title: Roland Orzabal

text: The band's debut album, "The Hurting" (1983), reached number one on the UK Albums Chart. Their second album, "Songs from the Big Chair" (1985), reached number one on the US "Billboard" 200, achieving multi-platinum status in both the UK and the US. "Songs from the Big Chair" included two "Billboard" Hot 100 number one hits: "Shout" and "Everybody Wants to Rule the World".


title: Roland Orzabal

text: After the release of their third album, "The Seeds of Love" (1989), Smith and Orzabal split in 1991. Orzabal continued recording under the Tears for Fears name, releasing the albums "Elemental" (1993) and "Raoul and the Kings of Spain" (1995). As Tears for Fears, Orzabal and Smith released "Everybody Loves a Happy Ending" in 2004. After almost a decade in development, the band's seventh album, "The Tipping Point", was released in February 2022.


title: Roland Orzabal

text: As a songwriter, Orzabal is a three-time Ivor Novello Award winner. His first award was in 1986 for "Songwriter of the Year" following the release of Tears for Fears' second album "Songs from the Big Chair".


title: Roland Orzabal

text: Orzabal and Smith were responsible for discovering pianist/vocalist Oleta Adams, whom they invited to collaborate on their 1989 album "The Seeds of Love". Adams appeared on several tracks on the album, most notably the hit single "Woman in Chains", which she performed as a duet with Orzabal. Orzabal then co-produced Adams' album "Circle of One" (1990). The album reached No. 1 in the UK and No. 20 in the US, and featured her transatlantic top ten hit "Get Here". Orzabal also co-wrote the lead track "Rhythm of Life" for the album, which was originally intended for "The Seeds of Love". As well as playing guitar and singing backing vocals on the track, he also appeared in the song's accompanying promo video.


title: Roland Orzabal

text: In 1999, Orzabal co-produced Icelandic singer-songwriter Emiliana Torrini's album "Love in the Time of Science", along with Tears for Fears associate Alan Griffiths. The pair also wrote two tracks for the album.


title: Roland Orzabal

text: Orzabal wrote the song "Mad World", recorded by Michael Andrews and Gary Jules for the film soundtrack "Donnie Darko" in 2001. Their version was released as a single in 2003 and became the Christmas number one single in the UK that year, ultimately becoming the year's biggest-selling single. The song was originally composed by Orzabal and was Tears for Fears' first hit single in 1982. In 2004, the song won Orzabal his second Ivor Novello Award; he was awarded as the songwriter of the Best Selling UK Single of 2003. In September 2021, Orzabal was awarded his third Ivor Novello Award along with Curt Smith for the Outstanding Song Collection by Tears for Fears.


title: Roland Orzabal

text: Orzabal wrote a novel, a romantic comedy entitled "Sex, Drugs & Opera", published in 2014. It tells the story of a middle-aged pop star, Solomon Capri, who is semi-retired but is approached to take part in the reality show "Popstar to Operastar". Capri sees the show as a way to rejuvenate his career and his waning marriage. The story was inspired by Orzabal's own experience; he was approached by the ITV show himself, though did not take part.


title: Roland Orzabal

text: In 1982, Orzabal married Caroline Johnston, whom he had been dating since his teenage years. Caroline sang the child vocal on the Tears for Fears song "Suffer the Children" from the band's debut album "The Hurting", and also drew the hands cover artwork for the 1983 re-release of "Pale Shelter". Roland and Caroline Orzabal had two sons. Caroline Orzabal died in July 2017 aged 62 after suffering from alcoholism-related dementia and cirrhosis, which came about after her menopause led to depression. Her death led the band to cancel its remaining tour dates that year.


title: Roland Orzabal

text: After the election of Margaret Thatcher in June 1987, Orzabal took interest in socialism. He then wrote the lyrics "Politician granny with your high ideals, have you no idea how the majority feels?" in the song "Sowing the Seeds of Love".


title: Roland Orzabal

text: Orzabal has a house in the Hollywood Hills, about 3 miles from bandmate Curt Smith. He also has a house in England.


title: Cross product

text: In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here formula_1), and is denoted by the symbol formula_2. Given two linearly independent vectors and , the cross product, (read "a cross b"), is a vector that is perpendicular to both and , and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with the dot product (projection product).


title: Cross product

text: If two vectors have the same direction or have the exact opposite direction from each other (that is, they are "not" linearly independent), or if either one has zero length, then their cross product is zero. More generally, the magnitude of the product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two perpendicular vectors is the product of their lengths.


title: Cross product

text: The cross product is anticommutative (that is, ) and is distributive over addition (that is, ). The space formula_1 together with the cross product is an algebra over the real numbers, which is neither commutative nor associative, but is a Lie algebra with the cross product being the Lie bracket.


title: Cross product

text: Like the dot product, it depends on the metric of Euclidean space, but unlike the dot product, it also depends on a choice of orientation (or "handedness") of the space (it's why an oriented space is needed). In connection with the cross product, the exterior product of vectors can be used in arbitrary dimensions (with a bivector or 2-form result) and is independent of the orientation of the space.


title: Cross product

text: The product can be generalized in various ways, using the orientation and metric structure just as for the traditional 3-dimensional cross product, one can, in dimensions, take the product of vectors to produce a vector perpendicular to all of them. But if the product is limited to non-trivial binary products with vector results, it exists only in three and seven dimensions. The cross-product in seven dimensions has undesirable properties (e.g. it fails to satisfy the Jacobi identity), however, so it is not used in mathematical physics to represent quantities such as multi-dimensional space-time. (See § Generalizations, below, for other dimensions.)


title: Cross product

text: The cross product of two vectors a and b is defined only in three-dimensional space and is denoted by . In physics and applied mathematics, the wedge notation is often used (in conjunction with the name "vector product"), although in pure mathematics such notation is usually reserved for just the exterior product, an abstraction of the vector product to dimensions.


title: Cross product

text: The cross product is defined as a vector c that is perpendicular (orthogonal) to both a and b, with a direction given by the right-hand rule and a magnitude equal to the area of the parallelogram that the vectors span.


title: Cross product

text: If the vectors a and b are parallel (that is, the angle "θ" between them is either 0° or 180°), by the above formula, the cross product of a and b is the zero vector 0.


title: Cross product

text: By convention, the direction of the vector n is given by the right-hand rule, where one simply points the forefinger of the right hand in the direction of a and the middle finger in the direction of b. Then, the vector n is coming out of the thumb (see the adjacent picture). Using this rule implies that the cross product is anti-commutative; that is, . By pointing the forefinger toward b first, and then pointing the middle finger toward a, the thumb will be forced in the opposite direction, reversing the sign of the product vector.


title: Cross product

text: As the cross product operator depends on the orientation of the space (as explicit in the definition above), the cross product of two vectors is not a "true" vector, but a "pseudovector". See for more detail.


title: Cross product

text: In 1842, William Rowan Hamilton discovered the algebra of quaternions and the non-commutative Hamilton product. In particular, when the Hamilton product of two vectors (that is, pure quaternions with zero scalar part) is performed, it results in a quaternion with a scalar and vector part. The scalar and vector part of this Hamilton product corresponds to the negative of dot product and cross product of the two vectors.


title: Cross product

text: In 1881, Josiah Willard Gibbs, and independently Oliver Heaviside, introduced the notation for both the dot product and the cross product using a period () and an "×" (), respectively, to denote them.


title: Cross product

text: In 1877, to emphasize the fact that the result of a dot product is a scalar while the result of a cross product is a vector, William Kingdon Clifford coined the alternative names scalar product and vector product for the two operations. These alternative names are still widely used in the literature.


title: Cross product

text: Both the cross notation () and the name cross product were possibly inspired by the fact that each scalar component of is computed by multiplying non-corresponding components of a and b. Conversely, a dot product involves multiplications between corresponding components of a and b. As explained below, the cross product can be expressed in the form of a determinant of a special matrix. According to Sarrus's rule, this involves multiplications between matrix elements identified by crossed diagonals.


title: Cross product

text: If (i, j,k) is a positively oriented orthonormal basis, the basis vectors satisfy the following equalities


title: Cross product

text: The anticommutativity of the cross product (and the obvious lack of linear independence) also implies that


title: Cross product

text: These equalities, together with the distributivity and linearity of the cross product (though neither follows easily from the definition given above), are sufficient to determine the cross product of any two vectors a and b. Each vector can be defined as the sum of three orthogonal components parallel to the standard basis vectors:


title: Cross product

text: This can be interpreted as the decomposition of into the sum of nine simpler cross products involving vectors aligned with i, j, or k. Each one of these nine cross products operates on two vectors that are easy to handle as they are either parallel or orthogonal to each other. From this decomposition, by using the above-mentioned equalities and collecting similar terms, we obtain:


title: Cross product

text: This determinant can be computed using Sarrus's rule or cofactor expansion. Using Sarrus's rule, it expands to


title: Cross product

text: The latter formula avoids having to change the orientation of the space when we inverse an orthonormal basis.


title: Cross product

text: The magnitude of the cross product can be interpreted as the positive area of the parallelogram having a and b as sides (see Figure 1):


title: Cross product

text: Indeed, one can also compute the volume "V" of a parallelepiped having a, b and c as edges by using a combination of a cross product and a dot product, called scalar triple product (see Figure 2):


title: Cross product

text: Since the result of the scalar triple product may be negative, the volume of the parallelepiped is given by its absolute value:


title: Cross product

text: Because the magnitude of the cross product goes by the sine of the angle between its arguments, the cross product can be thought of as a measure of "perpendicularity" in the same way that the dot product is a measure of "parallelism". Given two unit vectors, their cross product has a magnitude of 1 if the two are perpendicular and a magnitude of zero if the two are parallel. The dot product of two unit vectors behaves just oppositely: it is zero when the unit vectors are perpendicular and 1 if the unit vectors are parallel.


title: Cross product

text: Unit vectors enable two convenient identities: the dot product of two unit vectors yields the cosine (which may be positive or negative) of the angle between the two unit vectors. The magnitude of the cross product of the two unit vectors yields the sine (which will always be positive).


title: Cross product

text: If the cross product of two vectors is the zero vector (that is, ), then either one or both of the inputs is the zero vector, ( or ) or else they are parallel or antiparallel () so that the sine of the angle between them is zero ( or and ).


title: Cross product

text: Distributivity, linearity and Jacobi identity show that the R vector space together with vector addition and the cross product forms a Lie algebra, the Lie algebra of the real orthogonal group in 3 dimensions, SO(3).


title: Cross product

text: This can be the case where b and c cancel, but additionally where a and are parallel; that is, they are related by a scale factor "t", leading to:


title: Cross product

text: As cannot be simultaneously parallel (for the cross product to be 0) and perpendicular (for the dot product to be 0) to a, it must be the case that b and c cancel: .


title: Cross product

text: From the geometrical definition, the cross product is invariant under proper rotations about the axis defined by . In formulae:


title: Cross product

text: where formula_40 is a 3-by-3 matrix and formula_41 is the transpose of the inverse and formula_42 is the cofactor matrix. It can be readily seen how this formula reduces to the former one if formula_40 is a rotation matrix. If formula_40 is a 3-by-3 symmetric matrix applied to a generic cross product formula_45, the following relation holds true:


title: Cross product

text: The product rule of differential calculus applies to any bilinear operation, and therefore also to the cross product:


title: Cross product

text: The cross product is used in both forms of the triple product. The scalar triple product of three vectors is defined as


title: Cross product

text: It is the signed volume of the parallelepiped with edges a, b and c and as such the vectors can be used in any order that's an even permutation of the above ordering. The following therefore are equal:


title: Cross product

text: The vector triple product is the cross product of a vector with the result of another cross product, and is related to the dot product by the following formula


title: Cross product

text: The mnemonic "BAC minus CAB" is used to remember the order of the vectors in the right hand member. This formula is used in physics to simplify vector calculations. A special case, regarding gradients and useful in vector calculus, is


title: Cross product

text: The right-hand side is the Gram determinant of a and b, the square of the area of the parallelogram defined by the vectors. This condition determines the magnitude of the cross product. Namely, since the dot product is defined, in terms of the angle "θ" between the two vectors, as:


title: Cross product

text: which is the magnitude of the cross product expressed in terms of "θ", equal to the area of the parallelogram defined by a and b (see definition above).


title: Cross product

text: The combination of this requirement and the property that the cross product be orthogonal to its constituents a and b provides an alternative definition of the cross product.


title: Cross product

text: can be compared with another relation involving the right-hand side, namely Lagrange's identity expressed as:


title: Cross product

text: where a and b may be "n"-dimensional vectors. This also shows that the Riemannian volume form for surfaces is exactly the surface element from vector calculus. In the case where , combining these two equations results in the expression for the magnitude of the cross product in terms of its components:


title: Cross product

text: In R, Lagrange's equation is a special case of the multiplicativity of the norm in the quaternion algebra.


title: Cross product

text: It is a special case of another formula, also sometimes called Lagrange's identity, which is the three dimensional case of the Binet–Cauchy identity:


title: Cross product

text: The cross product conveniently describes the infinitesimal generators of rotations in R. Specifically, if n is a unit vector in R and "R"("φ", n) denotes a rotation about the axis through the origin specified by n, with angle φ (measured in radians, counterclockwise when viewed from the tip of n), then


title: Cross product

text: for every vector x in R. The cross product with n therefore describes the infinitesimal generator of the rotations about n. These infinitesimal generators form the Lie algebra so(3) of the rotation group SO(3), and we obtain the result that the Lie algebra R with cross product is isomorphic to the Lie algebra so(3).


title: Cross product

text: The vector cross product also can be expressed as the product of a skew-symmetric matrix and a vector:


title: Cross product

text: The columns [a] of the skew-symmetric matrix for a vector a can be also obtained by calculating the cross product with unit vectors. That is,


title: Cross product

text: This result can be generalized to higher dimensions using geometric algebra. In particular in any dimension bivectors can be identified with skew-symmetric matrices, so the product between a skew-symmetric matrix and vector is equivalent to the grade-1 part of the product of a bivector and vector. In three dimensions bivectors are dual to vectors so the product is equivalent to the cross product, with the bivector instead of its vector dual. In higher dimensions the product can still be calculated but bivectors have more degrees of freedom and are not equivalent to vectors.


title: Cross product

text: The above-mentioned triple product expansion (bac–cab rule) can be easily proven using this notation.


title: Cross product

text: As mentioned above, the Lie algebra R with cross product is isomorphic to the Lie algebra so(3), whose elements can be identified with the 3×3 skew-symmetric matrices. The map a → [a] provides an isomorphism between R and so(3). Under this map, the cross product of 3-vectors corresponds to the commutator of 3x3 skew-symmetric matrices.


title: Cross product

text: The cross product can alternatively be defined in terms of the Levi-Civita tensor "E" and a dot product "η", which are useful in converting vector notation for tensor applications:


title: Cross product

text: where the indices formula_76 correspond to vector components. This characterization of the cross product is often expressed more compactly using the Einstein summation convention as


title: Cross product

text: In a positively-oriented orthonormal basis "η" = δ (the Kronecker delta) and formula_78 (the Levi-Civita symbol). In that case, this representation is another form of the skew-symmetric representation of the cross product:


title: Cross product

text: In classical mechanics: representing the cross product by using the Levi-Civita symbol can cause mechanical symmetries to be obvious when physical systems are isotropic. (An example: consider a particle in a Hooke's Law potential in three-space, free to oscillate in three dimensions; none of these dimensions are "special" in any sense, so symmetries lie in the cross-product-represented angular momentum, which are made clear by the abovementioned Levi-Civita representation).


title: Cross product

text: The second and third equations can be obtained from the first by simply vertically rotating the subscripts, . The problem, of course, is how to remember the first equation, and two options are available for this purpose: either to remember the relevant two diagonals of Sarrus's scheme (those containing i), or to remember the xyzzy sequence.


title: Cross product

text: Since the first diagonal in Sarrus's scheme is just the main diagonal of the above-mentioned 3×3 matrix, the first three letters of the word xyzzy can be very easily remembered.


title: Cross product

text: Similarly to the mnemonic device above, a "cross" or X can be visualized between the two vectors in the equation. This may be helpful for remembering the correct cross product formula.


title: Cross product

text: If we want to obtain the formula for formula_87 we simply drop the formula_88 and formula_89 from the formula, and take the next two components down:


title: Cross product

text: When doing this for formula_91 the next two elements down should "wrap around" the matrix so that after the z component comes the x component. For clarity, when performing this operation for formula_91, the next two components should be z and x (in that order). While for formula_93 the next two components should be taken as x and y.


title: Cross product

text: For formula_87 then, if we visualize the cross operator as pointing from an element on the left to an element on the right, we can take the first element on the left and simply multiply by the element that the cross points to in the right hand matrix. We then subtract the next element down on the left, multiplied by the element that the cross points to here as well. This results in our formula_87 formula –


title: Cross product

text: The cross product has applications in various contexts. For example, it is used in computational geometry, physics and engineering.


title: Cross product

text: The cross product appears in the calculation of the distance of two skew lines (lines not in the same plane) from each other in three-dimensional space.


title: Cross product

text: The cross product can be used to calculate the normal for a triangle or polygon, an operation frequently performed in computer graphics. For example, the winding of a polygon (clockwise or anticlockwise) about a point within the polygon can be calculated by triangulating the polygon (like spoking a wheel) and summing the angles (between the spokes) using the cross product to keep track of the sign of each angle.


title: Cross product

text: In computational geometry of the plane, the cross product is used to determine the sign of the acute angle defined by three points formula_100 and formula_101. It corresponds to the direction (upward or downward) of the cross product of the two coplanar vectors defined by the two pairs of points formula_102 and formula_103. The sign of the acute angle is the sign of the expression


title: Cross product

text: In the "right-handed" coordinate system, if the result is 0, the points are collinear; if it is positive, the three points constitute a positive angle of rotation around formula_105 from formula_106 to formula_107, otherwise a negative angle. From another point of view, the sign of formula_108 tells whether formula_107 lies to the left or to the right of line formula_110


title: Cross product

text: The cross product is used in calculating the volume of a polyhedron such as a tetrahedron or parallelepiped.


title: Cross product

text: where is the position vector of the particle relative to the origin, is the linear momentum of the particle.


title: Cross product

text: Since position linear momentum and force are all "true" vectors, both the angular momentum and the moment of a force are "pseudovectors" or "axial vectors".


title: Cross product

text: The cross product frequently appears in the description of rigid motions. Two points "P" and "Q" on a rigid body can be related by:


title: Cross product

text: where formula_115 is the point's position, formula_116 is its velocity and formula_117 is the body's angular velocity.


title: Cross product

text: Since position formula_115 and velocity formula_116 are "true" vectors, the angular velocity formula_117 is a "pseudovector" or "axial vector".


title: Cross product

text: Since velocity force and electric field are all "true" vectors, the magnetic field is a "pseudovector".


title: Cross product

text: The trick of rewriting a cross product in terms of a matrix multiplication appears frequently in epipolar and multi-view geometry, in particular when deriving matching constraints.


title: Cross product

text: The cross product can be defined in terms of the exterior product. It can be generalized to an external product in other than three dimensions. This view allows a natural geometric interpretation of the cross product. In exterior algebra the exterior product of two vectors is a bivector. A bivector is an oriented plane element, in much the same way that a vector is an oriented line element. Given two vectors "a" and "b", one can view the bivector as the oriented parallelogram spanned by "a" and "b". The cross product is then obtained by taking the Hodge star of the bivector , mapping 2-vectors to vectors:


title: Cross product

text: This can be thought of as the oriented multi-dimensional element "perpendicular" to the bivector. Only in three dimensions is the result an oriented one-dimensional element – a vector – whereas, for example, in four dimensions the Hodge dual of a bivector is two-dimensional – a bivector. So, only in three dimensions can a vector cross product of "a" and "b" be defined as the vector dual to the bivector : it is perpendicular to the bivector, with orientation dependent on the coordinate system's handedness, and has the same magnitude relative to the unit normal vector as has relative to the unit bivector; precisely the properties described above.


title: Cross product

text: When physics laws are written as equations, it is possible to make an arbitrary choice of the coordinate system, including handedness. One should be careful to never write down an equation where the two sides do not behave equally under all transformations that need to be considered. For example, if one side of the equation is a cross product of two polar vectors, one must take into account that the result is an axial vector. Therefore, for consistency, the other side must also be an axial vector. More generally, the result of a cross product may be either a polar vector or an axial vector, depending on the type of its operands (polar vectors or axial vectors). Namely, polar vectors and axial vectors are interrelated in the following ways under application of the cross product:


title: Cross product

text: Because the cross product may also be a polar vector, it may not change direction with a mirror image transformation. This happens, according to the above relationships, if one of the operands is a polar vector and the other one is an axial vector (e.g., the cross product of two polar vectors). For instance, a vector triple product involving three polar vectors is a polar vector.


title: Cross product

text: Let (i, j,k) be an orthonormal basis. The vectors i, j and k don't depend on the orientation of the space. They can even be defined in the absence of any orientation. They can not therefore be axial vectors. But if i and j are polar vectors then k is an axial vector for i × j = k or j × i = k. This is a paradox.


title: Cross product

text: "Axial" and "polar" are "physical" qualifiers for "physical" vectors; that is, vectors which represent "physical" quantities such as the velocity or the magnetic field. The vectors i, j and k are mathematical vectors, neither axial nor polar. In mathematics, the cross-product of two vectors is a vector. There is no contradiction.


title: Cross product

text: The cross product can be seen as one of the simplest Lie products, and is thus generalized by Lie algebras, which are axiomatized as binary products satisfying the axioms of multilinearity, skew-symmetry, and the Jacobi identity. Many Lie algebras exist, and their study is a major field of mathematics, called Lie theory.


title: Cross product

text: For example, the Heisenberg algebra gives another Lie algebra structure on formula_123 In the basis formula_124 the product is formula_125


title: Cross product

text: In general, if a vector is represented as the quaternion , the cross product of two vectors can be obtained by taking their product as quaternions and deleting the real part of the result. The real part will be the negative of the dot product of the two vectors.


title: Cross product

text: A cross product for 7-dimensional vectors can be obtained in the same way by using the octonions instead of the quaternions. The nonexistence of nontrivial vector-valued cross products of two vectors in other dimensions is related to the result from Hurwitz's theorem that the only normed division algebras are the ones with dimension 1, 2, 4, and 8.


title: Cross product

text: In general dimension, there is no direct analogue of the binary cross product that yields specifically a vector. There is however the exterior product, which has similar properties, except that the exterior product of two vectors is now a 2-vector instead of an ordinary vector. As mentioned above, the cross product can be interpreted as the exterior product in three dimensions by using the Hodge star operator to map 2-vectors to vectors. The Hodge dual of the exterior product yields an -vector, which is a natural generalization of the cross product in any number of dimensions.


title: Cross product

text: The exterior product and dot product can be combined (through summation) to form the geometric product in geometric algebra.


title: Cross product

text: As mentioned above, the cross product can be interpreted in three dimensions as the Hodge dual of the exterior product. In any finite "n" dimensions, the Hodge dual of the exterior product of vectors is a vector. So, instead of a binary operation, in arbitrary finite dimensions, the cross product is generalized as the Hodge dual of the exterior product of some given vectors. This generalization is called external product.


title: Cross product

text: Interpreting the three-dimensional vector space of the algebra as the 2-vector (not the 1-vector) subalgebra of the three-dimensional geometric algebra, where formula_126, formula_127, and formula_128, the cross product corresponds exactly to the commutator product in geometric algebra and both use the same symbol formula_2. The commutator product is defined for 2-vectors formula_130 and formula_131 in geometric algebra as:


title: Cross product

text: The commutator product could be generalised to arbitrary multivectors in three dimensions, which results in a multivector consisting of only elements of grades 1 (1-vectors/true vectors) and 2 (2-vectors/pseudovectors). While the commutator product of two 1-vectors is indeed the same as the exterior product and yields a 2-vector, the commutator of a 1-vector and a 2-vector yields a true vector, corresponding instead to the left and right contractions in geometric algebra. The commutator product of two 2-vectors has no corresponding equivalent product, which is why the commutator product is defined in the first place for 2-vectors. Furthermore, the commutator triple product of three 2-vectors is the same as the vector triple product of the same three pseudovectors in vector algebra. However, the commutator triple product of three 1-vectors in geometric algebra is instead the negative of the vector triple product of the same three true vectors in vector algebra.


title: Cross product

text: Generalizations to higher dimensions is provided by the same commutator product of 2-vectors in higher-dimensional geometric algebras, but the 2-vectors are no longer pseudovectors. Just as the commutator product/cross product of 2-vectors in three dimensions correspond to the simplest Lie algebra, the 2-vector subalgebras of higher dimensional geometric algebra equipped with the commutator product also correspond to the Lie algebras. Also as in three dimensions, the commutator product could be further generalised to arbitrary multivectors.


title: Cross product

text: In the context of multilinear algebra, the cross product can be seen as the (1,2)-tensor (a mixed tensor, specifically a bilinear map) obtained from the 3-dimensional volume form, a (0,3)-tensor, by raising an index.


title: Cross product

text: In detail, the 3-dimensional volume form defines a product formula_134 by taking the determinant of the matrix given by these 3 vectors. By duality, this is equivalent to a function formula_135 (fixing any two inputs gives a function formula_136 by evaluating on the third input) and in the presence of an inner product (such as the dot product; more generally, a non-degenerate bilinear form), we have an isomorphism formula_137 and thus this yields a map formula_138 which is the cross product: a (0,3)-tensor (3 vector inputs, scalar output) has been transformed into a (1,2)-tensor (2 vector inputs, 1 vector output) by "raising an index".


title: Cross product

text: Translating the above algebra into geometry, the function "volume of the parallelepiped defined by formula_139" (where the first two vectors are fixed and the last is an input), which defines a function formula_136, can be "represented" uniquely as the dot product with a vector: this vector is the cross product formula_141 From this perspective, the cross product is "defined" by the scalar triple product, formula_142


title: Cross product

text: In the same way, in higher dimensions one may define generalized cross products by raising indices of the "n"-dimensional volume form, which is a formula_143-tensor.


title: Cross product

text: These products are all multilinear and skew-symmetric, and can be defined in terms of the determinant and parity.


title: Cross product

text: The formula_146-ary product can be described as follows: given formula_145 vectors formula_151 in formula_152 define their generalized cross product formula_153 as:


title: Cross product

text: This is the unique multilinear, alternating product which evaluates to formula_158, formula_159 and so forth for cyclic permutations of indices.


title: Cross product

text: In coordinates, one can give a formula for this formula_146-ary analogue of the cross product in R by:


title: Cross product

text: This formula is identical in structure to the determinant formula for the normal cross product in R except that the row of basis vectors is the last row in the determinant rather than the first. The reason for this is to ensure that the ordered vectors (v, ..., v, Λv) have a positive orientation with respect to (e, ..., e). If "n" is odd, this modification leaves the value unchanged, so this convention agrees with the normal definition of the binary product. In the case that "n" is even, however, the distinction must be kept. This formula_146-ary form enjoys many of the same properties as the vector cross product: it is alternating and linear in its arguments, it is perpendicular to each argument, and its magnitude gives the hypervolume of the region bounded by the arguments. And just like the vector cross product, it can be defined in a coordinate independent way as the Hodge dual of the wedge product of the arguments. Moreover, the product formula_163 satisfies the Filippov identity,


title: Cross product

text: In 1773, Joseph-Louis Lagrange used the component form of both the dot and cross products in order to study the tetrahedron in three dimensions.


title: Cross product

text: In 1843, William Rowan Hamilton introduced the quaternion product, and with it the terms "vector" and "scalar". Given two quaternions and , where u and v are vectors in R, their quaternion product can be summarized as . James Clerk Maxwell used Hamilton's quaternion tools to develop his famous electromagnetism equations, and for this and other reasons quaternions for a time were an essential part of physics education.


title: Cross product

text: In 1844, Hermann Grassmann published a geometric algebra not tied to dimension two or three. Grassmann develops several products, including a cross product represented then by . ("See also: exterior algebra.")


title: Cross product

text: In 1853, Augustin-Louis Cauchy, a contemporary of Grassmann, published a paper on algebraic keys which were used to solve equations and had the same multiplication properties as the cross product.


title: Cross product

text: In 1878, William Kingdon Clifford published "Elements of Dynamic", in which the term "vector product" is attested. In the book, this product of two vectors is defined to have magnitude equal to the area of the parallelogram of which they are two sides, and direction perpendicular to their plane. ("See also: Clifford algebra.")


title: Cross product

text: In 1881 lecture notes, Gibbs represents the cross product by formula_165 and calls it the "skew product". In 1901, Gibb's student Edwin Bidwell Wilson edits and extends these lecture notes into the textbook "Vector Analysis". Wilson keeps the term "skew product", but observes that the alternative terms "cross product" and "vector product" were more frequent.


title: Cross product

text: In 1908, Cesare Burali-Forti and Roberto Marcolongo introduce the vector product notation . This is used in France and other areas until this day, as the symbol formula_2 is already used to denote multiplication and the cartesian product.


title: Shohreh Aghdashloo

text: Shohreh Aghdashloo (, ; née Vaziri-Tabar (); 11 May 1952) is an Iranian and American actress. Following numerous starring roles on the stage, she made her film debut in "Chess of the Wind" (1976). Her next two films "The Report" (1977) and "Sooteh Delan" (1977) garnered critical acclaim and established Aghdashloo as one of Iran's leading ladies, although the films were banned in Iran itself.


title: Shohreh Aghdashloo

text: Aghdashloo moved to England during the Iranian Revolution in 1979 and then to the United States, subsequently becoming a U.S. citizen. After several years playing small roles in television and film, her performance in "House of Sand and Fog" (2003) brought her several film critics' awards and a nomination for an Academy Award for Best Supporting Actress. Her other film appearances include "The Exorcism of Emily Rose" (2005), "" and "The Nativity Story" (both 2006), "The Odd Life of Timothy Green" (2013) and "Star Trek Beyond" (2016).


title: Shohreh Aghdashloo

text: In television, she is best known for her roles as Dina Araz in the fourth season of "24" and as Chrisjen Avasarala on "The Expanse" (2015–2022). For her role as Sajida Talfah in the HBO miniseries "House of Saddam" (2008), she won the Primetime Emmy Award for Outstanding Supporting Actress in a Limited Series or Movie. In 2013, she released her autobiography titled "The Alley of Love and Yellow Jasmines".


title: Shohreh Aghdashloo

text: Aghdashloo was born Shohreh Vaziri-Tabar () in Tehran, the daughter of Effie ( alSadat) and Anushiravan Vaziri-Tabar. She has three brothers: Shahram, Shahriar and Shahrokh. Her stage name is from the family name of her first husband, painter Aydin Aghdashloo. After their marriage in 1972 when she was 19 and he was 31, she began attending theatre workshops, against the wishes of her family. She had always wanted to be an actress, and soon began playing leading roles in Iranian theatre and film. They did not have children and were divorced in 1979, when she left Iran for England at the start of the Iranian Revolution.


title: Shohreh Aghdashloo

text: Once Aghdashloo arrived in England, she earned a bachelor's degree in international relations at Brunel University because of her interest in politics after having to leave her home country. She was already familiar with England, as her parents had taken her to London as a child. She then continued to pursue her acting career, which brought her to Los Angeles. In 1987, Aghdashloo married actor/playwright Houshang Touzie. They have a daughter, Tara Touzie, born in 1989. She has since performed in a number of Touzie's plays, successfully taking them to national and international stages, primarily in the Iranian diaspora. Though born to a Muslim family, she has stated that she is non-practicing.


title: Shohreh Aghdashloo

text: Aghdashloo first began working as a theatre actress at the age of 19, when she starred in a theatrical adaptation of the novel "The Narrow Road to the Deep North" (1973). Aghdashloo made her American film debut in 1989 in a starring role in "Guests of Hotel Astoria". Her television debut came on September 25, 1990, in a guest role in the two-hour episode of the NBC television series "Matlock", titled "Nowhere to Turn: A Matlock Mystery Movie". In the years that followed Aghdashloo appeared on screen sporadically, including in the widely panned "Surviving Paradise" (2000), written and directed by Kamshad Kooshan.


title: Shohreh Aghdashloo

text: In 2001 Aghdashloo was cast opposite Ben Kingsley and Jennifer Connelly in director Vadim Perelman's "House of Sand and Fog" (2003) for which she was nominated for the Academy Award for Best Supporting Actress. Following this exposure Aghdashloo had a prominent recurring role in Season 4 of the Fox television series "24", playing Dina Araz, a terrorist undercover in Los Angeles as a well-to-do housewife and mother. In an interview with "Time" magazine, Aghdashloo stated that although she had previously resisted reinforcing the stereotype of Muslims as terrorists, the strength and complexity of the role convinced her to accept it. Iranian film scholar Hamid Naficy criticized Aghdashloo's acting in "the sensationalist film "The Stoning of Soraya M."" as "discredit[ing] her vow not to play in films that stereotype Middle Easterners, including Iranians." In the period that followed, Aghdashloo made guest appearances on several well-known television series, such as "Will & Grace", "ER" and "Grey's Anatomy". She also played supporting roles in films such as "" as Dr. Kavita Rao, "The Lake House", "The Nativity Story" as Elizabeth, and "The Sisterhood of the Traveling Pants 2".


title: Shohreh Aghdashloo

text: In 2008, Aghdashloo served as an official festival judge at the second annual Noor Iranian Film Festival in Los Angeles, while she also played the lead character of Zahra Khanum in the film "The Stoning of Soraya M.", marking her first leading role in a feature-length American film. In the same year, she also portrayed Sajida Talfah in the HBO original miniseries "House of Saddam" for which she received the Primetime Emmy Award for Outstanding Supporting Actress in a Limited Series or Movie. Speaking to a crowd of over 1,400 people at George Washington University's Lisner Auditorium on September 12, 2009, Aghdashloo, author Dr. Azar Nafisi, and Dr. Dwight Bashir, Associate Director for Policy at the United States Commission on International Religious Freedom, added their voices to those concerned about human rights in Iran and the persecution of Baháʼís in Iran. Aghdashloo's talk in particular was posted to YouTube. On October 9, 2010, the Public Affairs Alliance of Iranian Americans awarded Aghdashloo their Career Achievement Award during its first annual gala.


title: Shohreh Aghdashloo

text: Agdashloo continues to act in films, such as "The Odd Life of Timothy Green", "Septembers of Shiraz" and "Star Trek Beyond"; and on television, guest starring on series such as "House, M.D.", "The Simpsons", "Grimm", "" and "NCIS". She also voiced characters for the video games "Mass Effect 2", "Mass Effect 3", "Destiny" and "Destiny 2"; starred in the London revival of the play "The House of Bernarda Alba" at the Almeida Theatre as Bernarda Alba; and narrated the audiobook "And the Mountains Echoed", by Khaled Hosseini.


title: Shohreh Aghdashloo

text: Aghdashloo recently starred in Amazon Prime Video's acclaimed television series "The Expanse", as UN Deputy Undersecretary of Executive Administration Chrisjen Avasarala, a "smart and passionate member of a political family legacy who has risen high in the ranks of Earth's governing body without once standing for election".


title: Stalker (1979 film)

text: Stalker () is a 1979 Soviet science fiction art film directed by Andrei Tarkovsky with a screenplay written by Arkady and Boris Strugatsky, loosely based on their 1972 novel "Roadside Picnic". The film combines elements of science fiction with dramatic philosophical, psychological and theological themes.


title: Stalker (1979 film)

text: The film tells the story of an expedition led by a figure known as the "Stalker" (Alexander Kaidanovsky), who guides his two clients—a melancholic writer (Anatoly Solonitsyn) seeking inspiration, and a professor (Nikolai Grinko) seeking scientific discovery—through a hazardous wasteland to a mysterious restricted site known simply as the "Zone", where there supposedly exists a room which grants a person's innermost desires.


title: Stalker (1979 film)

text: "Stalker" was released by Goskino in May 1979. Upon release, the film garnered mixed reviews, but in subsequent years it has been recognized as a classic of world cinema, with the British Film Institute ranking it #29 on its list of the "100 Greatest Films of All Time". The film sold over 4 million tickets, mostly in the Soviet Union, against a budget of 1 million roubles.


title: Stalker (1979 film)

text: The meaning of the word "stalker" was derived from its use by the Strugatsky brothers in their novel "Roadside Picnic", upon which the movie is based. In "Roadside Picnic", "Stalker" was a common nickname for men engaged in the illegal enterprise of prospecting for and smuggling alien artifacts out of the "Zone". According to author Boris Strugatsky, "prospectors" and "trappers" were potential word choices before "stalker" was decided on, which was at least partially inspired by Rudyard Kipling's character "Stalky" in his "Stalky & Co." stories, of which both authors were fans. Their adaptation of the English word into Russian is pronounced slightly differently as "Stullker", and it came into common usage after being "coined" by the authors.


title: Stalker (1979 film)

text: In the film, a "stalker" is a professional guide to the Zone, someone having the ability and desire to cross the border into the dangerous and forbidden place with a specific goal.


title: Stalker (1979 film)

text: The protagonist (Alexander Kaidanovsky) works in an unnamed location as a "Stalker" leading people through the "Zone", an area in which the normal laws of physics do not apply and remnants of seemingly extraterrestrial activity lie undisturbed among its ruins. The Zone contains a place called the "Room", said to grant the wishes of anyone who steps inside. The area containing the Zone is shrouded in secrecy, sealed off by the government and surrounded by ominous hazards.


title: Stalker (1979 film)

text: At home with his wife and daughter, the Stalker's wife (Alisa Freindlich) begs him not to go into the Zone, but he dismissively rejects her pleas. In a rundown bar-café, the Stalker meets his next clients for a trip into the Zone, the Writer (Anatoly Solonitsyn) and the Professor (Nikolai Grinko).


title: Stalker (1979 film)

text: They evade the military blockade that guards the Zone by following a train inside the gate and ride into the heart of the Zone on a railway work car. The Stalker tells his clients they must do exactly as he says to survive the dangers which lie ahead and explains that the Zone must be respected and the straightest path is not always the shortest path. The Stalker tests for various "traps" by throwing metal nuts tied to strips of cloth ahead of them. He refers to a previous Stalker named "Porcupine", who had led his brother to his death in the Zone, visited the Room, come into possession of a large sum of money, and shortly afterwards committed suicide. The Writer is skeptical of any real danger, but the Professor generally follows the Stalker's advice.


title: Stalker (1979 film)

text: As they travel, the three men discuss their reasons for wanting to visit the Room. The Writer expresses his fear of losing his inspiration. The Professor seems less anxious, although he insists on carrying along a small backpack. The Professor admits he hopes to win a Nobel Prize for scientific analysis of the Zone. The Stalker insists he has no motive beyond the altruistic aim of aiding the desperate to their desires.


title: Stalker (1979 film)

text: After traveling through the tunnels, the three finally reach their destination: a decayed and decrepit industrial building. In a small antechamber, a phone rings. The surprised Professor decides to use the phone to telephone a colleague. As the trio approach the Room, the Professor reveals his true intentions in undertaking the journey. The Professor has brought a 20-kiloton bomb with him, and he intends to destroy the Room to prevent its use by evil men. The three men enter a physical and verbal standoff just outside the Room that leaves them exhausted.


title: Stalker (1979 film)

text: The Writer realizes that when Porcupine met his goal, despite his conscious motives, the room fulfilled Porcupine's secret desire for wealth rather than bring back his brother from death. This prompted the guilt-ridden Porcupine to commit suicide. The Writer tells them that no one in the whole world is able to know their true desires and as such it is impossible to use the Room for selfish reasons. The Professor gives up on his plan of destroying the Room. Instead, he disassembles his bomb and scatters its pieces. No one attempts to enter the Room.


title: Stalker (1979 film)

text: The Stalker, the Writer, and the Professor are met back at the bar-café by the Stalker's wife and daughter. After returning home, the Stalker tells his wife how humanity has lost its faith and belief needed for both traversing the Zone and living a good life. As the Stalker sleeps, his wife contemplates their relationship in a monologue delivered directly to the camera. In the last scene, Martyshka, the couple's deformed daughter, sits alone in the kitchen reading as a love poem by Fyodor Tyutchev is recited. She appears to use psychokinesis to push three drinking glasses across the table, one falling off. A train passes by where the Stalker's family lives, and the entire apartment shakes.


title: Stalker (1979 film)

text: In a review in "Slant Magazine", critic Nick Schager describes the film as a "dense, complex, often-contradictory, and endlessly pliable allegory about human consciousness, the necessity for faith in an increasingly secular, rational world, and the ugly, unpleasant dreams and desires that reside in the hearts of men", while conceding that the obliqueness of the imagery renders definitive interpretation "both pointless... [and] somewhat futile".


title: Stalker (1979 film)

text: Several critics have identified the nature of human desire as a central theme of the film. James Berardinelli interprets the film as suggesting that "one's innermost desire may not be what one thinks it is and that one may be better off not achieving it", while Schager describes the film as capturing "the essence of what man is made of... a yearning for something that's simultaneously beyond our reach and yet intrinsic to every one of us".


title: Stalker (1979 film)

text: Geoff Dyer argues the Stalker is "seeking asylum from the world", and says that "while the film may not be about the gulag, it is haunted by memories of the camps, from the overlap of vocabulary ("Zona", "the meat grinder") to the Stalker's Zek-style shaved head".


title: Stalker (1979 film)

text: The film's mysterious Zone has drawn comparisons with the Chernobyl Exclusion Zone that was established in 1986 (seven years after the release of the film) in the aftermath of the Chernobyl disaster, and some of the people employed to take care of the abandoned Chernobyl power plant referred to themselves as "stalkers". Though the film does not specify the origin of the Zone, near the end, in a shot of the Stalker with his family outside the Zone, what appears to be a power plant is visible in the background. The themes of nuclear radiation and environmental degradation would be revisited by Tarkovsky in his final film, "The Sacrifice".


title: Stalker (1979 film)

text: Midway in the film, the Stalker has an interior monologue in which he quotes the entire section 76 of Lao Tse's Tao Te Ching, the text of which characterizes softness and pliancy as qualities of a newborn, hence, new life; hardness and strength, on the contrary, are qualities nearing death. ("Man, when he enters life, is soft and weak. When he dies he is hard and strong.")


title: Stalker (1979 film)

text: After reading the novel "Roadside Picnic", by Arkady and Boris Strugatsky, Tarkovsky initially recommended it to a friend, the film director Mikhail Kalatozov, thinking Kalatozov might be interested in adapting it into a film. Kalatozov abandoned the project when he could not obtain the rights to the novel. Tarkovsky then became very interested in adapting the novel and expanding its concepts. He hoped it would allow him to make a film which conformed to the classical Aristotelian unity; a single action, on a single location, within 24 hours (single point in time).


title: Stalker (1979 film)

text: Tarkovsky viewed the idea of the Zone as a dramatic tool to draw out the personalities of the three protagonists, particularly the psychological damage from everything that happens to the idealistic views of the Stalker as he finds himself unable to make others happy: "This, too, is what Stalker is about: the hero goes through moments of despair when his faith is shaken; but every time he comes to a renewed sense of his vocation to serve people who have lost their hopes and illusions." The film departs considerably from the novel. According to an interview with Tarkovsky in 1979, the film has basically nothing in common with the novel except for the two words "Stalker" and "Zone".


title: Stalker (1979 film)

text: Yet, several similarities remain between the novel and the film. In both works, the Zone is guarded by a police or military guard, apparently authorized to use deadly force. The Stalker in both works tests the safety of his path by tossing nuts and bolts tied with scraps of cloth, verifying that gravity is working as usual. A character named Porcupine is a mentor to Stalker. In the novel, frequent visits to the Zone increase the likelihood of abnormalities in the visitor's offspring. In the book, the Stalker's daughter has light hair all over her body, while in the film she is crippled and has psychokinetic abilities. The 'meat grinder', a particularly perilous location, is mentioned in both film and the book. Neither in the novel nor in the film do the women enter the Zone — indeed, the film features a female character who is introduced as wishing to enter the Zone, but who is dismissed by the Stalker prior to departure. Finally, the target of the expedition in both works is a wish-granting device.


title: Stalker (1979 film)

text: In "Roadside Picnic", the site was specifically described as the site of alien visitation; the name of the novel derives from a metaphor proposed by a character who compares the visit to a roadside picnic. The closing monologue by the Stalker's wife at the end of the film has no equivalent in the novel. An early draft of the screenplay was published as a novel "Stalker" that differs substantially from the finished film.


title: Stalker (1979 film)

text: In an interview on the MK2 DVD, the production designer, Rashit Safiullin, recalled that Tarkovsky spent a year shooting all the outdoor scenes. However, when the crew returned to Moscow, they found that the film had been improperly developed and their footage was unusable. The film had been shot on new Kodak 5247 stock with which Soviet laboratories were not very familiar. Even before the film stock problem was discovered, relations between Tarkovsky and "Stalker"s first cinematographer, Georgy Rerberg, had deteriorated. After seeing the poorly developed material, Tarkovsky fired Rerberg. Safiullin contends that Tarkovsky was so despondent at having to discard all the outdoor work that he wanted to abandon further work on the film.


title: Stalker (1979 film)

text: After the loss of the film stock, the Soviet film boards wanted to shut the film down, but Tarkovsky came up with a solution: he asked to be allowed to make a two-part film, which meant additional deadlines and more funds. Tarkovsky ended up reshooting almost all of the film with a new cinematographer, Alexander Knyazhinsky. According to Safiullin, the finished version of "Stalker" is completely different from the one Tarkovsky originally shot.


title: Stalker (1979 film)

text: The documentary film "Rerberg and Tarkovsky: The Reverse Side of "Stalker"" by Igor Mayboroda offers a different interpretation of the relationship between Rerberg and Tarkovsky. Rerberg felt that Tarkovsky was not ready for this script. He told Tarkovsky to rewrite the script in order to achieve a good result. Tarkovsky ignored him and continued shooting. After several arguments, Tarkovsky sent Rerberg home. Ultimately, Tarkovsky shot "Stalker" three times, consuming over of film. People who have seen both the first version shot by Rerberg (as Director of Photography) and the final theatrical release say that they are almost identical. Tarkovsky sent home other crew members in addition to Rerberg, excluding them from the credits, as well.


title: Stalker (1979 film)

text: The central part of the film, in which the characters travel within the Zone, was shot in a few days at two deserted hydro power plants on the Jägala river near Tallinn, Estonia. The shot before they enter the Zone is an old Flora chemical factory in the center of Tallinn, next to the old Rotermann salt storage (now Museum of Estonian Architecture), and the former Tallinn Power Plant, now Tallinn Creative Hub, where a memorial plate of the film was set up in 2008. Some shots within the Zone were filmed in Maardu, next to the Iru Power Plant, while the shot with the gates to the Zone was filmed in Lasnamäe, next to Punane Street behind the Idakeskus. Other shots were filmed near the Tallinn–Narva highway bridge on the Pirita river.


title: Stalker (1979 film)

text: Several people involved in the film production, and possibly Tarkovsky himself, died from causes that some crew members attributed to the film's long shooting schedule in toxic locations. Sound designer Vladimir Sharun recalled:


title: Stalker (1979 film)

text: Like Tarkovsky's other films, "Stalker" relies on long takes with slow, subtle camera movement, rejecting the use of rapid montage. The film contains 142 shots in 163 minutes, with an average shot length of more than one minute and many shots lasting for more than four minutes. Almost all of the scenes not set in the Zone are in sepia or a similar high-contrast brown monochrome.


title: Stalker (1979 film)

text: The "Stalker" film score was composed by Eduard Artemyev, who had also composed the scores for Tarkovsky's previous films "Solaris" and "Mirror". For "Stalker", Artemyev composed and recorded two different versions of the score. The first score was done with an orchestra alone but was rejected by Tarkovsky. The second score that was used in the final film was created on a synthesizer along with traditional instruments that were manipulated using sound effects.


title: Stalker (1979 film)

text: In the final film score, the boundaries between music and sound were blurred, as natural sounds and music interact to the point where they are indistinguishable. In fact, many of the natural sounds were not production sounds but were created by Artemyev on his synthesizer.


title: Stalker (1979 film)

text: For Tarkovsky, music was more than just a parallel illustration of the visual image. He believed that music distorts and changes the emotional tone of a visual image while not changing the meaning. He also believed that in a film with complete theoretical consistency music will have no place and that instead music is replaced by sounds. According to Tarkovsky, he aimed at this consistency and moved into this direction in "Stalker" and "Nostalghia".


title: Stalker (1979 film)

text: In addition to the original monophonic soundtrack, the Russian Cinema Council (Ruscico) created an alternative 5.1 surround sound track for the 2001 DVD release. In addition to remixing the mono soundtrack, music and sound effects were removed and added in several scenes. Music was added to the scene where the three are traveling to the Zone on a motorized draisine. In the opening and the final scene Beethoven's "Ninth Symphony" was removed and in the opening scene in Stalker's house ambient sounds were added, changing the original soundtrack, in which this scene was completely silent except for the sound of a train.


title: Stalker (1979 film)

text: Initially, Tarkovsky had no clear understanding of the musical atmosphere of the final film and only an approximate idea where in the film the music was to be. Even after he had shot all the material he continued his search for the ideal film score, wanting a combination of Oriental and Western music. In a conversation with Artemyev he explained that he needed music that reflects the idea that although the East and the West can coexist, they are not able to understand each other. One of Tarkovsky's ideas was to perform Western music on Oriental instruments (or vice versa). Artemyev proposed to try this idea with the motet "Pulcherrima Rosa" by an anonymous 14th century Italian composer dedicated to the Virgin Mary.


title: Stalker (1979 film)

text: In its original form Tarkovsky did not perceive the motet as suitable for the film and asked Artemyev to give it an Oriental sound. Later, Tarkovsky proposed to invite musicians from Armenia and Azerbaijan and to let them improvise on the melody of the motet. A musician was invited from Azerbaijan who played the main melody on a tar based on mugham, accompanied by orchestral background music written by Artemyev. Tarkovsky, who, unusually for him, attended the full recording session, rejected the final result as not what he was looking for.


title: Stalker (1979 film)

text: Rethinking their approach, they finally found the solution in a theme that would create a state of inner calmness and inner satisfaction, or as Tarkovsky said "space frozen in a dynamic equilibrium". Artemyev knew about a musical piece from Indian classical music where a prolonged and unchanged background tone is performed on a tanpura. As this gave Artemyev the impression of frozen space, he used this inspiration and created a background tone on his synthesizer similar to the background tone performed on the tanpura. The tar then improvised on the background sound, together with a flute as a European, Western instrument. To mask the obvious combination of European and Oriental instruments he passed the foreground music through the effect channels of his SYNTHI 100 synthesizer. These effects included modulating the sound of the flute and lowering the speed of the tar, so that what Artemyev called "the life of one string" could be heard. Tarkovsky was amazed by the result, especially liking the sound of the tar, and used the theme without any alterations in the film.


title: Stalker (1979 film)

text: The title sequence is accompanied by Artemyev's main theme. The opening sequence of the film showing Stalker's room is mostly silent. Periodically one hears what could be a train. The sound becomes louder and clearer over time until the sound and the vibrations of objects in the room give a sense of a train's passing by without the train being visible. This aural impression is quickly subverted by the muffled sound of Beethoven's Symphony No. 9. The source of this music is unclear, thus setting the tone for the blurring of reality in the film. For this part of the film Tarkovsky was also considering music by Richard Wagner or the "Marseillaise".


title: Stalker (1979 film)

text: In an interview with Tonino Guerra in 1979, Tarkovsky said that he wanted: "...music that is more or less popular, that expresses the movement of the masses, the theme of humanity's social destiny...But this music must be barely heard beneath the noise, in a way that the spectator is not aware of it."


title: Stalker (1979 film)

text: The journey into the Zone on a motorized rail car features a disconnection between the visual image and the sound. The presence of the rail car is registered only through the clanking sound of the wheels on the tracks. Neither the rail car nor the scenery passing by is shown, since the camera is focused on the faces of the characters. This disconnection draws the audience into the inner world of the characters and transforms the physical journey into an inner journey. This effect on the audience is reinforced by Artemyev's synthesizer effects, which make the clanking wheels sound less and less natural as the journey progresses. When the three arrive in the Zone initially, it appears to be silent. Only after some time, and only slightly audibly can one hear the sound of a distant river, the sound of the blowing wind, or the occasional cry of an animal. These sounds grow richer and more audible while the Stalker makes his first venture into the Zone, as if the sound draws him towards the Zone. The sparseness of sounds in the Zone draws attention to specific sounds, which, as in other scenes, are largely disconnected from the visual image. Animals can be heard in the distance but are never shown. A breeze can be heard, but no visual reference is shown. This effect is reinforced by occasional synthesizer effects which meld with the natural sounds and blur the boundaries between artificial and alien sounds and the sounds of nature.


title: Stalker (1979 film)

text: During the journey in the Zone, the sound of water becomes more and more prominent, which, combined with the visual image, presents the Zone as a drenched world. In an interview Tarkovsky dismissed the idea that water has a symbolic meaning in his films, saying that there was so much rain in his films because it is always raining in Russia. In another interview, on the film "Nostalghia", however, he said "Water is a mysterious element, a single molecule of which is very photogenic. It can convey movement and a sense of change and flux." Emerging from the tunnel called the "meat grinder" by the Stalker, they arrive at the entrance of their destination, the room. Here, as in the rest of the film, sound is constantly changing and not necessarily connected to the visual image. The journey in the Zone ends with the three sitting in the room, silent, with no audible sound. When the sound resumes, it is again the sound of water but with a different timbre, softer and gentler, as if to give a sense of catharsis and hope. The transition back to the world outside the Zone is supported by sound. While the camera still shows a pool of water inside the Zone, the audience begins to hear the sound of a train and Ravel's "Boléro", reminiscent of the opening scene. The soundscape of the world outside the Zone is the same as before, characterized by train wheels, foghorns of a ship and train whistles. The film ends as it began, with the sound of a train passing by, accompanied by the muffled sound of Beethoven's Symphony No. 9, this time the "Ode to Joy" from the final moments of the symphony. As in the rest of the film the disconnect between the visual image and the sound leaves the audience unclear whether the sound is real or an illusion.


title: Stalker (1979 film)

text: Upon its release the film's reception was less than favorable. Officials at Goskino, a government group otherwise known as the State Committee for Cinematography, were critical of the film. On being told that "Stalker" should be faster and more dynamic, Tarkovsky replied:


title: Stalker (1979 film)

text: The Goskino representative then stated that he was trying to give the point of view of the audience. Tarkovsky supposedly retorted:


title: Stalker (1979 film)

text: More recently, reviews of the film have been highly positive. It earned a place in the British Film Institute's "100 Greatest Films of All Time" poll conducted for "Sight & Sound" in September 2012. The group's critics listed "Stalker" at joint #29. Directors ranked it at #30. In "The Guardian", Geoff Dyer described the film as "synonymous both with cinema's claims to high art and a test of the viewer's ability to appreciate it as such". Critic Derek Adams of the "Time Out Film Guide" has compared "Stalker" to Francis Ford Coppola's "Apocalypse Now", also released in 1979, and argued that "as a journey to the heart of darkness" "Stalker" looks "a good deal more persuasive than Coppola's." "Slant Magazine" reviewer Nick Schager has praised the film as an "endlessly pliable allegory about human consciousness".


title: Stalker (1979 film)

text: In 2018, the film was voted the 49th greatest non-English-language film of all time in a poll by BBC Culture involving 209 critics in 43 countries.


title: Stalker (1979 film)

text: On review aggregator Rotten Tomatoes, the film is rated at 100% based on 41 reviews with an average rating of 8.6/10. Its critical consensus states, ""Stalker" is a complex, oblique parable that draws unforgettable images and philosophical musings from its sci-fi/thriller setting."


title: Stalker (1979 film)

text: The film was awarded the "Prize of the Ecumenical Jury" at the Cannes Film Festival, and the "Audience Jury Award – Special Mention" at Fantasporto, Portugal.


title: Babylon Berlin

text: Babylon Berlin is a German neo-noir television series. Created, written, and directed by Tom Tykwer, Achim von Borries, and Hendrik Handloegten. It is loosely based on novels by German author Volker Kutscher.


title: Babylon Berlin

text: The series premiered on 13 October 2017 on Sky 1, a German-language entertainment channel broadcast by Sky Deutschland. The first release consisted of a continuous run of 16 episodes, with the first eight officially known as Season 1, and the second eight known as Season 2. The second run of 12 episodes, officially known as Season 3, premiered on 24 January 2020 on Sky 1. Season 4, consisting of 12 episodes, premiered on 8 October 2022.


title: Babylon Berlin

text: The series is set in Berlin during the latter years of the Weimar Republic, beginning in 1929. It follows Gereon Rath (Volker Bruch), a police inspector on assignment from Cologne who is on a secret mission to dismantle an extortion ring, and Charlotte Ritter (Liv Lisa Fries), police clerk by day, prostitute by night, who aspires to become a police inspector.


title: Babylon Berlin

text: The series was co-directed by Tom Tykwer, , and Achim von Borries, who also wrote the scripts. The 16 episodes of the first two seasons were adapted by Tykwer, von Borries and Handloegten from the novel "Der nasse Fisch" ("The Wet Fish") (2008) by Volker Kutscher and were filmed over eight months beginning in May 2016.


title: Babylon Berlin

text: German public broadcaster ARD and pay TV channel Sky co-produced the series, a first time collaboration in German television. As part of the arrangement, Sky broadcast the series first, and ARD started broadcasts by free-to-air television on 30 September 2018. Netflix purchased rights for the United States, Canada, and Australia, where the series became available in 2018 with English dubbing and subtitles.


title: Babylon Berlin

text: The series is described as the most expensive television drama series in Germany, with a budget of €40 million that increased to €55 million due to reshoots.


title: Babylon Berlin

text: The third season of "Babylon Berlin" was filmed over six months from late 2018 to May 2019. At the 32nd European Film Awards in December 2019, showrunners Achim von Borries, Henk Handloegten and Tom Tykwer stated that the third season was in post-production and that a fourth season was planned.


title: Babylon Berlin

text: The third season was developed loosely around the second novel in Volker Kutscher's trilogy "The Silent Death". The showrunners chose to diverge from the source material to better address the social and political unrest during the time period as they felt that the Weimar Republic is often overlooked by both media and historical sources. The third season is set in late 1929 around the Black Tuesday stock market crash and navigates the rise of the subversive Black Reichswehr and Communist political groups as well as the advent of talkies.


title: Babylon Berlin

text: In a January 2020 interview with "Berliner Zeitung", actress Liv Lisa Fries said that production would likely begin on the fourth season in late 2020 or early 2021. Planning and writing for the fourth season, based on the novel "Goldstein", began in October 2020. Filming began in early 2021 and was completed in September 2021, with the production having shot for 129 days at Studio Babelsberg and at locations around Berlin. "Season 4" is set in late 1930 and early 1931. It premiered on 8 October 2022.


title: Babylon Berlin

text: The creators of "Babylon Berlin" have stated in numerous interviews that they intend to end the series at the year 1933, with the assumption of power by Hitler and the National Socialist German Workers Party. While the novels are set one per year, and have currently reached 1937, the seasons of the series have not followed that model, with Seasons 1, 2 and 3 all set in 1929 and Season 4 set in 1930–1.


title: Babylon Berlin

text: We decided to go on until 1933... if you call the show Babylon Berlin, it is about this special city in a very special time. And this special time, the Babylon times, the free and liberated times, just ended in 1933.


title: Babylon Berlin

text: We always said it was over in 1933. If there is a final season, it would be the first months after the so-called seizure of power before the Reichstag fire. The National Socialists had turned the country upside down so fundamentally that the Babylonian in Berlin was over. After that we don't want to go on.


title: Babylon Berlin

text: In an interview with "The Wall Street Journal", one of the show's co-creators, Tom Tykwer, spoke about the era:


title: Babylon Berlin

text: At the time people did not realize how absolutely unstable this new construction of society which the Weimar Republic represented was. It interested us because the fragility of democracy has been put to the test quite profoundly in recent years... By 1929, new opportunities were arising. Women had more possibilities to take part in society, especially in the labour market as Berlin became crowded with new thinking, new art, theatre, music and journalistic writing.


title: Babylon Berlin

text: Nonetheless, Tykwer insisted that he and his co-directors were determined not to idealize the Weimar Republic: "People tend to forget that it was also a very rough era in German history. There was a lot of poverty, and people who had survived the war were suffering from a great deal of trauma."


title: Babylon Berlin

text: In the first season, communists, Soviets and especially Trotskyists play a prominent role (the Soviet ambassador to Germany from 1923 to 1930 was former Trotsky ally Nikolay Krestinsky). The show depicts what became known as Blutmai, violence between Communist demonstrators and members of the Berlin Police in early May 1929, and extra-legal paramilitary formations promoted by the German Army, known as the Black Reichswehr. In the first season, the Soviet ambassador in Berlin, who appears to be a loyal Stalinist, is involved in the massacre of Trotskyists in the printing shop, who were buried in a mass grave outside the city. According to Nathaniel Flakin, this event never happened. Nazi Party leader Adolf Hitler, on the other hand, is only mentioned in passing during the first two seasons of Babylon Berlin.


title: Babylon Berlin

text: Babelsberg Studio constructed a massive addition to its Metropolitan Backlot for the filming of the series and for future productions. This permanent standing set is billed as one of the largest in Europe. The set includes recreations of various Berlin neighbourhoods, from a range of economic classes. It also includes the large exterior of the night club "Moka Efti".


title: Babylon Berlin

text: In addition, the series was filmed throughout Berlin and at other locations in the surrounding state of Brandenburg. Numerous scenes were filmed on Alexanderplatz in front of the historic . The police headquarters, once located directly behind it, and other surrounding buildings, were destroyed in WWII, but were recreated with computer simulations. The Rotes Rathaus (Berlin City Hall) was used for most closeup scenes involving the exterior of the police headquarters, because their red brick appearance and architectural style are very similar. Interiors of the police headquarters lobby were filmed at the Rathaus Schöneberg, including scenes with its paternoster elevator, while the elegant Ratskeller restaurant in the same building was used as the nearby café "" in multiple scenes. Other interior scenes in the police headquarters were filmed in the historic .


title: Babylon Berlin

text: Interior scenes in the "Moka Efti" were filmed at the 'Delphi Cinema' in Berlin-Weissensee. Bar Tausend, in Berlin served as the show's Holländer Bar. A lengthy suspense sequence set during a performance of "The Threepenny Opera", was filmed at the historic Theater am Schiffbauerdamm, where the play actually ran at the time. The in Prenzlauer Berg was used for scenes of Anno and Helga's wedding. The headquarters of the Katholischer Studentenverein Askania-Burgundia Berlin, located in a villa in Dahlem, were used for the residence of Councillor Benda and his family. The atrium of the was used as Dr. Schmidt's psychiatric clinic. The interiors and exteriors of the historic former were used as numerous locations in the series, including as the exterior of the Soviet Embassy. Because the complex was empty at the time of filming, it was also used as the production headquarters, and to house the show's thousands of costumes. Other scenes were filmed on Museum Island, in the Hermannplatz U-Bahn station, at the , and the Church of the Redeemer on the Havel river in Potsdam.


title: Babylon Berlin

text: Portions of the series were also filmed in the state of North Rhine-Westphalia. Scenes set on the estate of the Nyssen family were filmed at Schloss Drachenburg, a castle in the Rhineland. The in Cologne was used as the Anhalter Güterbahnhof. The Landschaftspark Duisburg-Nord, a disused steel plant near Duisburg, was used as the factory adjacent to Bruno Wolter's apartment, in which numerous sequences take place.


title: Babylon Berlin

text: Scenes involving a steam train were filmed in the state of Bavaria at the Bavarian Railway Museum near Nördlingen.


title: Babylon Berlin

text: A number of new locations were introduced in Season 3. Berlin's Old City Hall served as the interior and exterior of the Berlin Stock Exchange. The Ullsteinhaus was used as the editorial offices of the "" newspaper, which were actually located there at the time. The Kammergericht in Berlin served as the Ministry of the Reichswehr. The Cafe Grosz doubled for the historic Romanisches Café, destroyed in WWII. The District Council Hall of the was used for the court room for Greta's trial. The Gästehaus am Lehnitzsee, a hotel housed in the historic , the pre-WWII mansion of Louis Adlon, manager of the famed Hotel Adlon, was used as the villa of Edgar and Esther Kasabian. The exterior of Gereon & Helga Rath's apartment was filmed at Woelckpromenade in Berlin-Weißensee.


title: Babylon Berlin

text: In 2018, the show formed an in-house band, The Moka Efti Orchestra, to perform the original music from the show. The group plays period-era music in a variety of styles ranging from ragtime to klezmer. Named after the nightclub featured in "Babylon Berlin", The Moka Efti Orchestra is a fourteen-member group and is fronted by the Lithuanian actress Severija Janušauskaitė as Svetlana Sorokina. In the first double episode of the first season, Janušauskaitė's character, crossdressing as the male singer Nikoros, performs the main theme of the series, "Zu Asche, zu Staub" in the Moka Efti cabaret. This song was later released and charted on the German singles chart.


title: Babylon Berlin

text: The group performed in concert in May 2018 and, due to popular demand, toured the country later that year. With the release of the third season of the show, the musical group released their debut album "Erstausgabe" (English: "First Edition").


title: Babylon Berlin

text: In addition to period music, "Dance Away", from the 1979 album "Manifesto" by Roxy Music, plays occasionally in the background (adapted to the style of the period) and also included is an adaptation of "These Foolish Things" and, in the Season Two finale, a Russian version of "Gloomy Sunday". Singer Bryan Ferry of Roxy Music appears toward the end of the first season as a cabaret singer performing "Bitter-Sweet", half in English, half in German, from the 1974 album "Country Life".


title: Babylon Berlin

text: A major action sequence in season two takes place during a performance of "The Threepenny Opera". The song "Die Morität von Mackie Messer" ("The Ballad of Mack the Knife") is featured in that scene, and also as a plot device. Two different characters hum the tune, giving detective Rath clues to the unfolding plot.


title: Babylon Berlin

text: "Babylon Berlin" premiered in Germany on 13 October 2017 (Sky 1) and in the United Kingdom and the Republic of Ireland on Sunday, 5 November 2017 (Sky Atlantic). The series debuted in Australia, Canada, and the United States on 30 January 2018 (Netflix). Broadcasting on the German TV channel Das Erste started Sunday 30 September 2018. The Swedish broadcast began on 19 June 2019 on SVT.


title: Babylon Berlin

text: After early indications of a late 2019 premiere, the third season premiered in Germany on Sky 1 in January 2020; and subsequently on German public television station ARD in October 2020. The international distribution rights for the third season were sold to more than one hundred countries and many different networks including Netflix, HBO Europe, and Viaplay in early 2019.


title: Babylon Berlin

text: In territories where the show is distributed by Netflix, the third season was released in its entirety on 1 March 2020.


title: Babylon Berlin

text: The first and second seasons, of eight episodes each, were written as one story (covering the first novel of the Kutscher book series) and filmed as one production. They premiered as one block, numbered 1–16 and have been broadcast throughout the world en bloc. In addition, all 16 episodes of both seasons were made available simultaneously on Netflix. In many territories the show was broadcast as a season comprising eight double-length episodes.


title: Babylon Berlin

text: The second block of 12 episodes are officially known as "Season 3" but were broadcast as "Season 2" in some territories where the previous episodes premiered as one block.


title: Babylon Berlin

text: The second-season episodes were written and directed by Henk Handloegten, Achim von Borries, and Tom Tykwer.


title: Babylon Berlin

text: On Rotten Tomatoes the first season holds approval rating of 100% based on 30 reviews, with the critics consensus reading: ""Babylon Berlin"s humor and humanity pair nicely with its hypnotic visuals, resulting in a show that dazzles within its oversaturated genre." As of April 2019, "Babylon Berlin" was the highest rated non-English language show on Sky TV.


title: Babylon Berlin

text: Carolin Ströbele of "Die Zeit" praised the pilot, saying that it "is highly dynamic and unites sex, crime and history in a pleasantly unobtrusive manner." Christian Buss, cultural critic from "Der Spiegel", praised the series for staying true to the tradition of "typically German angst cinema", in the vein of 1920s silent movies such as Fritz Lang's "Metropolis" or Robert Wiene's "The Cabinet of Dr. Caligari". "It could be that "Babylon Berlin" is the first big German TV production since "Das Boot" which enjoys really relevant success abroad. Let's not be shy to say it: we [Germans] are big again – as the world champions of angst."


title: Babylon Berlin

text: The series itself received several awards in 2018. These included a Bambi in the category "Beste Serie des Jahres (Best series of the year)", four awards at the Deutscher Fernsehpreis (best dramatical series; best cinematography for Frank Griebe, Bernd Fischer and Philip Haberlandt; best musical score for Johnny Klimek and Tom Tykwer; and best production design for Pierre-Yves Gayraud and Uli Hanisch), a special Bavarian TV Award and a Romy for TV event of the year. In the same year, everyone majorly involved with the production of the series won a Grimme-Preis, including Volker Bruch, Liv Lisa Fries, Peter Kurth, the three directors and several members of the technical team. Bruch also won a Goldene Kamera in the category Best German actor for his portrayal of Gereon Rath.


title: Babylon Berlin

text: The series' opening title sequence, created by German designer Saskia Marka and featuring a theme composed by Johnny Klimek and Tom Tykwer, was named the best title sequence of 2018 by industry website Art of the Title.


title: Babylon Berlin

text: In December 2019, the European Film Academy awarded the series with the inaugural Achievement in Fiction Series Award at the European Film Awards.


title: Marshall Plan

text: The Marshall Plan (officially the European Recovery Program, ERP) was an American initiative enacted in 1948 to provide foreign aid to Western Europe. The United States transferred over $13 billion (equivalent of about $ in ) in economic recovery programs to Western European economies after the end of World War II. Replacing an earlier proposal for a Morgenthau Plan, it operated for four years beginning on April 3, 1948. The goals of the United States were to rebuild war-torn regions, remove trade barriers, modernize industry, improve European prosperity and prevent the spread of communism. The Marshall Plan proposed the reduction of interstate barriers and the economic integration of the European Continent while also encouraging an increase in productivity as well as the adoption of modern business procedures.


title: Marshall Plan

text: The Marshall Plan aid was divided among the participant states roughly on a per capita basis. A larger amount was given to the major industrial powers, as the prevailing opinion was that their resuscitation was essential for the general European revival. Somewhat more aid per capita was also directed toward the Allied nations, with less for those that had been part of the Axis or remained neutral. The largest recipient of Marshall Plan money was the United Kingdom (receiving about 26% of the total). The next highest contributions went to France (18%) and West Germany (11%). Some eighteen European countries received Plan benefits. Although offered participation, the Soviet Union refused Plan benefits and also blocked benefits to Eastern Bloc countries, such as Romania and Poland. The United States provided similar aid programs in Asia but they were not part of the Marshall Plan.


title: Marshall Plan

text: Its role in rapid recovery has been debated. The Marshall Plan's accounting reflects that aid accounted for about 3% of the combined national income of the recipient countries between 1948 and 1951, which means an increase in GDP growth of less than half a percent.


title: Marshall Plan

text: Graham T. Allison states that "the Marshall Plan has become a favorite analogy for policy-makers. Yet few know much about it." Some new studies highlight not only the role of economic cooperation but approach the Marshall Plan as a case concerning strategic thinking to face some typical challenges in policy, as problem definition, risk analysis, decision support to policy formulation, and program implementation.


title: Marshall Plan

text: In 1947, two years after the end of the war, industrialist Lewis H. Brown wrote, at the request of General Lucius D. Clay, "A Report on Germany", which served as a detailed recommendation for the reconstruction of post-war Germany, and served as a basis for the Marshall Plan. The initiative was named after United States Secretary of State George C. Marshall. The plan had bipartisan support in Washington, where the Republicans controlled Congress and the Democrats controlled the White House with Harry S. Truman as president. The Plan was largely the creation of State Department officials, especially William L. Clayton and George F. Kennan, with help from the Brookings Institution, as requested by Senator Arthur Vandenberg, chairman of the United States Senate Committee on Foreign Relations. Marshall spoke of an urgent need to help the European recovery in his address at Harvard University in June 1947. The purpose of the Marshall Plan was to aid in the economic recovery of nations after World War II and secure US geopolitical influence over Western Europe. To combat the effects of the Marshall Plan, the USSR developed its own economic recovery program, known as the Molotov Plan.


title: Marshall Plan

text: The phrase "equivalent of the Marshall Plan" is often used to describe a proposed large-scale economic rescue program.


title: Marshall Plan

text: The reconstruction plan, developed at a meeting of the participating European states, was drafted on June 5, 1947. It offered the same aid to the Soviet Union and its allies, but they refused to accept it, under Soviet pressure (as was the case for Finland's rejection) as doing so would allow a degree of US control over the communist economies. The Soviet Union prevented its satellite states (i.e., East Germany, Poland, etc.) from accepting. Secretary Marshall became convinced Stalin had no interest in helping restore economic health in Western Europe.


title: Marshall Plan

text: President Harry Truman signed the Marshall Plan on April 3, 1948, granting $5 billion in aid to 16 European nations. During the four years, the plan was in effect, the United States donated $17 billion (equivalent to $ billion in ) in economic and technical assistance to help the recovery of the European countries that joined the Organisation for European Economic Co-operation. The $17 billion was in the context of a US GDP of $258 billion in 1948, and on top of $17 billion in American aid to Europe between the end of the war and the start of the Plan that is counted separately from the Marshall Plan. The Marshall Plan was replaced by the Mutual Security Plan at the end of 1951; that new plan gave away about $7.5 billion annually until 1961 when it was replaced by another program.


title: Marshall Plan

text: The ERP addressed each of the obstacles to postwar recovery. The plan looked to the future and did not focus on the destruction caused by the war. Much more important were efforts to modernize European industrial and business practices using high-efficiency American models, reducing artificial trade barriers, and instilling a sense of hope and self-reliance.


title: Marshall Plan

text: By 1952, as the funding ended, the economy of every participant state had surpassed pre-war levels; for all Marshall Plan recipients, output in 1951 was at least 35% higher than in 1938. Over the next two decades, Western Europe enjoyed unprecedented growth and prosperity, but economists are not sure what proportion was due directly to the ERP, what proportion indirectly, and how much would have happened without it.


title: Marshall Plan

text: A common American interpretation of the program's role in European recovery was expressed by Paul Hoffman, head of the Economic Cooperation Administration, in 1949 when he told Congress Marshall aid had provided the "critical margin" on which other investment needed for European recovery depended. The Marshall Plan was one of the first elements of European integration, as it erased trade barriers and set up institutions to coordinate the economy on a continental level—that is, it stimulated the total political reconstruction of Western Europe.


title: Marshall Plan

text: By the end of World War II, much of Europe was devastated. Sustained aerial bombardment during the war had badly damaged most major cities, and industrial facilities were especially hard-hit. Millions of refugees were in temporary camps. The region's trade flows had been thoroughly disrupted; millions were in refugee camps living on aid from the United States, which was provided by the United Nations Relief and Rehabilitation Administration and other agencies. Food shortages were severe, especially in the harsh winter of 1946–47. From July 1945 through June 1946, the United States shipped 16.5 million tons of food, primarily wheat, to Europe and Japan. It amounted to one-sixth of the American food supply and provided 35 trillion calories, enough to provide 400 calories a day for one year to 300 million people.


title: Marshall Plan

text: Especially damaged was transportation infrastructure, as railways, bridges, and docks had been specifically targeted by airstrikes, while much merchant shipping had been sunk. Although most small towns and villages had not suffered as much damage, the destruction of transportation left them economically isolated. None of these problems could be easily remedied, as most nations engaged in the war had exhausted their treasuries in the process.


title: Marshall Plan

text: The only major powers whose infrastructure had not been significantly harmed in World War II were the United States and Canada. They were much more prosperous than before the war but exports were a small factor in their economy. Much of the Marshall Plan aid would be used by the Europeans to buy manufactured goods and raw materials from the United States and Canada.


title: Marshall Plan

text: Most of Europe's economies were recovering slowly, as unemployment and food shortages led to strikes and unrest in several nations. Agricultural production was 83% of 1938 levels, industrial production was 88%, and exports 59%. Exceptions were the United Kingdom, the Netherlands and France, where by the end of 1947 production had already been restored to pre-war levels before the Marshall Plan. Italy and Belgium would follow by the end of 1948.


title: Marshall Plan

text: In Germany in 1945–46 housing and food conditions were bad, as the disruption of transport, markets, and finances slowed a return to normality. In the West, the bombing had destroyed 5,000,000 houses and apartments, and 12,000,000 refugees from the east had crowded in.


title: Marshall Plan

text: Food production was two-thirds of the pre-war level in 1946–48, while normal grain and meat shipments no longer arrived from the East. The drop in food production can be attributed to a drought that killed a major portion of the wheat crop while a severe winter destroyed the majority of the wheat crop the following year. This caused most Europeans to rely on a 1,500 calorie per day diet. Furthermore, the large shipments of food stolen from occupied nations during the war no longer reached Germany. Industrial production fell more than half and reached pre-war levels at the end of 1949.


title: Marshall Plan

text: While Germany struggled to recover from the destruction of the War, the recovery effort began in June 1948, moving on from emergency relief. The currency reform in 1948 was headed by the military government and helped Germany to restore stability by encouraging production. The reform revalued old currency and deposits and introduced new currency. Taxes were also reduced and Germany prepared to remove economic barriers.


title: Marshall Plan

text: During the first three years of occupation of Germany, the UK and US vigorously pursued a military disarmament program in Germany, partly by removal of equipment but mainly through an import embargo on raw materials, part of the Morgenthau Plan approved by President Franklin D. Roosevelt.


title: Marshall Plan

text: Nicholas Balabkins concludes that "as long as German industrial capacity was kept idle the economic recovery of Europe was delayed." By July 1947 Washington realized that economic recovery in Europe could not go forward without the reconstruction of the German industrial base, deciding that an "orderly, prosperous Europe requires the economic contributions of a stable and productive Germany." In addition, the strength of Moscow-controlled communist parties in France and Italy worried Washington.


title: Marshall Plan

text: In the view of the State Department under President Harry S Truman, the United States needed to adopt a definite position on the world scene or fear losing credibility. The emerging doctrine of containment (as opposed to rollback) argued that the United States needed to substantially aid non-communist countries to stop the spread of Soviet influence. There was also some hope that the Eastern Bloc nations would join the plan, and thus be pulled out of the emerging Soviet bloc, but that did not happen.


title: Marshall Plan

text: In January 1947, Truman appointed retired General George Marshall as Secretary of State. In July 1947 Marshall scrapped Joint Chiefs of Staff Directive 1067, which was based on the Morgenthau Plan which had decreed "take no steps looking toward the economic rehabilitation of Germany [or] designed to maintain or strengthen the German economy." The new plan JCS 1779 stated that "an orderly and prosperous Europe requires the economic contributions of a stable and productive Germany." The restrictions placed on German heavy industry production were partly ameliorated; permitted steel production levels were raised from 25% of pre-war capacity to a new limit placed at 50% of pre-war capacity.


title: Marshall Plan

text: With a threatening Greece, and Britain financially unable to continue its aid, the President announced his Truman Doctrine on March 12, 1947, "to support free peoples who are resisting attempted subjugation by armed minorities or by outside pressures", with an aid request for consideration and decision, concerning Greece and Turkey. Herbert Hoover noted that "The whole economy of Europe is interlinked with German economy through the exchange of raw materials and manufactured goods. The productivity of Europe cannot be restored without the restoration of Germany as a contributor to that productivity." Hoover's report led to a realization in Washington that a new policy was needed; "almost any action would be an improvement on current policy." In Washington, the Joint Chiefs declared that the "complete revival of German industry, particularly coal mining" was now of "primary importance" to American security.