title: Circumscribed circle

text: In coastal navigation, a triangle's circumcircle is sometimes used as a way of obtaining a position line using a sextant when no compass is available. The horizontal angle between two landmarks defines the circumcircle upon which the observer lies.


title: Circumscribed circle

text: In the Euclidean plane, it is possible to give explicitly an equation of the circumcircle in terms of the Cartesian coordinates of the vertices of the inscribed triangle. Suppose that


title: Circumscribed circle

text: are the coordinates of points . The circumcircle is then the locus of points formula_2 in the Cartesian plane satisfying the equations


title: Circumscribed circle

text: guaranteeing that the points are all the same distance from the common center of the circle. Using the polarization identity, these equations reduce to the condition that the matrix


title: Circumscribed circle

text: has a nonzero kernel. Thus the circumcircle may alternatively be described as the locus of zeros of the determinant of this matrix:


title: Circumscribed circle

text: we then have formula_7 where formula_8 and – assuming the three points were not in a line (otherwise the circumcircle is that line that can also be seen as a generalized circle with at infinity) – formula_9


title: Circumscribed circle

text: This formula only works in three dimensions as the cross product is not defined in other dimensions, but it can be generalized to the other dimensions by replacing the cross products with following identities:


title: Circumscribed circle

text: Without loss of generality this can be expressed in a simplified form after translation of the vertex to the origin of the Cartesian coordinate systems, i.e., when formula_15 In this case, the coordinates of the vertices formula_16 and formula_17 represent the vectors from vertex to these vertices. Observe that this trivial translation is possible for all triangles and the circumcenter formula_18 of the triangle follow as


title: Circumscribed circle

text: where are the lengths of the sides of the triangle and formula_22 is the semiperimeter. The expression formula_23 above is the area of the triangle, by Heron's formula. Trigonometric expressions for the diameter of the circumcircle include


title: Circumscribed circle

text: In any given triangle, the circumcenter is always collinear with the centroid and orthocenter. The line that passes through all of them is known as the Euler line.


title: Circumscribed circle

text: The useful minimum bounding circle of three points is defined either by the circumcircle (where three points are on the minimum bounding circle) or by the two points of the longest side of the triangle (where the two points define a diameter of the circle). It is common to confuse the minimum bounding circle with the circumcircle.


title: Circumscribed circle

text: The circumcircle of three collinear points is the line on which the three points lie, often referred to as a "circle of infinite radius". Nearly collinear points often lead to numerical instability in computation of the circumcircle.


title: Circumscribed circle

text: Circumcircles of triangles have an intimate relationship with the Delaunay triangulation of a set of points.


title: Circumscribed circle

text: where is the incircle radius and is the circumcircle radius; hence the circumradius is at least twice the inradius (Euler's triangle inequality), with equality only in the equilateral case.


title: Circumscribed circle

text: If median , altitude , and internal bisector all emanate from the same vertex of a triangle with circumradius , then


title: Circumscribed circle

text: Carnot's theorem states that the sum of the distances from the circumcenter to the three sides equals the sum of the circumradius and the inradius. Here a segment's length is considered to be negative if and only if the segment lies entirely outside the triangle.


title: Circumscribed circle

text: If a triangle has two particular circles as its circumcircle and incircle, there exist an infinite number of other triangles with the same circumcircle and incircle, with any point on the circumcircle as a vertex. (This is the case of Poncelet's porism). A necessary and sufficient condition for such triangles to exist is the above equality formula_31


title: Circumscribed circle

text: Quadrilaterals that can be circumscribed have particular properties including the fact that opposite angles are supplementary angles (adding up to 180° or π radians).


title: Circumscribed circle

text: For a cyclic polygon with an odd number of sides, all angles are equal if and only if the polygon is regular. A cyclic polygon with an even number of sides has all angles equal if and only if the alternate sides are equal (that is, sides are equal, and sides are equal).


title: Circumscribed circle

text: A cyclic pentagon with rational sides and area is known as a Robbins pentagon; in all known cases, its diagonals also have rational lengths.


title: Circumscribed circle

text: In any cyclic -gon with even , the sum of one set of alternate angles (the first, third, fifth, etc.) equals the sum of the other set of alternate angles. This can be proven by induction from the case, in each case replacing a side with three more sides and noting that these three new sides together with the old side form a quadrilateral which itself has this property; the alternate angles of the latter quadrilateral represent the additions to the alternate angle sums of the previous -gon.


title: Circumscribed circle

text: Let one -gon be inscribed in a circle, and let another -gon be tangential to that circle at the vertices of the first -gon. Then from any point on the circle, the product of the perpendicular distances from to the sides of the first -gon equals the product of the perpendicular distances from to the sides of the second -gon.


title: Circumscribed circle

text: Let a cyclic -gon have vertices on the unit circle. Then for any point on the minor arc , the distances from to the vertices satisfy


title: Circumscribed circle

text: For a regular -gon, if formula_33 are the distances from any point on the circumcircle to the vertices , then


title: Circumscribed circle

text: Any regular polygon is cyclic. Consider a unit circle, then circumscribe a regular triangle such that each side touches the circle. Circumscribe a circle, then circumscribe a square. Again circumscribe a circle, then circumscribe a regular pentagon, and so on. The radii of the circumscribed circles converge to the so-called "polygon circumscribing constant"


title: Arise (Sepultura album)

text: Arise is the fourth studio album by Brazilian heavy metal band Sepultura, released in 1991 by Roadrunner Records. Upon its release, the album received top reviews from heavy metal magazines such as "Rock Hard", "Kerrang!" and "Metal Forces". "Arise" is considered Sepultura's finest hour among longtime fans. While the music on "Arise" was mostly in the same death/thrash style as their previous album, "Beneath the Remains", it was clear that the Sepultura sound was acquiring an experimental edge.


title: Arise (Sepultura album)

text: The album presented their first incursions with industrial music, hardcore punk and Latin percussion. The tour (1991–1992) that supported the album was the group's longest at that time, totalling 220 shows in 39 countries. During this trek, the album went gold in Indonesia—the band's first music industry certification. By the tour's end, "Arise" had achieved platinum sales worldwide.


title: Arise (Sepultura album)

text: In August 1990, the band travelled to Florida to work on the album. Scott Burns reprised his role as producer and audio engineer, and now with a major advantage: Sepultura were at his home studio, Morrisound, a studio properly equipped to record their music style. Their label Roadrunner granted a $40,000 budget, which helped explain the album's improved production values. That allowed drummer Igor Cavalera and Burns, for example, to spend a whole week just testing the drum kit's tunings and experimenting with microphone practice. A rerecording of "Troops of Doom" took place in the first days but ended up released in the reissue of "Schizophrenia".


title: Arise (Sepultura album)

text: Although lead guitarist Andreas Kisser stated that "Arise" "took a lot of the same direction" as their previous album, "Beneath the Remains", it was clear that their music had somehow changed. Sepultura's usual breakneck pace became toned down a bit; drummer Igor Cavalera started using groove-laden rhythms. According to metal specialist Don Kaye, the album "represented the band taking their initial death/thrash sound to its logical conclusion."


title: Arise (Sepultura album)

text: "Arise" also found the band opening up to non-metal influences. Bands such as Einstürzende Neubauten, Nine Inch Nails, The Young Gods, and Ministry were already part of Sepultura's listening habits, and slight touches of industrial music can be traced through the use of samples and sound effects. A trademark of a later phase—Latin percussion and "tribal" drumming—made its first appearance on the song "Altered State". The band's old love for hardcore punk is evident on "Subtraction" and "Desperate Cry".


title: Arise (Sepultura album)

text: Just one day after finishing the recording of "Arise", the band embarked on a small headlining tour with extreme metallers Obituary and Sadus. That was the start of the longest promotional tour of Sepultura's career, a worldwide affair that would span two full years. In January 1991, they were invited to play for at the Brazilian music festival Rock in Rio 2 where their performance was watched by a 70,000-strong crowd.


title: Arise (Sepultura album)

text: Before heading out of Brazil on a mid-1991 European tour, Sepultura performed one more concert in São Paulo, the country's largest city. It took place at Praça Charles Miller (in front of Estádio do Pacaembu), on May 11. Local military police expected 10,000 to attend. 30,000 showed up instead, making crowd management nearly impossible. Six people were hurt, 18 were arrested and one was murdered with an axe. A week before, a young man was stabbed to death at a Ramones concert in São Paulo, during a brawl between headbangers and skinheads. These events were followed by a huge mainstream media backlash throughout the country against rock music.


title: Arise (Sepultura album)

text: Sepultura's three-month tour with thrash metal groups Sacred Reich and Heathen was a critical success. For the first time they appeared on the cover of best-selling British heavy metal magazine "Kerrang!" and major pop weeklies such as "Melody Maker" and "NME" published long feature articles on the group. While in Spain Sepultura recorded their "Under Siege" video, which included their Barcelona concert and interview footage with all four members of the band. After Europe, they embarked on the North American tour New Titans on the Block with Napalm Death, Sick of It All and Sacred Reich. Max Cavalera has recalled that, before signing on to the New Titans on the Block tour, Sepultura was supposed to be the opening act for the Clash of the Titans tour featuring Megadeth, Slayer and Anthrax, but they "got kicked out" and were replaced by Alice in Chains. Sepultura wrapped up the year doing a brief German tour with Motörhead and Morbid Angel in December.


title: Arise (Sepultura album)

text: Sepultura then managed to secure a slot in two of the most sought after rock tours of 1992. One was done with ex-Black Sabbath singer Ozzy Osbourne, who was promoting his multi-platinum solo album "No More Tears" while the second tour was with industrial metal stalwarts Ministry and influential alternative metal/noise rock unit Helmet. Both of these American acts had just released the most successful records of their careers – "" and "Meantime".


title: Arise (Sepultura album)

text: A remastered version of "Arise" was released by Roadrunner in 1997, with added notes by music critic Don Kaye and four bonus tracks, previously released on the compilation The Roots Of Sepultura: a cover version of Motörhead's "Orgasmatron", a rough mix of "Desperate Cry" and two previously unreleased songs. A previously unavailable photo shoot from the "Arise" period was also included in the expanded CD booklet.


title: Arise (Sepultura album)

text: "Arise" garnered praise from a wide variety of sources. By the time of its release, major Brazilian newspapers were already aware of the band's existence, and advance copies sent to them were generally met with positive reviews. Artur G. Couto Duarte, writing for "O Estado de Minas", described Sepultura's soundscapes as "stories describing barren worlds where disease, hunger, torture and death reign supreme". "Folha de S.Paulo"'s Sérgio Sá Leitão pointed out Sepultura's increasing compositional skills, drawing attention to how the band's occasional use of restraint benefited their songs as a whole.


title: Arise (Sepultura album)

text: The international pop press also took notice of Brazil's premiere metal group. Top British weeklies such as the "Melody Maker" and "NME" wrote lengthy articles on the band, praising them. A "Melody Maker" journalist wrote: "Sepultura is [...] a Brazilian metal band which seems to be in the verge of getting big – maybe even bigger than Slayer, their only true rival." Genre-specific magazines also reacted positively to the group. Germany's "Thrash" elected Sepultura the best band in the world, defeating major contenders Metallica and Slayer. Sepultura were also prominently featured on the biggest metal publications of the time, such as "Kerrang!", "Rock Hard" and "Metal Forces". "Select" gave the album a five out of five rating, referring to it as a "a classic example of rock music as pure cathartic release" and that "few metal LPs released this year, if any, will triumph over "Arise"."


title: Arise (Sepultura album)

text: "Arise" was the first Sepultura record to enter the "Billboard" charts, at number 145. It was also the first to gain a music certification—"Arise" went gold in 1992 for selling 25,000 copies in Indonesia. By 1993, the album had sold 1 million units around the globe. In 2001, it won a second certification: silver in the United Kingdom, for selling in excess of 60,000 copies.


title: Arise (Sepultura album)

text: Throughout the years, "Arise" has been continuously praised by the music press, not only as a landmark release of Sepultura's career, but of extreme metal in general. In November 1996, "Q" magazine stated that ""Arise" remains their thrash high water mark, sounding like an angry man throwing tools at a urinal while reading the Book of Revelations ["sic"]." AllMusic contributor Eduardo Rivadavia considered "Arise" as "a classic of the death metal genre." The album also appeared in the book "1001 Albums You Must Hear Before You Die" (2006), edited by writer Robert Dimery. In January 2016, 25 years since the album's release, "Arise" was inducted into the Decibel Magazine Hall of Fame, becoming the third Sepultura album to receive such award, the previous two being "Roots" and "Beneath the Remains". This induction would make Sepultura the first band to have at least three of their albums featured in the Decibel Hall of Fame. Decibel Magazine would further go on to proclaim "Arise" as the greatest album of 1991. Adam McCann of Metal Digest noted, "The band had created a monster with their previous album "Beneath the Remains", but "Arise" was the album which broke them through to the big mainstream MTV era with tracks like 'Dead Embryonic Cells', 'Desperate Cry' and the title track which would lay the foundation for Sepultura's mid 90's success with the band poised to conquer the world. Many people regard "Arise" as the bands last truly great album."


title: Mathematical economics

text: Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.


title: Mathematical economics

text: Mathematics allows economists to form meaningful, testable propositions about wide-ranging and complex subjects which could less easily be expressed informally. Further, the language of mathematics allows economists to make specific, positive claims about controversial or contentious subjects that would be impossible without mathematics. Much of economic theory is currently presented in terms of mathematical economic models, a set of stylized and simplified mathematical relationships asserted to clarify assumptions and implications.


title: Mathematical economics

text: Formal economic modeling began in the 19th century with the use of differential calculus to represent and explain economic behavior, such as utility maximization, an early economic application of mathematical optimization. Economics became more mathematical as a discipline throughout the first half of the 20th century, but introduction of new and generalized techniques in the period around the Second World War, as in game theory, would greatly broaden the use of mathematical formulations in economics.


title: Mathematical economics

text: This rapid systematizing of economics alarmed critics of the discipline as well as some noted economists. John Maynard Keynes, Robert Heilbroner, Friedrich Hayek and others have criticized the broad use of mathematical models for human behavior, arguing that some human choices are irreducible to mathematics.


title: Mathematical economics

text: The use of mathematics in the service of social and economic analysis dates back to the 17th century. Then, mainly in German universities, a style of instruction emerged which dealt specifically with detailed presentation of data as it related to public administration. Gottfried Achenwall lectured in this fashion, coining the term statistics. At the same time, a small group of professors in England established a method of "reasoning by figures upon things relating to government" and referred to this practice as "Political Arithmetick". Sir William Petty wrote at length on issues that would later concern economists, such as taxation, Velocity of money and national income, but while his analysis was numerical, he rejected abstract mathematical methodology. Petty's use of detailed numerical data (along with John Graunt) would influence statisticians and economists for some time, even though Petty's works were largely ignored by English scholars.


title: Mathematical economics

text: The mathematization of economics began in earnest in the 19th century. Most of the economic analysis of the time was what would later be called classical economics. Subjects were discussed and dispensed with through algebraic means, but calculus was not used. More importantly, until Johann Heinrich von Thünen's "The Isolated State" in 1826, economists did not develop explicit and abstract models for behavior in order to apply the tools of mathematics. Thünen's model of farmland use represents the first example of marginal analysis. Thünen's work was largely theoretical, but he also mined empirical data in order to attempt to support his generalizations. In comparison to his contemporaries, Thünen built economic models and tools, rather than applying previous tools to new problems.


title: Mathematical economics

text: Meanwhile, a new cohort of scholars trained in the mathematical methods of the physical sciences gravitated to economics, advocating and applying those methods to their subject, and described today as moving from geometry to mechanics.


title: Mathematical economics

text: These included W.S. Jevons who presented paper on a "general mathematical theory of political economy" in 1862, providing an outline for use of the theory of marginal utility in political economy. In 1871, he published "The Principles of Political Economy", declaring that the subject as science "must be mathematical simply because it deals with quantities". Jevons expected that only collection of statistics for price and quantities would permit the subject as presented to become an exact science. Others preceded and followed in expanding mathematical representations of economic problems.


title: Mathematical economics

text: Augustin Cournot and Léon Walras built the tools of the discipline axiomatically around utility, arguing that individuals sought to maximize their utility across choices in a way that could be described mathematically. At the time, it was thought that utility was quantifiable, in units known as utils. Cournot, Walras and Francis Ysidro Edgeworth are considered the precursors to modern mathematical economics.


title: Mathematical economics

text: Cournot, a professor of mathematics, developed a mathematical treatment in 1838 for duopoly—a market condition defined by competition between two sellers. This treatment of competition, first published in "Researches into the Mathematical Principles of Wealth", is referred to as Cournot duopoly. It is assumed that both sellers had equal access to the market and could produce their goods without cost. Further, it assumed that both goods were homogeneous. Each seller would vary her output based on the output of the other and the market price would be determined by the total quantity supplied. The profit for each firm would be determined by multiplying their output and the per unit Market price. Differentiating the profit function with respect to quantity supplied for each firm left a system of linear equations, the simultaneous solution of which gave the equilibrium quantity, price and profits. Cournot's contributions to the mathematization of economics would be neglected for decades, but eventually influenced many of the marginalists. Cournot's models of duopoly and Oligopoly also represent one of the first formulations of non-cooperative games. Today the solution can be given as a Nash equilibrium but Cournot's work preceded modern game theory by over 100 years.


title: Mathematical economics

text: While Cournot provided a solution for what would later be called partial equilibrium, Léon Walras attempted to formalize discussion of the economy as a whole through a theory of general competitive equilibrium. The behavior of every economic actor would be considered on both the production and consumption side. Walras originally presented four separate models of exchange, each recursively included in the next. The solution of the resulting system of equations (both linear and non-linear) is the general equilibrium. At the time, no general solution could be expressed for a system of arbitrarily many equations, but Walras's attempts produced two famous results in economics. The first is Walras' law and the second is the principle of tâtonnement. Walras' method was considered highly mathematical for the time and Edgeworth commented at length about this fact in his review of "Éléments d'économie politique pure" (Elements of Pure Economics).


title: Mathematical economics

text: Walras' law was introduced as a theoretical answer to the problem of determining the solutions in general equilibrium. His notation is different from modern notation but can be constructed using more modern summation notation. Walras assumed that in equilibrium, all money would be spent on all goods: every good would be sold at the market price for that good and every buyer would expend their last dollar on a basket of goods. Starting from this assumption, Walras could then show that if there were n markets and n-1 markets cleared (reached equilibrium conditions) that the nth market would clear as well. This is easiest to visualize with two markets (considered in most texts as a market for goods and a market for money). If one of two markets has reached an equilibrium state, no additional goods (or conversely, money) can enter or exit the second market, so it must be in a state of equilibrium as well. Walras used this statement to move toward a proof of existence of solutions to general equilibrium but it is commonly used today to illustrate market clearing in money markets at the undergraduate level.


title: Mathematical economics

text: Tâtonnement (roughly, French for "groping toward") was meant to serve as the practical expression of Walrasian general equilibrium. Walras abstracted the marketplace as an auction of goods where the auctioneer would call out prices and market participants would wait until they could each satisfy their personal reservation prices for the quantity desired (remembering here that this is an auction on "all" goods, so everyone has a reservation price for their desired basket of goods).


title: Mathematical economics

text: Only when all buyers are satisfied with the given market price would transactions occur. The market would "clear" at that price—no surplus or shortage would exist. The word "tâtonnement" is used to describe the directions the market takes in "groping toward" equilibrium, settling high or low prices on different goods until a price is agreed upon for all goods. While the process appears dynamic, Walras only presented a static model, as no transactions would occur until all markets were in equilibrium. In practice, very few markets operate in this manner.


title: Mathematical economics

text: Edgeworth introduced mathematical elements to Economics explicitly in "", published in 1881. He adopted Jeremy Bentham's felicific calculus to economic behavior, allowing the outcome of each decision to be converted into a change in utility. Using this assumption, Edgeworth built a model of exchange on three assumptions: individuals are self-interested, individuals act to maximize utility, and individuals are "free to recontract with another independently of...any third party".


title: Mathematical economics

text: Given two individuals, the set of solutions where both individuals can maximize utility is described by the "contract curve" on what is now known as an Edgeworth Box. Technically, the construction of the two-person solution to Edgeworth's problem was not developed graphically until 1924 by Arthur Lyon Bowley. The contract curve of the Edgeworth box (or more generally on any set of solutions to Edgeworth's problem for more actors) is referred to as the core of an economy.


title: Mathematical economics

text: Edgeworth devoted considerable effort to insisting that mathematical proofs were appropriate for all schools of thought in economics. While at the helm of "The Economic Journal", he published several articles criticizing the mathematical rigor of rival researchers, including Edwin Robert Anderson Seligman, a noted skeptic of mathematical economics. The articles focused on a back and forth over tax incidence and responses by producers. Edgeworth noticed that a monopoly producing a good that had jointness of supply but not jointness of demand (such as first class and economy on an airplane, if the plane flies, both sets of seats fly with it) might actually lower the price seen by the consumer for one of the two commodities if a tax were applied. Common sense and more traditional, numerical analysis seemed to indicate that this was preposterous. Seligman insisted that the results Edgeworth achieved were a quirk of his mathematical formulation. He suggested that the assumption of a continuous demand function and an infinitesimal change in the tax resulted in the paradoxical predictions. Harold Hotelling later showed that Edgeworth was correct and that the same result (a "diminution of price as a result of the tax") could occur with a discontinuous demand function and large changes in the tax rate.


title: Mathematical economics

text: From the later-1930s, an array of new mathematical tools from the differential calculus and differential equations, convex sets, and graph theory were deployed to advance economic theory in a way similar to new mathematical methods earlier applied to physics. The process was later described as moving from mechanics to axiomatics.


title: Mathematical economics

text: Vilfredo Pareto analyzed microeconomics by treating decisions by economic actors as attempts to change a given allotment of goods to another, more preferred allotment. Sets of allocations could then be treated as Pareto efficient (Pareto optimal is an equivalent term) when no exchanges could occur between actors that could make at least one individual better off without making any other individual worse off. Pareto's proof is commonly conflated with Walrassian equilibrium or informally ascribed to Adam Smith's Invisible hand hypothesis. Rather, Pareto's statement was the first formal assertion of what would be known as the first fundamental theorem of welfare economics. These models lacked the inequalities of the next generation of mathematical economics.


title: Mathematical economics

text: In the landmark treatise "Foundations of Economic Analysis" (1947), Paul Samuelson identified a common paradigm and mathematical structure across multiple fields in the subject, building on previous work by Alfred Marshall. "Foundations" took mathematical concepts from physics and applied them to economic problems. This broad view (for example, comparing Le Chatelier's principle to tâtonnement) drives the fundamental premise of mathematical economics: systems of economic actors may be modeled and their behavior described much like any other system. This extension followed on the work of the marginalists in the previous century and extended it significantly. Samuelson approached the problems of applying individual utility maximization over aggregate groups with comparative statics, which compares two different equilibrium states after an exogenous change in a variable. This and other methods in the book provided the foundation for mathematical economics in the 20th century.


title: Mathematical economics

text: Restricted models of general equilibrium were formulated by John von Neumann in 1937. Unlike earlier versions, the models of von Neumann had inequality constraints. For his model of an expanding economy, von Neumann proved the existence and uniqueness of an equilibrium using his generalization of Brouwer's fixed point theorem. Von Neumann's model of an expanding economy considered the matrix pencil " A - λ B " with nonnegative matrices A and B; von Neumann sought probability vectors "p" and "q" and a positive number "λ" that would solve the complementarity equation


title: Mathematical economics

text: along with two inequality systems expressing economic efficiency. In this model, the (transposed) probability vector "p" represents the prices of the goods while the probability vector q represents the "intensity" at which the production process would run. The unique solution "λ" represents the rate of growth of the economy, which equals the interest rate. Proving the existence of a positive growth rate and proving that the growth rate equals the interest rate were remarkable achievements, even for von Neumann. Von Neumann's results have been viewed as a special case of linear programming, where von Neumann's model uses only nonnegative matrices. The study of von Neumann's model of an expanding economy continues to interest mathematical economists with interests in computational economics.


title: Mathematical economics

text: In 1936, the Russian–born economist Wassily Leontief built his model of input-output analysis from the 'material balance' tables constructed by Soviet economists, which themselves followed earlier work by the physiocrats. With his model, which described a system of production and demand processes, Leontief described how changes in demand in one economic sector would influence production in another. In practice, Leontief estimated the coefficients of his simple models, to address economically interesting questions. In production economics, "Leontief technologies" produce outputs using constant proportions of inputs, regardless of the price of inputs, reducing the value of Leontief models for understanding economies but allowing their parameters to be estimated relatively easily. In contrast, the von Neumann model of an expanding economy allows for choice of techniques, but the coefficients must be estimated for each technology.


title: Mathematical economics

text: In mathematics, mathematical optimization (or optimization or mathematical programming) refers to the selection of a best element from some set of available alternatives. In the simplest case, an optimization problem involves maximizing or minimizing a real function by selecting input values of the function and computing the corresponding values of the function. The solution process includes satisfying general necessary and sufficient conditions for optimality. For optimization problems, specialized notation may be used as to the function and its input(s). More generally, optimization includes finding the best available element of some function given a defined domain and may use a variety of different computational optimization techniques.


title: Mathematical economics

text: Economics is closely enough linked to optimization by agents in an economy that an influential definition relatedly describes economics "qua" science as the "study of human behavior as a relationship between ends and scarce means" with alternative uses. Optimization problems run through modern economics, many with explicit economic or technical constraints. In microeconomics, the utility maximization problem and its dual problem, the expenditure minimization problem for a given level of utility, are economic optimization problems. Theory posits that consumers maximize their utility, subject to their budget constraints and that firms maximize their profits, subject to their production functions, input costs, and market demand.


title: Mathematical economics

text: Economic equilibrium is studied in optimization theory as a key ingredient of economic theorems that in principle could be tested against empirical data. Newer developments have occurred in dynamic programming and modeling optimization with risk and uncertainty, including applications to portfolio theory, the economics of information, and search theory.


title: Mathematical economics

text: Optimality properties for an entire market system may be stated in mathematical terms, as in formulation of the two fundamental theorems of welfare economics and in the Arrow–Debreu model of general equilibrium (also discussed below). More concretely, many problems are amenable to analytical (formulaic) solution. Many others may be sufficiently complex to require numerical methods of solution, aided by software. Still others are complex but tractable enough to allow computable methods of solution, in particular computable general equilibrium models for the entire economy.


title: Mathematical economics

text: Linear and nonlinear programming have profoundly affected microeconomics, which had earlier considered only equality constraints. Many of the mathematical economists who received Nobel Prizes in Economics had conducted notable research using linear programming: Leonid Kantorovich, Leonid Hurwicz, Tjalling Koopmans, Kenneth J. Arrow, Robert Dorfman, Paul Samuelson and Robert Solow. Both Kantorovich and Koopmans acknowledged that George B. Dantzig deserved to share their Nobel Prize for linear programming. Economists who conducted research in nonlinear programming also have won the Nobel prize, notably Ragnar Frisch in addition to Kantorovich, Hurwicz, Koopmans, Arrow, and Samuelson.


title: Mathematical economics

text: Linear programming was developed to aid the allocation of resources in firms and in industries during the 1930s in Russia and during the 1940s in the United States. During the Berlin airlift (1948), linear programming was used to plan the shipment of supplies to prevent Berlin from starving after the Soviet blockade.


title: Mathematical economics

text: Extensions to nonlinear optimization with inequality constraints were achieved in 1951 by Albert W. Tucker and Harold Kuhn, who considered the nonlinear optimization problem:


title: Mathematical economics

text: In allowing inequality constraints, the Kuhn–Tucker approach generalized the classic method of Lagrange multipliers, which (until then) had allowed only equality constraints. The Kuhn–Tucker approach inspired further research on Lagrangian duality, including the treatment of inequality constraints. The duality theory of nonlinear programming is particularly satisfactory when applied to convex minimization problems, which enjoy the convex-analytic duality theory of Fenchel and Rockafellar; this convex duality is particularly strong for polyhedral convex functions, such as those arising in linear programming. Lagrangian duality and convex analysis are used daily in operations research, in the scheduling of power plants, the planning of production schedules for factories, and the routing of airlines (routes, flights, planes, crews).


title: Mathematical economics

text: "Economic dynamics" allows for changes in economic variables over time, including in dynamic systems. The problem of finding optimal functions for such changes is studied in variational calculus and in optimal control theory. Before the Second World War, Frank Ramsey and Harold Hotelling used the calculus of variations to that end.


title: Mathematical economics

text: Following Richard Bellman's work on dynamic programming and the 1962 English translation of L. Pontryagin "et al".'s earlier work, optimal control theory was used more extensively in economics in addressing dynamic problems, especially as to economic growth equilibrium and stability of economic systems, of which a textbook example is optimal consumption and saving. A crucial distinction is between deterministic and stochastic control models. Other applications of optimal control theory include those in finance, inventories, and production for example.


title: Mathematical economics

text: It was in the course of proving of the existence of an optimal equilibrium in his 1937 model of economic growth that John von Neumann introduced functional analytic methods to include topology in economic theory, in particular, fixed-point theory through his generalization of Brouwer's fixed-point theorem. Following von Neumann's program, Kenneth Arrow and Gérard Debreu formulated abstract models of economic equilibria using convex sets and fixed–point theory. In introducing the Arrow–Debreu model in 1954, they proved the existence (but not the uniqueness) of an equilibrium and also proved that every Walras equilibrium is Pareto efficient; in general, equilibria need not be unique. In their models, the ("primal") vector space represented "quantities" while the "dual" vector space represented "prices".


title: Mathematical economics

text: In Russia, the mathematician Leonid Kantorovich developed economic models in partially ordered vector spaces, that emphasized the duality between quantities and prices. Kantorovich renamed "prices" as "objectively determined valuations" which were abbreviated in Russian as "o. o. o.", alluding to the difficulty of discussing prices in the Soviet Union.


title: Mathematical economics

text: Even in finite dimensions, the concepts of functional analysis have illuminated economic theory, particularly in clarifying the role of prices as normal vectors to a hyperplane supporting a convex set, representing production or consumption possibilities. However, problems of describing optimization over time or under uncertainty require the use of infinite–dimensional function spaces, because agents are choosing among functions or stochastic processes.


title: Mathematical economics

text: John von Neumann's work on functional analysis and topology broke new ground in mathematics and economic theory. It also left advanced mathematical economics with fewer applications of differential calculus. In particular, general equilibrium theorists used general topology, convex geometry, and optimization theory more than differential calculus, because the approach of differential calculus had failed to establish the existence of an equilibrium.


title: Mathematical economics

text: However, the decline of differential calculus should not be exaggerated, because differential calculus has always been used in graduate training and in applications. Moreover, differential calculus has returned to the highest levels of mathematical economics, general equilibrium theory (GET), as practiced by the "GET-set" (the humorous designation due to Jacques H. Drèze). In the 1960s and 1970s, however, Gérard Debreu and Stephen Smale led a revival of the use of differential calculus in mathematical economics. In particular, they were able to prove the existence of a general equilibrium, where earlier writers had failed, because of their novel mathematics: Baire category from general topology and Sard's lemma from differential topology. Other economists associated with the use of differential analysis include Egbert Dierker, Andreu Mas-Colell, and Yves Balasko. These advances have changed the traditional narrative of the history of mathematical economics, following von Neumann, which celebrated the abandonment of differential calculus.


title: Mathematical economics

text: John von Neumann, working with Oskar Morgenstern on the theory of games, broke new mathematical ground in 1944 by extending functional analytic methods related to convex sets and topological fixed-point theory to economic analysis. Their work thereby avoided the traditional differential calculus, for which the maximum–operator did not apply to non-differentiable functions. Continuing von Neumann's work in cooperative game theory, game theorists Lloyd S. Shapley, Martin Shubik, Hervé Moulin, Nimrod Megiddo, Bezalel Peleg influenced economic research in politics and economics. For example, research on the fair prices in cooperative games and fair values for voting games led to changed rules for voting in legislatures and for accounting for the costs in public–works projects. For example, cooperative game theory was used in designing the water distribution system of Southern Sweden and for setting rates for dedicated telephone lines in the USA.


title: Mathematical economics

text: Earlier neoclassical theory had bounded only the "range" of bargaining outcomes and in special cases, for example bilateral monopoly or along the contract curve of the Edgeworth box. Von Neumann and Morgenstern's results were similarly weak. Following von Neumann's program, however, John Nash used fixed–point theory to prove conditions under which the bargaining problem and noncooperative games can generate a unique equilibrium solution. Noncooperative game theory has been adopted as a fundamental aspect of experimental economics, behavioral economics, information economics, industrial organization, and political economy. It has also given rise to the subject of mechanism design (sometimes called reverse game theory), which has private and public-policy applications as to ways of improving economic efficiency through incentives for information sharing.


title: Mathematical economics

text: In 1994, Nash, John Harsanyi, and Reinhard Selten received the Nobel Memorial Prize in Economic Sciences their work on non–cooperative games. Harsanyi and Selten were awarded for their work on repeated games. Later work extended their results to computational methods of modeling.


title: Mathematical economics

text: Agent-based computational economics (ACE) as a named field is relatively recent, dating from about the 1990s as to published work. It studies economic processes, including whole economies, as dynamic systems of interacting agents over time. As such, it falls in the paradigm of complex adaptive systems. In corresponding agent-based models, agents are not real people but "computational objects modeled as interacting according to rules" ... "whose micro-level interactions create emergent patterns" in space and time. The rules are formulated to predict behavior and social interactions based on incentives and information. The theoretical assumption of mathematical "optimization" by agents markets is replaced by the less restrictive postulate of agents with "bounded" rationality "adapting" to market forces.


title: Mathematical economics

text: ACE models apply numerical methods of analysis to computer-based simulations of complex dynamic problems for which more conventional methods, such as theorem formulation, may not find ready use. Starting from specified initial conditions, the computational economic system is modeled as evolving over time as its constituent agents repeatedly interact with each other. In these respects, ACE has been characterized as a bottom-up culture-dish approach to the study of the economy. In contrast to other standard modeling methods, ACE events are driven solely by initial conditions, whether or not equilibria exist or are computationally tractable. ACE modeling, however, includes agent adaptation, autonomy, and learning. It has a similarity to, and overlap with, game theory as an agent-based method for modeling social interactions. Other dimensions of the approach include such standard economic subjects as competition and collaboration, market structure and industrial organization, transaction costs, welfare economics and mechanism design, information and uncertainty, and macroeconomics.


title: Mathematical economics

text: The method is said to benefit from continuing improvements in modeling techniques of computer science and increased computer capabilities. Issues include those common to experimental economics in general and by comparison and to development of a common framework for empirical validation and resolving open questions in agent-based modeling. The ultimate scientific objective of the method has been described as "test[ing] theoretical findings against real-world data in ways that permit empirically supported theories to cumulate over time, with each researcher's work building appropriately on the work that has gone before".


title: Mathematical economics

text: Over the course of the 20th century, articles in "core journals" in economics have been almost exclusively written by economists in academia. As a result, much of the material transmitted in those journals relates to economic theory, and "economic theory itself has been continuously more abstract and mathematical." A subjective assessment of mathematical techniques employed in these core journals showed a decrease in articles that use neither geometric representations nor mathematical notation from 95% in 1892 to 5.3% in 1990. A 2007 survey of ten of the top economic journals finds that only 5.8% of the articles published in 2003 and 2004 both lacked statistical analysis of data and lacked displayed mathematical expressions that were indexed with numbers at the margin of the page.


title: Mathematical economics

text: Between the world wars, advances in mathematical statistics and a cadre of mathematically trained economists led to econometrics, which was the name proposed for the discipline of advancing economics by using mathematics and statistics. Within economics, "econometrics" has often been used for statistical methods in economics, rather than mathematical economics. Statistical econometrics features the application of linear regression and time series analysis to economic data.


title: Mathematical economics

text: Ragnar Frisch coined the word "econometrics" and helped to found both the Econometric Society in 1930 and the journal "Econometrica" in 1933. A student of Frisch's, Trygve Haavelmo published "The Probability Approach in Econometrics" in 1944, where he asserted that precise statistical analysis could be used as a tool to validate mathematical theories about economic actors with data from complex sources. This linking of statistical analysis of systems to economic theory was also promulgated by the Cowles Commission (now the Cowles Foundation) throughout the 1930s and 1940s.


title: Mathematical economics

text: The roots of modern econometrics can be traced to the American economist Henry L. Moore. Moore studied agricultural productivity and attempted to fit changing values of productivity for plots of corn and other crops to a curve using different values of elasticity. Moore made several errors in his work, some from his choice of models and some from limitations in his use of mathematics. The accuracy of Moore's models also was limited by the poor data for national accounts in the United States at the time. While his first models of production were static, in 1925 he published a dynamic "moving equilibrium" model designed to explain business cycles—this periodic variation from over-correction in supply and demand curves is now known as the cobweb model. A more formal derivation of this model was made later by Nicholas Kaldor, who is largely credited for its exposition.


title: Mathematical economics

text: Much of classical economics can be presented in simple geometric terms or elementary mathematical notation. Mathematical economics, however, conventionally makes use of calculus and matrix algebra in economic analysis in order to make powerful claims that would be more difficult without such mathematical tools. These tools are prerequisites for formal study, not only in mathematical economics but in contemporary economic theory in general. Economic problems often involve so many variables that mathematics is the only practical way of attacking and solving them. Alfred Marshall argued that every economic problem which can be quantified, analytically expressed and solved, should be treated by means of mathematical work.


title: Mathematical economics

text: Economics has become increasingly dependent upon mathematical methods and the mathematical tools it employs have become more sophisticated. As a result, mathematics has become considerably more important to professionals in economics and finance. Graduate programs in both economics and finance require strong undergraduate preparation in mathematics for admission and, for this reason, attract an increasingly high number of mathematicians. Applied mathematicians apply mathematical principles to practical problems, such as economic analysis and other economics-related issues, and many economic problems are often defined as integrated into the scope of applied mathematics.


title: Mathematical economics

text: This integration results from the formulation of economic problems as stylized models with clear assumptions and falsifiable predictions. This modeling may be informal or prosaic, as it was in Adam Smith's "The Wealth of Nations", or it may be formal, rigorous and mathematical.


title: Mathematical economics

text: Broadly speaking, formal economic models may be classified as stochastic or deterministic and as discrete or continuous. At a practical level, quantitative modeling is applied to many areas of economics and several methodologies have evolved more or less independently of each other.


title: Mathematical economics

text: The great appeal of mathematical economics is that it brings a degree of rigor to economic thinking, particularly around charged political topics. For example, during the discussion of the efficacy of a corporate tax cut for increasing the wages of workers, a simple mathematical model proved beneficial to understanding the issues at hand.


title: Mathematical economics

text: As an intellectual exercise, the following problem was posed by Prof. Greg Mankiw of Harvard University:An open economy has the production function formula_11, where formula_12 is output per worker and formula_13 is capital per worker. The capital stock adjusts so that the after-tax marginal product of capital equals the exogenously given world interest rate formula_14...How much will the tax cut increase wages?To answer this question, we follow John H. Cochrane of the Hoover Institution. Suppose an open economy has the production function:formula_15Where the variables in this equation are:


title: Mathematical economics

text: The standard choice for the production function is the Cobb-Douglas production function:formula_20where formula_21 is the factor of productivity - assumed to be a constant. A corporate tax cut in this model is equivalent to a tax on capital. With taxes, firms look to maximize:formula_22where formula_23 is the capital tax rate, formula_24 is wages per worker, and formula_14 is the exogenous interest rate. Then the first-order optimality conditions become:formula_26Therefore, the optimality conditions imply that:formula_27Define total taxes formula_28. This implies that taxes per worker formula_29 are:formula_30Then the change in taxes per worker, given the tax rate, is:formula_31To find the change in wages, we differentiate the second optimality condition for the per worker wages to obtain:formula_32Assuming that the interest rate is fixed at formula_14, so that formula_34, we may differentiate the first optimality condition for the interest rate to find:formula_35For the moment, let's focus only on the static effect of a capital tax cut, so that formula_36. If we substitute this equation into equation for wage changes with respect to the tax rate, then we find that:formula_37Therefore, the static effect of a capital tax cut on wages is:formula_38Based on the model, it seems possible that we may achieve a rise in the wage of a worker greater than the amount of the tax cut. But that only considers the static effect, and we know that the dynamic effect must be accounted for. In the dynamic model, we may rewrite the equation for changes in taxes per worker with respect to the tax rate as:formula_39Recalling that formula_40, we have that:formula_41Using the Cobb-Douglas production function, we have that:formula_42Therefore, the dynamic effect of a capital tax cut on wages is:formula_43If we take formula_44, then the dynamic effect of lowering capital taxes on wages will be even larger than the static effect. Moreover, if there are positive externalities to capital accumulation, the effect of the tax cut on wages would be larger than in the model we just derived. It is important to note that the result is a combination of:


title: Mathematical economics

text: This result showing that, under certain assumptions, a corporate tax cut can boost the wages of workers by more than the lost revenue does not imply that the magnitude is correct. Rather, it suggests a basis for policy analysis that is not grounded in handwaving. If the assumptions are reasonable, then the model is an acceptable approximation of reality; if they are not, then better models should be developed.


title: Mathematical economics

text: Now let's assume that instead of the Cobb-Douglas production function we have a more general constant elasticity of substitution (CES) production function:formula_45where formula_46; formula_47 is the elasticity of substitution between capital and labor. The relevant quantity we want to calculate is formula_48"," which may be derived as:formula_49Therefore, we may use this to find that:formula_50Therefore, under a general CES model, the dynamic effect of a capital tax cut on wages is:formula_51We recover the Cobb-Douglas solution when formula_52. When formula_53, which is the case when perfect substitutes exist, we find that formula_54 - there is no effect of changes in capital taxes on wages. And when formula_55, which is the case when perfect complements exist, we find that formula_56 - a cut in capital taxes increases wages by exactly one dollar.


title: Mathematical economics

text: Friedrich Hayek contended that the use of formal techniques projects a scientific exactness that does not appropriately account for informational limitations faced by real economic agents.


title: Mathematical economics

text: Heilbroner stated that "some/much of economics is not naturally quantitative and therefore does not lend itself to mathematical exposition."


title: Mathematical economics

text: Philosopher Karl Popper discussed the scientific standing of economics in the 1940s and 1950s. He argued that mathematical economics suffered from being tautological. In other words, insofar as economics became a mathematical theory, mathematical economics ceased to rely on empirical refutation but rather relied on mathematical proofs and disproof. According to Popper, falsifiable assumptions can be tested by experiment and observation while unfalsifiable assumptions can be explored mathematically for their consequences and for their consistency with other assumptions.


title: Mathematical economics

text: Sharing Popper's concerns about assumptions in economics generally, and not just mathematical economics, Milton Friedman declared that "all assumptions are unrealistic". Friedman proposed judging economic models by their predictive performance rather than by the match between their assumptions and reality.


title: Mathematical economics

text: In response to these criticisms, Paul Samuelson argued that mathematics is a language, repeating a thesis of Josiah Willard Gibbs. In economics, the language of mathematics is sometimes necessary for representing substantive problems. Moreover, mathematical economics has led to conceptual advances in economics. In particular, Samuelson gave the example of microeconomics, writing that "few people are ingenious enough to grasp [its] more complex parts... "without" resorting to the language of mathematics, while most ordinary individuals can do so fairly easily "with" the aid of mathematics."


title: Mathematical economics

text: Some economists state that mathematical economics deserves support just like other forms of mathematics, particularly its neighbors in mathematical optimization and mathematical statistics and increasingly in theoretical computer science. Mathematical economics and other mathematical sciences have a history in which theoretical advances have regularly contributed to the reform of the more applied branches of economics. In particular, following the program of John von Neumann, game theory now provides the foundations for describing much of applied economics, from statistical decision theory (as "games against nature") and econometrics to general equilibrium theory and industrial organization. In the last decade, with the rise of the internet, mathematical economists and optimization experts and computer scientists have worked on problems of pricing for on-line services --- their contributions using mathematics from cooperative game theory, nondifferentiable optimization, and combinatorial games.


title: Mathematical economics

text: Robert M. Solow concluded that mathematical economics was the core "infrastructure" of contemporary economics:


title: Mathematical economics

text: Economics is no longer a fit conversation piece for ladies and gentlemen. It has become a technical subject. Like any technical subject it attracts some people who are more interested in the technique than the subject. That is too bad, but it may be inevitable. In any case, do not kid yourself: the technical core of economics is indispensable infrastructure for the political economy. That is why, if you consult [a reference in contemporary economics] looking for enlightenment about the world today, you will be led to technical economics, or history, or nothing at all.


title: Martha Bernays

text: Martha Bernays ( , ; 26 July 1861 – 2 November 1951) was the wife of Austrian psychoanalyst Sigmund Freud.


title: Martha Bernays

text: Bernays was the second daughter of Emmeline and Berman Bernays. Her paternal grandfather Isaac Bernays was a Chief Rabbi of Hamburg.


title: Martha Bernays

text: Martha Bernays was raised in an observant Orthodox Jewish family, the daughter of Berman Bernays (1826–1879) and Emmeline Philipp (1830–1910). Her grandfather, Isaac Bernays, was the chief rabbi of Hamburg and a distant relative of the German Romantic poet Heinrich Heine and whom Heine frequently mentioned in letters. Isaac's son, Michael Bernays (1834–1897), Martha's uncle, converted to Christianity at an early age and was professor of German at the University of Munich. Although the Bernays and Freud families were well-acquainted - her elder brother Eli married Freud's younger sister, for example - the latter were more liberal Jews, and Freud in particular had no time for ritual observances. Martha told a cousin that "not being allowed to light the Sabbath lights on the first Friday night after her marriage was one of the more upsetting experiences of her life". She was also the aunt of Edward Bernays, Austrian-born American publicist and "father of public relations". Her maternal cousins were brothers Julius Philipp and Oscar Philipp, founders of Philipp Brothers, which became the largest metal trading company in the world.


title: Martha Bernays

text: Sigmund Freud and Martha met in April 1882 and after a four-year engagement (1882–1886) they were married on 14 September 1886 in Hamburg.


title: Martha Bernays

text: Freud and Bernays's love letters sent during the engagement years, according to Freud's official biographer Ernest Jones, who read all the letters, "would be a not unworthy contribution to the great love literature of the world." Freud sent over 900 (lengthy) letters to his fiancée, which chart the ups and downs of a tempestuous relationship, marred by outbreaks of jealousy on his part as well as affirmations that "I love you with a kind of passionate enchantment".


title: Martha Bernays

text: Their eventual marriage was a much more harmonious affair: Martha consoling herself after his death with the thought that "in the 53 years of our marriage there was not a single angry word between us". The couple had six children: Mathilde (born 1887), Jean-Martin (born 1889), Oliver (born 1891), Ernst (born 1892), Sophie (born 1893), and Anna (born 1895).


title: Martha Bernays

text: Martha Freud died in 1951. She was cremated at Golders Green Crematorium and her ashes placed in the Freud Corner, into the same ancient Greek funeral urn that holds her husband's ashes.


title: Martha Bernays

text: The young Martha Bernays was a slim and attractive woman who was also a charmer, intelligent, well-educated and fond of reading (as she remained throughout her life). As a married woman, she ran her household efficiently, and was indeed almost obsessive about punctuality and dirt. Firm but loving with her children, she spread an atmosphere of peaceful joie de vivre through the household (at least according to the French analyst René Laforgue). However, Martha was not able to establish a strong connection with her youngest daughter, Anna.


title: Martha Bernays

text: Bernays's younger sister, Minna Bernays, was very close to the young couple, and moved in with them in the 1890s, to set up what has (jokingly) been called a ménage à trois. Sigmund and Minna would sometimes holiday together; and the suggestion has periodically been made that she in fact became Freud's mistress. Jung for example reported (late in life) that from Minna he "learned that Freud was in love with her and that their relationship was indeed very intimate". Freud historian Peter Swales "became notorious when, in 1981, he maintained that Freud had had a secret affair with his wife Martha’s younger sister Minna Bernays ... and had arranged for her to have an abortion after she became pregnant."


title: Martha Bernays

text: This claim was (and is) controversial. The publication of a hotel log from 1898 registering the pair as "Dr Sigm Freud u frau" in a double room prompted some Freud scholars, including his defender Peter Gay, to regard the conjecture of Freud and Minna having an affair as possibly accurate. Other proponents of the affair, however — relying on their analysis of Freud's own autobiographical writings — believe that it was consummated only in 1900.


title: Martha Bernays

text: Opponents point to the unlikelihood of such a betrayal taking place between sisters as close as Minna and Martha, especially given the mores of the time; and to the less sensational possibility of the hotel simply being full at the time. Pending publication of the Freud/Minna correspondence for the period 1893–1910, the truth behind such speculations may not be known for sure.


title: Martha Bernays

text: What does seem certain is that Martha herself in no way knew of, or colluded in, any such affair. Freud described her as thoroughly good, where he and Minna were more self-willed and wild; and for better or worse her commitment to conventional morality, domestic duty and family values is clear. (Her husband too had shocked André Breton by his lack of any Bohemianism, and considered a sexually promiscuous woman as "simply a "Haderlump" [a ragamuffin]".) Martha's attitude to infidelity is perhaps best illustrated by her reaction to their friend Stefan Zweig's leaving his wife Friderike for a younger woman: six years after Zweig's death in 1942, Martha wrote to his widow that she still resented "our friend's infidelity to you!"


title: High Court of Australia

text: The High Court of Australia is Australia's apex court. It exercises original and appellate jurisdiction on matters specified within Australia's Constitution.


title: High Court of Australia

text: The High Court was established following passage of the "Judiciary Act 1903". It derives its authority from Chapter III of the Australian Constitution, which vests it responsibility for the judicial power of the Commonwealth. Important legal instruments pertaining to the High Court include the "Judiciary Act 1903" and the "High Court of Australia Act 1979".


title: High Court of Australia

text: Its bench is composed of seven justices, including a Chief Justice, currently Susan Kiefel. Justices of the High Court are appointed by the Governor-General on the advice of the Prime Minister and are appointed permanently until their mandatory retirement at age 70, unless they retire earlier.


title: High Court of Australia

text: The court has resided in Canberra since 1980, following the construction of a purpose-built High Court Building, located in the Parliamentary Triangle and overlooking Lake Burley Griffin. Sittings of the court previously rotated between state capitals, particularly Melbourne and Sydney, and the court continues to regularly sit outside Canberra.


title: High Court of Australia

text: "The High Court's jurisdiction is divided in its exercise between constitutional and federal cases which loom so largely in the public eye, and the great body of litigation between man and man, or even man and government, which has nothing to do with the Constitution, and which is the principal preoccupation of the court."


title: High Court of Australia

text: The broad jurisdiction of the High Court means that it has an important role in Australia's legal system.


title: High Court of Australia

text: Its original jurisdiction is determined by section 75 and 76 of Australia's constitution. Section 75 confers original jurisdiction in all matters:


title: High Court of Australia

text: Constitutional matters, referred to in section 76(i), have been conferred to the High Court by section 30 of the "Judiciary Act 1903". Whilst it may seem that the inclusion of constitutional matters in section 76 means that the High Court's original jurisdiction regarding constitutional matters could be removed; In practice, section 75(iii) (suing the Commonwealth) and section 75(iv) (conflicts between states) are broad enough that many constitutional matters would still be within jurisdiction. The original constitutional jurisdiction of the High Court is now well established: the Australian Law Reform Commission has described the inclusion of constitutional matters in section 76 rather than section 75 as "an odd fact of history." The 1998 Constitutional Convention recommended an amendment to the constitution to prevent the possibility of the jurisdiction being removed by Parliament. Failure to proceed on this issue suggests that it was considered highly unlikely that Parliament would ever take this step.


title: High Court of Australia

text: The word 'matter' in section 75 and section 76 has been understood to mean that the High Court is unable to give merely advisory opinions.


title: High Court of Australia

text: The court is empowered by section 73 of the Constitution to hear appeals from the Supreme Courts of the States and Territories; as well as any court exercising federal jurisdiction. It may also hear appeals of decisions made in an exercise of its own original jurisdiction.


title: High Court of Australia

text: The High Court's appellate jurisdiction is limited by the "Judiciary Act", which requires 'special leave' to be granted before the hearing of an appeal. Special leave may only be granted where a question of law is raised which is of public importance, involves a conflict between courts or "is in the interests of the administration of justice".


title: High Court of Australia

text: Special leave hearings are typically presided over by a panel of two or three justices of the High Court. Parties are typically limited to an oral submission of 20 minutes, in addition to any written submissions.


title: High Court of Australia

text: Appeals to the United Kingdom's Privy Council was a notable controversy when Australia's constitution was drafted. Section 74 of the constitution as it was put to voters, stated that there would be no appeals to the privy council in any matter involving the Constitution of the Commonwealth or State Government.


title: High Court of Australia

text: The section as enacted by the Imperial Parliament was different. It prohibited appeals on constitutional matters, excepting where the High Court certified it appropriate for the appeal to be determined by Privy Council. This occurred only once, and the High Court has said it would never again grant a certificate of appeal.


title: High Court of Australia

text: On non-constitutional matters, the Privy Council regularly heard appeals against High Court decisions. In some cases the Council acknowledged that the Australian common law had developed differently from English law and thus did not apply its own principles. Other times it followed English authority, and overruled decisions of the High Court.


title: High Court of Australia

text: This arrangement led to tensions between the High Court and the Privy Council. In "Parker v R" (1964), Owen Dixon CJ led a unanimous judgment rejecting the authority of the House of Lords decision in "DPP v Smith", writing: "I shall not depart from the law on this matter as we have long since laid it down in this Court and I think that Smith's case should not be used in Australia as authority at all". The Privy Council overturned this by enforcing the UK precedent upon the High Court the following year.


title: High Court of Australia

text: Thirteen High Court judges have heard cases as part of the Privy Council. Sir Isaac Isaacs is the only judge to have sat on an appeal from the High Court, in 1936 after his retirement as Governor-General. Sir Garfield Barwick insisted on an amendment to Privy Council procedure to allow dissent; however he exercised that only once. The appeals mostly related to decisions from other Commonwealth countries, although they occasionally included appeals from a State Supreme Court.


title: High Court of Australia

text: Section 74 allowed parliament to prevent appeals to the Privy Council. It did so in 1968 with the "Privy Council (Limitation of Appeals) Act 1968", which closed off all appeals to the Privy Council in matters involving federal legislation. In 1975, the "Privy Council (Appeals from the High Court) Act 1975" was passed, which closed all routes of appeal from the High Court; excepting for those in which a certificate of appeal would be granted by the High Court.


title: High Court of Australia

text: In 1986, with the passing of the Australia Act by both the UK Parliament and the Parliament of Australia (with the request and consent of the Australian States), appeals to the Privy Council from state Supreme Courts were closed off, leaving the High Court as the only avenue of appeal. In 2002, Chief Justice Murray Gleeson said that the "combined effect" of the legislation and the announcement in "Kirmani" "has been that s 74 has become a dead letter, and what remains of s 74 after the legislation limiting appeals to the Privy Council will have no further effect".


title: High Court of Australia

text: Following an agreement between Nauru and Australia signed on 6 September 1976, the High Court became Nauru's apex court. It was empowered to hear appeals from the Supreme Court of Nauru in both criminal and civil cases; but not constitutional matters. There were a total of five appeals to the High Court under this agreement in the first 40 years of its operation. In 2017, however, this jumped to 13 appeals, most relating to asylum seekers. At the time some legal commentators argued that this appellate jurisdiction sat awkwardly with the High Court's other responsibilities, and ought be renegotiated or repealed. Anomalies included the need to apply Nauruan law and customary practice, and that special leave hearings were not required.


title: High Court of Australia

text: Nauruan politicians had expressed publicly that the Nauru government was unhappy about these arrangements. Of particular concern was a decision of the High Court in October 2017, which quashed an increase in sentence imposed upon political protestors by the Supreme Court of Nauru. The High Court had remitted to the Supreme Court 'differently constituted, for hearing according to law'.


title: High Court of Australia

text: On Nauru's 50th anniversary of independence, Baron Waqa declared to parliament that '[s]everance of ties to Australia’s highest court is a logical step towards full nationhood and an expression of confidence in Nauru’s ability to determine its own destiny.' An additional reason for cutting ties articulated by Justice Minister David Adeang was the cost of appeals to the High Court. Nauru then exercised an option under its agreement with Australia to end its appellate arrangement with 90 days notice. The option was exercised on 12 December 2017 and the High Court's jurisdiction ended 12 March 2018. This termination did not become publicly known until after the Supreme Court had reheard the case of the protesters, and again imposed increased sentences.


title: High Court of Australia

text: Following Earl Grey's 1846 proposal to federate the colonies, a 1849 report from the Privy Council suggested a national court be created. In 1856, the Governor of South Australia, Richard MacDonnell, suggested to the Government of South Australia that they consider establishing a court to hear appeals from the Supreme Courts in each colony. In 1860 the South Australian Parliament passed legislation encouraging MacDonnell to put the idea to the other colonies. However, only Victoria considered the proposal.


title: High Court of Australia

text: At a Melbourne inter-colonial conference held in 1870, the idea of an inter-colonial court was against raised. A Royal Commission was established in Victoria to investigate options for establishing such a court, and a draft bill was put forward. This draft bill however completely excluded appeals to the Privy Council, causing a reaction in London which prevented any serious attempts to implement the bill through the British Imperial Parliament.


title: High Court of Australia

text: Another draft bill was proposed in 1880 for the establishment of an Australasian Court of Appeal. The proposed court would consist of one judge from each of the colonial Supreme Courts, who would serve one-year terms. However, the proposed court allowed for appeals to the Privy Council, which was disliked by some of the colonies, and the bill was abandoned.


title: High Court of Australia

text: The idea of a federal Supreme Court was raised during the Constitutional Conventions of the 1890s. A proposal for a Supreme Court of Australia was included in a 1891 draft. It was proposed to enable the court to hear appeals from the State Supreme courts, with appeals to the Privy Council only occurring on assent from the British monarch. It was proposed that the Privy Council be prevented from hearing appeals on constitutional matters.


title: High Court of Australia

text: This draft was largely the work of Sir Samuel Griffith, then the Premier of Queensland. The Attorney-General of Tasmania Andrew Inglis Clark also contributed to the constitution's judicial clauses. Clark's most significant contribution was to give the court its own constitutional authority, ensuring a separation of powers. The original formulation of Griffith, Barton and Kingston provided only that the parliament could establish a court.


title: High Court of Australia

text: The draft was later amended at various conventions. In Adelaide the court's proposed name was changed to be the 'High Court of Australia'.


title: High Court of Australia

text: Many people opposed the idea of the new court completely replacing the Privy Council. Commercial interests, particularly subsidiaries of British companies preferred to operate under the unified jurisdiction of the British courts, and petitioned the conventions to that effect. Others argued that Australian judges were of a poorer quality than those of the English, and than the inevitable divergence in law that would occur without the oversight of the Privy Council; would put the legal system at risk.


title: High Court of Australia

text: Some politicians (e.g. George Dibbs) supported a retention of Privy Council supervision; whereas others, including Alfred Deakin, supported the design of the court as it was. Inglis Clark took the view that the possibility of divergence was a good thing, for the law could adapt appropriately to Australian circumstances. Despite this debate, the draft's judicial sections remained largely unchanged.


title: High Court of Australia

text: After the draft had been approved by the electors of the colonies, it was taken to London in 1899 for the assent of the British Imperial Parliament. The issue of Privy Council appeals remained a sticking point however; with objections made by Secretary of State for the Colonies, Joseph Chamberlain, the Chief Justice of South Australia, Sir Samuel Way, and Samuel Griffith, among others. In October 1899, Griffith made representations to Chamberlain soliciting suggestions from British ministers for alterations to the draft, and offered alterations of his own. Indeed, such was the effect of these and other representations that Chamberlain called for delegates from the colonies to come to London to assist with the approval process, with a view to their approving any alterations that the British government might see fit to make; delegates were sent, including Deakin, Barton and Charles Kingston, although they were under instructions that they would never agree to changes.


title: High Court of Australia

text: After intense lobbying both in Australia and in the United Kingdom, the Imperial Parliament finally approved the draft constitution. The draft as passed included an alteration to section 74, in a compromise between the two sides. It allowed for a general right of appeal from the High Court to the Privy Council, but the Parliament of Australia could make laws restricting this avenue. In addition, appeals in "inter se" matters were not as of right, but had to be certified by the High Court.


title: High Court of Australia

text: The High Court was not immediately established after Australia came into being. Some members of the First Parliament, including Sir John Quick, then one of the leading legal experts in Australia, opposed legislation to set up the court. Even H. B. Higgins, who was himself later appointed to the court, objected to setting it up, on the grounds that it would be impotent while Privy Council appeals remained, and that in any event there was not enough work for a federal court to make it viable.


title: High Court of Australia

text: The then Attorney-General Alfred Deakin introduced the "Judiciary Bill" to the House of Representatives in 1902. Prior efforts had been continually delayed by opponents in the parliament, and the success of the bill is generally attributed to Deakin's passion and persistence. Deakin proposed that the court be composed of five judges, specially selected to the court. Opponents instead proposed that the court should be made up of state Supreme Court justices, taking turns to sit on the High Court on a rotation basis, as had been mooted at the Constitutional Conventions a decade before. Deakin eventually negotiated amendments with the opposition, reducing the number of judges from five to three, and eliminating financial benefits such as pensions.


title: High Court of Australia

text: At one point, Deakin threatened to resign as Attorney-General due to the difficulties he faced. In his three and a half hour second reading speech to the House of Representatives, Deakin said:"The federation is constituted by distribution of powers, and it is this court which decides the orbit and boundary of every power... It is properly termed the keystone of the federal arch... The statute stands and will stand on the statute-book just as in the hour in which it was assented to. But the nation lives, grows and expands. Its circumstances change, its needs alter, and its problems present themselves with new faces. [The High Court] enables the Constitution to grow and be adapted to the changeful necessities and circumstances of generation after generation that the High Court operates."


title: High Court of Australia

text: Deakin's friend, painter Tom Roberts, who viewed the speech from the public gallery, declared it Deakin's "magnum opus". The Judiciary Act 1903 was finally passed on 25 August 1903, and the first three justices, Chief Justice Sir Samuel Griffith and Justices Sir Edmund Barton and Richard O'Connor were appointed on 5 October of that year. On 6 October, the court held its first sitting in the Banco Court in the Supreme Court of Victoria.


title: High Court of Australia

text: On 12 October 1906, the size of the High Court was increased to five justices, and Deakin appointed H. B. Higgins and Isaac Isaacs to the High Court. Following a court-packing attempt by the Labor Prime Minister Andrew Fisher In February 1913, the bench was increased again to a total to seven. Charles Powers and Albert Bathurst Piddington were appointed. These appointments generated an outcry, however, and Piddington resigned on 5 April 1913 after serving only one month as High Court justice.


title: High Court of Australia

text: The High Court continued its Banco location in Melbourne until 1928, until a dedicated courtroom was built in Little Bourke Street, next to the Supreme Court of Victoria. That space provided the court's Melbourne sitting place and housed the court's principal registry until 1980. The court also sat regularly in Sydney, sharing space in the Criminal Courts of Darlinghurst Courthouse, before a dedicated courtroom was constructed next door in 1923.


title: High Court of Australia

text: The court travelled to other cities across the country, where it would use facilities of the respective Supreme Courts. Deakin had envisaged that the court would sit in many different locations, so as to truly be a federal court. Shortly after the court's creation, Chief Justice Griffith established a schedule for sittings in state capitals: Hobart in February, Brisbane in June, Perth in September, and Adelaide in October. It has been said that Griffith established this schedule because those were the times of year he found the weather most pleasant in each city.


title: High Court of Australia

text: The tradition of special sittings remains to this day, although they are dependent on the court's caseload. There are annual sittings in Perth, Adelaide and Brisbane for up to a week each year, and sittings in Hobart occur once every few years. Sittings outside of these special occurrences are conducted in Canberra.


title: High Court of Australia

text: The court's operations were marked by various anomalies during World War II. The Chief Justice, Sir John Latham, served from 1940 to 1941 as Australia's first ambassador to Japan; however his activities in that role were limited by a pact Japan had entered with the Axis powers prior to his arrival in Tokyo. Owen Dixon was also absent for several years of his appointment, whilst he was serving as Australia's minister to the United States in Washington. Sir George Rich acted as Chief Justice during Latham's absence.


title: High Court of Australia

text: From 1952, with the appointment of Sir Owen Dixon as Chief Justice, the court entered a period of stability. After World War II, the court's workload continued to grow, particularly from the 1960s onwards, putting pressures on the court. Sir Garfield Barwick, who was Attorney-General from 1958 to 1964, and from then until 1981 Chief Justice, proposed that more federal courts be established, as permitted under the Constitution. In 1976 the Federal Court of Australia was established, with a general federal jurisdiction, and in more recent years the Family Court and Federal Magistrates Court have been set up to reduce the court's workload in specific areas.


title: High Court of Australia

text: In 1968, appeals to the Privy Council in matters involving federal legislation were barred. In 1986, with the passage of the "Australia Acts" direct appeals to the Privy Council from state Supreme Courts were also closed off.


title: High Court of Australia

text: The life tenure of High Court Justices was ended in 1977. A national referendum in May 1977 approved the "Constitution Alteration (Retirement of Judges) Act" (Cth), which upon its commencement on 29 July 1977 amended section 72 of the Constitution so as require that all Justices appointed from then on must retire on attaining the age of 70 years.


title: High Court of Australia

text: The "High Court of Australia Act 1979" (Cth), which commenced on 21 April 1980, gave the High Court power to administer its own affairs and prescribed the qualifications for, and method of appointment of, its Justices.


title: High Court of Australia

text: Historical periods of the High Court are commonly denoted by reference to the Chief Justice of the time. It ought be noted however, that the Chief Justice is not always the most influential figure on the Court.


title: High Court of Australia

text: The first Court under Chief Justice Griffith laid the foundations of Australia's constitutional law. The court was conscious of its position as Australia's new court of appeal, and made efforts to establish its authority at the top of Australia's court hierarchy. In "Deakin v Webb" (1904) It criticised the Victorian Supreme Court for following a Privy Council decision about the Constitution of Canada instead of its own authority.


title: High Court of Australia

text: In its early years Griffith and other federalists on the bench were dominant. Their decisions were occasionally at odds with nationalist judges such as Sir Isaac Isaacs and H. B. Higgins in 1906. With the death of Justice Richard O'Connor, in 1912; the nationalists achieved majority and Griffith's influence began to decline.


title: High Court of Australia

text: The early constitutional law decisions of the Griffith court was influenced by US Constitutional law.


title: High Court of Australia

text: An important doctrine peculiar to the Griffith court was that of the Reserved State powers. Under this doctrine, the Commonwealth parliament's legislative powers were to be interpreted narrowly; so as to avoid intruding on areas of power traditionally exercised by the State Parliaments prior to federation. Anthony Mason has noted that this doctrine doctrine probably helped smooth the transition to a federal system of government and "by preserving a balance between the constituent elements of the Australian federation, probably conformed to community sentiment, which at that stage was by no means adjusted to the exercise of central power."


title: High Court of Australia

text: Griffith and Sir Edmund Barton were frequently consulted by the States' governors-general, including on the exercise of the reserve powers.


title: High Court of Australia

text: Adrian Knox became Chief Justice on 18 October 1919. Justice Edmund Barton died soon after, leaving no original members. During the Knox Court, Justice Isaacs Isaacs had strong influence.


title: High Court of Australia

text: Under the Knox Court the Engineers case was decided, ending the Reserved State powers doctrine. The decision had lasting significance for the federal balance in Australia's political arrangements. Another significant decision was "Roche v Kronheimer", in which the court relied upon the defence power to uphold federal legislation seeking to implement Australia's obligations under the Treaty of Versailles.


title: High Court of Australia

text: Sir Isaac Isaacs was Chief Justice for only forty-two weeks; he left the court to be appointed Governor-General. He was ill for most of his term, and few significant cases were decided in this time.


title: High Court of Australia

text: Sir Frank Gavan Duffy was Chief Justice for four years from 1931; but he was already 78 when appointed to the position. He was not influential, and only participated in 40% of the cases during his tenure. For the most part he gave short judgements, or joined in the judgements of his colleagues. His frequent absence resulted in many tied decisions which have no lasting value as precedent.


title: High Court of Australia

text: John Latham was elevated to Chief Justice in 1935. His tenure is most notable for the court's interpretation of wartime legislation, and the subsequent transition back to peace.


title: High Court of Australia

text: Most legislation was upheld as enabled by the defence power. The Curtin Labor government's legislation was rarely successfully challenged, with the court recognizing a necessity that the defence power permit the federal government to govern strongly.


title: High Court of Australia

text: The court allowed for the establishment of a national income tax scheme in the "First Uniform Tax case", and upheld legislation declaring the pacifist Jehovah's Witnesses denomination to be a subversive organisation.


title: High Court of Australia

text: Following the war, the court reigned in the scope of the defence power. It struck down several key planks of the Chifley Labor government's reconstruction program, notably an attempt to nationalise the banks in the Bank Nationalisation case (1948), and an attempt to establish a comprehensive medical benefits scheme in the First Pharmaceutical Benefits case (1945).


title: High Court of Australia

text: During his tenure the court experienced what some have described as a 'Golden Age'. Dixon had strong influence on the court during this period. The court experienced a marked increase in the number of joint judgements, many of which were led by Dixon. The era has also been noted for the presence of generally good relations between the court's judges.


title: High Court of Australia

text: During Dixon's time, the court came to adopt in majority several of the views he had expressed in minority years prior.


title: High Court of Australia

text: Among other things, the Barwick court is known for controversially deciding several cases on tax avoidance and tax evasion, almost always deciding against the taxation office. Led by Barwick himself in most judgments, the court distinguished between avoidance (legitimately minimising one's tax obligations) and evasion (illegally evading obligations). The decisions effectively nullified the anti-avoidance legislation and led to the proliferation of avoidance schemes in the 1970s, a result which drew much criticism upon the court.


title: High Court of Australia

text: Among the Gibbs court's notable jurisprudence is an interpretive expansion of the Commonwealth's legislative powers. Scholars have also noted a tendency away from the traditions of legalism and conservatism that characterised the Dixon and Barwick courts.


title: High Court of Australia

text: The Mason court is known for being one of the most legally liberal benches of the court. It was a notably stable court, with the only change in its bench being the appointment of McHugh following Wilson's retirement.


title: High Court of Australia

text: Some of the decisions of the court in this time were politically controversial. Scholars have noted that the Mason court has tended to receive 'high praise and stringent criticism in equal measure'.


title: High Court of Australia

text: This era is also notable for originating Australia's implied freedom of political communication jurisprudence; through the cases "ACT v Cth" and "Theophanous".


title: High Court of Australia

text: Murray Gleeson was appointed Chief Justice in 1998. The Gleeson Court has been regarded as a relatively conservative period of the court's history.


title: High Court of Australia

text: Legal scholars have noted a shift in judicial style within the Kiefel court to one that attempts broad consensus. The frequency of dissenting judgements has decreased; and there have been relatively fewer decisions of a 4–3 split. Extrajudicially, Kiefel has expressed sympathy for judicial practices that maximise consensus and minimise dissent.


title: High Court of Australia

text: Additionally, it has been noted that Kiefel, Keane, and Bell frequently deliver a joint judgement when a unanimous consensus is not reached; often resulting in their decisions being determinative of the majority. This recent practice of the court has been criticized by the scholar Jeremy Gans, with comparisons drawn to the 'Four Horsemen' era of the US Supreme Court.


title: High Court of Australia

text: High Court Justices are appointed on the advice of the Prime Minister by the Governor-General in Council. The Prime Minister is typically assisted in this process by the Attorney-General for Australia.


title: High Court of Australia

text: Since 1979, it has been a requirement that State Governments have a consultative role in the appointment process. Some reformers have advocated for States having a determinative role.


title: High Court of Australia

text: The only constitutional requirement for a High Court justice is that they be under the compulsory retirement age of 70. However, the High Court of Australia Act requires that an appointee be a Judge of a federal, state or territory court; or have been an Australian legal practitioner for at least five years. The Australian Constitution does not prevent dual citizens from sitting as High Court judges.


title: High Court of Australia

text: The appointment process for Australian apex Justices is relatively uncontroversial and apolitical. Nevertheless, some appointments to the High Court display clear political influence. Three Justices had previously been conservative politicians prior to their promotion to Chief Justice; and Justices Evatt, McTiernan, and Murphy were all Labor party politicians at some stage in their careers prior to being elevated to the bench by a Labor prime minister.


title: High Court of Australia

text: The first High Court bench consisted of three justices; Samuel Griffith, Edmund Barton, and Richard O'Connor.


title: High Court of Australia

text: According to the contemporary press, among those considered and overlooked were Henry Higgins, Isaac Isaacs, Andrew Clark, John Downer, Josiah Symon, and George Wise.


title: High Court of Australia

text: Barton and O'Connor were both members of the federal parliament's government bench. Each appointee had participated in the drafting of Australia's constitution. All three have been described as relatively conservative justices for the time; and were strongly influenced in by United States law in their constitutional jurisprudence.


title: High Court of Australia

text: In 1906 at the request of the Justices, two seats were added to the bench; with Isaacs and Higgins being appointed.


title: High Court of Australia

text: After O'Connor's death in 1912, an amendment was made to the "Judiciary Act" expanding the bench to seven. However, these seats were left vacant for most of 1930.


title: High Court of Australia

text: Following Isaacs retirement in 1931, his seat was left empty and an amendment to the "Judiciary Act" reduced the number of seats to six. This however led to some decisions being split three-all.


title: High Court of Australia

text: With the appointment of Justice Webb in 1946, the court returned to seven seats; and since then the court has had a full bench of seven Justices.


title: High Court of Australia

text: The vast majority of the High Court's fifty-six appointees have been men. Seven women have been appointed in the court's history.


title: High Court of Australia

text: Michael Kirby was the first openly gay justice of the Court. He was replaced by Virginia Bell, who is the first person on the bench to identify as a lesbian.


title: High Court of Australia

text: Twenty-eight appointees have been residents of New South Wales, twenty-five of which graduated from Sydney Law School. Sixteen have come from Victoria, eight from Queensland, and four from Western Australia. No resident of South Australia, Tasmania, or any of the Territories has ever been appointed to the bench.


title: High Court of Australia

text: The majority of Justices have been of Protestant backgrounds, with a smaller number of a Catholic background. Two Jewish members have been appointed, Sir Isaac Isaacs and James Edelman, making them the only members of the court to have a faith background other than Christianity. However, many justices have refrained from commenting publicly upon their religious views.


title: High Court of Australia

text: Almost all judges on the High Court have "taken silk" in some form prior to their appointment, in the form of appointment to King's Counsel (KC), Queen's Counsel (QC) or Senior Counsel (SC). The exceptions are Starke, McTiernan, Webb, Walsh, Kirby, French, Edelman and Jagot.


title: High Court of Australia

text: While thirteen historical justices of the court have previously served in a Parliament; no parliamentarian has been appointed to the Court since Lionel Murphy in 1975.


title: High Court of Australia

text: Salaries are determined by the Remuneration Tribunal. The regular justices receive $551,880, while the Chief justice receives $608,150. High Court judicial compensation is constitutionally protected from decrease during appointment.