those texts. All we have is quotations by later philosophers, historians, and the occasional textual fragment.

Thales

Anaximander

Pythagoras

Heraclitus of Ephesus

Xenophanes, Parmenides, and the other Eleatic philosophers

Leucippus, Democritus and the other Atomists

Protagoras and the Sophists

Socrates:

Plato:

Aristotle:

Later Hellenistic Philosophers:

Cicero

Zeno of Citium, Epictetus

Epicurus, Lucretius

Empedocles

The Neo-Platonists: Ammonius Saccas, Plotinus, Porphyry, Proclus, Iamblichus)

Marcus Aurelius

Schools of Thought in Hellenistic Period.

Cynicism

Hedonism

Eclecticism

Neo-Platonism

Skepticism

Stoicism

The spread of Christianity through the Roman world ushers in the end of the Helinistic philosophy and ushered in the beginnings of Mediaeval Philosophy.

Ancient Philosophy -- Eastern

Vedic Philosophy

In the east, Indian philosophy begins with the Vedas where questions related to laws of nature, the origin of the universe and the place of man in it are asked. In the famous Rigvedic Hymn of Creation the poet says:

"Whence all creation had its origin, he, whether he fashioned it or whether he did not, he, who surveys it all from highest heaven, he knows--or maybe even he does not know."

In the Vedic view, creation is ascribed to the self-consciousness of the primeval person (Purusha). This leads to the inquiry of the one being that underlies the diversity of empirical phenomena and the origin of all things. Cosmic order is termed rta and causal law by karma. Nature (prakriti) is taken to have three qualities (sattva, rajas, and tamas).

Vedas

Upanishads

Hinduism

Classical Indian Philosophy

In classical times, these inquiries were systemized in six schools of philosophy. The questions asked were:

What is the ontological nature of consciousness?

How is cognition itself experienced?

Is mind (chit) intentional or not?

Does cognition have its own structure?

The six schools of Indian philosophy are:

Mimamsa

Samkhya

Yoga

Vaisheshika

Nyaya

Vedanta

Chinese philosophy

In China, less emphasis was laid upon materialism as a basis for reflecting upon the world and more on conduct, manners and social behaviour as is evidence in Taoism and Confucianism.

Chinese philosophy -- Confucianism, Taoism, Legalism

Buddhist philosophy arose in India but contributions to it were made in China, Japan, and Korea also.

Eastern philosophy

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Ancient philosophy."

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Class warfare

(From Wikipedia, the free Encyclopedia)

This article is about the general phenomena of Class warfare. See Class War for information about the newspaper/organisation of that name.

Class warfare is a long-used term to describe social and political conflicts between classeses - groups of disproportionately different financial status. Financial status includes all assests a person has ownership of.

Money is the way modern societies quantify the work of its society. Since many economic systems have historically allowed money to be the property of individuals, these people can retain to their own dictates a power over those of lesser financial means - particularly those of the working class, who live in service of the upper class if we define the upper class meaning those with the means of production and the working class as those who work for the upper class.

Thus a socio-political imbalance exists between individuals of extreme wealth, and those with little or no wealth. The interests of those in whom power is established will often dramatically conflict with the interests and needs of the working class.

Furthermore, since the mechanisms by which wealthy peoples will increase or maintain their financial status are related and similar to another, they tend to develop similar political needs, and act in concert as a political group to those ends.

This is of course, is in direct contradiction to the wants, and often needs, of the greater majority. The only means by which people have in modern times made progress against this imbalance has been through democracy, and the institutionalized respect and protection of personal liberties.

Fundamentally, there is little difference between the class warfare that existed between the Victorian era monarchy and the common public, and a modern Corporation and its workers, who may own part or most of the corperation.

-- Unionss are a modern incarnation of public will in class warfare. Representing a political group of like minded working people, unions have revolutionised health and safety standards in industrial economies. Corporations are companies that exist as perpetual entities. Their function is as a vehicle for business enterprise, while transcending the bounds of mortality and liability that accompany an individual-owned enterprise.

See also: class envy, exploitation, exploitation of the working class, labor struggles, classes, sharecropping system, taxation class struggle class conflict economic stratification

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Class warfare."

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Class Warfare

(From Wikipedia, the free Encyclopedia)

Class Warfare is a book of interviews with Noam Chomsky conducted by David Barsamian. It was first published in the UK by Pluto Press in 1996.

The contents runs as follows:

• Introduction
• Looking Ahead: Tenth Anniversary Interview (an interview conducted ten years since Barsamian first interviewed Chomsky)
• Rollback: The Return of Predatory Capitalism
• History and Memory
• The Federal Reserve Board
• Take from the Needy and Give to the Greedy
• Israel: Rewarding the Cop on the Beat

See also class warfare

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Class Warfare."

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Classical

(From Wikipedia, the free Encyclopedia)

The word classical has several meanings:

• Pertaining to the societies of ancient Greece or Rome. For example, the Greek and Latin languages, classical architecture and the cult of the Olympian gods. See also Greek mythology and Roman mythology.

• The style of court music prevelant in the 18th. and early 19th centuries, in between the Baroque and Romantic periods. See classical music.

• Any mode of scientific thought prevelant at the time of some radical new innovation. For example, the physics of Isaac Newton is described as "classical", since its assumptions have been challenged by the theories of relativity and quantum mechanics. See also classical mechanics.

  Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Classical."

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Classical antiquity

(From Wikipedia, the free Encyclopedia)

Classical antiquity is a broad and perhaps misleading term for a long period of European history, that begins roughly with the earliest recorded Greek poetry of Homer, and continues through the rise of Christianity and the fall of the Western Roman Empire.

Such a wide sampling of history and territory covers many rather disparate cultures and periods. "Classical antiquity" typically refers to an idealized vision of later people, of what was, in Lord Byron's words,

the glory that was Greece, the grandeur that was Rome!

Reverence for classical antiquity was formerly much greater in Western Europe than it is today. Respect for the "ancients" of Greece and Rome affected politics, philosophy, sculpture, literature, theatre, education, and even architecture.

In politics, the presence of a Roman Emperor was felt to be desirable long after the empire fell. This tendency reached its peak when Charlemagne was crowned "Roman Emperor" in the year 800, an act which led to the formation of the Holy Roman Empire. The notion that an emperor is a monarch who outranks a mere king dates from this period. In this political ideal, there would always be a Roman Empire, a state whose jurisdiction extended to the entire civilised world.

Epic poetry in Latin continued to be written and circulated well into the nineteenth century. John Milton and even Arthur Rimbaud got their first poetic educations in Latin. Genres like epic poetry, pastoral verse, and the endless use of characters and themes from Greek mythology left a deep mark on Western literature.

In architecture, there have been several Greek Revivals, which seem more inspired in retrospect by Roman architecture than Greek. Still, one needs only to look at Washington, DC to see a city filled with large marble buildings with façades made out to look like Roman temples, with columns constructed in the classical orders of architecture.

In philosophy, the efforts of St Thomas Aquinas were derived largely from the thought of Aristotle, despite the intervening change in religion from paganism to Christianity. Greek and Roman authorities such as Hippocrates and Galen formed the foundation of the practice of medicine even longer than Greek thought prevailed in philosophy. In the French theatre, tragedians such as Molière and Racine wrote plays on mythological or classical historical subjects and subjected them to the strict rules of the Three Unities derived from a remark by Aristotle. The desire to dance like a latter-day vision of how the ancient Greeks did it moved Isadora Duncan to create her brand of ballet.

"Classical antiquity," then, is the contemporary vision of Greek and Roman culture by their admirers from the more recent past. It remains a vision that many people in the twenty-first century continue to find compelling.

Articles that discuss various aspects of classical antiquity include:

• Greece
  • Greek mythology
  • Greek religion
    • Hellênismos
  • Greco-Roman religion
  • Greek philosophy
  • History of Greece
  • Early Helladic
  • Middle Helladic
  • Late Helladic
  • Hellenic Greece
  • Hellenistic Greece
  • Magna Graecia
  • Byzantium
  • Greek language
    • Ionic Greek
    • Doric Greek
    • Attic Greek
  • Greek literature
    • Greek Anthology

• Rome
  • Roman Kingdom
  • Roman Republic
  • Roman Empire
  • Roman mythology
  • Roman religion
  • Roman culture
  • Roman law
  • Roman Senate
  • Roman Emperors
  • Classical Rome
  • Latin
    • Classical Latin
    • Latin literature

• Other
  • Classical architecture
  • Classical orders
  • Classical education

    Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Classical antiquity."

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Classical architecture

(From Wikipedia, the free Encyclopedia)

From the point of view of modern times, the ancient civilizations of the Mediterranean sometimes seem to blend smoothly into one melange we call “the Classical.” This stylistic designation elides the 8 or 10 centuries the period spans and the remarkable changes in technology and architectural design that take place. While later architects reviving classical forms in the Renaissance or the Neo-classical styles picked what they wanted to imitate, it is essential to separate the parts.

A working division can be made into:

Greek architecture before Alexander the Great

Hellenistic architecture

Roman architecture

Only Greek Architecture before Alexander (who died in 323 B.C.) carries any ethnic designation. The ancient Greeks were notoriously dismissive of barbaroi, those who spoke Greek non-natively or (even worse!) not at all. The incredible conquests of Alexander and the subsequent application of a veneer of Greek city states to a base of Egyptian, Semitic, and even Iranian populations produced an important change. Though Greek-speaking remained the touchstone of whether one was a member of civilized culture or not, the ethnic diversification of the Hellenistic world is clear. The formal elements of classical Greek architecture were applied to temples for gods never worshipped in Greece.

The Romans can be seen as the latest Hellenistic empire. Pre-imperial architecture is more or less Etruscan with some Greek elements. By the time the Romans conquered mainland Greece in the 2nd century B.C. they were importing Greek craftsmen to build major public buildings. The term “Roman Art” and “Roman Architecture” has no ethnic meaning of “Italic Romans.” Most art historians assume that it has the ethnic meaning of “Greek-speaking slave” or “Greek-speaking free laborer,” in fact.

The elements of classical architecture turn out to be just that -- elements that can be applied in radically different architectural contexts than those for which they were developed The classical orders -- doric, ionic, and corinthian -- have a kind of meaning or stylistic developmental history in 5th century B.C. Greece that can be passed over or shifted in 1st century A.D. Gaul, which is why they have been revived over and over again since then.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Classical architecture."

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Classical Chinese

(From Wikipedia, the free Encyclopedia)

Classical Chinese (文言 wényán, literal meaning: "literary language") is a style of writing the Chinese language which uses alternate sets of characters and grammar which resembles Chinese as it was written historically. It was used for almost all formal correspondence before the 20th century, not only in China but also in Korea and Japan.

It is in contrast to bai hua which is a writing style that uses characters used in modern spoken Chinese. In practice there is a socially accepted continuum between bai hua and wen yan. A person writing a letter might include wen yan expressions and phrases to express that the matter being discussed is formal or serious and important. A letter written completely in wen yan would be considered stylistically odd, but not incorrect and certainly not uneducated.

Most Chinese people with at least a middle school education are able to read basic wen yan, because the ability to read (but not write) wen yan is part of the Chinese middle school and high school curriculum and is part of the college entrance examination. Classical Chinese is taught primarily by presenting a classical Chinese work and including a bai hua gloss which explains the meaning of phrases. Tests on classical Chinese are typically essentially translation exercises which ask the student to express the meaning of a paragraph in bai hua, using multiple choice.

In addition, many works of literature in wen yan (such as Tang poetry) have major cultural influences. However, even with knowledge of grammar and vocabulary, wen yan can be extremely difficult to decipher because of its heavy use of literature references and allusions.

Wen yan is distinguished from bai hua by the use of different characters, and a style which is extremely concise and pacted. The terms which are different in wen yan tend to be transition and grammatical words. A sentence which may take 20 characters in bai hua can often be rendered in wen yan in four or five. In addition to grammar and vocabulary differences, wen yan can be distinguished by an effort to maintain parallelism and rhythm, even in prose works, and its extensive use of allusions which also contribute to the brief style.

Wen yan was the primary form used in Chinese literary works until the May Fourth Movement, and was also heavily used in Japan and Korea. Exceptions to the use of wen yan were vernacular novels such as The Dream of the Red Chamber, which was considered low class at the time. Today, pure classical Chinese is occasionally used in formal or ceremonial occasions. The anthem San Min Chu-i, for example, is in wen yan. Most often, people will, in certain situations, add classical terms to writing in order to make it seem more formal. Ironically, Classical Chinese was used to write the Hunman jeong-eum in which the modern Korean alphabet (Hangul) was promulgated and the essay by Hu Shi in which he argued against using Classical Chinese and in favor of bai hua.

Classical Chinese is unique for today being an almost purely literary language. Classical Chinese characters are generally read with modern Mandarin Chinese sounds in which many different characters have become homonyms. This makes most Classical Chinese literature unintelligible when read with Mandarin pronunciations. However, some other Chinese dialects are closer to Classical Chinese, and in the subjective opinion of many Chinese, Classical Chinese literature, especially poetry, sounds better when read with a southern dialect such as Cantonese.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Classical Chinese."

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Classical economics

(From Wikipedia, the free Encyclopedia)

Classical economics is a school of economic thought whose major developers include William Petty, Adam Smith, David Ricardo, and John Stuart Mill. It is seen by many as the first modern school of economic thought.

It tended to stress the benefits of trade, an analysis organized around the natural price of commodities, and either the cost of production theory of value or the labor theory of value.

It was largely displaced by marginalist schools of thought (such as the Austrian School) who saw value to derive from the marginal utility that consumers found in a good rather than the cost of the inputs that made up the product. Ironically, considering the attachment of many classical economists to the free market, the largest school of economic thought that still adheres to classical forms is the Marxist school. This may be due to the fact that Karl Marx died before marginalist theories were widely accepted.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Classical economics."

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Classical genetics

(From Wikipedia, the free Encyclopedia)

Classical genetics consists of the techniques and methodologies of genetics that predate the advent of molecular biology. After the discovery of the genetic code and such tools of cloning as restriction enzymes, the avenues of investigation open to geneticists were greatly broadened. Some classical genetic ideas have been supplanted with the mechanistic understanding brought by molecular discoveries, but many remain intact and in use. Classical genetics is often contrasted with reverse genetics, and aspects of molecular biology are sometimes referred to as molecular genetics.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Classical genetics."

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Classical guitar

(From Wikipedia, the free Encyclopedia)

A Classical guitar is a Musical instrument from the guitar family. Also called Spanish guitar.

The classical guitar is distinguished by a number of features.

• It is an acoustic instrument. The sound is amplified by a sound box.
• It has six strings. A few classical guitars have eight or more strings to expand the bass scale, allowing lute music written for lutes with more than six courses of strings to be played.
• The strings are made from catgut (made from sheep intestine, despite the name), or much more commonly these days nylon, as opposed to the metal strings found in some other forms of guitar. These strings have a much lower tension than steel strings. The lower three strings ('bass strings') are wound with metal, commonly silver or bronze. Some less common stringings use a fourth wound string.
• Because of the low tension of the strings the neck can be made entirely of wood, not requiring a steel truss road.
• The neck tends to be broader than with steel string guitars, making more complex work easier, but requiring a left hand position which ultimately makes the guitar less stable to hold. The fretboard is flat, not curved.
• The strings are usually plucked with the fingers. Serious players shape their fingernails so that they contact the string in a certain way to achieve the desired tone.

Classical guitars can be equipped with an electronic pickup, which is sometimes used by performers in noisy environments. Either a piezoelectric pickup is placed under the bridge, or a microphone is suspended within the body.

The heyday of the classical guitar repertoire lies in the 19th century. Some guitar composers are:

• Dionisio Aguado 1784-1849
• Leo Brouwer 1939-
• Matteo Carcassi 1792-1853
• Fernando Carulli 1770-1841
• Mario Castelnuovo-Tedesco 1895-1968
• Napoleon Coste 1806-1883
• Mauro Giuliani 1780-1840
• Luigi Legnani 1790-1877
• Miguel Llobet 1878-1937
• Joaquin Rodrigo 1901-1999
• Fernando Sor 1778-1839
• Francisco Tarrega 1852-1909
• Heitor Villa-Lobos 1887-1959

Because of the relative scarcity of pieces, guitarists often play transcriptions of music originally written for other instruments. Lute transcriptions from the baroque era are common, because the fingering of the lute is similar.

Classical guitar players:

• Manuel Barrueco
• Ben Bolt
• Julian Bream 1933
• Charo
• Eric Hamilton
• Andrés Segovia 1893-1987
• Narciso Yepes 1927-1997
• John Williams 1941
• Pepé Romero
• Angél Romero

  Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Classical guitar."

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Classical mechanics

(From Wikipedia, the free Encyclopedia)

Classical mechanics is the physics of forces, acting upon bodies. It is often referred to as "Newtonian mechanics" after Newton and his laws of motion. Classical mechanics is subdivided into statics (which deals with objects in equilibrium) and dynamics (which deals with objects in motion).

Classical mechanics produces very accurate results within the domain of everyday experience. It is superseded by relativistic mechanics for systems moving at large velocities near the speed of light, quantum mechanics for systems at small distance scales, and relativistic quantum field theory for systems with both properties. Nevertheless, classical mechanics is still very useful, because (i) it is much simpler and easier to apply than these other theories, and (ii) it has a very large range of approximate validity. Classical mechanics can be used to describe the motion of human-sized objects (such as tops and baseballs), many astronomical objects (such as planets and galaxies), and even certain microscopic objects (such as organic molecules.)

Although classical mechanics is roughly compatible with other "classical" theories such as classical electrodynamics and thermodynamics, there are inconsistencies that were discovered in the late 19th century that can only be resolved by more modern physics. In particular, classical nonrelativistic electrodynamics predicts that the speed of light is a constant relative to an aether medium, a prediction that is difficult to reconcile with classical mechanics and which led to the development of special relativity. When combined with classical thermodynamics, classical mechanics leads to the Gibbs paradox in which entropy is not a well-defined quantity and to the ultraviolet catastrophe in which a blackbody is predicted to emit infinite amounts of energy. The effort at resolving these problems led to the development of quantum mechanics.

Description of the theory

We will now introduce the basic concepts of classical mechanics. For simplicity, we only deal with a point particle, which is an object with negligible size. The motion of a point particle is characterized by a small number of parameters: its position, mass, and the forces applied on it. We will discuss each of these parameters in turn.

In reality, the kind of objects which classical mechanics can describe always have a non-zero size. True point particles, such as the electron, are properly described by quantum mechanics. Objects with non-zero size have more complicated behavior than our hypothetical point particles, because their internal configuration can change - for example, a baseball can spin while it is moving. However, we will be able to use our results for point particles to study such objects by treating them as composite objects, made up of a large number of interacting point particles. We can then show that such composite objects behave like point particles, provided they are small compared to the distance scales of the problem, which indicates that our use of point particles is self-consistent.

Position and its derivatives

The position of a point particle is defined with respect to an arbitrary fixed point in space, which is sometimes called the origin, O. It is defined as the vector r from O to the particle. In general, the point particle need not be stationary, so r is a function of t, the time elapsed since an arbitrary initial time. The velocity, or the rate of change of position with time, is defined as

.

The acceleration, or rate of change of velocity, is

.

The acceleration vector can be changed by changing its magnitude, changing its direction, or both. If the magnitude of v decreases, this is sometimes referred to as deceleration; but generally any change in the velocity, including deceleration, is simply referred to as acceleration.

Forces; Newton's Second Law

Newton's second law relates the mass and velocity of a particle to a vector quantity known as the force. Suppose m is the mass of a particle and F is the vector sum of all applied forces (i.e. the net applied force.) Then Newton's second law states that

.

The quantity mv is called the momentum. Typically, the mass m is constant in time, and Newton's law can be written in the simplified form

where a is the acceleration, as defined above. It is not always the case that m is independent of t. For example, the mass of a rocket decreases as its propellant is ejected. Under such circumstances, the above equation is incorrect and the full form of Newton's second law must be used.

Newton's second law is insufficient to describe the motion of a particle. In addition, we require a description of F, which is to be obtained by considering the particular physical entities with which our particle is interacting. For example, a typical resistive force may be modelled as a function of the velocity of the particle, say

with λ a positive constant. Once we have independent relations for each force acting on a particle, we can substitute it into Newton's second law to obtain an ordinary differential equation, which is called the equation of motion. Continuing our example, suppose that friction is the only force acting on the particle. Then the equation of motion is

.

This can be integrated to obtain

where v₀ is the initial velocity. This means that the velocity of this particle decays exponentially to zero as time progresses. This expression can be further integrated to obtain the position r of the particle as a function of time.

Important forces include the gravitational force and the Lorentz force for electromagnetism. In addition, Newton's third law can sometimes be used to deduce the forces acting on a particle: if we know that particle A exerts a force F on another particle B, it follows that B must exert an equal and opposite reaction force, -F, on A.

Energy

If a force F is applied to a particle that achieves a displacement δr, the work done by the force is the scalar quantity

.

Suppose the mass of the particle is constant, and δW_total is the total work done on the particle, which we obtain by summing the work done by each applied force. From Newton's second law, we can show that

,

where T is called the kinetic energy. For a point particle, it is defined as

.

For extended objects composed of many particles, the kinetic energy of the composite body is the sum of the individual particles' kinetic energies.

A particular class of forces, known as conservative forces, can be expressed as the gradient of a scalar function, known as the potential energy and denoted V:

.

Suppose all the forces acting on a particle are conservative, and V is the total potential energy, obtained by summing the potential energies corresponding to each force. Then

.

This result is known as the conservation of energy, and states that the total energy, , is constant in time. It is often useful, because most commonly encountered forces are conservative.

Further results

Newton's laws provide many important results for composite bodies. See angular momentum.

There are two important alternative formulations of classical mechanics: Lagrangian mechanics and Hamiltonian mechanics. They are equivalent to Newtonian mechanics, but are often more useful for solving problems. These, and other modern formulations, usually bypass the concept of "force", instead referring to other physical quantities, such as energy, for describing mechanical systems.

History

The Greeks and Aristotle in particular were the first to propose that there are abstract principles governing nature.

One of the first scientists who suggested abstract laws was Galileo Galilei who also performed the famous experiment of dropping two canon balls from the tower of Pisa (The theory, and the practice showed that they both hit the ground at the same time).

Sir Isaac Newton was the first to propose the three laws of motion (the law of inertia, the second law mentioned above, and the law of action and reaction), and to prove that these laws govern both everyday objects and celestial objects.

Newton also developed the calculus which is necessary to perform the mathematical calculations involved in classical mechanics.

After Newton the field became more mathematical and more abstract.

See also

Edmund Halley -- List of equations in classical mechanics

Further Reading

• Feynman, R, Six Easy Pieces.
• ---, Six Not So Easy Pieces.
• ---, Lectures on Physics.
• Kleppner, D. and Kolenkow, R. J., An Introduction to Mechanics, McGraw-Hill (1973).

  Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Classical mechanics."

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Classical music

(From Wikipedia, the free Encyclopedia)

This article attempts to characterize Western classical music, particularly in comparison with other forms of music popular in Western societies. Further information on classical music can be found in the cross references given below. For articles on the classical music of other cultures, see classical music (disambiguation)

The nature of classical music

In a Western context, "classical music" is a somewhat imprecise term, but there are a number of ways that classical music is identified.

First, classical music is a written musical tradition, preserved in music notation, as opposed to being transmitted in recordings or as folklore. While differences between particular peformances of a classical work are recognized, a work of classical music is generally held to transcend any particular performance thereof. Works that are centuries old can be, and often are, performed far more often than works recently composed. The use of notation is an effective method for classical music because all active participants in the classical music tradition are able to read music. Normally, this ability comes from formal training, which usually begins with learning to play an instrument, and sometimes continues with instruction in music theory and composition. However, there are many passive participants in classical music who enjoy it without being able to read it or perform it.

Another important characteristic of classical music is that it is felt by many to represent a form of "high" culture. Particular works of classical music are often venerated, even to extremes--thus, for instance, the 18th century writer E. T. A. Hoffmann loved Wolfgang Amadeus Mozart's music so much that he changed his middle name to Amadeus. Performances of classical music take place in a relatively solemn atmosphere, with the audience maintaining (ideally) silence during the performance, so that everyone can hear each note and nuance. The performers usually dress formally, a practice which is often taken as a gesture of respect for the music, and performers normally do not engage in casual banter or other direct involvement with the audience.

The other side of concept of "high culture", of course, is snobbery, and participation in classical music has for centuries been, for some, the result of a desire for prestige.

Because classical music represents high culture, parents over the last several centuries have often made sure that their children receive classical music training. They are often motivated by a belief that such training will permit their children to lead richer, fuller lives; or by a belief that such training instills a useful sense of self-discipline.

Written transmission, along with the veneration bestowed on classical works, has important implications for the performance of classical music. To a fair degree, performers are expected to perform a work in a way that realizes the original intentions of the composer, which are often stated quite explicitly (down to the level of small, note-by-note details) in the musical score. Indeed, deviations from the composer's intentions are sometimes condemned as outright ethical lapses. Yet the opposite trend--admiration of performers for new "interpretations" of the composer's work, can be seen, and it is not unknown for a composer to praise a performer for achieving a better realization of the composer's original intent than the composer was able to imagine. Thus, classical music performers often achieve very high reputations for their musicianship, even if they do not compose themselves.

Another consequence of the veneration of the composer's written score is that improvisation plays a relatively minor role in classical music--in sharp contrast to traditions like jazz, where improvisation is central. Improvisation in classical music performance was far more common during the Baroque era, and recently the performance of such music by modern classical musicians has been enriched by a revival of the old improvisational practices. During the Classical period, Mozart and Beethoven sometimes improvised the cadenzas to their piano concertos--but tended to write out the cadenzas when other soloists were to perform them.

Art music and concert music are terms sometimes used as synonyms of classical music.

Classical music as "music of the classical era"

See main article: Classical music era

In music history, a different meaning of the term classical music is often used: it designates music from a period in musical history covering approximately Haydn to Beethoven -- roughly, 1750-1800. When used in this sense, the initial C of Classical music is sometimes capitalized to avoid confusion.

Classical music and popular music

The relationship (particularly, the relative value) of classical music and popular music is a controversial question. Some partisans of classical music may claim that classical music constitutes art and popular music only light entertainment. However, many popular works show a high level of artistry and musical innovation and many classical works are unabashedly crowd-pleasing.

It might be argued that, at least on the average, classical works have greater musical complexity. In particular, classical music usually involves more modulation (changing of keys), less outright repetition, and a wider use of musical phrases that are not default length--that is, four or eight bars long (however, much minimalist music goes against these tendencies). Also, it is normally only in classical music that long works (30 minutes to three hours) are built up hierarchically from smaller units (usually called movements).

This not to say that popular music is always simpler than classical. Both jazz and rap make use of rhythms more complex than would appear in the average classical work, and popular music sometimes uses certain complex chordss that would be quite unusual in a classical music.

Classical and popular music are distinguished to some extent by their choice of instruments. For the most part, the instruments used in classical music are nonelectrical and were invented prior to the mid-1800's (often, much earlier). They consist of the instruments found in an orchestra, together with a few other solo instruments (piano, harpsichord, organ). The electric guitar plays an extremely prominent role in popular music, but plays almost no role in classical music, even classical music of the 20th and 21st centuries. Both classical and popular musicians have experimented for the last several decades with electrical or electronic instruments (for instance, the synthesizer), and instruments from other cultures (such as the gamelan).

One last difference between classical and popular music is worth observing. New performers entering the field of popular music are expected, virtually without exception, to be young and sexually attractive. Older performers are sometimes successful, but typically their following consists largely of fans who encountered them when they were young. In the case of classical music, it is likewise a professional advantage for beginning performers to be attractive, but there is no rigid requirement in this regard. Older performers continue to attract new listeners, and indeed, artists such as Vladimir Horowitz and Artur Rubinstein performed before enthusiastic audiences in advanced old age. Further, a number of opera singers attract enthusiastic followings despite being quite stout or even obese.

A phenomenon that arose in the last century is "cross-over"--the popularity, usually temporary, of certain classical works among people who ordinarily do not listen to classical music. Often this is due to the appearance of a classical work in a filmscore. Some classical works that achieved crossover status in the twentieth century include the Canon in D by Johann Pachelbel, the Symphony No. 3 by Henryk Górecki, Joseph Haydn's Trumpet Concerto (popularized by the trumpeter Wynton Marsalis), and the second movement of Mozart's Piano Concerto, K. 457 (from its appearance in a 1967 film entitled Elvira Madigan). Even atonal music, which tends to be less popular among classical enthusiasts, has a strong niche in popular culture, since (as Charles Rosen has noted) it is widely used in film and television scores "to depict an approaching menace".

An interesting speculation is whether works of popular music are likely to achieve the kind of permanence that works of classical music have achieved. Prior to the advent of audio recordings, this was not a possibility, since popular works are generally identified with the performance of the artist who created them. However, since high-quality audio recordings have now existed for over fifty years, the possibility of popular works achieving some kind of permanent, enshrined, status now presents itself, and is probably happening now in the case of the most outstanding artists.

Periods of classical music

• Early music
• Medieval European music
• Renaissance music
• Baroque music
• Classical music era
• Romantic music
• Impressionist music
• Expressionist music
• Nationalist music
• Modern classical music
• Contemporary music

Other genres of classical music

• Film music
• Electronic art music

Composers of classical music

• List of classical music composers

Terms of classical music

• Polyphony
• Tonality
• Atonality
• Musical tuning
• Counterpoint
• Timbre
• Melody
• Harmony
• Rhythm
• Musical form
• Musical Interpretation
• Musical voices
• Musical color
• Tone Row

  Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Classical music."

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Classical music era

(From Wikipedia, the free Encyclopedia)

The classical music era in Western music occurred in the second half of the 18th century. Although the term classical music is used as a blanket term meaning all kinds of music in a certain tradition, it can also mean this particular era within that tradition.

The classical music era falls between the Baroque and the Romantic periods. Amongst its earliest composers were Joseph Haydn and Carl Philipp Emanuel Bach. The best known composer from this period is Wolfgang Amadeus Mozart. The last classical composers are generally taken to be Ludwig van Beethoven, who after writing in a classical style in his early works, pushed its conventions and forms into new territory, and Franz Schubert, who served as a bridge between the Classical and Romantic Era.

Classical music itself is distinguished by the use of dynamic contrast to accent suspension and return to the tonic. Earlier composers did not have as many tools of dynamic contrast; later composers found more varied uses for those tools.

Classical-period music is distinguishable from Baroque music by its plainness of style, without the heavy and complex Baroque figurations, and from Romantic music by its general emotional coolness and its regularity of form. Forms pioneered in the classical period include the symphony and the string quartet; the concerto also saw considerable development.

Composers of the classical era

• Juan Crisostomo de Arriaga
• Ludwig van Beethoven
• Luigo Boccherini
• Luigi Cherubini
• Domenico Cimarosa
• Franz Danzi
• John Field
• Christoph Willibald Gluck
• Franz Joseph Haydn
• Johann Nepomuk Hummel (1778 - 1837)
• Joseph Martin Kraus
• Wolfgang Amadeus Mozart (1756-1791)
• Niccolò Paganini
• Antonio Salieri
• Franz Schubert
• Fernando Sor (1778-1839)
• Louis Spohr
• Carl Maria von Weber (although chronologically Classical, his music tends to be Romantic)

  Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Classical music era."

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Classical physics

(From Wikipedia, the free Encyclopedia)

Classical physics typically included all of physics before the theory of relativity and the quantum theory came into existence. Nowadays, it includes relativistic theories as well, and something non-classical would involve some quantum phenomenon. Classical physics is characterized by the philosophy of strict determinism unlike the quantum laws (wavefunction collapse, in particular). Thus, it includes all of classical mechanics (the Newton's laws of motion, Lagrangian and Hamiltonian formalisms, Maxwell's Equations of electrodynamics, the laws of thermodynamics, etc...) and also the special and general theories of relativity.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Classical physics."

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Classicism

(From Wikipedia, the free Encyclopedia)

Classicism in the theatre was developed by 17th century French playwrights from what they judged to be the rules of Greek classical theatre, including the Three Unities of time, place and action.

• Unity of time referred to the need for the entire action of the play to take place in a fictional 24-hour period
• Unity of place was as it sounds, the action had to unfold in a single location
• Unity of action meant that the play should be constructed around a single 'plot-line' , such as a tragic love affair or a conflict between honour and duty.

The language also had to be of the most exalted kind, excluding 'low-life' characters and smutty jokes.

Classicists did not approve of Shakespeare, who broke all these rules and plenty more.

Examples of classicist playwrights:

• Pierre Corneille
• Jean Racine

Victor Hugo was among the first french playwrights to break these conventions.

See also:

• Neoclassicism
• Renaissance Classicism

  Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Classicism."

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Classics

(From Wikipedia, the free Encyclopedia)

In its classic sense, "classics", when used as a singular noun, means the study of the language, literature, history, art, and other aspects of ancient Greece and Rome, during the time frame of classical antiquity. As a plural noun "classics" are books written in ancient Greece and Rome. The study of classics is a primary subject for the humanities, and the people reading classics are sometimes called humanists.

• Ancient Greece

Greek language

Greek mythology

Greek literature

Greek architecture

• Ancient Rome

Latin

Roman mythology

Latin literature

Rhetoric

• Post-Classical Scholarship

Humanism

Philology

Classics can also mean (typically in non-academic contexts) classic books.

See also: Classics basic topics

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Classics."

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Logic

(From Wikipedia, the free Encyclopedia)

Roughly speaking, logic is the study of prescriptive systems of reasoning, that is, systems proposed as guides for how people (as well, perhaps, as other intelligent beings/machines/systems) ought to reason. Logic says which forms of inference are valid and which are not. Traditionally, logic is studied as a branch of philosophy, but it can also be considered a branch of mathematics. How people actually reason is usually studied under other headings, including cognitive psychology.

Logos: some words about logic

Logic is traditionally divided into deductive reasoning, concerned with what follows logically from given premises, and inductive reasoning, concerned with how we can go from some number of observed events to a reliable generalization.

As a science, logic defines the structure of statement and argument and devises formulae by which these are codified. Implicit in a study of logic is the understanding of what makes a good argument and what arguments are fallacious.

Philosophical logic deals with formal descriptions of natural language. Most philosophers assume that the bulk of "normal" proper reasoning can be captured by logic, if one can find the right method for translating ordinary language into that logic.

Following are more specific discussions of some systems of logic. See also: list of topics in logic.

Aristotelian logic

Aristotelian logic was pioneered by Aristotle. Although it is possible that Aristotle was taught by someone else, the earliest study of reasoning can be attributed to Aristotle. Aristotle and his followers held that two of the most important principles of logic are the law of non-contradiction and the law of excluded middle. This kind of logic is now given various names to distinguish it from more recent systems of logic, e.g., Aristotelian logic or classical two-valued logic.

The law of non-contradiction states that no proposition is both true and false and law of excluded middle states that a proposition must either be true or false. In combination, these laws require two truth values that are mutually exclusive. A proposition can be either true or false, but cannot be both at the same time.

Some have considered classical logic to be just like a mathematical theory, and in particular the laws of non-contradiction and the excluded middle to be simply axioms of the theory, which have to be assumed without proof. In fact this is not so:

• Assume the law of non-contradiction is false. This means it can still be true, so therefore it is true (it is only the law of non-contradiction that prevents " can be" from necessarily becoming "is"). Therefore classical logic still remains valid.

• Assume the law of the excluded middle is not true. It does not follow that the law of the excluded middle is false, or indeed that any other proposition of classical logic which was true is now false.

• More generally, consider the proposition: "The validity of Rule X is fundamental to the validity of logic. Unless you assume the validity of Rule X, logic is not valid". Now assume that Rule X (whatever it might be) is false. The conclusion that logic is not valid has to follow by logical reasoning. But if logic is not valid, this reasoning is also invalid, and the conclusion cannot be drawn. Thus, the validity of logic is independent of the assumption of validity of any of its supposed laws. (This is an argument by self reference.)

A better way to look at these laws is that, without them, the logic still remains valid, but a whole lot of illogic becomes valid as well. Thus, those laws are simply filters for stripping away the illogic, and leaving only the part that doesn't depend on them—the logic.

Formal logic

See also Propositional calculus

Formal logic, also called symbolic logic, is concerned primarily with the structure of reasoning. Formal logic deals with the relationships between concepts and provides a way to compose proofs of statements. In formal logic, concepts are rigorously defined, and sentences are translated into a precise, compact, and unambiguous symbolic notation.

Some examples of symbolic notation are:

p: 1 + 2 = 3

This statement defines p is 1 + 2 = 3 and that is true.

Two propositions can be combined using conjunction, disjunction or conditional. They are called binary logical operators. Such combined propositions are called compound propositions. For example,

p: 1 + 1 = 2 and "logic is the study of reasoning."

In this case, and is a conjunction. The two propositions can differ totally from each other.

In mathematics and computer science, one may want to state a proposition depending on some variables:

p: n is an odd integer.

This proposition can be either true or false according to the variable n.

A proposition with free variables is called propositional function with domain of discourse D. To form an actual proposition, one uses quantifiers. For every n, or for some n, can be specified by quantifiers: either the universal quantifier or the existential quantifier. For example,

for all n in D, P(n).

This can be written also as:

The standard situation in mathematical analysis since Weierstrass, the quantifications for all ... there exists or there exists ... such that for all (and more complex analogues) can be expressed, instead of symbols. This may be done for clarity in certain cases also.

Mathematical logic

Mathematical logic is the use of formal logic to study mathematical reasoning. At the beginning of the twentieth century, philosophical logicians including (Frege, Russell) attempted to prove that mathematics could be entirely reduced to logic. They held that in discovering the "logical form" of a sentence, you were somehow revealing the "right" way to say it, or uncovering some previously hidden essence. The reduction failed, but in the process, logic took on much of the notation and methodology of mathematics, and nowadays logic is accepted as an accurate way to describe mathematical reasoning.

Philosophical logic

Philosophical logic is essentially a continuation of the traditional discipline that was called "Logic" before it was supplanted by the invention of Mathematical logic. It is concerned with the elucidation of ideas such as reference, predication, identity, truth, quantification, existence, and others. Philosophical logic has a much greater concern with the connection between natural language and logic. See Philosophical logic.

Predicate logic

See also First-order predicate calculus

Gottlob Frege, in his Begriffsschrift, discovered a way to rearrange many sentences to make their logical form clear, to show how sentences relate to one another in certain respects. Prior to Frege, formal logic had not been successful beyond the level of sentential logic: it could represent the structure of sentences composed of other sentences using such words as "and", "or", and "not," but it could not break sentences down into smaller parts. It could not show how "Cows are animals" entails "Parts of cows are parts of animals."

Sentential logic explains the workings of words such as "and", "but", "or", "not", "if-then", "if and only if", and "neither-nor". Frege expanded logic to include words such as "all", "some", and "none". He showed how we can introduce variables and "quantifiers" to rearrange sentences.

• "All humans are mortal" becomes "All things x are such that, if x is a human then x is mortal." which may be written symbolically

• "Some humans are vegetarian" becomes "There exists some (at least one) thing x such that x is human and x is vegetarian" which may be written symbolically

.

Frege treats simple sentences without subject nouns as predicates and applies them to "dummy objects" (x). The logical structure in discourse about objects can then be operated on according to the rules of sentential logic, with some additional details for adding and removing quantifiers. Frege's work started contemporary formal logic.no,

Frege adds to sentential logic (1) the vocabulary of quantifiers (upside-down A, backward E) and variables, (2) a semantics that explains that the variables denote individual objects and the quantifiers have something like the force of "all" "some" in relation to those objects, and (3) methods for using these in language. To introduce an "All" quantifier, you assume an arbitrary variable, prove something that must hold true of it, and then prove that it didn't matter which variable you chose, that would have held true. An "All" quantifier can be removed by applying the sentence to any particular object at all. A "Some" (exists) quantifier can be added to a sentence true of any object at all; it can be removed in favor of a term about which you are not already presupposing any information.

Multi-valued Logic

The logics discussed above are all "bivalent" or "two-valued"; that is, the semantics for each of these languages will assign to every sentence either the value "True" or the value "False."

Systems which do not always make this distinction are known as non-Aristotelian logics, or multi-valued logics.

In the early 20th century Jan Łukasiewicz investigated the extension of the traditional true/false values to include a third value, "possible".

Logics such as fuzzy logic have since been devised with an infinite number of "degrees of truth", e.g., represented by a real number between 0 and 1. Bayesian probability can be interpreted as a system of logic where probability is the subjective truth value.

Logic and computers

Logic is extensively used in the fields of artificial intelligence, and computer science.

In the 1950s and 1960s, researchers predicted that when human knowledge could be expressed using logic with mathematical notation, it would be possible to create a machine that reasons, or artificial intelligence. This turned out to be more difficult than expected because of the complexity of human reasoning. Logic programming is an attempt to make computers do logical reasoning and Prolog programming language is commonly used for it.

In symbolic logic and mathematical logic, proofs by humans can be computer-assisted. Using automated theorem proving the machines can find and check proofs, as well as work with proofs too lengthy to be written out by hand.

In computer science, Boolean algebra is the basis of hardware design, as well as much software design.

Logic Puzzles

A large class of elementary logical puzzles can be solved using the laws of boolean algebra and logic truth tables. Familiarity with boolean algebra and its simplification process is a prerequisite to understand the following examples.

Example

On the Keikei Island, there lived two kinds of people -- knights and knaves. The knights always tell the truth, but the knaves always tell a lie.

John and Bill are residents of the Keikie Island.

Example 1

John says: We are both knaves.

Who is who?

Example 2

John: If Bill is a knave then I'm a knight.

Bill: We are different.

Who is who?

Example 3

Logician: Are you both knights? John: Yes or No. Logician: Are you both knaves? John: Yes or No.

Who is who?

Solution to Example 1

We can use Boolean algebra to deduce who's who as follows:

Let J be true if John is a knight and let B be true if Bill is a knight. Now, either John is a knight and what he said was true, or John is not a knight and what he said was false. Tranlating that into Boolean algebra, we get:

Simplification Process:

by de Morgan's theorem.

Therefore John is a knave and Bill is a knight. Although most people can solve this puzzle without using Boolean algebra, the example still serves as a powerful testament of the power of Boolean algebra in sovling logic puzzles.

See also analytic proposition; college logic; argument form; validity; soundness; cogency; deduction and induction; lambda calculus; modus ponens; affirming the consequent; modus tollens; disjunctive syllogism, faith, Scientific method; fuzzy logic; history of logic; set theory

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Logic."

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Neoclassicism

(From Wikipedia, the free Encyclopedia)

Neoclassicism (sometimes rendered as Neo-Classicism) is the name given to distinct movements in the visual arts, literature and music.

Visual and literary neoclassicism

In visual art, neoclassicism began as a reaction against the Baroque, and a desire to return to perceived "purity" of the arts of Ancient Greece and Rome, and to a lesser extent the examples of Renaissance Classicism.

Neoclassicism first gained influence in France in the 17th century, and continued to be a major force in art through the 19th century and beyond, although from the late 19th century on has often been considered anti-modern or even reactionary in some art circles.

Noted neoclassical artists have included painter Jean Auguste Dominique Ingres and sculptor Antonio Canova. Neoclassical architecture includes the Smith Tower. Known writers of the period have included Daniel Defoe, Jonathan Swift, Alexander Pope and John Dryden.

Neo-classicism in music

In music, neo-classicism was a 20th century development, particularly popular in the period between the two World Wars, in which composers drew inspiration from music of the 18th century. The term is somewhat misleading, because inspiration was as much drawn from the Baroque period as the Classical - for this reason, music which draws influence specifically from the Baroque is sometimes termed neo-baroque.

Neo-classicism can be seen as a reaction to the prevailing trend of 19th century Romanticism to sacrifice internal balance and order in favour of more overtly emotional writing. Neo-classicism makes a return to balanced forms and often emotional restraint, as well as 18th century compositional processes and techniques. However, in the use of modern instrumental resources such as the full orchestra, which had greatly expanded since the 18th century, and advanced harmony, neo-classical works are distinctly 20th century.

Igor Stravinsky composed some of the best known neo-classical works - in his ballet Pulcinella, for example, he used themes which he believed to be by Giovanni Pergolesi (it later transpired that many of them were not, though they were by contemporaries). Paul Hindemith was another neo-classicist, as was Bohuslav Martinu, who revived the Baroque concerto grosso form.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Neoclassicism."

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Synonyms within Context: Classical

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Modern Usage: Classical

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Commercial Usage: Classical

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Image Slideshow: Classical

Photos: Classical More pictures...

Illustrations: Classical More pictures...

Computer Images: Classical More pictures...

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Photo Album: Classical

Thumbnail	Description & Credit	Thumbnail	Description & Credit
	Veranda and doorway. Photograph by L.D. Andrew, May 1936. (Reproduction Number: HABS, GA,108-COLM,4-1) Begun in 1859 for the wealthy Scottish immigrant James A. Rankin but not completed until after the Civil War, this town house combines different building materials and details from a number of historical architectural styles. The ironwork shown here on the veranda is based on the Gothic architecture of medieval England and France. The Corinthian columns of the doorway behind it, on the other hand, call to mind the classical architecture of ancient Greece and Rome. The Rankin House is an excellent example of Eclecticism architecture, the term used to describe the mixing of different styles and materials in buildings. Credit: Library of Congress.		Classical allegory of the arts with female figures representing painting, sculpture, and architecture. Credit: Library of Congress.
	Woman in classical garb with palm leading emigrants (?). Credit: Library of Congress.		Young girl and young man in classical dress and reading a scroll are flanked by soldiers, while a girl strews flowers in front of a bearded old man. Credit: Library of Congress.
	Tropical ballet tries classic New York, N.Y. --a group of the Katherine Dunham dancers are shown in mid-air during a rehearsal of the classical ballet, "Mozart's Sonata in D Major," which they will present at the annual dinner of the Spanish Refugee Appea. Credit: Library of Congress.		Re-photograph of the series "The Seven Words" mounted in elaborately carved frame of classical columns and inscription on architrave. Credit: Library of Congress.
	Room with piano, potted palms, and classical statues and friezes. Credit: Library of Congress.		Classical sculpture gallery, Worcester Art Museum. Credit: Library of Congress.
	Outdoor dance performance with dancers in classical drapery, possibly in Long Island. Credit: Library of Congress.		Miscellaneous interiors. Fireplace with mantel carved with mythological and classical motifs. Credit: Library of Congress.
Source: pictures compiled by the editor from various references; see picture credits.

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Digital Photo Gallery: Classical
 

"Classical Fountain" by Erika Thorpe Commentary: "Fountain in Seaport Village, San Diego."	"English phonebooth" by Kevin Blomqvist Commentary: "A classical english phonebooth in london."
Source: photographs selected by the editor, with permission from the photographers.

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Sounds Captioned with "Classical".

Play	Caption	Play	Caption
	High Classical era work for piano similar to that of works by Bach.		A typical classical guitar etude for solo guitar.
	Classical period piano work featuring melody and chordal accompaniment.		A guitar duet played in a classical guitar style.
	Low pedal point with classical synthesized string harmony for melody.		A classical guitar playing a solo work for guitar.
	A quick piano excerpt stylized in the High Classical era style.
Source: compiled by the editor from various references; see credits.

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Familiar Quotations: Classical

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Historic Usage: Classical

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Use in Literature: Classical

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Non-Fiction Usage: Classical

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Usage Frequency: Classical

Source: compiled by the editor from several corpora; see credits.

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Expressions: Classical

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Frequency of Internet Keywords: Classical

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Modern Translation: Classical

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Ancestral Language Translations: Classical

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Derivations & Misspellings: Classical

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Rhyming with "Classical"

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