History.

Ancient.

The earliest enamel all used the cloisonné technique, placing the enamel within small cells with gold walls. This had been used as a technique to hold pieces of stone and gems tightly in place since the 3rd millenium BC, for example in Mesopotamia, and then Egypt. Enamel seems likely to have developed as a cheaper method of achieving similar results.  The earliest undisputed objects known to use enamel are a group of Mycenaean rings from Cyprus, dated to the 13th century BC. Although Egyptian pieces, including jewellery from the Tomb of Tutankhamun of c. 1325 BC, are frequently described as using "enamel", many scholars doubt the glass paste was sufficiently melted to be properly so described, and use terms such as "glass-paste". It seems possible that in Egyptian conditions the melting point of the glass and gold were too close to make enamel a viable technique. Nonetheless, there appear to be a few actual examples of enamel, perhaps from the Third Intermediate Period of Egypt (beginning 1070 BC) on. But it remained rare in both Egypt and Greece.  The technique appears in the Kuban during the Scythian period, and was perhaps carried by the Sarmatians to the ancient Celts. Red enamel is used in 26 places on the Battersea Shield (c.350–50 BC), probably as an imitation of the red Mediterranean coral, which is used on the Witham Shield (400-300 BC). Pliny the Elder mentions the Celts' use of the technique on metal, which the Romans in his day hardly knew. The Staffordshire Moorlands Pan is a 2nd century AD souvenir of Hadrian's Wall, made for the Roman military market, which has swirling enamel decoration in a Celtic style. In Britain, probably through preserved Celtic craft skills, enamel survived until the hanging bowls of early Anglo-Saxon art.  A problem that adds to the uncertainty over early enamel is artefacts (typically excavated) that appear to have been prepared for enamel, but have now lost whatever filled the cloisons or backing to a champlevé piece. This occurs in several different regions, from ancient Egypt to Anglo-Saxon England. Once enamel becomes more common, as in medieval Europe after about 1000, the assumption that enamel was originally used becomes safer.

Medieval and Renaissance Europe.

In European art history, enamel was at its most important in the Middle Ages, beginning with the Late Romans and then the Byzantine, who began to use cloisonné enamel in imitation of cloisonné inlays of precious stones. The Byzantine enamel style was widely adopted by the "barbarian" peoples of Migration Period northern Europe. The Byzantines then began to use cloisonné more freely to create images; this was also copied in Western Europe.  Mosan metalwork often included enamel plaques of the highest quality in reliquaries and other large works of goldsmithing. Limoges enamel was made in Limoges, France, the most famous centre of vitreous enamel production in Western Europe, though Spain also made a good deal. Limoges became famous for champlevé enamels from the 12th century onwards, producing on a large scale, and then (after a period of reduced production) from the 15th century retained its lead by switching to painted enamel on flat metal plaques. The champlevé technique was considerably easier and very widely practiced in the Romanesque period. In Gothic art the finest work is in basse-taille and ronde-bosse techniques, but cheaper champlevé works continued to be produced in large numbers for a wider market.  Painted enamel remained in fashion for over a century, and in France developed into a sophisticated Renaissance and the Mannerist style, seen on objects such as large display dishes, ewers, inkwells and in small portraits. After it fell from fashion it continued as a medium for portrait miniatures, spreading to England and other countries. This continued until the early 19th century.  A Russian school developed, which used the technique on other objects, as in the Renaissance, and for relatively cheap religious pieces such as crosses and small icons.

China.

From either Byzantium or the Islamic world, the cloisonné technique reached China in the 13–14th centuries. The first written reference to cloisonné is in a book from 1388, where it is called "Dashi ('Muslim') ware". No Chinese pieces that are clearly from the 14th century are known; the earliest datable pieces are from the reign of the Xuande Emperor (1425–35), which, since they show a full use of Chinese styles, suggest considerable experience in the technique.  Cloisonné remained very popular in China until the 19th century and is still produced today. The most elaborate and most highly valued Chinese pieces are from the early Ming Dynasty, especially the reigns of the Xuande Emperor and Jingtai Emperor (1450–57), although 19th century or modern pieces are far more common. Starting from the mid-19th century, the Japanese also produced large quantities of very high technical quality.

Later.

Persians used this method for colouring and ornamenting the surface of metals by fusing over it brilliant colours that are decorated in an intricate design and called it Meenakari. The French traveller, Jean Chardin, who toured Iran during the Safavid period, made a reference to an enamel work of Isfahan, which comprised a pattern of birds and animals on a floral background in light blue, green, yellow and red. Gold has been used traditionally for Meenakari jewellery as it holds the enamel better, lasts longer and its lustre brings out the colours of the enamels. Silver, a later introduction, is used for artifacts like boxes, bowls, spoons, and art pieces while copper which is used for handicraft products was introduced only after the Gold Control Act, which compelled the Meenakars to look for a material other than gold, was enforced in India. Initially, the work of Meenakari often went unnoticed as this art was traditionally used as a backing for the famous kundan or stone-studded jewellery. This also allowed the wearer to reverse the jewellery as also promised a special joy in the secret of the hidden design. More recently, the bright, jewel-like colors have made enamel a favoured choice for jewellery designers, including the Art Nouveau jewellers, for designers of bibelots such as the eggs of Peter Carl Fabergé and the enameled copper boxes of the Battersea enamellers, and for artists such as George Stubbs and other painters of portrait miniatures.  A resurgence in enamel-based art took place near the end of the 20th century in the Soviet Union, led by artists like Alexei Maximov and Leonid Efros. In Australia, abstract artist Bernard Hesling brought the style into prominence with his variously sized steel plates.  Enamel was first applied commercially to sheet iron and steel in Austria and Germany in about 1850. Industrialization increased as the purity of raw materials increased and costs decreased. The wet application process started with the discovery of the use of clay to suspend frit in water. Developments that followed during the 20th century include enamelling-grade steel, cleaned-only surface preparation, automation, and ongoing improvements in efficiency, performance, and quality.

Properties.

Vitreous enamel can be applied to most metals. Most modern industrial enamel is applied to steel in which the carbon content is controlled to prevent unwanted reactions at the firing temperatures. Enamel can also be applied to gold, silver, copper, aluminium, stainless steel, and cast iron.  Vitreous enamel has many useful properties: it is smooth, hard, chemically resistant, durable, scratch resistant (5–6 on the Mohs scale), has long-lasting colour fastness, is easy to clean, and cannot burn. Enamel is glass, not paint, so it does not fade under ultraviolet light. A disadvantage of enamel is a tendency to crack or shatter when the substrate is stressed or bent, but modern enamels are relatively chip- and impact-resistant because of good thickness control and coefficients of thermal expansion well-matched to the metal.  The Buick automobile company was founded by David Dunbar Buick with wealth earned by his development of improved enamelling processes, c. 1887, for sheet steel and cast iron. Such enameled ferrous material had, and still has, many applications: early 20th century and some modern advertising signs, interior oven walls, cooking pots, housing and interior walls of major kitchen appliances, housing and drums of clothes washers and dryers, sinks and cast iron bathtubs, farm storage silos, and processing equipment such as chemical reactors and pharmaceutical process tanks. Structures such as filling stations, bus stations and Lustron Houses had walls, ceilings and structural elements made of enamelled steel.  One of the most widespread modern uses of enamel is in the production of quality chalk-boards and marker-boards (typically called 'blackboards' or 'whiteboards') where the resistance of enamel to wear and chemicals ensures that 'ghosting', or unerasable marks, do not occur, as happens with polymer boards. Since standard enamelling steel is magnetically attractive, it may also be used for magnet boards. Some new developments in the last ten years include enamel/non-stick hybrid coatings, sol-gel functional top-coats for enamels, enamels with a metallic appearance, and easy-to-clean enamels.  The key ingredient of vitreous enamel is finely ground glass called frit. Frit for enamelling steel is typically an alkali borosilicate glass with a thermal expansion and glass temperature suitable for coating steel. Raw materials are smelted together between into a liquid glass that is directed out of the furnace and thermal shocked with either water or steel rollers into frit.  Colour in enamel is obtained by the addition of various minerals, often metal oxides cobalt, praseodymium, iron, or neodymium. The latter creates delicate shades ranging from pure violet through wine-red and warm grey. Enamel can be transparent, opaque or opalescent (translucent). Different enamel colours can be mixed to make a new colour, in the manner of paint.  There are various types of frit, which may be applied in sequence. A ground coat is applied first; it usually contains smelted-in transition metal oxides such as cobalt, nickel, copper, manganese, and iron that facilitate adhesion to the metal. Next, clear and semi-opaque frits that contain material for producing colours are applied.

Techniques of artistic enameling.

Variants, and less common techniques are:

Industrial enamel application.

On sheet steel, a ground coat layer is applied to create adhesion. The only surface preparation required for modern ground coats is degreasing of the steel with a mildly alkaline solution. White and coloured second "cover" coats of enamel are applied over the fired ground coat. For electrostatic enamels, the coloured enamel powder can be applied directly over a thin unfired ground coat "base coat" layer that is co-fired with the cover coat in a very efficient two-coat/one-fire process.  The frit in the ground coat contains smelted-in cobalt and/or nickel oxide as well as other transition metal oxides to catalyse the enamel-steel bonding reactions. During firing of the enamel at between, iron oxide scale first forms on the steel. The molten enamel dissolves the iron oxide and precipitates cobalt and nickel. The iron acts as the anode in an electrogalvanic reaction in which the iron is again oxidised, dissolved by the glass, and oxidised again with the available cobalt and nickel limiting the reaction. Finally, the surface becomes roughened with the glass anchored into the holes.

Building cladding.

Enamel coatings applied to steel panels offer protection to the core material whether cladding road tunnels, underground stations, building superstructures or other applications. It can also be specified as a curtain walling. Qualities of this structural material include:

Vitreous enamel, also called porcelain enamel, is a material made by fusing powdered glass to a substrate by firing, usually between. The powder melts, flows, and then hardens to a smooth, durable vitreous coating. The word comes from the Latin, meaning "glass".

Smalt (nebo také email) je křemičitá tavenina příbuzná sklu, ale i porcelánu, která po zahřátí na vysokou teplotu vytvoří na kovu celistvý ochranný povlak hladkého a lesklého charakteru. Teplotou výpalu v peci vykazuje vlastnosti na rozhraní skla a porcelánu. I když je smalt křehký, dokáže bez změny barvy i lesku přečkat stovky let. Dodnes se vyrábí smaltované cedule pro označení ulic a čísel domů.


Introduction.

Carl Friedrich Gauss in his 1827 "Disquisitiones generales circa superficies curvas" ("General investigations of curved surfaces") considered a surface parametrically, with the Cartesian coordinates,, and of points on the surface depending on two auxiliary variables and. Thus a parametric surface is (in today's terms) a vector-valued function  depending on an ordered pair of real variables, and defined in an open set in the -plane. One of the chief aims of Gauss's investigations was to deduce those features of the surface which could be described by a function which would remain unchanged if the surface underwent a transformation in space (such as bending the surface without stretching it), or a change in the particular parametric form of the same geometrical surface.  One natural such invariant quantity is the length of a curve drawn along the surface. Another is the angle between a pair of curves drawn along the surface and meeting at a common point. A third such quantity is the area of a piece of the surface. The study of these invariants of a surface led Gauss to introduce the predecessor of the modern notion of the metric tensor.

Arc length.

If the variables and are taken to depend on a third variable,, taking values in an interval, then will trace out a parametric curve in parametric surface. The arc length of that curve is given by the integral  where formula_3 represents the Euclidean norm. Here the chain rule has been applied, and the subscripts denote partial derivatives:  The integrand is the restriction to the curve of the square root of the (quadratic) differential  where  The quantity in () is called the line element, while is called the first fundamental form of. Intuitively, it represents the principal part of the square of the displacement undergone by when is increased by units, and is increased by units.  Using matrix notation, the first fundamental form becomes

Coordinate transformations.

Suppose now that a different parameterization is selected, by allowing and to depend on another pair of variables and. Then the analog of () for the new variables is The chain rule relates,, and to,, and via the matrix equation  where the superscript T denotes the matrix transpose. The matrix with the coefficients,, and arranged in this way therefore transforms by the Jacobian matrix of the coordinate change  A matrix which transforms in this way is one kind of what is called a tensor. The matrix  with the transformation law () is known as the metric tensor of the surface.

Invariance of arclength under coordinate transformations.

first observed the significance of a system of coefficients,, and, that transformed in this way on passing from one system of coordinates to another. The upshot is that the first fundamental form () is "invariant" under changes in the coordinate system, and that this follows exclusively from the transformation properties of,, and. Indeed, by the chain rule,  so that

Length and angle.

Another interpretation of the metric tensor, also considered by Gauss, is that it provides a way in which to compute the length of tangent vectors to the surface, as well as the angle between two tangent vectors. In contemporary terms, the metric tensor allows one to compute the dot product of tangent vectors in a manner independent of the parametric description of the surface. Any tangent vector at a point of the parametric surface can be written in the form  for suitable real numbers and. If two tangent vectors are given:  then using the bilinearity of the dot product,  This is plainly a function of the four variables,,, and. It is more profitably viewed, however, as a function that takes a pair of arguments and which are vectors in the -plane. That is, put  This is a symmetric function in and, meaning that  It is also bilinear, meaning that it is linear in each variable and separately. That is,  for any vectors,,, and in the plane, and any real numbers and.  In particular, the length of a tangent vector is given by  and the angle between two vectors and is calculated by

Area.

The surface area is another numerical quantity which should depend only on the surface itself, and not on how it is parameterized. If the surface is parameterized by the function over the domain in the -plane, then the surface area of is given by the integral  where denotes the cross product, and the absolute value denotes the length of a vector in Euclidean space. By Lagrange's identity for the cross product, the integral can be written  where is the determinant.

Definition.

Let be a smooth manifold of dimension ; for instance a surface (in the case ) or hypersurface in the Cartesian space. At each point there is a vector space, called the tangent space, consisting of all tangent vectors to the manifold at the point. A metric tensor at is a function which takes as inputs a pair of tangent vectors and at, and produces as an output a real number (scalar), so that the following conditions are satisfied:  A metric tensor field on assigns to each point of a metric tensor in the tangent space at in a way that varies smoothly with. More precisely, given any open subset of manifold and any (smooth) vector fields and on, the real function  is a smooth function of.

Components of the metric.

The components of the metric in any basis of vector fields, or frame, are given by  The functions form the entries of an symmetric matrix,. If are two vectors at, then the value of the metric applied to and is determined by the coefficients () by bilinearity:  Denoting the matrix by and arranging the components of the vectors and into column vectors and,  where and denote the transpose of the vectors and, respectively. Under a change of basis of the form  for some invertible matrix, the matrix of components of the metric changes by as well. That is,  or, in terms of the entries of this matrix,  For this reason, the system of quantities is said to transform covariantly with respect to changes in the frame.

Metric in coordinates.

A system of real-valued functions, giving a local coordinate system on an open set in, determines a basis of vector fields on  The metric has components relative to this frame given by  Relative to a new system of local coordinates, say  the metric tensor will determine a different matrix of coefficients,  This new system of functions is related to the original by means of the chain rule  so that  Or, in terms of the matrices and,  where denotes the Jacobian matrix of the coordinate change.

Signature of a metric.

Associated to any metric tensor is the quadratic form defined in each tangent space by  If is positive for all non-zero, then the metric is positive-definite at. If the metric is positive-definite at every, then is called a Riemannian metric. More generally, if the quadratic forms have constant signature independent of, then the signature of is this signature, and is called a pseudo-Riemannian metric. If is connected, then the signature of does not depend on.  By Sylvester's law of inertia, a basis of tangent vectors can be chosen locally so that the quadratic form diagonalizes in the following manner  for some between 1 and. Any two such expressions of (at the same point of ) will have the same number of positive signs. The signature of is the pair of integers, signifying that there are positive signs and negative signs in any such expression. Equivalently, the metric has signature if the matrix of the metric has positive and negative eigenvalues.  Certain metric signatures which arise frequently in applications are:

Inverse metric.

Let be a basis of vector fields, and as above let be the matrix of coefficients One can consider the inverse matrix, which is identified with the inverse metric (or "conjugate" or "dual metric"). The inverse metric satisfies a transformation law when the frame is changed by a matrix via  The inverse metric transforms "contravariantly", or with respect to the inverse of the change of basis matrix. Whereas the metric itself provides a way to measure the length of (or angle between) vector fields, the inverse metric supplies a means of measuring the length of (or angle between) covector fields; that is, fields of linear functionals.  To see this, suppose that is a covector field. To wit, for each point, determines a function defined on tangent vectors at so that the following linearity condition holds for all tangent vectors and, and all real numbers and :  As varies, is assumed to be a smooth function in the sense that  is a smooth function of for any smooth vector field.  Any covector field has components in the basis of vector fields. These are determined by  Denote the row vector of these components by  Under a change of by a matrix, changes by the rule  That is, the row vector of components transforms as a "covariant" vector.  For a pair and of covector fields, define the inverse metric applied to these two covectors by  The resulting definition, although it involves the choice of basis, does not actually depend on in an essential way. Indeed, changing basis to gives  So that the right-hand side of equation () is unaffected by changing the basis to any other basis whatsoever. Consequently, the equation may be assigned a meaning independently of the choice of basis. The entries of the matrix are denoted by, where the indices and have been raised to indicate the transformation law ().

Raising and lowering indices.

In a basis of vector fields, any smooth tangent vector field can be written in the form  for some uniquely determined smooth functions. Upon changing the basis by a nonsingular matrix, the coefficients change in such a way that equation () remains true. That is,  Consequently,. In other words, the components of a vector transform "contravariantly" (that is, inversely or in the opposite way) under a change of basis by the nonsingular matrix. The contravariance of the components of is notationally designated by placing the indices of in the upper position.  A frame also allows covectors to be expressed in terms of their components. For the basis of vector fields define the dual basis to be the linear functionals such that  That is,, the Kronecker delta. Let  Under a change of basis for a nonsingular matrix, transforms via  Any linear functional on tangent vectors can be expanded in terms of the dual basis  where denotes the row vector. The components transform when the basis is replaced by in such a way that equation () continues to hold. That is,  whence, because, it follows that. That is, the components transform "covariantly" (by the matrix rather than its inverse). The covariance of the components of is notationally designated by placing the indices of in the lower position.  Now, the metric tensor gives a means to identify vectors and covectors as follows. Holding fixed, the function  of tangent vector defines a linear functional on the tangent space at. This operation takes a vector at a point and produces a covector. In a basis of vector fields, if a vector field has components, then the components of the covector field in the dual basis are given by the entries of the row vector  Under a change of basis, the right-hand side of this equation transforms via  so that : transforms covariantly. The operation of associating to the (contravariant) components of a vector field the (covariant) components of the covector field, where  is called lowering the index.  To "raise the index", one applies the same construction but with the inverse metric instead of the metric. If are the components of a covector in the dual basis, then the column vector  has components which transform contravariantly:  Consequently, the quantity does not depend on the choice of basis in an essential way, and thus defines a vector field on. The operation () associating to the (covariant) components of a covector the (contravariant) components of a vector given is called raising the index. In components, () is

Induced metric.

Let be an open set in, and let be a continuously differentiable function from into the Euclidean space, where. The mapping is called an immersion if its differential is injective at every point of. The image of is called an immersed submanifold. More specifically, for, which means that the ambient Euclidean space is, the induced metric tensor is called the first fundamental form.  Suppose that is an immersion onto the submanifold. The usual Euclidean dot product in is a metric which, when restricted to vectors tangent to, gives a means for taking the dot product of these tangent vectors. This is called the induced metric.  Suppose that is a tangent vector at a point of, say  where are the standard coordinate vectors in. When is applied to, the vector goes over to the vector tangent to given by  (This is called the pushforward of along.) Given two such vectors, and, the induced metric is defined by  It follows from a straightforward calculation that the matrix of the induced metric in the basis of coordinate vector fields is given by  where is the Jacobian matrix:

Intrinsic definitions of a metric.

The notion of a metric can be defined intrinsically using the language of fiber bundles and vector bundles. In these terms, a metric tensor is a function  from the fiber product of the tangent bundle of with itself to such that the restriction of to each fiber is a nondegenerate bilinear mapping  The mapping () is required to be continuous, and often continuously differentiable, smooth, or real analytic, depending on the case of interest, and whether can support such a structure.

Metric as a section of a bundle.

By the universal property of the tensor product, any bilinear mapping () gives rise naturally to a section of the dual of the tensor product bundle of with itself  The section is defined on simple elements of by  and is defined on arbitrary elements of by extending linearly to linear combinations of simple elements. The original bilinear form is symmetric if and only if where is the braiding map.  Since is finite-dimensional, there is a natural isomorphism  so that is regarded also as a section of the bundle of the cotangent bundle with itself. Since is symmetric as a bilinear mapping, it follows that is a symmetric tensor.

Metric in a vector bundle.

More generally, one may speak of a metric in a vector bundle. If is a vector bundle over a manifold, then a metric is a mapping  from the fiber product of to which is bilinear in each fiber:  Using duality as above, a metric is often identified with a section of the tensor product bundle. (See metric (vector bundle).)

Tangent–cotangent isomorphism.

The metric tensor gives a natural isomorphism from the tangent bundle to the cotangent bundle, sometimes called the musical isomorphism. This isomorphism is obtained by setting, for each tangent vector,  the linear functional on which sends a tangent vector at to. That is, in terms of the pairing between and its dual space,  for all tangent vectors and. The mapping is a linear transformation from to. It follows from the definition of non-degeneracy that the kernel of is reduced to zero, and so by the rank–nullity theorem, is a linear isomorphism. Furthermore, is a symmetric linear transformation in the sense that  for all tangent vectors and.  Conversely, any linear isomorphism defines a non-degenerate bilinear form on by means of  This bilinear form is symmetric if and only if is symmetric. There is thus a natural one-to-one correspondence between symmetric bilinear forms on and symmetric linear isomorphisms of to the dual.  As varies over, defines a section of the bundle of vector bundle isomorphisms of the tangent bundle to the cotangent bundle. This section has the same smoothness as : it is continuous, differentiable, smooth, or real-analytic according as. The mapping, which associates to every vector field on a covector field on gives an abstract formulation of "lowering the index" on a vector field. The inverse of is a mapping which, analogously, gives an abstract formulation of "raising the index" on a covector field.  The inverse defines a linear mapping  which is nonsingular and symmetric in the sense that  for all covectors,. Such a nonsingular symmetric mapping gives rise (by the tensor-hom adjunction) to a map  or by the double dual isomorphism to a section of the tensor product

Arclength and the line element.

Suppose that is a Riemannian metric on. In a local coordinate system,, the metric tensor appears as a matrix, denoted here by, whose entries are the components of the metric tensor relative to the coordinate vector fields.  Let be a piecewise-differentiable parametric curve in, for. The arclength of the curve is defined by  In connection with this geometrical application, the quadratic differential form  is called the first fundamental form associated to the metric, while is the line element. When is pulled back to the image of a curve in, it represents the square of the differential with respect to arclength.  For a pseudo-Riemannian metric, the length formula above is not always defined, because the term under the square root may become negative. We generally only define the length of a curve when the quantity under the square root is always of one sign or the other. In this case, define  Note that, while these formulas use coordinate expressions, they are in fact independent of the coordinates chosen; they depend only on the metric, and the curve along which the formula is integrated.

The energy, variational principles and geodesics.

Given a segment of a curve, another frequently defined quantity is the (kinetic) energy of the curve:  This usage comes from physics, specifically, classical mechanics, where the integral can be seen to directly correspond to the kinetic energy of a point particle moving on the surface of a manifold. Thus, for example, in Jacobi's formulation of Maupertuis' principle, the metric tensor can be seen to correspond to the mass tensor of a moving particle.  In many cases, whenever a calculation calls for the length to be used, a similar calculation using the energy may be done as well. This often leads to simpler formulas by avoiding the need for the square-root. Thus, for example, the geodesic equations may be obtained by applying variational principles to either the length or the energy. In the latter case, the geodesic equations are seen to arise from the principle of least action: they describe the motion of a "free particle" (a particle feeling no forces) that is confined to move on the manifold, but otherwise moves freely, with constant momentum, within the manifold.

Canonical measure and volume form.

In analogy with the case of surfaces, a metric tensor on an -dimensional paracompact manifold gives rise to a natural way to measure the -dimensional volume of subsets of the manifold. The resulting natural positive Borel measure allows one to develop a theory of integrating functions on the manifold by means of the associated Lebesgue integral.  A measure can be defined, by the Riesz representation theorem, by giving a positive linear functional on the space of compactly supported continuous functions on. More precisely, if is a manifold with a (pseudo-)Riemannian metric tensor, then there is a unique positive Borel measure such that for any coordinate chart, for all supported in. Here is the determinant of the matrix formed by the components of the metric tensor in the coordinate chart. That is well-defined on functions supported in coordinate neighborhoods is justified by Jacobian change of variables. It extends to a unique positive linear functional on by means of a partition of unity.  If is in addition oriented, then it is possible to define a natural volume form from the metric tensor. In a positively oriented coordinate system the volume form is represented as where the are the coordinate differentials and denotes the exterior product in the algebra of differential forms. The volume form also gives a way to integrate functions on the manifold, and this geometric integral agrees with the integral obtained by the canonical Borel measure.

Examples.

Euclidean metric.

The most familiar example is that of elementary Euclidean geometry: the two-dimensional Euclidean metric tensor. In the usual coordinates, we can write  The length of a curve reduces to the formula:  The Euclidean metric in some other common coordinate systems can be written as follows.  Polar coordinates :  So by trigonometric identities.  In general, in a Cartesian coordinate system on a Euclidean space, the partial derivatives are orthonormal with respect to the Euclidean metric. Thus the metric tensor is the Kronecker delta δ in this coordinate system. The metric tensor with respect to arbitrary (possibly curvilinear) coordinates is given by

The round metric on a sphere.

The unit sphere in comes equipped with a natural metric induced from the ambient Euclidean metric, through the process explained in the induced metric section. In standard spherical coordinates, with the colatitude, the angle measured from the -axis, and the angle from the -axis in the -plane, the metric takes the form  This is usually written in the form

Lorentzian metrics from relativity.

In flat Minkowski space (special relativity), with coordinates  the metric is, depending on choice of metric signature,  For a curve with—for example—constant time coordinate, the length formula with this metric reduces to the usual length formula. For a timelike curve, the length formula gives the proper time along the curve.  In this case, the spacetime interval is written as  The Schwarzschild metric describes the spacetime around a spherically symmetric body, such as a planet, or a black hole. With coordinates  we can write the metric as  where (inside the matrix) is the gravitational constant and represents the total mass-energy content of the central object.

In the mathematical field of differential geometry, one definition of a metric tensor is a type of function which takes as input a pair of tangent vectors and at a point of a surface (or higher dimensional differentiable manifold) and produces a real number scalar in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space. In the same way as a dot product, metric tensors are used to define the length of and angle between tangent vectors. Through integration, the metric tensor allows one to define and compute the length of curves on the manifold.

V matematice je metrický tenzor zpravidla tenzorové pole druhého řádu na hladké varietě, které dává do souvislosti souřadnice a vzdálenost. Jinými slovy, zvolíme na tečném bandlu hladké variety tenzorové pole druhého řádu. V daném bodě variety přiřadí toto pole dvěma vektorům z tečného prostoru reálné číslo.


Structure.

Structurally, the text comprises seven sections divided (in most printed editions) into three volumes: parts 1–2, parts 3–4, and parts 5–7. At one level, the "Gulag Archipelago" traces the history of the system of forced labor camps that existed in the Soviet Union from 1918 to 1956. Solzhenitsyn begins with V. I. Lenin's original decrees which were made shortly after the October Revolution; they established the legal and practical framework for a series of camps where political prisoners and ordinary criminals would be sentenced to forced labor. The book then describes and discusses the waves of purges and the assembling of show trials in the context of the development of the greater Gulag system; Solzhenitsyn gives particular attention to its purposive legal and bureaucratic development.  The narrative ends in 1956 at the time of Nikita Khrushchev's Secret Speech ("On the Personality Cult and its Consequences"). Khrushchev gave the speech at the 20th Congress of the Communist Party of the Soviet Union, denouncing Stalin's personality cult, his autocratic power, and the surveillance that pervaded the Stalin era. Although Khrushchev's speech was not published in the Soviet Union for a long time, it was a break with the most atrocious practices of the Gulag system.  Despite the efforts by Solzhenitsyn and others to confront the legacy of the Gulag, the realities of the camps remained a taboo subject until the 1980s. Solzhenitsyn was also aware that although many practices had been stopped, the basic structure of the system had survived and it could be revived and expanded by future leaders. While Khrushchev, the Communist Party, and the Soviet Union's supporters in the West viewed the Gulag as a deviation of Stalin, Solzhenitsyn and many among the opposition tended to view it as a systemic fault of Soviet political culture – an inevitable outcome of the Bolshevik political project.  Parallel to this historical and legal narrative, Solzhenitsyn follows the typical course of a "zek" (a slang term for an inmate), derived from the widely used abbreviation "z/k" for ""zakliuchennyi"" (prisoner) through the Gulag, starting with arrest, show trial, and initial internment; transport to the "archipelago"; the treatment of prisoners and their general living conditions; slave labor gangs and the technical prison camp system; camp rebellions and strikes (see Kengir uprising); the practice of internal exile following the completion of the original prison sentence; and the ultimate (but not guaranteed) release of the prisoner. Along the way, Solzhenitsyn's examination details the trivial and commonplace events of an average prisoner's life, as well as specific and noteworthy events during the history of the Gulag system, including revolts and uprisings.  Solzhenitsyn also states:  There had been works about the Soviet prison/camp system before, and its existence had been known to the Western public since the 1930s. However, never before had the general reading public been brought face to face with the horrors of the Gulag in this way. The controversy surrounding this text, in particular, was largely due to the way Solzhenitsyn definitively and painstakingly laid the theoretical, legal, and practical origins of the Gulag system at Lenin's feet, not Stalin's. According to Solzhenitsyn's testimony, Stalin merely amplified a concentration camp system that was already in place. This is significant, as many Western intellectuals viewed the Soviet concentration camp system as a "Stalinist aberration".

Publication.

After the KGB had confiscated Solzhenitsyn's materials in Moscow, during 1965–1967, the preparatory drafts of "The Gulag Archipelago" were turned into finished typescript, sometimes in hiding at his friends' homes in the Moscow region and elsewhere. While held at the KGB's Lubyanka Prison in 1945, Solzhenitsyn had befriended Arnold Susi, a lawyer and former Estonian Minister of Education, who had been taken captive after the Soviet Union occupied Estonia in 1940. Solzhenitsyn entrusted Susi with the original typed and proofread manuscript of the finished work, after copies had been made of it both on paper and on microfilm. Arnold Susi's daughter, Heli Susi, subsequently kept the "master copy" hidden from the KGB in Estonia until the dissolution of the Soviet Union in 1991.  In 1973 the KGB seized one of only three existing copies of the text still on Soviet soil. This was achieved after interrogating Elizaveta Voronyanskaya, one of Solzhenitsyn's trusted typists who knew where the typed copy was hidden; within days of her release by the KGB she hanged herself (3 August 1973). Although he had earlier wanted it published in Russia first, after Solzhenitsyn learned of her death, he decided the next month, September, to allow its publication in Paris.  The first edition of the work was published (in Russian) by the French publishing house Éditions du Seuil a few days after Christmas 1973; they had received a go-ahead from Solzhenitsyn but had decided to release the work about ten days earlier than he had expected. News of the nature of the work immediately caused a stir, and translations into many other languages followed within the next few months, sometimes produced in a race against time. American Thomas Whitney produced the English version; the English and French translations of Volume I appeared in the spring and summer of 1974.  Solzhenitsyn had wanted the manuscript to be published in Russia first, but knew this was impossible under conditions then extant. The work had a profound effect internationally. Not only did it provoke energetic debate in the West; a mere six weeks after the work had left Parisian presses Solzhenitsyn himself was forced into exile.  Because possession of the manuscript incurred the risk of a long prison sentence for "anti-Soviet activities", Solzhenitsyn never worked on the manuscript in complete form. Since he was under constant KGB surveillance, Solzhenitsyn worked on only parts of the manuscript at any one time, so as not to put the full book into jeopardy if he happened to be arrested. For this reason, he secreted the various parts of the work throughout Moscow and the surrounding suburbs, in the care of trusted friends. Sometimes when he was purportedly visiting them on social calls he actually worked on the manuscript in their homes. During much of this time, Solzhenitsyn lived at the dacha of the world-famous cellist Mstislav Rostropovich, and due to the reputation and standing of the musician, despite the elevated scrutiny of the Soviet authorities, Solzhenitsyn was reasonably safe from KGB searches there.  Solzhenitsyn did not think this series would be his defining work, as he considered it journalism and history rather than high literature. However, with the possible exception of "One Day in the Life of Ivan Denisovich", it is his best-known and most popular work, at least in the West.  Finished in 1968, "The Gulag Archipelago" was microfilmed and smuggled out to Solzhenitsyn's main legal representative, Dr Fritz Heeb of Zürich, to await publication (a later paper copy, also smuggled out, was signed by Heinrich Böll at the foot of each page to prove against possible accusations of a falsified work).  Solzhenitsyn was aware that there was a wealth of material and perspectives about Gulag to be continued in the future, but he considered the book finished for his part. The royalties and sales income for the book were transferred to the Solzhenitsyn Aid Fund for aid to former camp prisoners, and this fund, which had to work in secret in its native country, managed to transfer substantial amounts of money to those ends in the 1970s and 1980s.

Impact and reception.

Beginning in 2009, Russian schools issued the book as required reading. In an exchange with Natalia Solzhenitsyn (Aleksandr Solzhenitsyn's second wife) Russian president Vladimir Putin called the book "much-needed." while the Russian Ministry of Education said that the book showed "vital historical and cultural heritage on the course of 20th-century domestic history." Arseny Roginsky, then head of the human-rights organization Memorial, welcomed Mr. Putin's backing for the Solzhenitsyn textbook.  Natalia Solzhenitsyn, for her part, created an abridged version for Russian high-school students, including her probing introduction about the unique nature of Solzhenitsyn's "experiment in literary investigation".  Novelist Doris Lessing said that the book "brought down an empire" while Michael Scammell similarly said that the book was a gesture that "amounted to a head-on challenge to the Soviet state, calling its very legitimacy into question and demanding revolutionary change." The philosopher Isaiah Berlin said that, "Until the Gulag, the Communists and their allies had persuaded their followers that denunciations of the regime were largely bourgeois propaganda." while the American diplomat George F. Kennan, said that the book was “the most powerful single indictment of a political regime ever to be levied in modern times.” Tom Butler-Bowdon has described the book as a "Solzhenitsyn's monument to the millions tortured and murdered in Soviet Russia between the Bolshevik Revolution and the 1950s."  An edition of The Book Show said that the book helped expose the brutality of the Soviet system.  Psychologist Jordan Peterson has said that "The Gulag Archipelago" is the most important book of the twentieth century.  Historian and archival researcher Stephen G. Wheatcroft describes the book as "a fine literary masterpiece, a sharp political indictment against the Soviet regime, and has had tremendous importance in raising the issue of Soviet repression in the Russian consciousness." He also said that the book was essentially a "literary and political work", and "never claimed to place the camps in a historical or social-scientific quantitative perspective" but that in the case of qualitative estimates, Solzhenitsyn, according to Wheatcroft, gave his high estimate as he wanted to challenge the Soviet authorities to show that "that the scale of the camps was less than this."  Parallels have been drawn between the book and the treatment of Liao Yiwu, a dissident who, according to the AFP, is dubbed the "Chinese Solzhenitsyn." David Aikman has asserted that Yiwu is the first Chinese dissident writer to "come up with a very detailed account of prison conditions including torture in China in the same way that [Soviet dissident Aleksandr] Solzhenitsyn did in “The Gulag Archipelago,”."  UCLA historian J. Arch Getty writes of Solzhenitsyn's methodology that "Such documentation is methodically unacceptable in other fields of history" while also arguing that "The work is of limited value to the serious student of the 1930s for it provides no important new information or original analytical framework." Gabor Rittersporn shares Getty's criticism saying "he is inclined to give priority to vague reminiscences and hearsay [...] [and] inevitably [leads] towards selective bias". Vadim Rogovin wrote that "using the circumstance that the memoirs from prisoners in Stalin’s camps which had been given to him to read had never been published, Solzhenitsyn took plenty of license in outlining their contents and interpreting them".  In an interview with German weekly "Die Zeit", British historian Orlando Figes asserted that many gulag inmates he interviewed for his research identified so strongly with the book's contents that they became unable to distinguish between their own experiences and what they read: ""The Gulag Archipelago" spoke for a whole nation and was the voice of all those who suffered".  Former Communist Party member, dissident and historian, Roy Medvedev has referred to the book as "extremely contradictory". However, in a review for the book he described it as without parallel, saying, "I believe there are few who will get up from their desks after reading this book the same as when they opened its first page. In this regard I have nothing with which to compare Solzhenitsyn's book either in Russian or world literature."  Mustafa Akyol drew a parallel between the book and the current situation in Xinjiang.

Television documentary.

On 12 December 2009, the Russian channel "Rossiya K" showed the French television documentary "L'Histoire Secrète de l'Archipel du Goulag" made by Jean Crépu and Nicolas Miletitch and translated it into Russian under the title "Taynaya Istoriya “Arkhipelaga GULAG”" ("Secret History: The Gulag Archipelago"). The documentary covers events related to the writing and publication of "The Gulag Archipelago".

The Gulag Archipelago: An Experiment in Literary Investigation (, "Arkhipelag GULAG") is a three-volume, non-fiction text written between 1958 and 1968 by Russian writer and historian Aleksandr Solzhenitsyn. It was first published in 1973, followed by an English translation the following year. It covers life in what is often known as the Gulag, the Communist Soviet forced labour camp system, through a narrative constructed from various sources including reports, interviews, statements, diaries, legal documents, and Solzhenitsyn's own experience as a Gulag prisoner. In Russian, the term GULAG (ГУЛАГ) is an acronym for Main Directorate of Camps (Главное управление лагерей).

Souostroví Gulag (rusky: "Архипелаг ГУЛАГ") je jedním z nejznámějších děl popisujících vězeňský systém Sovětského svazu. Jeho autor – Alexandr Solženicyn – čerpal ze zkušenosti svého vlastního uvěznění i rozsáhlého výzkumu, stejně tak i z dobových autentických dokumentů. Kniha byla napsána mezi lety 1958 a 1968, na západě publikována v roce 1973, v Československu před rokem 1989 obíhala v samizdatových vydáních, v Sovětském svazu oficiálně vydána v roce 1989. Žánrově pak tato kniha stojí na pomezí románu, literatury faktu a autentického dokumentu.


Details.

"Up" saw R.E.M. move into electronic music-influenced territory after delivering "New Adventures in Hi-Fi" in 1996. Ending a 10-year relationship with co-producer Scott Litt, the band engaged the production assistance of Pat McCarthy, who was assisted on most tracks by engineer Nigel Godrich, Radiohead's producer. The single "Daysleeper" became a Top 10 UK hit, and "Lotus", The Beach Boys-influenced "At My Most Beautiful" and "Suspicion" were also released as singles.  "There are certain things I set out to do," Michael Stipe noted. "Rough ideas that I wanted to play around with. One of them was the religious-spiritual versus science-technology-modern-age. There are several songs on the record that, to me, address that. I don't know how other people are going to take them. It's taking off a little bit from 'Undertow' and 'New Test Leper', with the freedom of 'E-Bow the Letter' and 'Country Feedback' – songs that just come out. What I really wanted was more of that automatic, unconscious stuff... greatly inspired by Patti Smith and various others... Bert Downs said the record's about people falling down and getting back up again. He said there's a lot of that imagery. I'm like, 'Really?'"  Breaking with a tradition that stretched back to the band's 1983 debut, "Murmur", Stipe elected to have his complete lyrics included in "Up"'s CD booklet, a practice he would maintain on all subsequent R.E.M. studio albums. "[Mike Mills] was reading the lyrics," he explained, "and he said, 'These are really great – we should print them on the record sleeve.' It was a really good night and there were eight or nine songs on the wall. I said, 'Yeah, we will'... I thought it was a nice way of saying that we are a different band now."  R.E.M. subsequently admitted that they came close to breaking up while recording the album.

Sales and critical reception.

"Up" reached #3 in the U.S. (with 16 weeks on the "Billboard" 200) and #2 in the UK, but didn't have the staying power of the band's more-recent albums, and thus had the band's lowest sales in years. "The things that we have to do creatively for the band may not be the most commercial things," Mike Mills observed. "That isn't the point. The point is to keep it fresh and interesting and alive."  "It will certainly sound strange to those who only own "Automatic for the People" and repeat-play the hits," wrote Danny Eccleston in a 4-star review for "Q". "Conversely, anyone who has a healthy number of R.E.M. records – let's say four – and plays them regularly, should manage to listen to "Up" without his head exploding or tossing herself off a tall building or any of the weird things people are meant to do when faced with music they don't quite understand. This is R.E.M. after all. We couldn't even hear the lyrics until album five."  Although R.E.M. initially intended not to tour for the album, after many successful promotional concerts upon the album's release, the band quickly arranged a four-month arena tour of Europe and America during the summer of 1999. As of March 2007, "Up" has sold 664,000 units in the U.S.  In 2005, Warner Bros. Records issued an expanded two-disc edition of "Up" which includes a CD, a DVD-Audio disc containing a 5.1-channel surround sound mix of the album done by Elliot Scheiner, and the original CD booklet with expanded liner notes.

Accolades.

In 1999, "Nude as the News" ranked the album at number 74 in its list of "The 100 Most Compelling Albums of the Decade." That same year, Australian magazine "Juice" ranked it at number 38 in its list of the "100 Greatest Albums of the '90s." In 2005, journalist Jude Rogers included the album in "The Word"'s list "Hidden Treasure: Great Underrated Albums of Our Time," whose inductions were chosen by celebrities. It also appeared in at least 22 magazine lists of the greatest albums of 1998.

Track listing.

All songs by Peter Buck, Mike Mills and Michael Stipe, except "Hope" by Buck, Mills, Stipe and Leonard Cohen.  Up Side  Down Side  Notes Cohen was not directly involved in the writing of "Hope" but was given a writing credit by the band due to similarities in melody and lyrical pattern to his "Suzanne".

Studio B-sides.

Two non-album tracks from the "Up" sessions appeared as single-only releases, as well as alternate versions of four album tracks.

Up is the eleventh studio album by American rock band R.E.M., released on October 26, 1998 by Warner Bros. Records. It was the band's first album without original drummer Bill Berry, who retired from the group in October 1997, and recorded as a three-piece. In his place, R.E.M. used session drummers and drum machines. It is also their second longest record with total track time of 64 minutes, 1 minute shorter than their previous and last album recorded with Bill Berry, "New Adventures in Hi-Fi". The band has said that the album probably would have sounded the same with Berry, as first rehearsals and sessions with him have commenced, but his departure almost broke them and "hung over" on the resulting late recordings with drum machines and session drummers like Barrett Martin and Joey Waronker.

Up je album kapely R.E.M. vydané v roce 1998. Jde o první album, na kterém se nepodílel bubeník Bill Berry, zakládající člen kapely, kterou opustil v říjnu 1997. Místo něj použila kapela elektronické bubny a studiové bubeníky.


Premise.

Setting and characters.

The show follows the exploits of four boys, Stan Marsh, Kyle Broflovski, Eric Cartman and Kenny McCormick. The boys live in the fictional small town of South Park, located within the real-life South Park basin in the Rocky Mountains of central Colorado. The town is also home to an assortment of frequent characters such as students, families, elementary school staff, and other various residents, who tend to regard South Park as a bland, quiet place to live. Prominent settings on the show include the local elementary school, bus stop, various neighborhoods and the surrounding snowy landscape, actual Colorado landmarks, and the shops and businesses along the town's main street, all of which are based on the appearance of similar locations in Fairplay, Colorado. Stan is portrayed as the everyman of the group, as the show's website describes him as an "average, American 4th grader". Kyle is the lone Jew among the group, and his portrayal in this role is often dealt with satirically. Stan is modeled after Parker, while Kyle is modeled after Stone. They

Themes and style.

Each episode opens with a tongue-in-cheek all persons fictitious disclaimer: "All characters and events in this show—even those based on real people—are entirely fictional. All celebrity voices are impersonated...poorly. The following program contains coarse language and due to its content it should not be viewed by anyone."  "South Park" was the first weekly program to be rated TV-MA, and is generally intended for adult audiences. The boys and most other child characters use strong profanity, with only the most taboo words being bleeped during a typical broadcast. Parker and Stone perceive this as the manner in which real-life small boys speak when they are alone.  "South Park" commonly makes use of carnivalesque and absurdist techniques, numerous running gags, violence, sexual content, offhand pop-cultural references, and satirical portrayal of celebrities.  Early episodes tended to be shock value-oriented and featured more slapstick-style humor. While social satire had been used on the show occasionally earlier on, it became more prevalent as the series progressed, with the show retaining some of its focus on the

Development.

Parker and Stone met in film class at the University of Colorado in 1992 and discovered a shared love of Monty Python, which they often cite as one of their primary inspirations. They created an animated short entitled "The Spirit of Christmas". The film was created by animating construction paper cutouts with stop motion, and features prototypes of the main characters of "South Park", including a character resembling Cartman but named "Kenny", an unnamed character resembling what is today Kenny, and two near-identical unnamed characters who resemble Stan and Kyle. Fox Broadcasting Company (FOX) executive and mutual friend Brian Graden commissioned Parker and Stone to create a second short film as a video Christmas card. Created in 1995, the second "The Spirit of Christmas" short resembled the style of the later series more closely. To differentiate between the two homonymous shorts, the first short is often referred to as "Jesus vs. Frosty", and the second short as "Jesus vs. Santa". Graden sent copies of the video to several of his friends, and from there it was copied and distributed, including on the internet, where it became one of the first viral videos.

Production.

Except for the pilot episode, which was produced using cutout animation, all episodes of "South Park" are created with the use of software, primarily Autodesk Maya. As opposed to the pilot, which took three months to complete, and other animated sitcoms, which are traditionally hand-drawn by companies in South Korea in a process that takes roughly eight to nine months, individual episodes of "South Park" take significantly less time to produce. Using computers as an animation method, the show's production staff were able to generate an episode in about three weeks during the first seasons. Now, with a staff of about 70 people, episodes are typically completed in one week, with some in as little as three to four days. Nearly the entire production of an episode is accomplished within one set of offices, which were originally at a complex in Westwood, Los Angeles, California, and are now part of South Park Studios in Culver City, California. Parker and Stone have been the show's executive producers throughout its entire history. Debbie Liebling, who was Senior Vice President of original programming and development for Comedy Central, also served as an executive producer during the show's first five seasons, coordinating the show's production efforts between South Park Studios and Comedy Central's headquarters in New York City. During its early stages, finished episodes of "South Park" were hastily recorded to D-2 to be sent to Comedy Central for airing in just a few days' time. Scripts are not written before a season begins. Production of an episode begins on a Thursday, with the show's writing consultants brainstorming with Parker and Stone. Former staff writers include Pam Brady, who has since written scripts for the films "Hot Rod", "Hamlet 2" and "" (with Parker and Stone), and Nancy Pimental, who served as co-host of "Win Ben Stein's Money" and wrote the film "The Sweetest Thing" after her tenure with the show during its first three seasons. Television producer and writer Norman Lear, an idol of both Parker and Stone, served as a guest writing consultant for the season seven (2003) episodes "Cancelled" and "I'm a Little Bit Country". During the 12th and 13th seasons, "Saturday Night Live" actor and writer Bill Hader served as a creative consultant and co-producer.  After exchanging ideas, Parker will write a script, and from there the entire team of animators, editors, technicians, and sound engineers will each typically work 100–120 hours in the ensuing week. Since the show's fourth season (2000), Parker has assumed most of the show's directorial duties, while Stone relinquished his share of the directing to focus on handling the coordination and business aspects of the production. On Wednesday, a completed episode is sent to Comedy Central's headquarters via satellite uplink, sometimes just a few hours before its air time of 10 PM Eastern Time.  Parker and Stone state that subjecting themselves to a one-week deadline creates more spontaneity amongst themselves in the creative process, which they feel results in a funnier show. The schedule also allows "South Park" to both stay more topical and respond more quickly to specific current events than other satiric animated shows. One of the earliest examples of this was in the season four (2000) episode "Quintuplets 2000", which references the United States Border Patrol's raid of a house during the Elián González affair, an event which occurred only four days before the episode originally aired. The season nine (2005) episode "Best Friends Forever" references the Terri Schiavo case, and originally aired in the midst of the controversy and less than 12 hours before she died. A scene in the season seven (2003) finale "It's Christmas in Canada" references the discovery of dictator Saddam Hussein in a "spider hole" and his subsequent capture, which happened a mere three days prior to the episode airing. The season 12 (2008) episode "About Last Night..." revolves around Barack Obama's victory in the 2008 presidential election, and aired less than 24 hours after Obama was declared the winner, using segments of dialogue from Obama's real victory speech.  On October 16, 2013, the show failed to meet their production deadline for the first time ever, after a power outage on October 15 at the production studio prevented the episode, season 17's "", from being finished in time. The episode was rescheduled to air a week later on October 23, 2013. In July 2015, "South Park" was renewed through 2019; extending the show through season 23 with 307 episodes overall. On September 12, 2019, the show was renewed for seasons 24 through 26 until 2022.

Distribution.

International.

Internationally, "South Park" is broadcast in India, New Zealand, and several countries throughout Europe and Latin America on channels that are divisions of Comedy Central and ViacomCBS Domestic Media Networks, both subsidiaries of ViacomCBS. In distribution deals with Comedy Central, other independent networks also broadcast the series in other international markets. In Australia, the show

Syndication.

"South Park" entered broadcast syndication in 2003. Episodes further edited for content

Home media.

Complete seasons of "South Park" have been regularly released on their entirety on DVD since 2002, with season twenty-one being the most recently released. Several other themed DVD compilations have been released by Rhino Entertainment and Comedy

Streaming.

In March 2008, Comedy Central made every episode of "South Park" available for free full-length on-demand legal streaming on the official South Park Studios website. From March 2008 until December 2013 new episodes were added to the site the day following their debut, and an uncensored version was posted the following day. The episode stayed up for the remainder of the week, then taken down, and added to the site three weeks later.  Within a week, the site served more than a million streams of full episodes, and the number grew to 55 million by October 2008. Legal issues prevent the U.S. content from being accessible outside the U.S., so local servers have been set up in other countries. In September 2009, a South Park Studios website with streaming episodes was launched in the UK and Ireland. In Canada, episodes were available for streaming from The Comedy Network's website, though due to digital rights restrictions, they are no longer available.  In July 2014 it was announced that Hulu had signed

Re-rendered episodes.

From its debut in 1997 to the season twelve finale in 2008 the series had been natively produced in 480i standard definition. In 2009 the series switched to being natively produced in 1080i high definition with the beginning of the thirteenth season. Since this, all seasons originally produced in standard definition with 4:3 aspect ratio have been remastered by South Park Studios, being fully re-rendered in 1080i 16:9 high definition. The re-rendered versions

Reception.

Ratings.

When "South Park" debuted, it was a huge ratings success for Comedy Central and is seen as being largely responsible for the success of the channel, with Herzog crediting it for putting the network "on the map".  The show's first episode, "Cartman Gets an Anal Probe", earned a Nielsen rating of 1.3 (980,000 viewers), at the time considered high for a cable program. The show instantly generated buzz among television viewers, and mass viewing parties began assembling on college campuses. By the time the eighth episode, "Starvin' Marvin", aired — three months after the show debuted — ratings and viewership had tripled, and "South Park" was already the most successful show in Comedy Central's history. When the tenth episode "Damien" aired the following February, viewership increased another 33 percent. The episode earned a 6.4 rating, which at the time was over 10 times the average rating earned by a cable show aired in prime time. The ratings peaked with the second episode of season two, "Cartman's Mom Is Still a Dirty Slut", which aired on April 22, 1998. The episode earned an 8.2 rating (6.2 million viewers) and, at the time, set a record as

Recognitions and awards.

In 2004, Channel 4 voted "South Park" the third-greatest cartoon of all time. In 2007, "Time" magazine included the show on its list of the "100 Best TV Shows of All Time", proclaiming it as "America's best source of rapid-fire satire for [the past] decade". The same year, "Rolling Stone" declared it to be the funniest show on television since its debut 10 years prior. In 2008, "South Park" was named the 12th-greatest TV show of the past 25 years by "Entertainment Weekly", while AOL declared it as having the "most astute" characters of any show in history when naming it the 16th-best television comedy series of all time. In 2011, "South Park" was voted number one in the "25 Greatest Animated TV Series" poll by "Entertainment Weekly". The character of Cartman ranked 10th on TV Guide's 2002 list of the "Top 50 Greatest Cartoon Characters", 198th on VH1's "200 Greatest Pop Culture Icons", 19th on Bravo's "100 Greatest TV Characters" television special in 2004, and second on

Criticism.

The show's frequent depiction of taboo subject matter, general toilet humor, accessibility to younger viewers, disregard for conservative sensibilities, negative depiction of liberal causes, and portrayal of religion for comic effect have generated controversy and debate over the course of its run.  As the series became popular, students in two schools were barred from wearing "South Park"-related T-shirts, and the headmaster of a UK public school asked parents not to let their children watch the programme after eight- and nine-year-old children voted the "South Park" character Cartman as

Controversies.

The show further lampooned the controversy surrounding its use of profanity, as well as the media attention surrounding the network show "Chicago Hope"<nowiki>'s</nowiki> singular use of the word "shit", with the season five premiere "It Hits the Fan", in which the word "shit" is said 162 times without being bleeped for censorship purposes, while also appearing uncensored in written form. In the days following the show's original airing, 5,000 disapproving e-mails were sent to Comedy Central. Despite its 43 uncensored uses of the racial slur "nigger", the season 11 episode "With Apologies to Jesse Jackson" generated relatively little controversy, as most in the black community and the NAACP praised the episode for its context and its comedic way of conveying other races' perceptions of how black people feel when hearing the word.  Specific controversies regarding the show have included an April Fools' Day prank played on its viewers in 1998, its depiction of the Virgin Mary in the season nine (2005) finale "Bloody Mary" that angered several Catholics, its depiction of Steve Irwin with a stingray barb stuck in his chest in the episode "Hell on Earth 2006", which originally aired less than two months after Irwin was killed in the same fashion, and Comedy Central's censorship of the depiction of Muhammad in the season 10 episode "Cartoon Wars Part II" in the wake of the "Jyllands-Posten" Muhammad cartoons controversy.  The season nine (2005) episode "Trapped in the Closet" denounces Scientology as nothing more than "a

Influence and legacy.

Cultural.

Commentary made in episodes has been interpreted as statements Parker and Stone are attempting to make to the viewing public, and these opinions have been subject to much critical analysis in the media and literary world within the framework of popular philosophical, theological, social, and political concepts. Since "South Park" debuted, college students have written term papers and doctoral theses analyzing the show, while Brooklyn College offers a course called ""South Park" and Political Correctness".  Soon after one of Kenny's trademark deaths on the show, other characters would typically shout "Oh my God, they killed Kenny!". The exclamation quickly became a popular catchphrase, while the running gag of Kenny's recurring deaths are one of the more recognized hallmarks among viewers of modern television. Cartman's exclamations of "Respect my authori-tah!" and "Screw you guys...I'm going home!" became catchphrases as well, and during the show's earlier seasons, were highly popular in the lexicon of viewers. Cartman's eccentric intonation of "Hey!" was included in the 2002 edition of "The Oxford Dictionary of Catchphrases".  In

Political.

While some conservatives have condemned "South Park" for its vulgarity, a growing population of people who hold center-right political beliefs, including teenagers and young adults, have embraced the show for its tendency to mock liberal viewpoints and lampoon liberal celebrities and icons. Political commentator Andrew Sullivan dubbed the group "South Park" Republicans, or "South Park" conservatives. Sullivan averred that members of the group are "extremely skeptical of political correctness but also are socially liberal on many issues", though he says the phrase applied to them is meant to be more of a casual indication of beliefs than a strong partisan label. Brian C. Anderson describes the group as "generally characterized by holding strong libertarian beliefs and rejecting more conservative social policy", and notes that although the show makes "wicked fun of conservatives", it is "at the forefront of a conservative revolt

Franchise.

Film.

In 1999, less than two years after the series first aired, a was released. The film, a musical comedy, was directed by Parker, who co-wrote the script with Stone and Pam Brady. The film was generally well received by critics, and

Shorts.

As a tribute to the Dead Parrot sketch, a short that features Cartman attempting to return a dead Kenny to a shop run by Kyle aired during a 1999 BBC television special commemorating the 30th anniversary of "Monty Python's Flying Circus". "South Park" parodied Scientology in a short that aired as part of the 2000 MTV Movie Awards. The short was entitled "The Gauntlet" and also poked fun at John Travolta, a Scientologist. The four main characters were featured in the documentary film "The Aristocrats", listening to Cartman tell his version of the

Music.

"", a compilation of original songs from the show, characters performing cover songs, and tracks performed by guest artists was released in 1998, while "Mr. Hankey's Christmas Classics", a compilation of songs performed by the characters in the

Merchandising.

Merchandising related to the show is an industry which generates several million dollars a year. In 1998, the top-selling specialty T-shirt in the United States was based on "South Park", and US$30 million in T-shirt sales was reached during the show's first season.  A "South

References.

Further Reading

South Park is an American animated sitcom created by Trey Parker and Matt Stone and developed by Brian Graden for the Comedy Central television network. The series revolves around four boys—Stan Marsh, Kyle Broflovski, Eric Cartman, and Kenny McCormick—and their exploits in and around the titular Colorado town. The show became infamous for its profanity and dark, surreal humor that satirizes a wide range of topics towards a mature audience.

Městečko South Park (v anglickém originále South Park) je americký komediální animovaný seriál, který vytvořili Trey Parker a Matt Stone. V USA jej vysílá stanice Comedy Central od roku 1997. V Česku ho v letech 1997–2004 vysílaly stanice HBO a TV Nova až do 6. série. Od roku 2012 navázala Nova na svém kanále Fanda 7. sérií a od roku 2015 seriál vysílá Prima Comedy Central.


Life.

Early life.

Galbraith was born on October 15, 1908, to Canadians of Scottish descent, Sarah Catherine (Kendall) and Archibald "Archie" Galbraith, in Iona Station, Ontario, Canada, and was raised in Dunwich Township, Ontario. He had three siblings: Alice, Catherine, and Archibald William (Bill). By the time he was a teenager, he had adopted the name Ken, and later disliked being called John. Galbraith grew to be a very tall man, attaining a height of.  His father was a farmer and school teacher. His mother, a homemaker and a community activist, died when he was fourteen years old. The family farm was located on Thomson Line. Both of his parents were supporters of the United Farmers of Ontario in the 1920s.  His early years were spent at a one-room school which is still standing, on 9468 Willey Road, in Iona Station. Later, he went to Dutton High School and St. Thomas High School. In 1931, Galbraith graduated with a Bachelor of Science

Second World War.

The United States went into WWII with an economy still not fully recovered from the Great Depression. Because wartime production needs mandated large budget deficits and an accommodating monetary policy, inflation and a runaway wage-price spiral was seen as likely. As a part of a team charged with keeping inflation from crippling the war effort, Galbraith served as a deputy head of the Office of Price Administration (OPA) during the Second World War in 1941–1943. The OPA directed the process of stabilization of prices and rents.  On May 11, 1941, President Roosevelt signed the Executive Order 8734 which created the Office of Price Administration and Civilian Supply (OPACS). On August 28, 1941, an Executive Order 8875 transformed OPACS into the Office of Price Administration (OPA). After the US entered WWII in December 1941, OPA was tasked with

Postwar.

In February 1946, Galbraith took a leave of absence from his magazine work for a senior position in the State Department as director of the Office of Economic Security Policy where he was nominally in charge of economic affairs regarding Germany, Japan, Austria, and South Korea. He was distrusted by the senior diplomats so he was relegated to routine work with few opportunities to make policy. Galbraith favored détente with the Soviet Union, along with Secretary of State James F. Byrnes and General Lucius D. Clay, a military governor of the US Zone in Germany from 1947 to 1949, but they were out of step with the containment policy then being developed by George Kennan and favored by the majority of the US major policymakers. After a disconcerting half-year, Galbraith resigned in September 1946 and went back to his magazine writing on economics issues. Later, he immortalized his frustration with "the ways of Foggy Bottom" in a satirical novel, "The Triumph" (1968). The postwar period also was memorable for Galbraith because of his work, along with Eleanor Roosevelt and Hubert Humphrey, to establish a progressive policy organization Americans for Democratic Action (ADA) in support of the cause of economic and social justice in 1947. In 1952, Galbraith's friends Arthur M. Schlesinger Jr. and George Ball recruited him to work as a speechwriter for the Democratic candidate, Adlai Stevenson. The involvement of several intellectuals from the ADA in the Stevenson campaign attracted controversy as the Republican Senator Joseph McCarthy accused the ADA intellectuals as being "tainted" by "well documented Red associations"; Galbraith later said one of his regrets was that McCarthy failed to condemn him as one of Stevenson's "red" advisers. During his time as an adviser to President John F. Kennedy, Galbraith was appointed United States Ambassador to India from 1961 to 1963. His rapport with President Kennedy was such that he regularly bypassed the State Department and sent his diplomatic cables directly to the president. Galbraith disliked his superior, the Secretary of State, Dean Rusk, writing to Kennedy that trying to communicate via Rusk was "like trying to fornicate through a mattress". In India, he became a confidant of Prime Minister Jawaharlal Nehru and extensively advised the Indian government on economic matters.  India was considered by Kennedy to be not just important in its own right, but because an Indian diplomat always served as the chief commissioner of the International Control Commission (ICC), and thus in this way, Galbraith came to be involved in American policy towards Southeast Asia from

Later life and recognition.

In 1972 he served as president of the American Economic Association. The "Journal of Post Keynesian Economics" benefited from Galbraith's support and he served as the chairman of its board from its beginning.  During the shooting of "The World at War", a British television documentary series (1973–74), Galbraith described his experiences in the Roosevelt war administration. Among other things, he spoke about the initial confusion during the first meeting of the major departmental leaders about kapok and its use. Galbraith also talked about rationing and especially about trickery during fuel allocation.  In December 1977, he met the Palauan senator Roman Tmetuchl and eventually became an unpaid adviser to the Palau Political Status Commission. He advocated for minimal financial requirement and infrastructure projects. In 1979 he addressed Palau's legislature and participated in a seminar for the delegates to the Palau Constitutional Convention. He

Family.

On September 17, 1937, Galbraith married Catherine Merriam Atwater, whom he met while she was a Radcliffe graduate student. Their marriage lasted for 68 years. The Galbraiths resided in Cambridge, Massachusetts, and had a summer home in Newfane, Vermont. They had four sons: J. Alan Galbraith is a partner in the Washington, DC, law firm Williams & Connolly; Douglas Galbraith died in childhood of leukemia; Peter W. Galbraith

Writings.

Even before becoming a president of the American Economic Association, Galbraith was considered as an iconoclast by many economists. This is partly because he rejected the technical analysis and mathematical modelling of neoclassical economics as being divorced from reality. Following Thorstein Veblen, he believed that economic activity could not be distilled into inviolable laws, but rather was a complex product of the cultural and political milieu in which it occurs. In particular, he posited that important factors, such as the separation between corporate ownership and management, oligopoly, and the influence of government and military spending had been largely neglected by most economists because they are not amenable to axiomatic descriptions. In this sense, he worked as much in political economy as in classical economics.  His work included several best selling books throughout the fifties and sixties. His major contribution to the field of economics is the so-called "American capitalism" trilogy: The "Affluent Society" (1958), "The New Industrial State" (1967), and "Economics and the Public Purpose" (1973). Written in a clear and concise style, they were comprehensible to lay readers, not just economists.  After his retirement from Harvard as the Paul M. Warburg Professor of Economics, Emeritus, he remained in the public spotlight by continuing to write 21 new books, as well as completing a script in 1977 for a major series on economics for PBS and BBC television—"The Age of Uncertainty", broadcast in 38 countries.  In addition to his books, he wrote hundreds of essays and a number of novels. Among his novels, "A Tenured Professor" achieved particular critical acclaim. Galbraith wrote book reviews, e.g., of "The Report from Iron Mountain on the Possibility and Desirability of Peace", a 1967 political satire, under the pen name of "Herschel McLandress", a name of a fictional Scottish mentor featured in the "Tenured Professor". He also used the pseudonym, Mark Épernay, when he published "The McLandress Dimension" in 1963.

Economics books.

Galbraith was an important figure in 20th-century institutional economics, and provided an exemplary "institutionalist" perspective on economic power. Among his numerous writings, Galbraith cherished "The New Industrial State" and "The Affluent Society" as his two best. As for the later works, economist and Galbraith friend Mike Sharpe visited him in 2004, on which occasion Galbraith gave Sharpe a copy of what would be Galbraith's last book, "The Economics of Innocent Fraud". Galbraith confided in Sharpe that "this is my best book", an assertion Galbraith delivered "a little mischievously."  After the beginning of the Great Recession of 2008, Galbraith's "The Great Crash, 1929" (1955) and other books containing warnings about the dangers of an unrestrained speculative mood without proper government oversight found an attentive readership again. In 2010, the Library of America published a new edition of Galbraith's major works, edited by his son, James K. Galbraith: "The Affluent Society & Other Writings, 1952–1967": "American Capitalism", "The Great Crash, 1929", "The Affluent Society", and "The New Industrial State". On this occasion, Bill Moyers interviewed James K. Galbraith about his father, his works, and his legacy.

American economy.

In "American Capitalism: The Concept of Countervailing Power", published in 1952, Galbraith concluded that the American economy was managed by a triumvirate of big business, big labor, and an activist government. Galbraith defined the actions of the industry lobby groups and unions as "countervailing power". He contrasted this arrangement with the period prior to the previous Depression, when big business had relatively free rein over the economy.  His 1955 bestseller "The Great Crash, 1929" describes the Wall Street meltdown of stock prices and how markets progressively become decoupled from reality in a speculative boom. The book is also a platform for Galbraith's humor and keen

New industrial state.

In 1966, Galbraith was invited by the BBC to present the Reith Lectures, a series of radio broadcasts, which he titled "The New Industrial State". Across six broadcasts, he explored the economics of production and the effect large corporations could have over the state.  In the print edition of "The New Industrial State" (1967), Galbraith expanded his analysis of the role of power in economic life, arguing that very few industries in the United States fit the model of perfect competition. A central concept of the book is the revised sequence. The

Financial bubbles.

In "A Short History of Financial Euphoria" (1990), he traces speculative bubbles through several centuries, and argues that they are inherent in the free market system because of "mass psychology" and the "vested interest in error that accompanies speculative euphoria." Also, financial memory is "notoriously short": what currently seems to be a "new financial instrument" is inevitably nothing of the sort. Galbraith cautions: "The world of finance hails the invention of the wheel over and over again, often in a slightly more unstable version." Crucial to his analysis is the assertion that the common factor in boom-and-bust is the creation of debt to finance speculation, which "becomes dangerously out of scale in relation to the underlying means of payment."

Legacy.

Galbraith's main ideas focused around the influence of the market power of large corporations. He believed that this market power weakened the widely accepted principle of consumer sovereignty, allowing corporations to be price makers, rather than price takers, allowing corporations with the strongest market power to increase the production of their goods beyond an efficient amount. He further believed that market power played a major role in inflation. He argued that corporations and trade unions could only increase prices to the extent that their market power allowed. He argued that in situations of excessive market power, price controls effectively controlled inflation, but cautioned against using them in markets that were basically efficient such as agricultural goods and housing. He noted that price controls were much easier to enforce in industries with relatively few buyers and sellers. Galbraith's view of market power was not entirely negative; he also noted that the power of US firms played a part in the success of the US economy.  In "The Affluent Society" Galbraith asserts that classical economic theory was true for the eras before the present, which were times of "poverty"; now, however, we have moved from an

Criticism of Galbraith's work.

Galbraith's work in general, and "The Affluent Society" in particular, have drawn sharp criticism from laissez-faire supporters since the time of their publications. Nobel-Memorial-Prize-winning economist Milton Friedman in "Friedman on Galbraith, and on curing the British disease" views Galbraith as a 20th-century version of the early-19th-century Tory radical of Great Britain. He asserts that Galbraith believes in the superiority of aristocracy and in its paternalistic authority, that consumers should not be allowed choice, and that all should be determined by those with "higher minds":  Many reformers—Galbraith is not alone in this—have as their basic objection to a free market that it frustrates them in achieving their reforms, because it enables people to have what they want, not what the reformers want. Hence every reformer has a strong tendency to be averse to a free market.  Nobel Prize-winning economist Robert Solow, in a review of "The New Industrial State", points at Galbraith's lack of empiricism and selectiveness in his use of evidence. He points out that "It may be unjust and pointless to consider the degree of literal truth of each of the assertions that

Memoirs.

The first edition of "The Scotch" was published in the UK under two alternative titles: as "Made to Last" and "The Non-potable Scotch: A Memoir of the Clansmen in Canada". It was illustrated by Samuel H. Bryant. Galbraith's account of his boyhood environment in Elgin County in

Honors.

John Kenneth Galbraith was one of the few people to receive both the World War II Medal of Freedom and the Presidential Medal of Freedom; respectively in 1946 from President Truman and in 2000 from President Bill Clinton. He was a recipient of Lomonosov Gold Medal in 1993 for his contributions to science. He also was appointed to the Order of Canada in 1997 and, in 2001, awarded the Padma Vibhushan, India's second highest civilian award, for his contributions to strengthening ties between India and the United States.  In 2010, he became the first economist to have his works included in the Library of America series.

Honorary degrees.

John Kenneth Galbraith received

John Kenneth Galbraith (October 15, 1908 – April 29, 2006), also known as Ken Galbraith, was a Canadian-American economist, public official and diplomat, and a leading proponent of 20th-century American liberalism. His books on economic topics were bestsellers from the 1950s through the 2000s, a time during which Galbraith fulfilled the role of public intellectual. As an economist, he leaned toward post-Keynesian economics from an institutionalist perspective.

John Kenneth Galbraith (15. října 1908, Iona Station, Ontario – 29. dubna 2006, Cambridge, Massachusetts) byl vlivný kanadsko-americký ekonom, harvardský profesor, spisovatel, veřejný intelektuál, ekonomický popularizátor, prezidentský poradce a velvyslanec USA v Indii.