Description.

A tuning fork is a fork-shaped acoustic resonator used in many applications to produce a fixed tone. The main reason for using the fork shape is that, unlike many other types of resonators, it produces a very pure tone, with most of the vibrational energy at the fundamental frequency. The reason for this is that the frequency of the first overtone is about = = times the fundamental (about octaves above it). By comparison, the first overtone of a vibrating string or metal bar is one octave above (twice) the fundamental, so when the string is plucked or the bar is struck, its vibrations tend to mix the fundamental and overtone frequencies. When the tuning fork is struck, little of the energy goes into the overtone modes; they also die out correspondingly faster, leaving a pure sine wave at the fundamental frequency. It is easier to tune other instruments with this pure tone.  Another reason for using the fork shape is that it can then be held at the base without dampening the oscillation. That is because its principal mode of vibration is symmetric, with the two prongs always moving in opposite directions, so that at the base where the two prongs meet there is a node (point of no vibratory motion) which can therefore be handled without removing energy from the oscillation (dampening). However, there is still a tiny motion induced in the handle in its longitudinal direction (thus at right angles to the oscillation of the prongs) which can be made audible using any sort of sound board. Thus by pressing the tuning fork's base against a sound board such as a wooden box, table top, or bridge of a musical instrument, this small motion, but which is at a high acoustic pressure (thus a very high acoustic impedance), is partly converted into audible sound in air which involves a much greater motion (particle velocity) at a relatively low pressure (thus low acoustic impedance). The pitch of a tuning fork can also be heard directly through bone conduction, by pressing the tuning fork against the bone just behind the ear, or even by holding the stem of the fork in ones teeth, conveniently leaving both hands free. Bone conduction using a tuning fork is specifically used in the Weber and Rinne tests for hearing in order to bypass the middle ear. If just held in open air, the sound of a tuning fork is very faint due to the acoustic impedance mismatch between the steel and air. Moreover, since the feeble sound waves emanating from each prong are 180° out of phase, those two opposite waves interfere, largely cancelling each other. Thus when a solid sheet is slid in between the prongs of a vibrating fork, the apparent volume actually "increases", as this cancellation is reduced, just as a loudspeaker requires a baffle in order to radiate efficiently.  Commercial tuning forks are tuned to the correct pitch at the factory, and the pitch and frequency in hertz is stamped on them. They can be retuned by filing material off the prongs. Filing the ends of the prongs raises the pitch, while filing the inside of the base of the prongs lowers it.  Currently, the most common tuning fork sounds the note of A = 440 Hz, the standard concert pitch that many orchestras use. That A is the pitch of the violin's second string, the first string of the viola, and an octave above the first string of the cello. Orchestras between 1750 and 1820 mostly used A = 423.5 Hz, though there were many forks and many slightly different pitches. Standard tuning forks are available that vibrate at all the pitches within the central octave of the piano, and also other pitches. Well-known tuning fork manufacturers include Ragg and John Walker, both of Sheffield, England.  Tuning fork pitch varies slightly with temperature, due mainly to a slight decrease in the modulus of elasticity of steel with increasing temperature. A change in frequency of 48 parts per million per °F (86 ppm per °C) is typical for a steel tuning fork. The frequency decreases (becomes flat) with increasing temperature. Tuning forks are manufactured to have their correct pitch at a standard temperature. The standard temperature is now, but is an older standard. The pitch of other instruments is also subject to variation with temperature change.

Calculation of frequency.

The frequency of a tuning fork depends on its dimensions and what it's made from:  where:  The ratio in the equation above can be rewritten as if the prongs are cylindrical with radius, and if the prongs have rectangular cross-section of width along the direction of motion.

Uses.

Tuning forks have traditionally been used to tune musical instruments, though electronic tuners have largely replaced them. Forks can be driven electrically by placing electronic oscillator-driven electromagnets close to the prongs.

In musical instruments.

A number of keyboard musical instruments use principles similar to tuning forks. The most popular of these is the Rhodes piano, in which hammers hit metal tines that vibrate in the magnetic field of a pickup, creating a signal that drives electric amplification. The earlier, un-amplified dulcitone, which used tuning forks directly, suffered from low volume.

In clocks and watches.

The quartz crystal that serves as the timekeeping element in modern quartz clocks and watches is in the form of a tiny tuning fork. It usually vibrates at a frequency of 32,768 Hz in the ultrasonic range (above the range of human hearing). It is made to vibrate by small oscillating voltages applied to metal electrodes plated on the surface of the crystal by an electronic oscillator circuit. Quartz is piezoelectric, so the voltage causes the tines to bend rapidly back and forth.  The Accutron, an electromechanical watch developed by Max Hetzel and manufactured by Bulova beginning in 1960, used a 360-hertz steel tuning fork as its timekeeper, powered by electromagnets attached to a battery-powered transistor oscillator circuit. The fork provided greater accuracy than conventional balance wheel watches. The humming sound of the tuning fork was audible when the watch was held to the ear.

Medical and scientific uses.

Alternatives to the common A=440 standard include philosophical or scientific pitch with standard pitch of C=512. According to Rayleigh, physicists and acoustic instrument makers used this pitch. The tuning fork John Shore gave to George Frideric Handel produces C=512.  Tuning forks, usually C512, are used by medical practitioners to assess a patient's hearing. This is most commonly done with two exams called the Weber test and Rinne test, respectively. Lower-pitched ones, usually at C128, are also used to check vibration sense as part of the examination of the peripheral nervous system.  Orthopedic surgeons have explored using a tuning fork (lowest frequency C=128) to assess injuries where bone fracture is suspected. They hold the end of the vibrating fork on the skin above the suspected fracture, progressively closer to the suspected fracture. If there is a fracture, the periosteum of the bone vibrates, and fire nociceptors (pain receptors) causing a local sharp pain. This can indicate a fracture, which the practitioner refers for medical X-ray. The sharp pain of a local sprain can give a false positive. Established practice, however, requires an X-ray regardless, because it's better than missing a real fracture while wondering if a response means a sprain. A systematic review published in 2014 in BMJ Open suggests that this technique is not reliable or accurate enough for clinical use.  Tuning forks also play a role in several alternative therapy practices, such as sonopuncture and polarity therapy.

Radar gun calibration.

A radar gun that measures the speed of cars or a ball in sports is usually calibrated with a tuning fork. Instead of the frequency, these forks are labeled with the calibration speed and radar band (e.g., X-band or K-band) they are calibrated for.

In gyroscopes.

Doubled and H-type tuning forks are used for tactical-grade Vibrating Structure Gyroscopes and various types of microelectromechanical systems.

Level Sensors.

Tuning fork forms the sensing part of Vibrating Point Level Sensors Point Level Sensors. The tuning fork is kept vibrating at its resonant frequency by a piezoelectric device. Upon coming in contact with solids, amplitude of oscillation goes down, the same is used as a switching parameter for detecting point level for solids. For liquids, the resonant frequency of tuning fork changes upon coming in contact with the liquids, change in frequency is used to detect level.

A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs (tines) formed from a U-shaped bar of elastic metal (usually steel). It resonates at a specific constant pitch when set vibrating by striking it against a surface or with an object, and emits a pure musical tone once the high overtones fade out. A tuning fork's pitch depends on the length and mass of the two prongs. They are traditional sources of standard pitch for tuning musical instruments.

音叉由弹性金属(多为钢)制成,末有一柄,两端分叉,型如拉丁字母‘U’。音叉拥有一固定的共振频率,受到敲击时则震动,在等待初始时的泛音列过去后,音叉发出的音响就具有固定的音高。一个音叉所发出的音高由它分叉部分的长度决定。


Formation.

Cyclogenesis is the development and strengthening of cyclonic circulations, or low-pressure areas, within the atmosphere. Cyclogenesis is the opposite of, and has an anticyclonic (high-pressure system) equivalent which deals with the formation of high-pressure areas—anticyclogenesis. Cyclogenesis is an umbrella term for several different processes, all of which result in the development of some sort of cyclone. Meteorologists use the term "cyclone" where circular pressure systems flow in the direction of the Earth's rotation, which normally coincides with areas of low pressure. The largest low-pressure systems are cold-core polar cyclones and extratropical cyclones which lie on the synoptic scale. Warm-core cyclones such as tropical cyclones, mesocyclones, and polar lows lie within the smaller mesoscale. Subtropical cyclones are of intermediate size. Cyclogenesis can occur at various scales, from the microscale to the synoptic scale. Larger-scale troughs, also called Rossby waves, are synoptic in scale. Shortwave troughs embedded within the flow around larger scale troughs are smaller in scale, or mesoscale in nature. Both Rossby waves and shortwaves embedded within the flow around Rossby waves migrate equatorward of the polar cyclones located in both the Northern and Southern hemispheres. All share one important aspect, that of upward vertical motion within the troposphere. Such upward motions decrease the mass of local atmospheric columns of air, which lowers surface pressure.  Extratropical cyclones form as waves along weather fronts due to a passing by shortwave aloft or upper level jet streak before occluding later in their life cycle as cold-core cyclones. Polar lows are small-scale, short-lived atmospheric low-pressure systems that occur over the ocean areas poleward of the main polar front in both the Northern and Southern Hemispheres. They are part of the larger class of mesoscale weather-systems. Polar lows can be difficult to detect using conventional weather reports and are a hazard to high-latitude operations, such as shipping and gas- and oil-platforms. They are vigorous systems that have near-surface winds of at least. Tropical cyclones form due to latent heat driven by significant thunderstorm activity, and are warm-core with well-defined circulations. Certain criteria need to be met for their formation. In most situations, water temperatures of at least are needed down to a depth of at least ; waters of this temperature cause the overlying atmosphere to be unstable enough to sustain convection and thunderstorms. Another factor is rapid cooling with height, which allows the release of the heat of condensation that powers a tropical cyclone. High humidity is needed, especially in the lower-to-mid troposphere; when there is a great deal of moisture in the atmosphere, conditions are more favorable for disturbances to develop. Low amounts of wind shear are needed, as high shear is disruptive to the storm's circulation. Lastly, a formative tropical cyclone needs a pre-existing system of disturbed weather, although without a circulation no cyclonic development will take place. Mesocyclones form as warm core cyclones over land, and can lead to tornado formation. Waterspouts can also form from mesocyclones, but more often develop from environments of high instability and low vertical wind shear.  In deserts, lack of ground and plant moisture that would normally provide evaporative cooling can lead to intense, rapid solar heating of the lower layers of air. The hot air is less dense than surrounding cooler air. This, combined with the rising of the hot air, results in a low-pressure area called a thermal low. Monsoon circulations are caused by thermal lows which form over large areas of land and their strength is driven by how land heats more quickly than the surrounding nearby ocean. This generates a steady wind blowing toward the land, bringing the moist near-surface air over the oceans with it. Similar rainfall is caused by the moist ocean-air being lifted upwards by mountains, surface heating, convergence at the surface, divergence aloft, or from storm-produced outflows at the surface. However the lifting occurs, the air cools due to expansion in lower pressure, which in turn produces condensation. In winter, the land cools off quickly, but the ocean keeps the heat longer due to its higher specific heat. The hot air over the ocean rises, creating a low-pressure area and a breeze from land to ocean while a large area of drying high pressure is formed over the land, increased by wintertime cooling. Monsoons resemble sea and land breezes, terms usually referring to the localized, diurnal (daily) cycle of circulation near coastlines everywhere, but they are much larger in scale - also stronger and seasonal.

Climatology.

Mid-latitudes and subtropics.

Large polar cyclones help determine the steering of systems moving through the mid-latitudes, south of the Arctic and north of the Antarctic. The Arctic oscillation provides an index used to gauge the magnitude of this effect in the Northern Hemisphere. Extratropical cyclones tend to form east of climatological trough positions aloft near the east coast of continents, or west side of oceans. A study of extratropical cyclones in the Southern Hemisphere shows that between the 30th and 70th parallels there are an average of 37 cyclones in existence during any 6-hour period. A separate study in the Northern Hemisphere suggests that approximately 234 significant extratropical cyclones form each winter. In Europe, particularly in the United Kingdom and in the Netherlands, recurring extratropical low-pressure weather systems are typically known as depressions. These tend to bring wet weather throughout the year. "Thermal lows" also occur during the summer over continental areas across the subtropics - such as the Sonoran Desert, the Mexican plateau, the Sahara, South America, and Southeast Asia. The lows are most commonly located over the Tibetan plateau and in the lee of the Rocky mountains.

Monsoon trough.

Elongated areas of low pressure form at the monsoon trough or intertropical convergence zone as part of the Hadley cell circulation. Monsoon troughing in the western Pacific reaches its zenith in latitude during the late summer when the wintertime surface ridge in the opposite hemisphere is the strongest. It can reach as far as the 40th parallel in East Asia during August and 20th parallel in Australia during February. Its poleward progression is accelerated by the onset of the summer monsoon which is characterized by the development of lower air pressure over the warmest part of the various continents. The large-scale thermal lows over continents help create pressure gradients which drive monsoon circulations. In the southern hemisphere, the monsoon trough associated with the Australian monsoon reaches its most southerly latitude in February, oriented along a west-northwest/east-southeast axis. Many of the world's rainforests are associated with these climatological low-pressure systems.

Tropical cyclone.

Tropical cyclones generally need to form more than or poleward of the 5th parallel north and 5th parallel south, allowing the Coriolis effect to deflect winds blowing towards the low-pressure center and creating a circulation. Worldwide, tropical cyclone activity peaks in late summer, when the difference between temperatures aloft and sea surface temperatures is the greatest. However, each particular basin has its own seasonal patterns. On a worldwide scale, May is the least active month while September is the most active month. November is the only month that activity in all the tropical cyclone basins is possible. Nearly one-third of the world's tropical cyclones form within the western Pacific Ocean, making it the most active tropical cyclone basin on Earth.

Associated weather.

Wind is initially accelerated from areas of high pressure to areas of low pressure. This is due to density (or temperature and moisture) differences between two air masses. Since stronger high-pressure systems contain cooler or drier air, the air mass is denser and flows towards areas that are warm or moist, which are in the vicinity of low-pressure areas in advance of their associated cold fronts. The stronger the pressure difference, or pressure gradient, between a high-pressure system and a low-pressure system, the stronger the wind. Thus, stronger areas of low pressure are associated with stronger winds.  The Coriolis force caused by the Earth's rotation is what gives winds around low-pressure areas (such as in hurricanes, cyclones, and typhoons) their counter-clockwise (anticlockwise) circulation in the northern hemisphere (as the wind moves inward and is deflected right from the center of high pressure) and clockwise circulation in the southern hemisphere (as the wind moves inward and is deflected left from the center of high pressure). A tropical cyclone differs from a hurricane or typhoon based only on geographic location. Note that a tropical cyclone is fundamentally different from a mid-latitude cyclone. A hurricane is a storm that occurs in the Atlantic Ocean and northeastern Pacific Ocean, a typhoon occurs in the northwestern Pacific Ocean, and a tropical cyclone occurs in the south Pacific or Indian Ocean. Friction with land slows down the wind flowing into low-pressure systems and causes wind to flow more inward, or flowing more ageostrophically, toward their centers. A low-pressure area is commonly associated with inclement weather, while a high-pressure area is associated with light winds and fair skies. Tornadoes are often too small, and of too short duration, to be influenced by the Coriolis force, but may be so-influenced when arising from a low-pressure system.

A low-pressure area, low area or low is a region on the topographic map where the air pressure is lower than that of surrounding locations. Low-pressure systems form under areas of wind divergence that occur in the upper levels of the atmosphere. The formation process of a low-pressure area is known as cyclogenesis. Within the field of meteorology, atmospheric divergence aloft occurs in two areas. The first area is on the east side of upper troughs, which form half of a Rossby wave within the Westerlies (a trough with large wavelength that extends through the troposphere). A second area of wind divergence aloft occurs ahead of embedded shortwave troughs, which are of smaller wavelength. Diverging winds aloft ahead of these troughs cause atmospheric lift within the troposphere below, which lowers surface pressures as upward motion partially counteracts the force of gravity.

低压区(英语:Low pressure area,符号为L)是大气中气压较邻近地区为低的地带。一般都是成螺旋状,是为气旋。在北半球低气压区域内的空气作逆时针方向旋转,在南半球则顺时针方向。偶尔也有一连串低压区连在一起,称为「低压槽」,因该区的大气压力比其两旁为低,所以称为槽,是为槽线取其陷下的意思。低压区一般都伴着云,或会有风、雨(通常雨势较大并夹杂着狂风雷暴)。


Terminology.

The philosophy of communitarianism originated in the 20th century, but the term "communitarian" was coined in 1841, by John Goodwyn Barmby, a leader of the British Chartist movement, who used it in referring to utopian socialists and other idealists who experimented with communal styles of life. However, it was not until the 1980s that the term "communitarianism" gained currency through association with the work of a small group of political philosophers. Their application of the label "communitarian" was controversial, even among communitarians, because, in the West, the term evokes associations with the ideologies of socialism and collectivism; so, public leaders — and some of the academics who champion this school of thought — usually avoid the term "communitarian", while still advocating and advancing the ideas of communitarianism.  The term is primarily used in two senses:  Czech and Slovak philosophers like Marek Hrubec, and Luboš Blaha extend communitarianism to social projects tied to the values and significance of community or collectivism, and to various types of socialism and communism (Christian, Utopian, Scientific), for example:

Origins.

While the term communitarian was coined only in the mid-nineteenth century, ideas that are communitarian in nature appear much earlier. They are found in some classical socialist doctrine (e.g. writings about the early commune and about workers' solidarity), and further back in the New Testament. Communitarianism has been traced back to early monasticism.  A number of early sociologists had strongly communitarian elements in their work, such as Ferdinand Tönnies in his comparison of Gemeinschaft (oppressive but nurturing communities) and Gesellschaft (liberating but impersonal societies), and Emile Durkheim's concerns about the integrating role of social values and the relations between the individual and society. Both authors warned of the dangers of anomie (normlessness) and alienation in modern societies composed of atomized individuals who had gained their liberty but lost their social moorings. Modern sociologists saw the rise of a mass society and the decline of communal bonds and respect for traditional values and authority in the United States as of the 1960s. Among those who raised these issues were Robert Nisbet (Twilight of Authority), Robert N. Bellah "Habits of the Heart", and Alan Ehrenhalt (The Lost City: The Forgotten Virtues Of Community In America). In his book Bowling Alone (2000), Robert Putnam documented the decline of "social capital" and stressed the importance of "bridging social capital," in which bonds of connectedness are formed across diverse social groups.  In the twentieth century communitarianism also began to be formulated as a philosophy by Dorothy Day and the Catholic Worker movement. In an early article the "Catholic Worker" clarified the dogma of the Mystical Body of Christ as the basis for the movement's communitarianism. Along similar lines, communitarianism is also related to the personalist philosophy of Emmanuel Mounier.  Responding to criticism that the term 'community' is too vague or cannot be defined, Amitai Etzioni, one of the leaders of the American communitarian movement, pointed out that communities can be defined with reasonable precision as having two characteristics: first, a web of affect-laden relationships among a group of individuals, relationships that often crisscross and reinforce one another (as opposed to one-on-one or chain-like individual relationships); and second, a measure of commitment to a set of shared values, norms, and meanings, and a shared history and identity – in short, a particular culture. Further, author David E. Pearson argued that "[t]o earn the appellation 'community,' it seems to me, groups must be able to exert moral suasion and extract a measure of compliance from their members. That is, communities are necessarily, indeed, by definition, coercive as well as moral, threatening their members with the stick of sanctions if they stray, offering them the carrot of certainty and stability if they don't."  What is specifically meant by "community" in the context of communitarianism can vary greatly between authors and time periods. Historically, communities have been small and localized. However, as the reach of economic and technological forces extended, more-expansive communities became necessary in order to provide effective normative and political guidance to these forces, prompting the rise of national communities in Europe in the 17th century. Since the late 20th century there has been some growing recognition that the scope of even these communities is too limited, as many challenges that people now face, such as the threat of nuclear war and that of global environmental degradation and economic crises, cannot be handled on a national basis. This has led to the quest for more-encompassing communities, such as the European Union. Whether truly supra-national communities can be developed is far from clear.  More modern communities can take many different forms, but are often limited in scope and reach. For example, members of one residential community are often also members of other communities – such as work, ethnic, or religious ones. As a result, modern community members have multiple sources of attachments, and if one threatens to become overwhelming, individuals will often pull back and turn to another community for their attachments. Thus, communitarianism is the reaction of some intellectuals to the problems of Western society, an attempt to find flexible forms of balance between the individual and society, the autonomy of the individual and the interests of the community, between the common good and freedom, rights and duties.

Communitarian philosophy.

In moral and political philosophy, communitarians are best known for their critiques of John Rawls' political liberalism, detailed at length in his book "A Theory of Justice". Communitarians criticize the image Rawls presents of humans as atomistic individuals, and stress that individuals who are well-integrated into communities are better able to reason and act in responsible ways than isolated individuals, but add that if social pressure to conform rises to high levels, it will undermine the individual self. Communitarians uphold the importance of the social realm, and communities in particular, though they differ in the extent to which their conceptions are attentive to liberty and individual rights. Even with these general similarities, communitarians, like members of many other schools of thought, differ considerably from one another. There are several distinct (and at times wildly divergent) schools of communitarian thought.  The following authors have communitarian tendencies in the philosophical sense, but have all taken pains to distance themselves from the political ideology known as communitarianism, which is discussed further below:

Academic communitarianism.

Whereas the classical liberalism of the Enlightenment can be viewed as a reaction to centuries of authoritarianism, oppressive government, overbearing communities, and rigid dogma, modern communitarianism can be considered a reaction to excessive individualism, understood as an undue emphasis on individual rights, leading people to become selfish or egocentric.  The close relation between the individual and the community was discussed on a theoretical level by Michael Sandel and Charles Taylor, among other academic communitarians, in their criticisms of philosophical liberalism, especially the work of the American liberal theorist John Rawls and that of the German Enlightenment philosopher Immanuel Kant. They argued that contemporary liberalism failed to account for the complex set of social relations that all individuals in the modern world are a part of. Liberalism is rooted in an untenable ontology that posits the existence of generic individuals and fails to account for social embeddedness. To the contrary, they argued, there are no generic individuals but rather only Germans or Russians, Berliners or Muscovites, or members of some other particularistic community. Because individual identity is partly constructed by culture and social relations, there is no coherent way of formulating individual rights or interests in abstraction from social contexts. Thus, according to these communitarians, there is no point in attempting to found a theory of justice on principles decided behind Rawls' veil of ignorance, because individuals cannot exist in such an abstracted state, even in principle.  Academic communitarians also contend that the nature of the political community is misunderstood by liberalism. Where liberal philosophers described the polity as a neutral framework of rules within which a multiplicity of commitments to moral values can coexist, academic communitarians argue that such a thin conception of political community was both empirically misleading and normatively dangerous. Good societies, these authors believe, rest on much more than neutral rules and procedures—they rely on a shared moral culture. Some academic communitarians argued even more strongly on behalf of such particularistic values, suggesting that these were the only kind of values which matter and that it is a philosophical error to posit any truly universal moral values.  In addition to Charles Taylor and Michael Sandel, other thinkers sometimes associated with academic communitarianism include Michael Walzer, Alasdair MacIntyre, Seyla Benhabib, and Shlomo Avineri.

Social capital.

Beginning in the late 20th century, many authors began to observe a deterioration in the social networks of the United States. In the book "Bowling Alone", Robert Putnam observed that nearly every form of civic organization has undergone drops in membership exemplified by the fact that, while more people are bowling than in the 1950s, there are fewer bowling leagues.  This results in a decline in "social capital", described by Putnam as "the collective value of all'social networks' and the inclinations that arise from these networks to do things for each other". According to Putnam and his followers, social capital is a key component to building and maintaining democracy.  Communitarians seek to bolster social capital and the institutions of civil society. The Responsive Communitarian Platform described it thus:  Many social goals require partnership between public and private groups. Though government should not seek to replace local communities, it may need to empower them by strategies of support, including revenue-sharing and technical assistance. There is a great need for study and experimentation with creative use of the structures of civil society, and public-private cooperation, especially where the delivery of health, educational and social services are concerned.

Positive rights.

Important to some supporters of communitarian philosophy is the concept of positive rights, which are rights or guarantees to certain things. These may include state-subsidized education, state-subsidized housing, a safe and clean environment, universal health care, and even the right to a job with the concomitant obligation of the government or individuals to provide one. To this end, communitarians generally support social security programs, public works programs, and laws limiting such things as pollution.  A common objection is that by providing such rights, communitarians violate the negative rights of the citizens; rights to "not" have something done for you. For example, taxation to pay for such programs as described above dispossesses individuals of property. Proponents of positive rights, by attributing the protection of negative rights to the society rather than the government, respond that individuals would not have any rights in the absence of societies—a central tenet of communitarianism—and thus have a social responsibility to give something back to it. Some have viewed this as a negation of natural rights. However, what is or is not a "natural right" is a source of contention in modern politics, as well as historically; for example, whether or not universal health care, private property or protection from polluters can be considered a birthright.  Alternatively, some agree that negative rights may be violated by a government action, but argue that it is justifiable if the positive rights protected outweigh the negative rights lost. In the same vein, supporters of positive rights further argue that negative rights are irrelevant in their absence. Moreover, some communitarians "experience this less as a case of being used for others' ends and more as a way of contributing to the purposes of a community I regard as my own".  Still other communitarians question the very idea of natural rights and their place in a properly functioning community. They claim that instead, claims of rights and entitlements creates a society unable to form cultural institutions and grounded social norms based on shared values. Rather, the liberalist claim to individual rights leads to a morality centered on individual emotivism, as ethical issues can no longer be solved by working through common understandings of the good. The worry here is that not only is society individualized, but so are moral claims.

Responsive communitarianism movement.

In the early 1990s, in response to the perceived breakdown in the moral fabric of society engendered by excessive individualism, Amitai Etzioni and William A. Galston began to organize working meetings to think through communitarian approaches to key societal issues. This ultimately took the communitarian philosophy from a small academic group, introduced it into public life, and recast its philosophical content.  Deeming themselves "responsive communitarians" in order to distinguish the movement from authoritarian communitarians, Etzioni and Galston, along with a varied group of academics (including Mary Ann Glendon, Thomas A. Spragens, James Fishkin, Benjamin Barber, Hans Joas, Philip Selznick, and Robert N. Bellah, among others) drafted and published The Responsive Communitarian Platform based on their shared political principles, and the ideas in it were eventually elaborated in academic and popular books and periodicals, gaining thereby a measure of political currency in the West. Etzioni later formed the Communitarian Network to study and promote communitarian approaches to social issues and began publishing a quarterly journal, "The Responsive Community".  The main thesis of responsive communitarianism is that people face two major sources of normativity: that of the common good and that of autonomy and rights, neither of which in principle should take precedence over the other. This can be contrasted with other political and social philosophies which derive their core assumptions from one overarching principle (such as liberty/autonomy for libertarianism). It further posits that a good society is based on a carefully crafted balance between liberty and social order, between individual rights and personal responsibility, and between pluralistic and socially established values.  Responsive communitarianism stresses the importance of society and its institutions above and beyond that of the state and the market, which are often the focus of other political philosophies. It also emphasizes the key role played by socialization, moral culture, and informal social controls rather than state coercion or market pressures. It provides an alternative to liberal individualism and a major counterpoint to authoritarian communitarianism by stressing that strong rights presume strong responsibilities and that one should not be neglected in the name of the other.  Following standing sociological positions, communitarians assume that the moral character of individuals tends to degrade over time unless that character is continually and communally reinforced. They contend that a major function of the community, as a building block of moral infrastructure, is to reinforce the character of its members through the community's "moral voice," defined as the informal sanction of others, built into a web of informal affect-laden relationships, which communities provide.

Influence.

Responsive communitarians have been playing a considerable public role, presenting themselves as the founders of a different kind of environmental movement, one dedicated to shoring up society (as opposed to the state) rather than nature. Like environmentalism, communitarianism appeals to audiences across the political spectrum, although it has found greater acceptance with some groups than others.  Although communitarianism is a small philosophical school, it has had considerable influence on public dialogues and politics. There are strong similarities between communitarian thinking and the Third Way, the political thinking of centrist Democrats in the United States, and the Neue Mitte in Germany. Communitarianism played a key role in Tony Blair's remaking of the British socialist Labour Party into "New Labour" and a smaller role in President Bill Clinton's campaigns. Other politicians have echoed key communitarian themes, such as Hillary Clinton, who has long held that to raise a child takes not just parents, family, friends and neighbors, but a whole village.  It has also been suggested that the compassionate conservatism espoused by President Bush during his 2000 presidential campaign was a form of conservative communitarian thinking, although he did not implement it in his policy program. Cited policies have included economic and rhetorical support for education, volunteerism, and community programs, as well as a social emphasis on promoting families, character education, traditional values, and faith-based projects.  President Barack Obama gave voice to communitarian ideas and ideals in his book "The Audacity of Hope", and during the 2008 presidential election campaign he repeatedly called upon Americans to "ground our politics in the notion of a common good," for an "age of responsibility," and for foregoing identity politics in favor of community-wide unity building. However, for many in the West, the term communitarian conjures up authoritarian and collectivist associations, so many public leaders – and even several academics considered champions of this school – avoid the term while embracing and advancing its ideas.  Reflecting the dominance of liberal and conservative politics in the United States, no major party and few elected officials openly advocate communitarianism. Thus there is no consensus on individual policies, but some that most communitarians endorse have been enacted. Nonetheless, there is a small faction of communitarians within the Democratic Party; prominent communitarians include Bob Casey Jr., Joe Donnelly, and Claire McCaskill. Many communitarian Democrats are part of the Blue Dog Coalition. A small communitarian faction within the Republican Party also exists. Rick Santorum is an example of a communitarian Republican. It is quite possible that the United States' right-libertarian ideological underpinnings have suppressed major communitarian factions from emerging.  Dana Milbank, writing in the "Washington Post", remarked of modern communitarians, "There is still no such thing as a card-carrying communitarian, and therefore no consensus on policies. Some, such as John DiIulio and outside Bush adviser Marvin Olasky, favor religious solutions for communities, while others, like Etzioni and Galston, prefer secular approaches."  In August 2011, the right-libertarian "Reason Magazine" worked with the Rupe organization to survey 1,200 Americans by telephone. The Reason-Rupe poll found that "Americans cannot easily be bundled into either the 'liberal' or 'conservative' groups". Specifically, 28% expressed conservative views, 24% expressed libertarian views, 20% expressed communitarian views, and 28% expressed liberal views. The margin of error was ±3.  A similar Gallup survey in 2011 included possible centrist/moderate responses. That poll reported that 17% expressed conservative views, 22% expressed libertarian views, 20% expressed communitarian views, 17% expressed centrist views, and 24% expressed liberal views. The organization used the terminology "the bigger the better" to describe communitarianism.  The Pakistan Tehreek-e-Insaf party, founded and led by Imran Khan, is considered the first political party in the world which has declared communitarianism as one of their official ideologies.

Comparison to other political philosophies.

Early communitarians were charged with being, in effect, social conservatives. However, many contemporary communitarians, especially those who define themselves as responsive communitarians, fully realize and often stress that they do not seek to return to traditional communities, with their authoritarian power structure, rigid stratification, and discriminatory practices against minorities and women. Responsive communitarians seek to build communities based on open participation, dialogue, and truly shared values. Linda McClain, a critic of communitarians, recognizes this feature of the responsive communitarians, writing that some communitarians do "recognize the need for careful evaluation of what is good and bad about [any specific] tradition and the possibility of severing certain features... from others." And R. Bruce Douglass writes, "Unlike conservatives, communitarians are aware that the days when the issues we face as a society could be settled on the basis of the beliefs of a privileged segment of the population have long since passed."  One major way the communitarian position differs from the social conservative one is that although communitarianism's ideal "good society" reaches into the private realm, it seeks to cultivate only a limited set of core virtues through an organically developed set of values rather than having an expansive or holistically normative agenda given by the state. For example, American society favors being religious over being atheist, but is rather neutral with regard to which particular religion a person should follow. There are no state-prescribed dress codes, "correct" number of children to have, or places one is expected to live, etc. In short, a key defining characteristic of the ideal communitarian society is that in contrast to a liberal state, it creates shared formulations of the good, but the scope of this good is much smaller than that advanced by authoritarian societies."  Authoritarian governments often embrace extremist ideologies and rule with brute force, accompanied with severe restrictions on personal freedom, political and civil rights. Authoritarian governments are overt about the role of the government as director and commander. Civil society and democracy are not generally characteristic of authoritarian regimes.

Criticism.

Liberal theorists such as Simon Caney disagree that philosophical communitarianism has any interesting criticisms to make of liberalism. They reject the communitarian charges that liberalism neglects the value of community, and holds an "atomized" or asocial view of the self.  According to Peter Sutch the principal criticisms of communitarianism are:  However, he goes on to show that such arguments cannot be leveled against the particular communitarian theories of Michael Walzer and Mervyn Frost.  Other critics emphasize close relation of communitarianism to neoliberalism and new policies of dismantling the welfare state institutions through development of the third sector.

Communitarianism is a philosophy that emphasizes the connection between the individual and the community. Its overriding philosophy is based upon the belief that a person's social identity and personality are largely molded by community relationships, with a smaller degree of development being placed on individualism. Although the community might be a family, communitarianism usually is understood, in the wider, philosophical sense, as a collection of interactions, among a community of people in a given place (geographical location), or among a community who share an interest or who share a history. Communitarianism usually opposes extreme individualism and disagrees with extreme "laissez-faire" policies that neglect the stability of the overall community.

社群主义(英语:communitarianism)是一种提倡民主却与个人主义、自由主义对立的政治哲学,又称为“社区主义”、“共同体主义”、“合作主义”等。 社群主义强调个人与群体之间的联系。这种信念来源于认为自我、社会认同、人格等概念都是由社群建构的,与个人主义的观点有很大分歧。尽管社群可以小到以一个家庭为单位,但社群主义经常在更广大的视角下被理解:拥有共同利益、历史文化、居住地理区域的不同人群的互动。


Synonyms.

"Tone quality" and "tone color" are synonyms for "timbre", as well as the ""texture" attributed to a single instrument". However, the word texture can also refer to the type of music, such as multiple, interweaving melody lines versus a singable melody accompanied by subordinate chords. Hermann von Helmholtz used the German "Klangfarbe" ("tone color"), and John Tyndall proposed an English translation, "clangtint", but both terms were disapproved of by Alexander Ellis, who also discredits "register" and "color" for their pre-existing English meanings. The sound of a musical instrument may be described with words such as "bright", "dark", "warm", "harsh", and other terms. There are also colors of noise, such as pink and white. In visual representations of sound, timbre corresponds to the shape of the image, while loudness corresponds to brightness; pitch corresponds to the y-shift of the spectrogram.

ASA definition.

The Acoustical Society of America (ASA) Acoustical Terminology definition 12.09 of timbre describes it as "that attribute of auditory sensation which enables a listener to judge that two nonidentical sounds, similarly presented and having the same loudness and pitch, are dissimilar", adding, "Timbre depends primarily upon the frequency spectrum, although it also depends upon the sound pressure and the temporal characteristics of the sound".

Attributes.

Timbre has been called "...the psychoacoustician's multidimensional waste-basket category for everything that cannot be labeled pitch or loudness." (; "cf." and ).  Many commentators have attempted to decompose timbre into component attributes. For example, J. F. Schouten (1968, 42) describes the "elusive attributes of timbre" as "determined by at least five major acoustic parameters", which Robert finds, "scaled to the concerns of much contemporary music":  An example of a tonal sound is a musical sound that has a definite pitch, such as pressing a key on a piano; a sound with a noiselike character would be white noise, the sound similar to that produced when a radio is not tuned to a station.  See also Psychoacoustic evidence below.

Harmonics.

The richness of a sound or note a musical instrument produces is sometimes described in terms of a sum of a number of distinct frequencies. The lowest frequency is called the "fundamental frequency", and the pitch it produces is used to name the note, but the fundamental frequency is not always the dominant frequency. The dominant frequency is the frequency that is most heard, and it is always a multiple of the fundamental frequency. For example, the dominant frequency for the transverse flute is double the fundamental frequency. Other significant frequencies are called overtones of the fundamental frequency, which may include harmonics and partials. Harmonics are whole number multiples of the fundamental frequency, such as ×2, ×3, ×4, etc. Partials are other overtones. There are also sometimes subharmonics at whole number "divisions" of the fundamental frequency. Most instruments produce harmonic sounds, but many instruments produce partials and inharmonic tones, such as cymbals and other indefinite-pitched instruments.  When the tuning note in an orchestra or concert band is played, the sound is a combination of 440 Hz, 880 Hz, 1320 Hz, 1760 Hz and so on. Each instrument in the orchestra or concert band produces a different combination of these frequencies, as well as harmonics and overtones. The sound waves of the different frequencies overlap and combine, and the balance of these amplitudes is a major factor in the characteristic sound of each instrument.  William Sethares wrote that just intonation and the western equal tempered scale are related to the harmonic spectra/timbre of many western instruments in an analogous way that the inharmonic timbre of the Thai renat (a xylophone-like instrument) is related to the seven-tone near-equal tempered pelog scale in which they are tuned. Similarly, the inharmonic spectra of Balinese metallophones combined with harmonic instruments such as the stringed rebab or the voice, are related to the five-note near-equal tempered slendro scale commonly found in Indonesian gamelan music.

Envelope.

The timbre of a sound is also greatly affected by the following aspects of its "envelope": attack time and characteristics, decay, sustain, release (ADSR envelope) and transients. Thus these are all common controls on professional synthesizers. For instance, if one takes away the attack from the sound of a piano or trumpet, it becomes more difficult to identify the sound correctly, since the sound of the hammer hitting the strings or the first blast of the player's lips on the trumpet mouthpiece are highly characteristic of those instruments. The envelope is the overall amplitude structure of a sound, so called because the sound just "fits" inside its envelope: what this means should be clear from a time-domain display of almost any interesting sound, zoomed out enough that the entire waveform is visible.

In music history.

Instrumental timbre played an increasing role in the practice of orchestration during the eighteenth and nineteenth centuries. Berlioz and Wagner made significant contributions to its development during the nineteenth century. For example, Wagner’s “Sleep motif” from Act 3 of his opera "Die Walküre", features a descending chromatic scale that passes through a gamut of orchestral timbres. First the woodwind (flute, followed by oboe), then the massed sound of strings with the violins carrying the melody, and finally the brass (French horns).Debussy, who composed during the last decades of the nineteenth and the first decades of the twentieth centuries, has been credited with elevating further the role of timbre: "To a marked degree the music of Debussy elevates timbre to an unprecedented structural status; already in "Prélude à l'après-midi d'un faune" the "color" of flute and harp functions referentially".  Mahler’s approach to orchestration illustrates the increasing role of differentiated timbres in music of the early twentieth century. Norman describes the following passage from the Scherzo movement of his Sixth Symphony, as "a seven-bar link to the trio consisting of an extension in diminuendo of the repeated As... though now rising in a succession of piled octaves which moreover leap-frog with Cs added to the As. The lower octaves then drop away and only the Cs remain so as to dovetail with the first oboe phrase of the trio." During these bars, Mahler passes the repeated notes through a gamut of instrumental colors, mixed and single: starting with horns and pizzicato strings, progressing through trumpet, clarinet, flute, piccolo and finally, oboe: See also Klangfarbenmelodie.  In rock music from the late 1960s to the 2000s, the timbre of specific sounds is important to a song. For example, in heavy metal music, the sonic impact of the heavily amplified, heavily distorted power chord played on electric guitar through very loud guitar amplifiers and rows of speaker cabinets is an essential part of the style's musical identity. You could not take the heavily amplified electric guitar part and substitute it with the same notes played on a grand piano or pipe organ.

Psychoacoustic evidence.

Often, listeners can identify an instrument, even at different pitches and loudness, in different environments, and with different players. In the case of the clarinet, acoustic analysis shows waveforms irregular enough to suggest three instruments rather than one. David suggests that this implies that "[C]ertain strong regularities in the acoustic waveform of the above instruments must exist which are invariant with respect to the above variables." However, Robert Erickson argues that there are few regularities and they do not explain our "...powers of recognition and identification." He suggests borrowing the concept of subjective constancy from studies of vision and visual perception.  Psychoacoustic experiments from the 1960s onwards tried to elucidate the nature of timbre. One method involves playing pairs of sounds to listeners, then using a multidimensional scaling algorithm to aggregate their dissimilarity judgments into a timbre space. The most consistent outcomes from such experiments are that brightness or spectral energy distribution, and the "bite", or rate and synchronicity and rise time, of the attack are important factors.

Tristimulus timbre model.

The concept of tristimulus originates in the world of color, describing the way three primary colors can be mixed together to create a given color. By analogy, the musical tristimulus measures the mixture of harmonics in a given sound, grouped into three sections. It is basically a proposal of reducing a huge number of sound partials, that can amount to dozens or hundreds in some cases, down to only three values. The first tristimulus measures the relative weight of the first harmonic; the second tristimulus measures the relative weight of the second, third, and fourth harmonics taken together; and the third tristimulus measures the relative weight of all the remaining harmonics (;, ): More evidences, studies and applications would be needed regarding this type of representation, in order to validate it.

Brightness.

The term "brightness" is also used in discussions of sound timbres, in a rough analogy with visual brightness. Timbre researchers consider brightness to be one of the perceptually strongest distinctions between sounds, and formalize it acoustically as an indication of the amount of high-frequency content in a sound, using a measure such as the spectral centroid.

In music, timbre (, ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or tone. Timbre distinguishes different types of sound production, such as choir voices and musical instruments, such as string instruments, wind instruments, and percussion instruments. It also enables listeners to distinguish different instruments in the same category (e.g., an oboe and a clarinet, both woodwind instruments).

音色(timbre)是音的特色。不同音色的声音,即使在同一音高和同一响度的情况下,也能让人区分开来。同样的音高和响度配上不同的音色就好比同样色相和明度配上不同的色度一样。


History.

The technique of using a group of still cameras to freeze motion occurred before the invention of cinema itself with preliminary work by Etienne Jules Marey on chronophotography, later experimented by Eadweard Muybridge. In "Sallie Gardner at a Gallop" (1878), Muybridge analyzed the motion of a galloping horse by using a line of cameras to photograph the animal as it ran past. Eadweard Muybridge used still cameras placed along a racetrack, and each camera was actuated by a taut string stretched across the track; as the horse galloped past, the camera shutters snapped, taking one frame at a time. The original intent was to settle a debate Leland Stanford had engaged in, as to whether all four of the animal's legs would leave the ground when galloping. Muybridge later assembled the pictures into a rudimentary animation, by placing them on a glass disk which he spun in front of a light source. His zoopraxiscope may have been an inspiration for Thomas Edison to explore the idea of motion pictures.  Muybridge also took photos of actions from many angles at the same instant in time, to study how the human body went up stairs, for example. In effect, however, Muybridge had achieved the aesthetic opposite to modern bullet-time sequences, since his studies lacked the dimensionality of the later developments. A debt may also be owed to MIT professor Harold Edgerton, who, in the 1940s, captured now-iconic photos of bullets using xenon strobe lights to "freeze" motion.  Bullet-time as a concept was frequently developed in cel animation. One of the earliest examples is the shot at the end of the title sequence for the 1966 Japanese anime series "Speed Racer": as Speed leaps from the Mach Five, he freezes in mid-jump, and then the camera does an arc shot from front to sideways.  In 1980, Tim Macmillan started producing pioneering film and later, video, in this field while studying for a BA at the (then named) Bath Academy of Art using 16mm film arranged in a progressing circular arrangement of pinhole cameras. They were the first iteration of the Time-Slice' Motion-Picture Array Cameras" which he developed in the early 1990s when still cameras for the array capable of high image quality for broadcast and movie applications became available. In 1997 he founded Time-Slice Films Ltd. (UK). He applied the technique to his artistic practice in a video projection, titled "Dead Horse" in an ironic reference to Muybridge, that was exhibited at the London Electronic Arts Gallery in 1998 and in 2000 was nominated for the Citibank Prize for photography.  The first music video to use aspects of bullet-time was "Midnight Mover", a 1985 Accept video. In the 1990s, a morphing-based variation on time-slicing was employed by director Michel Gondry and the visual effects company BUF Compagnie in the music video for The Rolling Stones' "Like A Rolling Stone", and in a 1996 Smirnoff commercial the effect was used to depict slow-motion bullets being dodged. Similar time-slice effects were also featured in commercials for The Gap (which was directed by M. Rolston and again produced by BUF), and in feature films such as "Lost in Space" (1998) and "Buffalo '66" (1998) and the television program "The Human Body".  It is well-established for feature films' action scenes to be depicted using slow-motion footage, for example the gunfights in "The Wild Bunch" (directed by Sam Peckinpah) and the heroic bloodshed films of John Woo. Subsequently, the 1998 film "Blade" featured a scene that used computer generated bullets and slow-motion footage to illustrate characters' superhuman bullet-dodging reflexes. The 1999 film "The Matrix" combined these elements (gunfight action scenes, superhuman bullet-dodging, and time-slice effects), popularizing both the effect and the term "bullet-time". "The Matrix" version of the effect was created by John Gaeta and Manex Visual Effects. Rigs of still cameras were set up in patterns determined by simulations, and then shot either simultaneously (producing an effect similar to previous time-slice scenes) or sequentially (which added a temporal element to the effect). Interpolation effects, digital compositing, and computer generated "virtual" scenery were used to improve the fluidity of the apparent camera motion. Gaeta said of "The Matrix" use of the effect:  For artistic inspiration for bullet time, I would credit Otomo Katsuhiro, who co-wrote and directed "Akira", which definitely blew me away, along with director Michel Gondry. His music videos experimented with a different type of technique called view-morphing and it was just part of the beginning of uncovering the creative approaches toward using still cameras for special effects. Our technique was significantly different because we built it to move around objects that were themselves in motion, and we were also able to create slow-motion events that 'virtual cameras' could move around – rather than the static action in Gondry's music videos with limited camera moves.  Following "The Matrix", bullet time and other slow-motion effects were featured as key gameplay mechanics in various video games. While some games like Cyclone Studios' "", released in March 1999, featured slow-motion effects, Remedy Entertainment's 2001 video game "Max Payne" is considered to be the first true implementation of a bullet-time effect that enables the player to have added limited control (such as aiming and shooting) during the slow-motion mechanic; this mechanic was explicitly called "Bullet Time" in the game. The mechanic is also used extensively in the "F.E.A.R." series, combining it with squad-based enemy design encouraging the player to use bullet time to avoid being overwhelmed.  Bullet time was used for the first time in a live music environment in October 2009 for Creed's live DVD "Creed Live".

Technology.

The bullet time effect was originally achieved photographically by a set of still cameras surrounding the subject. The cameras are fired sequentially, or all at the same time, depending on the desired effect. Single frames from each camera are then arranged and displayed consecutively to produce an orbiting viewpoint of an action frozen in time or as hyper-slow-motion. This technique suggests the limitless perspectives and variable frame rates possible with a virtual camera. However, if the still array process is done with real cameras, it is often limited to assigned paths.  In "The Matrix", the camera path was pre-designed using computer-generated visualizations as a guide. Cameras were arranged, behind a green or blue screen, on a track and aligned through a laser targeting system, forming a complex curve through space. The cameras were then triggered at extremely close intervals, so the action continued to unfold, in extreme slow-motion, while the viewpoint moved. Additionally, the individual frames were scanned for computer processing. Using sophisticated interpolation software, extra frames could be inserted to slow down the action further and improve the fluidity of the movement (especially the frame rate of the images); frames could also be dropped to speed up the action. This approach provides greater flexibility than a purely photographic one. The same effect can also be simulated using pure CGI, motion capture and other approaches.  Bullet time evolved further through "The Matrix" series (1999–2003) with the introduction of high-definition computer-generated approaches like virtual cinematography and universal capture. Universal capture, a machine vision guided system, was the first ever motion picture deployment of an array of high definition cameras focused on a common human subject (actor, Neo) in order to create volumetric photography. Like the concept of bullet time, the subject could be viewed from any angle yet, at the same time, the depth based media could be recomposed as well as spatially integrated within computer generated constructs. It moved past a visual concept of a virtual camera to becoming an actual virtual camera. Virtual elements within the Matrix Trilogy utilized state-of-the-art image-based computer rendering techniques pioneered in Paul Debevec's 1997 film "The Campanile" and custom evolved for "The Matrix" by George Borshukov, an early collaborator of Debevec. Inspiration aside, virtual camera methodologies pioneered within the "Matrix" trilogy have been often credited as fundamentally contributing to capture approaches required for emergent virtual reality and other immersive experience platforms.  For many years, it has been possible to use computer vision techniques to capture scenes and render images of novel viewpoints sufficient for bullet time type effects. More recently, these have been formalized into what is becoming known as free viewpoint television (FTV). At the time of "The Matrix", FTV was not a fully mature technology. FTV is effectively the live action version of bullet time, without the slow motion.

Bullet time (also known as frozen moment, dead time, flow motion or time slice) is a visual effect or visual impression of detaching the time and space of a camera (or viewer) from those of its visible subject. It is a depth enhanced simulation of variable-speed action and performance found in films, broadcast advertisements, and realtime graphics within video games and other special media. It is characterized both by its extreme transformation of time (slow enough to show normally imperceptible and unfilmable events, such as flying bullets) and space (by way of the ability of the camera angle—the audience's point-of-view—to move around the scene at a normal speed while events are slowed). This is almost impossible with conventional slow motion, as the physical camera would have to move implausibly fast; the concept implies that only a "virtual camera", often illustrated within the confines of a computer-generated environment such as a virtual world or virtual reality, would be capable of "filming" bullet-time types of moments. Technical and historical variations of this effect have been referred to as time slicing, view morphing, "temps mort" (French: "dead time") and virtual cinematography.

子弹时间(英语:Bullet time)是一种使用在电影、电视广告或电脑游戏中,用计算机辅助的摄影技术模拟变速特效,例如强化的慢镜头、时间静止等效果。它的特点是不但在时间上极端变化(观众可以看到一些在平常不能见到的景象,如子弹缓慢飞过头顶,因此得名),而且在空间上极端变化:在慢镜头的同时拍摄角度(观众视角)也围绕场景旋转。


History.

The octonions were discovered in 1843 by John T. Graves, inspired by his friend William Rowan Hamilton's discovery of quaternions. Graves called his discovery octaves, and mentioned them in a letter to Hamilton dated 16 December 1843. He first published his result slightly later than Arthur Cayley's article. The octonions were discovered independently by Cayley and are sometimes referred to as Cayley numbers or the Cayley algebra. Hamilton described the early history of Graves' discovery.

Definition.

The octonions can be thought of as octets (or 8-tuples) of real numbers. Every octonion is a real linear combination of the unit octonions:  where formula_3 is the scalar or real element; it may be identified with the real number 1. That is, every octonion "x" can be written in the form with real coefficients formula_5.  Addition and subtraction of octonions is done by adding and subtracting corresponding terms and hence their coefficients, like quaternions. Multiplication is more complex. Multiplication is distributive over addition, so the product of two octonions can be calculated by summing the products of all the terms, again like quaternions. The product of each pair of terms can be given by multiplication of the coefficients and a multiplication table of the unit octonions, like this one (due to Cayley, 1845, and Graves, 1843):  Most off-diagonal elements of the table are antisymmetric, making it almost a skew-symmetric matrix except for the elements on the main diagonal, as well as the row and column for which formula_3 is an operand.  The table can be summarized as follows:  where formula_8 is the Kronecker delta and formula_9 is a completely antisymmetric tensor with value +1 when "ijk" = 123, 145, 176, 246, 257, 347, 365.  The above definition though is not unique, but is only one of 480 possible definitions for octonion multiplication with. The others can be obtained by permuting and changing the signs of the non-scalar basis elements formula_10. The 480 different algebras are isomorphic, and there is rarely a need to consider which particular multiplication rule is used.  Each of these 480 definitions is invariant up to signs under some 7-cycle of the points (1234567), and for each 7-cycle there are four definitions, differing by signs and reversal of order. A common choice is to use the definition invariant under the 7-cycle (1234567) with — by using the triangular multiplication diagram, or Fano plane, below (and instead of the multiplication table, above) — as it is particularly easy to remember the multiplication.  A variation of this sometimes used is to label the elements of the basis by the elements ∞, 0, 1, 2,..., 6, of the projective line over the finite field of order 7. The multiplication is then given by and, and all expressions obtained from this by adding a constant (mod 7) to all subscripts: in other words using the 7 triples (124) (235) (346) (450) (561) (602) (013). These are the nonzero codewords of the quadratic residue code of length 7 over the Galois field of two elements, "GF"(2). There is a symmetry of order 7 given by adding a constant mod 7 to all subscripts, and also a symmetry of order 3 given by multiplying all subscripts by one of the quadratic residues 1, 2, 4 mod 7.  The multiplication table for a geometric algebra of signature (−−−−) can be given in terms of the following 7 quaternionic triples (omitting the identity element): ("I","j","k"), ("i","J","k"), ("i","j","K"), ("I","J","K"), (∗"I","i","m"), (∗"J","j","m"), (∗"K","k","m") in which the lowercase items are vectors (mathematics and physics) and the uppercase ones are bivectors and (which is in fact the Hodge star operator). If the ∗ is forced to be equal to the identity then the multiplication ceases to be associative, but the ∗ may be removed from the multiplication table resulting in an octonion multiplication table.  In keeping associative and thus not reducing the 4-dimensional geometric algebra to an octonion one, the whole multiplication table can be derived from the equation for ∗. Consider the gamma matrices. The formula defining the fifth gamma matrix shows that it is the ∗ of a four-dimensional geometric algebra of the gamma matrices.

Cayley–Dickson construction.

A more systematic way of defining the octonions is via the Cayley–Dickson construction. Just as quaternions can be defined as pairs of complex numbers, the octonions can be defined as pairs of quaternions. Addition is defined pairwise. The product of two pairs of quaternions and is defined by where formula_12 denotes the conjugate of the quaternion "z". This definition is equivalent to the one given above when the eight unit octonions are identified with the pairs

Fano plane mnemonic.

A convenient mnemonic for remembering the products of unit octonions is given by the diagram, which represents the multiplication table of Cayley and Graves. This diagram with seven points and seven lines (the circle through 1, 2, and 3 is considered a line) is called the Fano plane. The lines are directional. The seven points correspond to the seven standard basis elements of Im(O) (see definition below). Each pair of distinct points lies on a unique line and each line runs through exactly three points.  Let be an ordered triple of points lying on a given line with the order specified by the direction of the arrow. Then multiplication is given by  together with cyclic permutations. These rules together with  completely defines the multiplicative structure of the octonions. Each of the seven lines generates a subalgebra of O isomorphic to the quaternions H.

Conjugate, norm, and inverse.

The "conjugate" of an octonion  is given by  Conjugation is an involution of O and satisfies (note the change in order).  The "real part" of "x" is given by  and the "imaginary part" by  The set of all purely imaginary octonions span a 7 dimension subspace of O, denoted Im(O).  Conjugation of octonions satisfies the equation  The product of an octonion with its conjugate,, is always a nonnegative real number:  Using this the norm of an octonion can be defined, as  This norm agrees with the standard Euclidean norm on R.  The existence of a norm on O implies the existence of inverses for every nonzero element of O. The inverse of is given by  It satisfies.

Properties.

Octonionic multiplication is neither commutative:  nor associative:  The octonions do satisfy a weaker form of associativity: they are alternative. This means that the subalgebra generated by any two elements is associative. Actually, one can show that the subalgebra generated by any two elements of O is isomorphic to R, C, or H, all of which are associative. Because of their non-associativity, octonions do not have matrix representations, unlike quaternions.  The octonions do retain one important property shared by R, C, and H: the norm on O satisfies  This equation means that the octonions form a composition algebra. The higher-dimensional algebras defined by the Cayley–Dickson construction (e.g., the sedenions) all fail to satisfy this property. They all have zero divisors.  Wider number systems exist which have a multiplicative modulus (e.g. 16-dimensional conic sedenions). Their modulus is defined differently from their norm, and they also contain zero divisors.  As shown by Hurwitz, R, C, H, and O are the only normed division algebras over the reals. These four algebras also form the only alternative, finite-dimensional division algebras over the reals (up to isomorphism).  Not being associative, the nonzero elements of O do not form a group. They do, however, form a loop, indeed a Moufang loop.

Commutator and cross product.

The commutator of two octonions "x" and "y" is given by  This is antisymmetric and imaginary. If it is considered only as a product on the imaginary subspace Im(O) it defines a product on that space, the seven-dimensional cross product, given by  Like the cross product in three dimensions this is a vector orthogonal to "x" and "y" with magnitude  But like the octonion product it is not uniquely defined. Instead there are many different cross products, each one dependent on the choice of octonion product.

Automorphisms.

An automorphism, "A", of the octonions is an invertible linear transformation of O which satisfies  The set of all automorphisms of O forms a group called "G". The group "G" is a simply connected, compact, real Lie group of dimension 14. This group is the smallest of the exceptional Lie groups and is isomorphic to the subgroup of Spin(7) that preserves any chosen particular vector in its 8-dimensional real spinor representation. The group Spin(7) is in turn a subgroup of the group of isotopies described below.  "See also": PSL(2,7) – the automorphism group of the Fano plane.

Isotopies.

An isotopy of an algebra is a triple of bijective linear maps "a", "b", "c" such that if then. For this is the same as an automorphism. The isotopy group of an algebra is the group of all isotopies, which contains the group of automorphisms as a subgroup.  The isotopy group of the octonions is the group Spin(R), with "a", "b", and "c" acting as the three 8-dimensional representations. The subgroup of elements where "c" fixes the identity is the subgroup Spin(R), and the subgroup where "a", "b", and "c" all fix the identity is the automorphism group "G".

Applications.

The octonions play a significant role in the classification and construction of other mathematical entities. For example, the exceptional Lie group G is the automorphism group of the octonions, and the other exceptional Lie groups F, E, E and E can be understood as the isometries of certain projective planes defined using the octonions. The set of self-adjoint formula_32 octonionic matrices, equipped with a symmetrized matrix product, defines the Albert algebra. In discrete mathematics, the octonions provide an elementary derivation of the Leech lattice, and thus they are closely related to the sporadic simple groups.  Applications of the octonions to physics have largely been conjectural. For example, in the 1970s, attempts were made to understand quarks by way of an octonionic Hilbert space. It is known that the octonions, and the fact that only four normed division algebras can exist, relates to the spacetime dimensions in which supersymmetric quantum field theories can be constructed. Also, attempts have been made to obtain the Standard Model of elementary particle physics from octonionic constructions, for example using the "Dixon algebra" formula_33.  Octonions have also arisen in the study of black hole entropy and quantum information science.  Octonions have been used in solutions to the hand eye calibration problem in robotics.  Deep octonion networks provide a means of efficient and compact expression in machine learning applications.

Integral octonions.

There are several natural ways to choose an integral form of the octonions. The simplest is just to take the octonions whose coordinates are integers. This gives a nonassociative algebra over the integers called the Gravesian octonions. However it is not a maximal order (in the sense of ring theory); there are exactly 7 maximal orders containing it. These 7 maximal orders are all equivalent under automorphisms. The phrase "integral octonions" usually refers to a fixed choice of one of these seven orders.  These maximal orders were constructed by, Dickson and Bruck as follows. Label the 8 basis vectors by the points of the projective line over the field with 7 elements. First form the "Kirmse integers" : these consist of octonions whose coordinates are integers or half integers, and that are half integers (that is, halves of odd integers) on one of the 16 sets of the extended quadratic residue code of length 8 over the field of 2 elements, given by ∅, (∞124) and its images under adding a constant mod 7, and the complements of these 8 sets. Then switch infinity and any one other coordinate; this operation creates a bijection of the Kirmse integers onto a different set, which is a maximal order. There are 7 ways to do this, giving 7 maximal orders, which are all equivalent under cyclic permutations of the 7 coordinates 0123456. (Kirmse incorrectly claimed that the Kirmse integers also form a maximal order, so he thought there were 8 maximal orders rather than 7, but as pointed out they are not closed under multiplication; this mistake occurs in several published papers.)  The Kirmse integers and the 7 maximal orders are all isometric to the E lattice rescaled by a factor of 1/. In particular there are 240 elements of minimum nonzero norm 1 in each of these orders, forming a Moufang loop of order 240.  The integral octonions have a "division with remainder" property: given integral octonions "a" and, we can find "q" and "r" with, where the remainder "r" has norm less than that of "b".  In the integral octonions, all left ideals and right ideals are 2-sided ideals, and the only 2-sided ideals are the principal ideals "nO" where "n" is a non-negative integer.  The integral octonions have a version of factorization into primes, though it is not straightforward to state because the octonions are not associative so the product of octonions depends on the order in which one does the products. The irreducible integral octonions are exactly those of prime norm, and every integral octonion can be written as a product of irreducible octonions. More precisely an integral octonion of norm "mn" can be written as a product of integral octonions of norms "m" and "n".  The automorphism group of the integral octonions is the group "G"(F) of order 12096, which has a simple subgroup of index 2 isomorphic to the unitary group "A"(3). The isotopy group of the integral octonions is the perfect double cover of the group of rotations of the E lattice.

In mathematics, the octonions are a normed division algebra over the real numbers, meaning it is a hypercomplex number system; Octonions are usually represented by the capital letter O, using boldface O or blackboard bold formula_1. Octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension. They are noncommutative and nonassociative, but satisfy a weaker form of associativity; namely, they are alternative. They are also power associative.

八元数是四元数的一个非结合推广,通常记为O,或formula_1。