text:
Division by zero

In mathematics, division by zero, division where the divisor (denominator) is 0|zero, is a unique and problematic special case. Using fraction notation, the general example can be written as $$\tfrac a0$$, where $$a$$ is the dividend (numerator).

The usual definition of the quotient in elementary arithmetic is the number which yields the dividend when multiplied by the divisor. That is, $$c = \tfrac ab$$ is equivalent to $$c \cdot b = a.$$ By this definition, the quotient $$q = \tfrac{a}{0}$$ is nonsensical, as the product $$q \cdot 0$$ is always $$0$$ rather than some other number $$a.$$ Following the ordinary rules of elementary algebra while allowing division by zero can create a mathematical fallacy, a subtle mistake leading to absurd results. To prevent this, the arithmetic of real numbers and more general numerical structures called fields leaves division by zero undefined, and situations where division by zero might occur must be treated with care. Since any number multiplied by zero is zero, the expression $\tfrac{0}{0}$ is also undefined.

Calculus studies the behavior of functions in the limit as their input tends to some value. When a real function can be expressed as a fraction whose denominator tends to zero, the output of the function becomes arbitrarily large, and is said to "tend to infinity", a type of mathematical singularity. For example, the reciprocal function, $$f(x) = \tfrac 1x,$$ tends to infinity as $$x$$ tends to $$0.$$ When both the numerator and the denominator tend to zero at the same input, the expression is said to take an indeterminate form, as the resulting limit depends on the specific functions forming the fraction and cannot be determined from their separate limits.

As an alternative to the common convention of working with fields such as the real numbers and leaving division by zero undefined, it is possible to define the result of division by zero in other ways, resulting in different number systems. For example, the quotient $$\tfrac{a}{0}$$ can be defined to equal zero; it can be defined to equal a new explicit point at infinity, sometimes denoted by the infinity symbol $\infty$; or it can be defined to result in signed infinity, with positive or negative sign depending on the sign of the dividend. In these number systems division by zero is no longer a special exception per se, but the point or points at infinity involve their own new types of exceptional behavior.

In computing, an error may result from an attempt to divide by zero. Depending on the context and the type of number involved, dividing by zero may evaluate to positive or negative infinity, a special not-a-number value, zero, generate an exception, display an error message, or crash or hang the program.

The meaning of division
The division $$N/D = Q$$ can be conceptually interpreted in several ways.

In quotitive division, the dividend $$N$$ is imagined to be split up into parts of size $$D$$ (the divisor), and the quotient $$Q$$ is the number of resulting parts. For example, imagine ten slices of bread are to be made into sandwiches, each requiring two slices of bread. A total of five sandwiches can be made ($\tfrac{10}{2}=5$). Now imagine instead that zero slices of bread are required per sandwich (perhaps a lettuce wrap). Arbitrarily many such sandwiches can be made from ten slices of bread, as the bread is irrelevant.

The quotitive concept of division lends itself to calculation by repeated subtraction: dividing entails counting how many times the divisor can be subtracted before the dividend runs out. Because no finite number of subtractions of zero will ever exhaust a non-zero dividend, calculating division by zero in this way never terminates. Such an interminable division-by-zero algorithm is physically exhibited by some mechanical calculators.

In partitive division, the dividend $$N$$ is imagined to be split into $$D$$ parts, and the quotient $$Q$$ is the resulting size of each part. For example, imagine ten cookies are to be divided among two friends. Each friend will receive five cookies ($\tfrac{10}{2}=5$). Now imagine instead that the ten cookies are to be divided among zero friends. How many cookies will each friend receive? Since there are no friends, this is an absurdity.

In another interpretation, the quotient $$Q$$ represents the ratio $$N:D.$$ For example, a cake recipe might call for ten cups of flour and two cups of sugar, a ratio of $$10:2$$ or, proportionally, $$5:1.$$ To scale this recipe to larger or smaller quantities of cake, a ratio of flour to sugar proportional to $$5:1$$ could be maintained, for instance one cup of flour and one-fifth cup of sugar, or fifty cups of flour and ten cups of sugar. Now imagine a sugar-free cake recipe calls for ten cups of flour and zero cups of sugar. The ratio $$10:0,$$ or proportionally $$1:0,$$ is perfectly sensible: it just means that the cake has no sugar. However, the question "How many parts flour for each part sugar?" still has no meaningful numerical answer.

A geometrical appearance of the division-as-ratio interpretation is the slope of a straight line in the Cartesian plane. The slope is defined to be the "rise" (change in vertical coordinate) divided by the "run" (change in horizontal coordinate) along the line. When this is written using the symmetrical ratio notation, a horizontal line has slope $$0:1$$ and a vertical line has slope $$1:0.$$ However, if the slope is taken to be a single real number then a horizontal line has slope $$\tfrac01 = 0$$ while an vertical line has an undefined slope, since in real-number arithmetic the quotient $$\tfrac10$$ is undefined. The real-valued slope $$\tfrac{y}{x}$$ of a line through the origin is the vertical coordinate of the intersection between the line and a vertical line at horizontal coordinate $$1,$$ dashed black in the figure. The vertical red and dashed black lines are parallel, so they have no intersection in the plane. Sometimes they are said to intersect at a point at infinity, and the ratio $$1:0$$ is represented by a new number $\infty$; see below. Vertical lines are sometimes said to have an "infinitely steep" slope.

Inverse of multiplication
Division is the inverse of multiplication, meaning that multiplying and then dividing by the same non-zero quantity, or vice versa, leaves an original quantity unchanged; for example $$(5 \times 3) / 3 = {}$$$$(5 / 3) \times 3 = 5$$. Thus a division problem such as $$\tfrac{6}{3} = {?}$$ can be solved by rewriting it as an equivalent equation involving multiplication, $${?}\times 3 = 6,$$ where $${?}$$ represents the same unknown quantity, and then finding the value for which the statement is true; in this case the unknown quantity is $$2,$$ because $$2\times 3 = 6,$$ so therefore $$\tfrac63 = 2.$$

An analogous problem involving division by zero, $$\tfrac{6}{0} = {?},$$ requires determining an unknown quantity satisfying $${?}\times 0 = 6.$$ However, any number multiplied by zero is zero rather than six, so there exists no number which can substitute for $${?}$$ to make a true statement.

When the problem is changed to $$\tfrac{0}{0} = {?},$$ the equivalent multiplicative statement is ${?}\times 0 = 0$; in this case any value can be substituted for the unknown quantity to yield a true statement, so there is no single number which can be assigned as the quotient $$\tfrac{0}{0}.$$

Because of these difficulties, quotients where the divisor is zero are traditionally taken to be undefined, and division by zero is not allowed.

Fallacies
A compelling reason for not allowing division by zero is that allowing it leads to fallacies.

When working with numbers, it is easy to identify an illegal division by zero. For example:

 * From $$0\times 1 = 0$$ and $$0\times 2 = 0$$ one gets $$0\times 1 = 0\times 2.$$ Cancelling $y = 1⁄x$ from both sides yields $$1 = 2$$, a false statement.

The fallacy here arises from the assumption that it is legitimate to cancel $1 : 0$ like any other number, whereas, in fact, doing so is a form of division by $0$.

Using algebra, it is possible to disguise a division by zero to obtain an invalid proof. For example:

This is essentially the same fallacious computation as the previous numerical version, but the division by zero was obfuscated because we wrote $0$ as $0$.

Early attempts
The Brāhmasphuṭasiddhānta of Brahmagupta (c. 598–668) is the earliest text to treat zero as a number in its own right and to define operations involving zero. According to Brahmagupta,

"A positive or negative number when divided by zero is a fraction with the zero as denominator. Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. Zero divided by zero is zero."

In 830, Mahāvīra unsuccessfully tried to correct the mistake Brahmagupta made in his book Ganita Sara Samgraha: "A number remains unchanged when divided by zero."

Bhāskara II's Līlāvatī (12th century) proposed that division by zero results in an infinite quantity,

"A quantity divided by zero becomes a fraction the denominator of which is zero. This fraction is termed an infinite quantity. In this quantity consisting of that which has zero for its divisor, there is no alteration, though many may be inserted or extracted; as no change takes place in the infinite and immutable God when worlds are created or destroyed, though numerous orders of beings are absorbed or put forth."

Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to $\tfrac{a}{0}$ is contained in Anglo-Irish philosopher George Berkeley's criticism of infinitesimal calculus in 1734 in The Analyst ("ghosts of departed quantities").

Calculus
Calculus studies the behavior of functions using the concept of a limit, the value to which a function's output tends as its input tends to some specific value. The notation $ \lim_{x \to c} f(x) = L$ means that the value of the function $$f$$ can be made arbitrarily close to $$L$$ by choosing $$x$$ sufficiently close to $$c.$$

In the case where the limit of the real function $$f$$ increases without bound as $$x$$ tends to $$c,$$ the function is not defined at $$x,$$ a type of mathematical singularity. Instead, the function is said to "tend to infinity", denoted $ \lim_{x \to c} f(x) = \infty,$ and its graph has the line $$x=c$$ as a vertical asymptote. While such a function is not formally defined for $$x = c,$$ and the infinity symbol $$\infty$$ in this case does not represent any specific real number, such limits are informally said to "equal infinity". If the value of the function decreases without bound, the function is said to "tend to negative infinity", $$-\infty.$$ In some cases a function tends to two different values when $$x$$ tends to $$c$$ from above ($x \to c^+$) and below ($x \to c^-$); such a function has two distinct one-sided limits.

A basic example of an infinite singularity is the reciprocal function, $$f(x) = 1/x,$$ which tends to positive or negative infinity as $$x$$ tends to $0$:

$$ \lim_{x \to 0^+} \frac1x = +\infty,\qquad \lim_{x \to 0^-} \frac1x = -\infty. $$

In most cases, the limit of a quotient of functions is equal to the quotient of the limits of each function separately,

$$ \lim_{x \to c} \frac{f(x)}{g(x)} = \frac{\displaystyle \lim_{x \to c} f(x)}{\displaystyle \lim_{x \to c} g(x)}. $$

However, when a function is constructed by dividing two functions whose separate limits are both equal to $$0,$$ then the limit of the result cannot be determined from the separate limits, so is said to take an indeterminate form, informally written $$\tfrac00.$$ (Another indeterminate form, $$\tfrac \infty \infty,$$ results from dividing two functions whose limits both tend to infinity.) Such a limit may equal any real value, may tend to infinity, or may not converge at all, depending on the particular functions. For example, in

$$ \lim_{x \to 1} \dfrac{x^2 - 1}{x - 1},$$

the separate limits of the numerator and denominator are $$0$$, so we have the indeterminate form $$\tfrac00$$, but simplifying the quotient first shows that the limit exists:

$$ \lim_{x \to 1} \frac{x^2 - 1}{x - 1} = \lim_{x \to 1} \frac{(x - 1)(x + 1)}{x - 1} = \lim_{x \to 1} (x + 1) = 2. $$

Extended real line
The affinely extended real numbers are obtained from the real numbers $$\R$$ by adding two new numbers $$+\infty$$ and $$-\infty,$$ read as "positive infinity" and "negative infinity" respectively, and representing points at infinity. With the addition of $$\pm \infty,$$ the concept of a "limit at infinity" can be made to work like a finite limit. When dealing with both positive and negative extended real numbers, the expression $$1/0$$ is usually left undefined. However, in contexts where only non-negative values are considered, it is often convenient to define $$1/0 = +\infty$$.

Projectively extended real line
The set $$\mathbb{R}\cup\{\infty\}$$ is the projectively extended real line, which is a one-point compactification of the real line. Here $$\infty$$ means an unsigned infinity or point at infinity, an infinite quantity that is neither positive nor negative. This quantity satisfies $$-\infty = \infty$$, which is necessary in this context. In this structure, $$\frac{a}{0} = \infty$$ can be defined for nonzero $x = 1$, and $$\frac{a}{\infty} = 0$$ when $1$ is not $$\infty$$. It is the natural way to view the range of the tangent function and cotangent functions of trigonometry: $x − 1$ approaches the single point at infinity as $x = 1$ approaches either $0$ or $x − 1$ from either direction.

This definition leads to many interesting results. However, the resulting algebraic structure is not a field, and should not be expected to behave like one. For example, $$\infty+\infty$$ is undefined in this extension of the real line.

Riemann sphere
The subject of complex analysis applies the concepts of calculus in the complex numbers. Of major importance in this subject is the extended complex numbers $$\C \cup\{\infty\},$$ the set of complex numbers with a single additional number appended, usually denoted by the infinity symbol $$\infty$$ and representing a point at infinity, which is defined to be contained in every exterior domain, making those its topological neighborhoods.

This can intuitively be thought of as wrapping up the infinite edges of the complex plane and pinning them together at the single point $$\infty,$$ a one-point compactification, making the extended complex numbers topologically equivalent to a sphere. This equivalence can be extended to a metrical equivalence by mapping each complex number to a point on the sphere via inverse stereographic projection, with the resulting spherical distance applied as a new definition of distance between complex numbers; and in general the geometry of the sphere can be studied using complex arithmetic, and conversely complex arithmetic can be interpreted in terms of spherical geometry. As a consequence, the set of extended complex numbers is often called the Riemann sphere. The set is usually denoted by the symbol for the complex numbers decorated by an asterisk, overline, tilde, or circumflex, for example $$\hat\C = \C \cup\{\infty\}.$$

In the extended complex numbers, for any nonzero complex number $$z,$$ ordinary complex arithmetic is extended by the additional rules $$\tfrac{z}{0}=\infty,$$ $$\tfrac{z}{\infty} = 0,$$ $$\infty + 0 = \infty,$$ $$\infty + z = \infty,$$ $$\infty \cdot z = \infty.$$ However, $$\tfrac{0}{0}$$, $$\tfrac{\infty}{\infty}$$, and $$0\cdot\infty$$ are left undefined.

Higher mathematics
The four basic operations – addition, subtraction, multiplication and division – as applied to whole numbers (positive integers), with some restrictions, in elementary arithmetic are used as a framework to support the extension of the realm of numbers to which they apply. For instance, to make it possible to subtract any whole number from another, the realm of numbers must be expanded to the entire set of integers in order to incorporate the negative integers. Similarly, to support division of any integer by any other, the realm of numbers must expand to the rational numbers. During this gradual expansion of the number system, care is taken to ensure that the "extended operations", when applied to the older numbers, do not produce different results. Loosely speaking, since division by zero has no meaning (is undefined) in the whole number setting, this remains true as the setting expands to the real or even complex numbers.

As the realm of numbers to which these operations can be applied expands there are also changes in how the operations are viewed. For instance, in the realm of integers, subtraction is no longer considered a basic operation since it can be replaced by addition of signed numbers. Similarly, when the realm of numbers expands to include the rational numbers, division is replaced by multiplication by certain rational numbers. In keeping with this change of viewpoint, the question, "Why can't we divide by zero?", becomes "Why can't a rational number have a zero denominator?". Answering this revised question precisely requires close examination of the definition of rational numbers.

In the modern approach to constructing the field of real numbers, the rational numbers appear as an intermediate step in the development that is founded on set theory. First, the natural numbers (including zero) are established on an axiomatic basis such as Peano's axiom system and then this is expanded to the ring of integers. The next step is to define the rational numbers keeping in mind that this must be done using only the sets and operations that have already been established, namely, addition, multiplication and the integers. Starting with the set of ordered pairs of integers, $a$ with $a$, define a binary relation on this set by $tan(x)$ if and only if $x$. This relation is shown to be an equivalence relation and its equivalence classes are then defined to be the rational numbers. It is in the formal proof that this relation is an equivalence relation that the requirement that the second coordinate is not zero is needed (for verifying transitivity).

Although division by zero cannot be sensibly defined with real numbers and integers, it is possible to consistently define it, or similar operations, in other mathematical structures.

Non-standard analysis
In the hyperreal numbers, division by zero is still impossible, but division by non-zero infinitesimals is possible. The same holds true in the surreal numbers.

Distribution theory
In distribution theory one can extend the function $\frac{1}{x}$ to a distribution on the whole space of real numbers (in effect by using Cauchy principal values). It does not, however, make sense to ask for a "value" of this distribution at x = 0; a sophisticated answer refers to the singular support of the distribution.

Linear algebra
In matrix algebra, square or rectangular blocks of numbers are manipulated as though they were numbers themselves: matrices can be added and multiplied, and in some cases, a version of division also exists. Dividing by a matrix means, more precisely, multiplying by its inverse. Not all matrices have inverses. For example, a matrix containing only zeros is not invertible.

One can define a pseudo-division, by setting a/b = ab+, in which b+ represents the pseudoinverse of b. It can be proven that if b−1 exists, then b+ = b−1. If b equals 0, then b+ = 0.

Abstract algebra
In abstract algebra, the integers, the rational numbers, the real numbers, and the complex numbers can be abstracted to more general algebraic structures, such as a commutative ring, which is a mathematical structure where addition, subtraction, and multiplication behave as they do in the more familiar number systems, but division may not be defined. Adjoining a multiplicative inverses to a commutative ring is called localization. However, the localization of every commutative ring at zero is the trivial ring, where $$0 = 1$$, so nontrivial commutative rings do not have inverses at zero, and thus division by zero is undefined for nontrivial commutative rings.

Nevertheless, any number system that forms a commutative ring can be extended to a structure called a wheel in which division by zero is always possible. However, the resulting mathematical structure is no longer a commutative ring, as multiplication no longer distributes over addition. Furthermore, in a wheel, division of an element by itself no longer results in the multiplicative identity element $$1$$, and if the original system was an integral domain, the multiplication in the wheel no longer results in a cancellative semigroup.

The concepts applied to standard arithmetic are similar to those in more general algebraic structures, such as rings and fields. In a field, every nonzero element is invertible under multiplication; as above, division poses problems only when attempting to divide by zero. This is likewise true in a skew field (which for this reason is called a division ring). However, in other rings, division by nonzero elements may also pose problems. For example, the ring Z/6Z of integers mod 6. The meaning of the expression $\frac{2}{2}$ should be the solution x of the equation $$2x = 2$$. But in the ring Z/6Z, 2 is a zero divisor. This equation has two distinct solutions, $+π⁄2$ and $−π⁄2$, so the expression $\frac{2}{2}$ is undefined.

In field theory, the expression $\frac{a}{b}$ is only shorthand for the formal expression ab−1, where b−1 is the multiplicative inverse of b. Since the field axioms only guarantee the existence of such inverses for nonzero elements, this expression has no meaning when b is zero. Modern texts, that define fields as a special type of ring, include the axiom ${(a, b)}$ for fields (or its equivalent) so that the zero ring is excluded from being a field. In the zero ring, division by zero is possible, which shows that the other field axioms are not sufficient to exclude division by zero in a field.

Floating-point arithmetic
In computing, most numerical calculations are done with floating-point arithmetic, which since the 1980s has been standardized by the IEEE 754 specification. In IEEE floating-point arithmetic, numbers are represented using a sign (positive or negative), a fixed-precision significand and an integer exponent. Numbers whose exponent is too large to represent instead "overflow" to positive or negative infinity (+∞ or −∞), while numbers whose exponent is too small to represent instead "underflow" to positive or negative zero (+0 or −0). A NaN (not a number) value represents undefined results.

In IEEE arithmetic, division of 0/0 or ∞/∞ results in NaN, but otherwise division always produces a well-defined result. Dividing any non-zero number by positive zero (+0) results in an infinity of the same sign as the dividend. Dividing any non-zero number by negative zero (−0) results in an infinity of the opposite sign as the dividend. This definition preserves the sign of the result in case of arithmetic underflow.

For example, using single-precision IEEE arithmetic, if x = −2−149, then x/2 underflows to −0, and dividing 1 by this result produces 1/(x/2) = −∞. The exact result −2150 is too large to represent as a single-precision number, so an infinity of the same sign is used instead to indicate overflow.

Integer arithmetic

Integer division by zero is usually handled differently from floating point since there is no integer representation for the result. CPUs differ in behavior: for instance x86 processors trigger a hardware exception, while PowerPC processors silently generate an incorrect result for the division and continue. Because of this inconsistency between platforms, the C and C++ programming languages consider the result of dividing by zero undefined behavior. In typical higher-level programming languages, such as Python, an exception is raised for attempted division by zero, which can be handled in another part of the program.

In proof assistants
Many proof assistants, such as Coq and Lean, define 1/0 = 0. This is due to the requirement that all functions are total. Such a definition does not create contradictions, as further manipulations (such as cancelling out) still require that the divisor is non-zero.

Historical accidents

 * On September 21, 1997, a division by zero error in the "Remote Data Base Manager" aboard USS Yorktown (CG-48) brought down all the machines on the network, causing the ship's propulsion system to fail.

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Boyacá Department

Boyacá is one of the thirty-two departments of Colombia, and the remnant of Boyacá State, one of the original nine states of the "United States of Colombia".

Boyacá is centrally located within Colombia, almost entirely within the mountains of the Eastern Cordillera to the border with Venezuela, although the western end of the department extends to the Magdalena River at the town of Puerto Boyacá. Boyacá borders to the north with the Department of Santander, to the northeast with the Bolivarian Republic of Venezuela and Norte de Santander, to the east with the departments of Arauca and Casanare. To the south, Boyacá borders the department of Cundinamarca and to the west with the Department of Antioquia covering a total area of 23189 sqkm. The capital of Boyacá is the city of Tunja.

Boyacá is known as "The Land of Freedom" because this region was the scene of a series of battles which led to Colombia's independence from Spain. The first one took place on 25 July 1819 in the Pantano de Vargas and the final and decisive battle known as the Battle of Boyacá was fought on 7 August 1819 at Puente de Boyacá.

Boyacá is home to three universities: the Universidad Pedagógica y Tecnológica de Colombia (UPTC), the Universidad de Boyacá (UNIBOYACA), and the Saint Thomas Aquinas University.

Etymology
The word Boyacá derived from the Chibcha word "Bojacá" which means "Near the cacique", or "Region of the royal mantle".

History
The territory of present-day Boyaca was during the Pre-Columbian time the domain of the Muisca indigenous peoples. The Muisca under the chiefdom of the zaque of Hunza lived mainly by agriculture and mining gold and emeralds.

The first European to discover the area was the Spaniard Gonzalo Jiménez de Quesada who conquered the northern Muisca living in the area led by last zaque Aquiminzaque and distributed the land in encomiendas and forced the indigenous people to work for him.

In 1539, Gonzalo Suárez Rendón, a Spanish conquistador, founded the city of Tunja and other sites where the indigenous people previously had their villages. Tunja became one of the main political and economic centers for the Spanish during the Viceroyalty of New Granada.

During the 19th century, Boyacá was battleground for numerous confrontations between the royalist and patriot armies led by Simón Bolívar during the Spanish colonies' war of independence from Spain. Two of the most decisive battles were the Battle of Boyacá and the Battle of Vargas Swamp (1819) won by the patriot forces against the royalists. In 1824 Gran Colombia created the Boyacá Department (Gran Colombia).

After the creation of the Granadine Confederation by 1858 the territory of now Boyaca became the Sovereign State of Boyacá. It was later rearranged in territory and administration and renamed as "Department of Boyaca" after a series of civil wars like the Colombian Civil War (1860–1862) and the Thousand Days War that struggled over a centralist or federalist system and political instability that changed to many constitutions (such as the Constitution of 1886), Boyaca finally acquired its current definition as territory.

Geography

Boyacá is located in the Andean Region in central Colombia, over the Cordillera Oriental mountain range and covers a total area of 23,189 km2. It borders other Colombian departments as follows: to the north Santander and Norte de Santander, to the east Arauca and Casanare, to the south Cundinamarca and a small part of Meta, and to the west Antioquia and Caldas. It has a territorial dispute with Norte de Santander and Cundinamarca.

The department of Boyacá covers a small portion of the Middle Magdalena valley of the Magdalena River to the west, the Cordillera Oriental mountain range with altitudes of 5,380 m above sea level (Sierra Nevada del Cocuy with 25 snow peaks), flat highland plateaux, and another small portion of territory by the eastern Llanos plains. Among its most prominent geographical features are the Range of the Zorro, Serrania de las Quinchas and the Andean plateaus of Rusia, Guantivá, Pisba, Chontales and Rechiniga.

The Altiplano Cundiboyacense, shared with the department of Cundinamarca, is densely populated with numerous valleys. The southern part is the Bogotá savanna. Boyacá is subdivided into 123 municipalities.

Many rivers originate in Boyacá, the most important are the Chicamocha River and Arauca River and tributaries to other important rivers such as the Magdalena and Meta.

Boyacá also has numerous lakes which include Lake Tota, Lake Sochagota and Lake Fúquene, shared with the department of Cundinamarca, the artificial Chivor Reservoir and others.

National parks
El Cocuy and Pisba National Parks are located in the northeast of Boyacá. Pisba National Park is shared with the department of Arauca. The flora and fauna sanctuary of Lake Iguaque is situated in the centre of the department. The most beautiful páramo in the world, Ocetá Páramo, is in northeast Boyacá.

Climate
The central area of the highlands has two rainy seasons; the first between April and June, and a second between October and November with an average of 1000 mm of rainfall per year. The rest of the year is considered to be the dry seasons with intermittent rainfall.

Provinces and municipalities

There are 13 provinces and two special districts in the Boyacá Department, listed below with their 123 municipalities. The department also has 123 corregimientos, 185 police inspectorates and numerous towns and small villages spread throughout the territory.

Municipalities are also grouped into 45 notary circuits with 53 notaries public. One circuit main registry based in the capital of the department; Tunja and 13 other minor registries spread across the territory.

{|
 * valign="top" width="33%"|

Central

 * 1) Cómbita
 * 2) Cucaita
 * 3) Chíquiza
 * 4) Chivatá
 * 5) Motavita
 * 6) Oicatá
 * 7) Siachoque
 * 8) Samacá
 * 9) Sora
 * 10) Soracá
 * 11) Sotaquirá
 * 12) Toca
 * 13) Tunja
 * 14) Tuta
 * 15) Ventaquemada

Northern

 * 1) Boavita
 * 2) Covarachía
 * 3) La Uvita
 * 4) San Mateo
 * 5) Sativanorte
 * 6) Sativasur
 * 7) Soatá
 * 8) Susacón
 * 9) Tipacoque

Western

 * 1) Briceño
 * 2) Buenavista
 * 3) Caldas
 * 4) Chiquinquirá
 * 5) Coper
 * 6) La Victoria
 * 7) Maripí
 * 8) Muzo
 * 9) Otanche
 * 10) Pauna
 * 11) Quipama
 * 12) Saboyá
 * 13) San Miguel de Sema
 * 14) San Pablo de Borbur
 * 15) Tununguá

Eastern

 * 1) Almeida
 * 2) Chivor
 * 3) Guateque
 * 4) Guayatá
 * 5) La Capilla
 * 6) Somondoco
 * 7) Sutatenza
 * 8) Tenza
 * valign="top" width="33%"|

Gutiérrez

 * 1) Chiscas
 * 2) El Cocuy
 * 3) El Espino
 * 4) Guacamayas
 * 5) Güicán
 * 6) Panqueba

La Libertad

 * 1) Labranzagrande
 * 2) Pajarito
 * 3) Paya
 * 4) Pisba

Lengupá

 * 1) Berbeo
 * 2) Campohermoso
 * 3) Miraflores
 * 4) Páez
 * 5) San Eduardo
 * 6) Zetaquirá

Márquez

 * 1) Boyacá
 * 2) Ciénega
 * 3) Jenesano
 * 4) Nuevo Colón
 * 5) Ramiriquí
 * 6) Rondón
 * 7) Tibaná
 * 8) Turmequé
 * 9) Úmbita
 * 10) Viracachá

Neira

 * 1) Chinavita
 * 2) Garagoa
 * 3) Macanal
 * 4) Pachavita
 * 5) San Luis de Gaceno
 * 6) Santa María

Ricaurte

 * 1) Arcabuco
 * 2) Chitaraque
 * 3) Gachantivá
 * 4) Moniquirá
 * 5) Ráquira
 * 6) Sáchica
 * 7) San José de Pare
 * 8) Santa Sofía
 * 9) Santana
 * 10) Sutamarchán
 * 11) Tinjacá
 * 12) Togüí
 * 13) Villa de Leyva
 * valign="top" width="33%"|

Sugamuxi

 * 1) Aquitania
 * 2) Cuítiva
 * 3) Firavitoba
 * 4) Gámeza
 * 5) Iza
 * 6) Mongua
 * 7) Monguí
 * 8) Nobsa
 * 9) Pesca
 * 10) Sogamoso
 * 11) Tibasosa
 * 12) Tópaga
 * 13) Tota

Tundama

 * 1) Belén
 * 2) Busbanzá
 * 3) Cerinza
 * 4) Corrales
 * 5) Duitama
 * 6) Floresta
 * 7) Paipa
 * 8) Santa Rosa de Viterbo
 * 9) Tutazá

Valderrama

 * 1) Betéitiva
 * 2) Chita
 * 3) Jericó
 * 4) Paz de Río
 * 5) Socotá
 * 6) Socha
 * 7) Tasco

Frontier District

 * 1) Cubará

Special Handling Zone

 * 1) Puerto Boyacá
 * }

title: Boyacá Department


text:
X-1

X-1 may refer to:

Aircraft

 * Bell X-1, the first aircraft to exceed the speed of sound in controlled level flight

Automobiles

 * Lada X-1, a 1981 Soviet concept MPV
 * McLaren X-1, a 2012 British one-off sports car based on the 12C

Cycles

 * Sinclair X-1, an electrically assisted faired recumbent bicycle
 * Yamaha X-1, a commuter-style motorbike

Watercraft

 * X-1 Submarine, the United States Navy's only midget submarine

Technology

 * Xbox One, a video game console
 * a one-lane PCI Express slot

Arts, entertainment, and media

 * X Minus One, a 1950s American radio show
 * X-Men (film), the first film in the X-Men franchise
 * X-One, monthly magazine produced by Imagine Publishing

Other

 * x−1, the multiplicative inverse of x (another way to denote 1⁄x, one divided by x)
 * Cygnus X-1 and Scorpius X-1, two astronomical x-ray sources
 * M82 X-1, a candidate intermediate-mass black hole detected in January 2006

title: X-1


text:
Compression artifact

A compression artifact (or artefact) is a noticeable distortion of media (including images, audio, and video) caused by the application of lossy compression. Lossy data compression involves discarding some of the media's data so that it becomes small enough to be stored within the desired disk space or transmitted (streamed) within the available bandwidth (known as the data rate or bit rate). If the compressor cannot store enough data in the compressed version, the result is a loss of quality, or introduction of artifacts. The compression algorithm may not be intelligent enough to discriminate between distortions of little subjective importance and those objectionable to the user.

The most common digital compression artifacts are DCT blocks, caused by the discrete cosine transform (DCT) compression algorithm used in many digital media standards, such as JPEG, MP3, and MPEG video file formats. These compression artifacts appear when heavy compression is applied, and occur often in common digital media, such as DVDs, common computer file formats such as JPEG, MP3 and MPEG files, and some alternatives to the compact disc, such as Sony's MiniDisc format. Uncompressed media (such as on Laserdiscs, Audio CDs, and WAV files) or losslessly compressed media (such as FLAC or PNG) do not suffer from compression artifacts.

The minimization of perceivable artifacts is a key goal in implementing a lossy compression algorithm. However, artifacts are occasionally intentionally produced for artistic purposes, a style known as glitch art or datamoshing.

Technically speaking, a compression artifact is a particular class of data error that is usually the consequence of quantization in lossy data compression. Where transform coding is used, it typically assumes the form of one of the basis functions of the coder's transform space.

Images

When performing block-based discrete cosine transform (DCT) coding for quantization, as in JPEG-compressed images, several types of artifacts can appear.
 * Ringing
 * Contouring
 * Posterizing
 * Staircase noise (aliasing) along curving edges
 * Blockiness in "busy" regions (block boundary artifacts, sometimes called (macro)blocking, quilting, or checkerboarding)

Other lossy algorithms, which use pattern matching to deduplicate similar symbols, are prone to introducing hard to detect errors in printed text. For example, the numbers "6" and "8" may get replaced. This has been observed to happen with JBIG2 in certain photocopier machines.

Block boundary artifacts
At low bit rates, any lossy block-based coding scheme introduces visible artifacts in pixel blocks and at block boundaries. These boundaries can be transform block boundaries, prediction block boundaries, or both, and may coincide with macroblock boundaries. The term macroblocking is commonly used regardless of the artifact's cause. Other names include blocking, tiling, mosaicing, pixelating, quilting, and checkerboarding.

Block-artifacts are a result of the very principle of block transform coding. The transform (for example the discrete cosine transform) is applied to a block of pixels, and to achieve lossy compression, the transform coefficients of each block are quantized. The lower the bit rate, the more coarsely the coefficients are represented and the more coefficients are quantized to zero. Statistically, images have more low-frequency than high-frequency content, so it is the low-frequency content that remains after quantization, which results in blurry, low-resolution blocks. In the most extreme case only the DC-coefficient, that is the coefficient which represents the average color of a block, is retained, and the transform block is only a single color after reconstruction.

Because this quantization process is applied individually in each block, neighboring blocks quantize coefficients differently. This leads to discontinuities at the block boundaries. These are most visible in flat areas, where there is little detail to mask the effect.

Image artifact reduction
Various approaches have been proposed to reduce image compression effects, but to use standardized compression/decompression techniques and retain the benefits of compression (for instance, lower transmission and storage costs), many of these methods focus on "post-processing"—that is, processing images when received or viewed. No post-processing technique has been shown to improve image quality in all cases; consequently, none has garnered widespread acceptance, though some have been implemented and are in use in proprietary systems. Many photo editing programs, for instance, have proprietary JPEG artifact reduction algorithms built-in. Consumer equipment often calls this post-processing "MPEG Noise Reduction".

Boundary artifact in JPEG can be turned into more pleasing "grains" not unlike those in high ISO photographic films. Instead of just multiplying the quantized coefficients with the quantisation step $Q$ pertaining to the 2D-frequency, intelligent noise in the form of a random number in the interval $[-Q/2; Q/2]$ can be added to the dequantized coefficient. This method can be added as an integral part to JPEG decompressors working on the trillions of existing and future JPEG images. As such it is not a "post-processing" technique.

The ringing issue can be reduced at encode time by overshooting the DCT values, clamping the rings away.

Posterization generally only happens at low quality, when the DC values are given too little importance. Tuning the quantization table helps.

Video
When motion prediction is used, as in MPEG-1, MPEG-2 or MPEG-4, compression artifacts tend to remain on several generations of decompressed frames, and move with the optic flow of the image, leading to a peculiar effect, part way between a painting effect and "grime" that moves with objects in the scene.

Data errors in the compressed bit-stream, possibly due to transmission errors, can lead to errors similar to large quantization errors, or can disrupt the parsing of the data stream entirely for a short time, leading to "break-up" of the picture. Where gross errors have occurred in the bit-stream, decoders continue to apply updates to the damaged picture for a short interval, creating a "ghost image" effect, until receiving the next independently compressed frame. In MPEG picture coding, these are known as "I-frames", with the 'I' standing for "intra". Until the next I-frame arrives, the decoder can perform error concealment.

Motion compensation block boundary artifacts
Block boundary discontinuities can occur at edges of motion compensation prediction blocks. In motion compensated video compression, the current picture is predicted by shifting blocks (macroblocks, partitions, or prediction units) of pixels from previously decoded frames. If two neighboring blocks use different motion vectors, there will be a discontinuity at the edge between the blocks.

Mosquito noise
Video compression artifacts include cumulative results of compression of the comprising still images, for instance ringing or other edge busyness in successive still images appear in sequence as a shimmering blur of dots around edges, called mosquito noise, as they resemble mosquitoes swarming around the object. The so-called "mosquito noise" is caused by the block-based discrete cosine transform (DCT) compression algorithm used in most video coding standards, such as the MPEG formats.

Video artifact reduction
The artifacts at block boundaries can be reduced by applying a deblocking filter. As in still image coding, it is possible to apply a deblocking filter to the decoder output as post-processing.

In motion-predicted video coding with a closed prediction loop, the encoder uses the decoder output as the prediction reference from which future frames are predicted. To that end, the encoder conceptually integrates a decoder. If this "decoder" performs a deblocking, the deblocked picture is then used as a reference picture for motion compensation, which improves coding efficiency by preventing a propagation of block artifacts across frames. This is referred to as an in-loop deblocking filter. Standards which specify an in-loop deblocking filter include VC-1, H.263 Annex J, H.264/AVC, and H.265/HEVC.

Audio
Lossy audio compression typically works with a psychoacoustic model—a model of human hearing perception. Lossy audio formats typically involve the use of a time/frequency domain transform, such as a modified discrete cosine transform. With the psychoacoustic model, masking effects such as frequency masking and temporal masking are exploited, so that sounds that should be imperceptible are not recorded. For example, in general, human beings are unable to perceive a quiet tone played simultaneously with a similar but louder tone. A lossy compression technique might identify this quiet tone and attempt to remove it. Also, quantization noise can be "hidden" where they would be masked by more prominent sounds. With low compression, a conservative psy-model is used with small block sizes.

When the psychoacoustic model is inaccurate, when the transform block size is restrained, or when aggressive compression is used, this may result in compression artifacts. Compression artifacts in compressed audio typically show up as ringing, pre-echo, "birdie artifacts", drop-outs, rattling, warbling, metallic ringing, an underwater feeling, hissing, or "graininess".

An example of compression artifacts in audio is applause in a relatively highly compressed audio file (e.g. 96 kbit/sec MP3). In general, musical tones have repeating waveforms and more predictable variations in volume, whereas applause is essentially random, therefore hard to compress. A highly compressed track of applause may have "metallic ringing" and other compression artifacts.

Artistic use
Compression artifacts may intentionally be used as a visual style, sometimes known as glitch art. Rosa Menkman's glitch art makes use of compression artifacts, particularly the discrete cosine transform blocks (DCT blocks) found in most digital media data compression formats such as JPEG digital images and MP3 digital audio. In still images, an example is Jpegs by German photographer Thomas Ruff, which uses intentional JPEG artifacts as the basis of the picture's style.

In video art, one technique used is datamoshing, where two videos are interleaved so intermediate frames are interpolated from two separate sources. Another technique involves simply transcoding from one lossy video format to another, which exploits the difference in how the separate video codecs process motion and color information. The technique was pioneered by artists Bertrand Planes in collaboration with Christian Jacquemin in 2006 with DivXPrime, Sven König, Takeshi Murata, Jacques Perconte and Paul B. Davis in collaboration with Paperrad, and more recently used by David OReilly and within music videos for Chairlift and by Nabil Elderkin in the "Welcome to Heartbreak" music video for Kanye West.

There is also a genre of internet memes where often nonsensical images are purposefully heavily compressed sometimes multiple times for comedic effect. Images created using this technique are often referred to as "deep fried."

title: Compression artifact


text:
Talk:Compression artifact

English dialects
For those searching using British spelling: Compression artefact. —Preceding unsigned comment added by 217.24.129.50 (talk • contribs)
 * Note that a redirect from the alternative spelling was added just minutes before the comment above was made. - dcljr (talk) 07:45, 17 February 2007 (UTC)

Audio section
Hi, the audio section looks a bit unprofessional; it seems to be a partial revert of a deletion I made a while back. I think it needs to be rewritten to become more precise and accurate. --Kjoonlee 03:37, 13 October 2006 (UTC)

Saying "aggressive" in the leading sentence sounds a bit NPOV, does it? - 88.73.236.209 00:50, 19 January 2007 (UTC)

Perhaps a mention should be made to the file size of audio files and the relation to kbs.--71.182.74.210 (talk) 23:51, 9 March 2009 (UTC)

Unclear
In its discussion of picture encoding, the article states:
 * Where predictive coding of motion pictures is used, as in MPEG-1, compression artifacts tend to remain on several generations of decompressed frames, leading to a "painting" effect being seen, as if the picture were being painted by an unseen artist's paint-brush.
 * Where motion prediction is used, as in MPEG-2 or MPEG-4, compression artifacts tend to move with the optic flow of the image, leading to a peculiar effect, part way between a painting effect and "grime" that moves with objects in the scene.

So, am I to understand that "predictive coding of motion pictures" and "motion prediction" are two different things? This should probably be explained a bit further. A quick glance through the linked articles didn't help. - dcljr (talk) 07:45, 17 February 2007 (UTC)

Yes, simple "predictive coding" of motion pictures and "motion prediction coding" of motion pictures are two slightly different things.

Simple "predictive coding" uses the last image to predict the next image, only painting the pixels that change, sending the new pixel colors. The "motion prediction coding" technique builds on top of it. It also paints only the pixels that change, but rather than sending the actual new pixel colors, it sends a message describing the "motion" of a block of pixels from the last image.

Say you have a movie that has scene with a white truck slowly moving left in front of a landscape.

If you transmit it using simple "predictive coding", and someone loses the signal in the middle of previous scene, then regains the signal in the middle of the picket fence scene, that person will see the white (at the leading edge of the truck) and the various landscape colors (at the trailing edge of the truck) slowly paint over the previous scene.

If you transmit it using "motion prediction", it will compress much smaller, but that person will see a truck-shaped cutout of the previous scene slowly moving left.

Please update the article to clarify the unclear parts. --76.209.28.72 21:02, 22 June 2007 (UTC)

Merge
I think JPEG artifacts should be merged into this article, as they are both practically the same thing, and this article is longer. -- AAA!  ( AAAA ) 07:45, 16 March 2007 (UTC)

A 42 kB thumbnail
The original image thumbnail is actually 7.95 kB now (I guess wikimedia's thumbnail generation has changed). That's smaller than the poor quality version below it, so can't really correct the size without making things confusing. —Preceding unsigned comment added by AbleRiver (talk • contribs) 16:11, 31 August 2007 (UTC)

Merger proposal (Datamoshing)
"Datamoshing" is a neologism (link to policy) for the purposeful manipulation of compression artifacts. The article is extremely short, and there are no real reliable sources that sup[port having a separate article. I suggest it be merged as a section here, until which time (if ever) it gains enough notability to be a stand alone article.--Cerejota (talk) 06:35, 2 March 2009 (UTC) (please use the appropriate section)
 * I support the merge proposal. I disagree with the characterization of the sources - the MTV link is detailed and from a respectable music journalism source. (I've removed the divisive merge-vote-heading-structure, as I don't anticipate this being a lengthy discussion/problem.) -- Quiddity (talk) 18:15, 2 March 2009 (UTC)
 * Support - Pointillist (talk) 15:13, 17 March 2009 (UTC)
 * 'Support - I support this as well because it is only a fad and will not be remembered. —Preceding unsigned comment added by 166.77.6.4 (talk) 21:59, 21 April 2009 (UTC)

Missing audio example
The last paragraph of the "Compression artifacts in audio coding" section appears to be missing the example.

"This highly compressed track of applause will illustrate the "metallic ringing" and other compression artifacts very well." —Preceding unsigned comment added by 151.151.73.168 (talk) 12:21, 5 May 2009 (UTC)

This image shows...
''This image shows the (accentuated) difference between a JPEG image and the original. Note especially the changes apparent on sharp edges.''

Excuse me. What original? — Preceding unsigned comment added by 98.204.138.111 (talk • contribs) 19:28, 26 April 2010
 * Indeed, the image was deleted last year. But even more absurd is that "the original" is linked to a JPEG file, which cannot possibly be the original - unless it's either a Lossless JPEG (which would be foolish as not many browsers support this) or a PNG file that nonetheless has been given a .jpg extension.
 * I think we need a new example. But what would be a good image to use that we have in a lossless format in the first place?  (OK, so scaling down a high-res JPEG to a size at which its artefacts become irrelevant and then saving that as a PNG would be another possibility.)  FWIW I've just made some JPEG artefact images of File:Lenna.png but not uploaded them yet.  I'm not sure what the right licensing label is for a derivative work of a fair use image.  But one of us could still create an image to use for this, thereby avoiding this issue. — Smjg (talk) 16:21, 25 April 2011 (UTC)

Merge of content from Macroblock
The Macroblock article used to include a section on generic block-coding artifacts, probably because "Macroblocking" is commonly used to refer to any and all block-coding artifacts. I have now integrated the content into this article. See also the discussion on the corresponding talk page Talk:Macroblock. Conquerist (talk) 20:36, 5 February 2014 (UTC)

Does color dithering count?

 * Dither
 * Floyd–Steinberg dithering

Does a GIF (animated or not) with dithering have a type of compression artifact? NoToleranceForIntolerance (talk) 22:42, 7 July 2016 (UTC)

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title: Talk:Compression artifact


text: User:Synthetik/Scratch/Prefectures of Japan


text:
Hans Florine

Hans Florine (born June 18, 1964) is an American rock climber, who holds the record for the number of ascents of Yosemite Valley's El Capitan and is known for holding the speed record on The Nose of Yosemite’s El Capitan 8 different times. Hans' last speed record on The Nose was accomplished with Alex Honnold for climbing The Nose in 2:23:46 (2 hours, 23 minutes and 46 seconds), on June 17, 2012. In addition to climbing El Capitan over 175 times, Hans also holds the record for the number of ascents of The Nose, climbing it more than 111 times.

El Capitan is traditionally climbed in three to five days. The Nose route is 2900 ft and features 31 pitches of strenuous, exposed climbing. This translates to a rate of roughly 5 minutes per pitch.

Florine is well regarded in the climbing community, and pioneered many of the methods currently used in speed climbing.

Climbing career
Florine started climbing as a teenager in 1983, and began competing in bouldering and speed competitions by 1986 at a time when competition climbing was not popular. He found that by speed climbing in competitions he was able to earn some gear and a tiny bit of money to fund his climbing, and by climbing quickly he could simply get more climbing in.

In 1990 Hans Teamed up with Steve Schneider to Climb The Nose route in a record 8 hours and 6 minutes. Approximately one week later Dave Schultz and Peter Croft climbed The Nose in 6 hours and 40 minutes. The following Year, 1991, Hans teamed up with Andres Puhvel and they climbed The Nose in 6:01. Approximately one week later Schultz and Croft climbed The Nose in 4:48. The following year Hans met Peter Croft at a slide show and suggested they climb The Nose together, and so they did.

Hans broke The Nose speed record with Yuji Hirayama in 2002, with a time of 2:48:55. This was bested by German brothers Alexander Huber and Thomas Huber in 2007, however, Florine and Hirayama regained the record with a time of 2:43:33 just six months later. They improved again to set a time of 2:37:05 (2 hours, 37 minutes and 5 seconds), on October 12, 2008.

On July 30, 2005, Florine also completed a solo ascent of The Nose in just 11 hours and 41 minutes. Solo ascents are characterized by climbing by yourself while using a rope for protection, and require one person to do all the work.

In 2018 he broke both his legs during a training run up The Nose after a piece of protection popped out of a crack. He and his partner Abraham Shreve were rescued by Yosemite Search and Rescue the next day.

Race against Pedro Hoffmeister
On May 18, 2019, Florine and Pete "Pedro" Hoffmeister raced in a NIAD ("Nose In A Day" - 3000 feet of rock climbing in one day). The race was titled "Super Local vs. Super Pro," and took place at The Columns, Skinner's Butte Park, in Eugene, Oregon. Both climbers were coming back from devastating injuries. Hoffmeister had the advantage of knowing all of the routes. Florine did not know the routes. Hoffmeister won the race, climbing 3000 feet, 64 routes, in 2:05:55. Florine clocked 2:27:05.

Notable ascents

 * The Nose of El Capitan: Former speed record with Steve Schneider, 1990. Time: 8:06
 * The Nose of El Capitan: Former speed record with Andres Puhvel, 1991. Time: 6:01
 * The Nose of El Capitan: Former speed record with Peter Croft, 1992. Time: 4:22
 * The Nose of El Capitan: Former speed record with Jim Herson, 2001. Time: 3:57:27
 * The Nose of El Capitan: Former speed record with Yuji Hirayama, 2002. Time: 2:48:55
 * The Nose of El Capitan: Former speed record with Yuji Hirayama, July 2, 2008. Time: 2:43:33
 * The Nose of El Capitan: Former speed record with Yuji Hirayama, October 12, 2008. Time: 2:37:05
 * The Nose of El Capitan: Former speed record with Alex Honnold, June 17, 2012. Time: 2:23:46 or 2:23:51

Competition Climbing
Florine has been climbing competitively since 1987. He has won 3 gold medals in X-Game speed climbing, in 1995, 1996 and 1997. He also won the US National championships at City Rock in Emeryville CA in 1990. He won two other national events in difficulty climbing, as well as 12 national titles in speed climbing. Hans won the first ever World Championships in Speed Climbing in Frankfurt Germany in 1991.

From 1991 until 1995 Hans was the Executive Director of The American Sport Climbing Federation. (ASCF) the ASCF was formed from a committee that was part of the American Alpine Club. Hans, along with Randy Hart organized and supported the first US Junior National Competition. The off shoot from that was the formation of the Junior Competitive Climbing Association, JCCA, which later eclipsed the ASCF, and effectively adopted it back in to form what later became https://usaclimbing.org/

Books

 * Climb On! Skills for More Efficient Climbing (How To Climb Series), Hans Florine with Bill Wright, Falcon Guides, 2001
 * Speed Climbing!, 2nd: How to Climb Faster and Better (How To Climb Series), Hans Florine with Bill Wright, Falcon Guides, 2004
 * On the Nose: A Lifelong Obsession with Yosemite’s Most Iconic Climb, Hans Florine with Jayme Moye, Falcon Guides, 2016

title: Hans Florine


text:
User:G~enwiki

Wikipedia newbie, so please be nice to me. You can see my own website at www.garethshouse.net.

Please ignore the following
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title: User:G~enwiki


text:
Magnificat

The Magnificat (Latin for "[My soul] magnifies [the Lord]") is a canticle, also known as the Song of Mary, the Canticle of Mary and, in the Byzantine tradition, the Ode of the Theotokos (Ἡ ᾨδὴ τῆς Θεοτόκου). It is traditionally incorporated into the liturgical services of the Catholic Church, the Eastern Orthodox Church, Lutheran Churches and the Anglican Communion. Its name comes from the incipit of the Latin version of the text.

The text of the canticle is taken from the Gospel of Luke where it is spoken by Mary upon the occasion of her Visitation to her cousin Elizabeth. In the narrative, after Mary greets Elizabeth, who is pregnant with John the Baptist, the latter moves within Elizabeth's womb. Elizabeth praises Mary for her faith (using words partially reflected in the Hail Mary), and Mary responds with what is now known as the Magnificat. Some ancient authorities have Elizabeth, rather than Mary, speaking the Magnificat.

The Magnificat is one of the eight most ancient Christian hymns and perhaps the earliest Marian hymn. Within the whole of Christianity, the canticle is most frequently recited within the Liturgy of the Hours. In Western Christianity, the Magnificat is most often sung or recited during the main evening prayer service: Vespers in the Catholic and Lutheran churches, and Evening Prayer (or Evensong) in Anglicanism. The traditional form is found the Book of Common Prayer (1662) and in Common Worship, as well as the Book of Common Prayer (1928) and Book of Common Prayer (1979) of the Episcopal Church (United States). In Eastern Christianity, the Magnificat is always sung at Matins. The Magnificat may also be sung during worship services, especially in the Advent season during which these verses are traditionally read.

Context
Mary's Magnificat, recorded only in Luke's Gospel, is one of four hymns, distilled from a collection of early Jewish-Christian canticles, which complement the promise-fulfillment theme of Luke's infancy narrative. These songs are Mary's Magnificat; Zechariah's Benedictus (1:67–79); the angels' Gloria in Excelsis Deo (2:13–14); and Simeon's Nunc dimittis (2:28–32). In form and content, these four canticles are patterned on the "hymns of praise" in Israel's Psalter. In structure, these songs reflect the compositions of pre-Christian contemporary Jewish hymnology. The first stanza displays graphically a characteristic feature of Hebrew poetry—synonymous parallelism—in ascribing praise to God: "my soul" mirrors "my spirit"; "proclaims the greatness" with "has found gladness"; "of the Lord" with "in God my Savior." The balance of the opening two lines bursts out into a dual Magnificat of declaring the greatness of and finding delight in God. The third stanza again demonstrates parallelism, but in this instance, three contrasting parallels: the proud are reversed by the low estate, the mighty by those of low degree, and the rich by the hungry.

Although there is some scholarly discussion of whether the historical Mary herself actually proclaimed this canticle, Luke portrays her as the singer of this song of reversals and the interpreter of the contemporary events taking place. Mary symbolizes both ancient Israel and the Lucan faith-community as the author/singer of the Magnificat.

The canticle echoes several biblical passages, but the most pronounced allusions are to the Song of Hannah, from the Books of Samuel. Scriptural echoes from the Torah, the Prophets, and the Writings complement the main allusions to Hannah's "magnificat of rejoicing". Along with the Benedictus, as well as several Old Testament canticles, the Magnificat is included in the Book of Odes, an ancient liturgical collection found in some manuscripts of the Septuagint.

As with other canticles and psalms, Western liturgical tradition usually adds the doxology known as Gloria Patri to the end of the Magnificat. This is not found in the original text.

Structure
In a style reminiscent of Old Testament poetry and song, Mary praises the Lord in alignment with this structure:

 * 1) Mary rejoices that she has the privilege of giving birth to the promised Messiah.
 * 2) She glorifies God for His power, holiness, and mercy.
 * 3) Mary looks forward to God transforming the world through the Messiah. The proud will be brought low, and the humble will be lifted up; the hungry will be fed, and the rich will go without.
 * 4) Mary exalts God because He has been faithful to His promise to Abraham (see God's promise to Abraham in ).

Catholic translation
Traditional
 * My soul doth magnify the Lord,
 * And my spirit hath rejoiced in God my Saviour
 * Because He hath regarded the humility of his handmaid: for behold from henceforth all generations shall call me blessed.
 * Because He that is mighty hath done great things to me, and holy is His name.
 * And His mercy is from generation unto generations to them that fear Him.
 * He hath shewed might in His arm: He hath scattered the proud in the conceit of their heart.
 * He hath put down the mighty from their seat, and hath exalted the humble.
 * He hath filled the hungry with good things, and the rich He hath sent empty away.
 * He hath received Israel His servant, being mindful of His mercy.
 * As He spoke to our fathers; to Abraham and his seed forever.

 * Glory be to the Father, and to the Son, and to the Holy Ghost,
 * As it was in the beginning is now, and ever shall be, world without end. Amen.

Modern
 * My soul proclaims the greatness of the Lord,
 * my spirit rejoices in God my Savior,
 * for He has looked with favor on His humble servant.

 * From this day all generations will call me blessed,
 * the Almighty has done great things for me,
 * and holy is His Name.

 * He has mercy on those who fear Him
 * in every generation.

 * He has shown the strength of his arm,
 * He has scattered the proud in their conceit.

 * He has cast down the mighty from their thrones,
 * and has lifted up the humble.

 * He has filled the hungry with good things,
 * and the rich He has sent away empty.

 * He has come to the help of His servant Israel
 * for He has remembered his promise of mercy,
 * the promise He made to our fathers,
 * to Abraham and his children for ever.

 * Glory to the Father, and to the Son, and to the Holy Spirit,
 * as it was in the beginning, is now, and will be for ever.
 * Amen, Alleluia.

Greek
The oldest (likely original) version of the Magnificat was written in Koine Greek.

 * Μεγαλύνει ἡ ψυχή μου τὸν Κύριον καὶ ἠγαλλίασεν τὸ πνεῦμά μου ἐπὶ τῷ Θεῷ τῷ σωτῆρί μου,
 * ὅτι ἐπέβλεψεν ἐπὶ τὴν ταπείνωσιν τῆς δούλης αὐτοῦ. ἰδοὺ γὰρ ἀπὸ τοῦ νῦν μακαριοῦσίν με πᾶσαι αἱ γενεαί,
 * ὅτι ἐποίησέν μοι μεγάλα ὁ δυνατός, καὶ ἅγιον τὸ ὄνομα αὐτοῦ, καὶ τὸ ἔλεος αὐτοῦ εἰς γενεὰς καὶ γενεὰς τοῖς φοβουμένοις αὐτόν.
 * Ἐποίησεν κράτος ἐν βραχίονι αὐτοῦ, διεσκόρπισεν ὑπερηφάνους διανοίᾳ καρδίας αὐτῶν·
 * καθεῖλεν δυνάστας ἀπὸ θρόνων καὶ ὕψωσεν ταπεινούς, πεινῶντας ἐνέπλησεν ἀγαθῶν καὶ πλουτοῦντας ἐξαπέστειλεν κενούς.
 * ἀντελάβετο Ἰσραὴλ παιδὸς αὐτοῦ, μνησθῆναι ἐλέους, καθὼς ἐλάλησεν πρὸς τοὺς πατέρας ἡμῶν τῷ Αβραὰμ καὶ τῷ σπέρματι αὐτοῦ εἰς τὸν αἰῶνα.

In Eastern Orthodox worship, the Ode of the Theotokos is accompanied by the following refrain sung between the verses (a sticheron) and a megalynarion, which is the second part of the Axion Estin hymn:
 * Τὴν τιμιωτέραν τῶν Χερουβὶμ καὶ ἐνδοξοτέραν ἀσυγκρίτως τῶν Σεραφίμ, τὴν ἀδιαφθόρως Θεὸν Λόγον τεκοῦσαν, τὴν ὄντως Θεοτόκον, σὲ μεγαλύνομεν.
 * ('You who are more to be honoured than the Cherubim and incomparably more glorious than the Seraphim, you who, uncorrupted, gave birth to God the Word, in reality the God-bearer, we exalt you.')

Amharic

In the Oriental Orthodox Church Scripture of Ethiopia according to the Ye' Luqas Wongel, Gospel of Luqas (Luke):

46፤ ማርያምም እንዲህ አለች።

47፤ ነፍሴ ጌታን ታከብረዋለች፥ መንፈሴም በአምላኬ በመድኃኒቴ ሐሴት ታደርጋለች፤

48፤ የባሪያይቱን ውርደት ተመልክቶአልና። እነሆም፥ ከዛሬ ጀምሮ ትውልድ ሁሉ ብፅዕት ይሉኛል፤

49፤ ብርቱ የሆነ እርሱ በእኔ ታላቅ ሥራ አድርጎአልና፤ ስሙም ቅዱስ ነው።

50፤ ምሕረቱም ለሚፈሩት እስከ ትውልድና ትውልድ ይኖራል።

51፤ በክንዱ ኃይል አድርጎአል፤ ትዕቢተኞችን በልባቸው አሳብ በትኖአል፤

52፤ ገዥዎችን ከዙፋናቸው አዋርዶአል፤ ትሑታንንም ከፍ አድርጎአል፤

53፤ የተራቡትን በበጎ ነገር አጥግቦአል፤ ባለ ጠጎችንም ባዶአቸውን ሰዶአቸዋል።

54-55፤ ለአባቶቻችን እንደ ተናገረ፥ ለአብርሃምና ለዘሩ ለዘላለም ምሕረቱ ትዝ እያለው እስራኤልን ብላቴናውን ረድቶአል።

Slavonic
The translation of the hymn into Church Slavonic is as follows:

Liturgical use

The text forms a part of the daily office in the Catholic Vespers service, the Lutheran Vespers service, and the Anglican services of Evening Prayer, according to both the Book of Common Prayer and Common Worship. In the Book of Common Prayer Evening Prayer service, it is usually paired with the Nunc dimittis. The Book of Common Prayer allows for an alternative to the Magnificat—the Cantate Domino, Psalm 98—and some Anglican rubrics allow for a wider selection of canticles, but the Magnificat and Nunc dimittis remain the most popular. In Anglican, Lutheran, and Catholic services, the Magnificat is generally followed by the Gloria Patri. It is also commonly used among Lutherans at the Feast of the Visitation (July 2).

In Eastern Orthodox liturgical practice, the Magnificat is always sung during the Matins service before the Irmos of the ninth ode of the canon (except on greater feasts of the Lord or the Theotokos, where the magnificat is excluded completely). After each biblical verse, i.e. as a sticheron, the following megalynarion or troparion is sung:

"More honourable than the Cherubim, and more glorious beyond compare than the Seraphim, without corruption thou gavest birth to God the Word: true Theotokos, we magnify thee."

As a canticle, the Magnificat has frequently been set to music. Most compositions were originally intended for liturgical use, especially for Vesper services and celebrations of the Visitation, but some are also performed in concert.

Indulgence
In the Catholic Church, the Enchiridion Indulgentiarum of 2004 provides for partial indulgence.

Musical settings
As the Magnificat is part of the sung Vespers, many composers, beginning in the Renaissance, set the words to music, for example Claudio Monteverdi in his Vespro della Beata Vergine (1610). Henry Dumont, André Campra (1713), Antoine-Esprit Blanchard (1741), Marc-Antoine Charpentier, 10 settings (H.72, H.73, H.74, H.75, H.76, H.77, H.78, H.79, H.80, H.81), François Giroust (12 settings), Vivaldi composed a setting of the Latin text for soloists, choir, and orchestra, as did Johann Sebastian Bach in his Magnificat (1723, rev. 1733). Other notable examples include C.P.E. Bach's Magnificat and two extant settings by Jan Dismas Zelenka (ZWV 106 is missing).

Anton Bruckner composed a Magnificat for soloists, choir, orchestra, and organ. Rachmaninoff and, more recently, John Rutter also composed a setting, inserting additions into the text.

Dieter Schnebel wrote a Magnificat in 1996/97 for small choir (schola), percussion and additional instruments ad libitum. Arvo Pärt composed a setting for choir a cappella. Kim André Arnesen's Magnificat for choir, strings, piano, and organ premiered in 2010. The Taizé Community have also composed an ostinato setting of the text.

Together with the Nunc dimittis, the Magnificat is a regular part of the Anglican Evensong. The "Mag and Nunc" has been set by many composers – such as Thomas Tallis, Ralph Vaughan Williams, Herbert Sumsion, Charles Wood and John Tavener – of Anglican church music, often for choir a cappella or choir and organ. Since the canticles are sung every day at some cathedrals, Charles Villiers Stanford wrote a Magnificat in every major key, and Herbert Howells published 18 settings over his career, including the Collegium Regale setting and the Magnificat and Nunc dimittis for St Paul's Cathedral.

An Eastern Orthodox setting of the Magnificat (text in Latin and English) is to be found in the 2011 All-night Vigil (Section 11) by the English composer Clive Strutt.

Maria Luise Thurmair wrote in 1954 the lyrics for a popular German ecumenical hymn based on the Magnificat, "Den Herren will ich loben", set to a 1613 melody by Melchior Teschner (that of Valet will ich dir geben). Timothy Dudley-Smith wrote "Tell Out, My Soul", a popular paraphrase of the Magnificat, in 1962. Krzysztof Penderecki composed an extended Magnificat for the 1200th anniversary of the Salzburg Cathedral in 1974, for bass soloist, men's and boys' voices, two mixed choirs and orchestra.

The oratorio Laudato si' composed in 2016 by Peter Reulein on a libretto by Helmut Schlegel includes the full Latin text of the Magnificat, expanded by writings of Clare of Assisi, Francis of Assisi and Pope Francis.

Society and politics
In Nicaragua, the Magnificat is a favorite prayer among many peasants and is often carried as a sacramental. During the Somoza years, campesinos were required to carry proof of having voted for Somoza; this document was mockingly referred to as a Magnificat.

title: Magnificat


text:
Galleon

Galleons were large, multi-decked sailing ships developed in Spain  and first used as armed cargo carriers by Europeans from the 16th to 18th centuries during the Age of Sail and were the principal vessels drafted for use as warships until the Anglo-Dutch Wars of the mid-1600s. Galleons generally carried three or more masts with a lateen fore-and-aft rig on the rear masts, were carvel built with a prominent squared off raised stern, and used square-rigged sail plans on their fore-mast and main-masts.

Such ships were the mainstay of maritime commerce into the early 19th century, and were often drafted into use as auxiliary naval war vessels—indeed, were the mainstay of contending fleets through most of the 150 years of the Age of Exploration—before the Anglo-Dutch wars brought purpose-built ship-rigged warships, ships of the line, that thereafter dominated war at sea during the remainder of the Age of Sail.

Etymology
The word galleon, "large ship", comes from Spanish galeón, "galleon", "armed merchant ship" or from Old French galion, "armed ship of burden" from Medieval Greek galea, "galley", to which the French or Spanish augmentative suffix -on is added. Another possible origin is the Old French word galie, "galley"; also from Medieval Greek galea. The galea was a warship of the Byzantine navy, and its name may be related to the Greek word galeos, "dogfish shark". The term was originally given to certain types of war galleys in the Middle Ages.

The Annali Genovesi mention galleons of 60, 64 and 80 oars, used for battle and on missions of exploration, in the 12th and 13th centuries. It is very likely that the galleons and galliots mentioned in the accounts of the crusades were the same vessels. In the early 16th century, the Venetian galleoni were a new class of galley used to hunt down pirates in the Mediterranean Sea.

Later, when the term started to be applied to sail-only vessels, it meant, like the English term "man-of-war", any large warship that was otherwise no different from the other sailing ships of the time.

History
During the 16th century, a lowering of the carrack's forecastle and elongation of the hull gave the ocean-going ships an unprecedented level of stability in the water, and reduced wind resistance at the front, leading to a faster, more maneuverable vessel. The galleon differed from the carrack and other older types primarily by being longer, lower and narrower, with a square tuck stern instead of a round tuck, and by having a snout or head projecting forward from the bows below the level of the forecastle. While carracks could be very large for the time, with some Portuguese carracks over 1,000 tons, galleons were generally smaller, usually under 500 tons although some Manila galleons were to reach a displacement of 2,000 tons.

Carracks also tended to be lightly armed and used for transporting cargo in all the fleets of other Western European states, while galleons were purpose-built warships, and were stronger, more heavily armed, and also cheaper to build (five galleons could cost around the same as three carracks) and were therefore a much better investment for use as warships or transports. Galleons' design changed and improved through the application of various innovations, and they were particularly linked with the military capabilities of the Atlantic sea powers. It was the captains of the Spanish navy, Pedro Menéndez de Avilés and Álvaro de Bazán, who designed the definitive long and relatively narrow hulled galleon in the 1550s.

The galleon was powered entirely by wind, using sails carried on three or four masts, with a lateen sail continuing to be used on the last (usually third and fourth) masts. They were used in both military and trade applications, most famously in the Spanish treasure fleet, and the Manila galleons. While carracks played the leading role in early global explorations, galleons also played a part in the 16th and 17th centuries. In fact, galleons were so versatile that a single vessel might be refitted for wartime and peacetime roles several times during its lifespan. The galleon was the prototype of all square-rigged ships with three or more masts for over two and a half centuries, including the later full-rigged ship.

The principal warships of the opposing English and Spanish fleets in the 1588 confrontation of the Spanish Armada and in the 1589 confrontation of the English Armada were galleons, with the modified English race-built galleons developed by John Hawkins proving their great utility in combat, while the capacious Spanish galleons, designed primarily as transports, showed great endurance in the battles and in the long and stormy return home.

Construction

Galleons were constructed from oak (for the keel), pine (for the masts) and various hardwoods for hull and decking. Hulls were usually carvel-built. The expenses involved in galleon construction were enormous. Hundreds of expert tradesmen (including carpenters, pitch-melters, blacksmiths, coopers, shipwrights, etc.) worked for months before a galleon was seaworthy. To cover the expense, galleons were often funded by groups of wealthy businessmen who pooled resources for a new ship. Therefore, most galleons were originally consigned for trade, although those captured by rival states were usually put into military service.

The most common gun used aboard a galleon was the demi-culverin, although gun sizes up to demi-cannon were possible.

Because of the long periods often spent at sea and poor conditions on board, many of the crew often perished during the voyage; therefore advanced rigging systems were developed so that the vessel could be sailed home by an active sailing crew a fraction of the size aboard at departure.

Distinguishing features

The most distinguishing features of the galleon include the long, prominent beak or beakhead followed by a foremast and mainmast, both noticeably taller than the single or double lateen-rigged mizzenmasts with their sloped lateen-rig yards, and below those the square quarter gallery at the stern. On average with three masts, in larger galleons, a fourth mast was added, usually another lateen-rigged mizzen, called the bonaventure mizzen.

The oldest English drawings
The oldest known scale drawings in England are in a manuscript called "Fragments of Ancient Shipwrightry" made in about 1586 by Mathew Baker, a master shipwright. This manuscript, held at the Pepysian Library, Magdalene College, Cambridge, provides an authentic reference for the size and shape of typical English galleons built during this period. Based on these plans, the Science Museum, London has built a 1:48 scale model ship that is an exemplar of galleons of this era.

Notable galleons

 * São João Baptista, nicknamed Botafogo, the most powerful warship when launched (1534) by the Portuguese; became famous during the Conquest of Tunis (1535), where it was commanded by Luís of Portugal, Duke of Beja.
 * "La Galga", the Assateague Spanish galleon that was shipwrecked in 1794; according to legend, the ancestors of the now famous Chincoteague ponies swam ashore from its hold.
 * Adler von Lübeck, the largest ship of its day when launched in 1566.
 * The Manila galleons, Spanish trading ships that sailed once or twice per year across the Pacific Ocean between Manila in the Philippines and Acapulco in New Spain (now Mexico); (1565–1815).
 * San Salvador, flagship vessel in Juan Rodríguez Cabrillo's 1542 exploration of present-day California in the United States.
 * San Pelayo, the large 906-ton galleon, which served as the flagship of Pedro Menéndez de Avilés during his expedition to establish St. Augustine, Florida in 1565. The vessel was so large it could not enter St. Augustine's harbor, so Menendez ordered it offloaded and sent it back to Hispaniola. At a later date her crew mutinied and sailed to Europe where the ship wrecked off the coast of Denmark.
 * Golden Hind, the ship in which Sir Francis Drake circumnavigated the globe 1577–1580.
 * Dainty, ship with which Sir Richard Hawkins sought to emulate the circumnavigation voyage of his cousin Francis Drake. She was captured by the Spanish in the action of Atacames Bay in 1594 and served in the Spanish Navy in the South American Pacific for several years.
 * Ark Raleigh was designed and built by Sir Walter Raleigh. She was later chosen by Lord Howard, admiral of the fleet to be the flagship of the English fleet in the fight against the Spanish Armada in 1588 and was summarily renamed Ark Royal.
 * Revenge, a galleon built in 1577, the flagship of Sir Francis Drake in the Battle of the Spanish Armada in 1588, was captured by a Spanish fleet off Flores in the Azores in 1591 and sank while being sailed back to Spain.
 * São Martinho, a Portuguese galleon, the flagship of Duke of Medina Sidonia, commander-in-chief of the Spanish Armada.
 * Santa Teresa, a Portuguese galleon, the flagship of Admiral Lope de Hoces at the Battle of the Downs, in 1639.
 * Triumph, the largest Elizabethan galleon; flagship of Sir Martin Frobisher in the Battle of the Spanish Armada.
 * San Juan Bautista (originally called Date Maru, 伊達丸 in Japanese). She crossed the Pacific Ocean from Japan to New Spain in 1614. She was of the Spanish galleon type, known in Japan as Nanban-Sen (南蛮船).
 * Nuestra Señora de la Concepción, a Spanish galleon, known to her crew as Cacafuego for her strong cannon. She was captured by Sir Francis Drake in 1578 and all her treasures were brought to England. She was holding treasures mined in one year by the Spanish in the Americas.
 * Padre Eterno, a Portuguese galleon launched in 1663. She was considered to be the biggest ship of her time, carrying 144 pieces of artillery with a displacement up to 2,000 tons.
 * Vasa, the only original galleon to be preserved. She sank in 1628 and was raised in 1961 for preservation as a museum ship.
 * Santa Luzia, a Portuguese galleon known for defeating a Dutch squadron single-handedly twice in 1650.
 * ''Galeon Adalucia, a replica galleon built in Spain in 2014.

title: Galleon


text:
User:Melmohor

Philosophy: English summary.(by El Mohor Mehdi)

Chapter 1 : foreword and interview

1.1 . What is the truth?

The truth corresponds to the reality at a given moment. It evolve with time.

1.2. Our truth.

Until now, it is the scientific truth that is the more successful but each of us has got his own convictions. By example, faith in god. Lots of people are sure of god’s existence while others don’t think so. We can say that education has a very big influence on our truth. Our truth would be the one of our parents. However, several persons find very innovative answers to their questions. So they can give a better version of the truth. It isn’t the result of education any longer but it becomes a kind of freedom, thus one of the realities. Actually, the truth is bond to the personality of each of us.

1.3 . True truth.

There is no true truth. There is just one true truth bond to space and time in which we are. We can decide that one thing is true for us. For example: if I say “I love my husband”, it is a truth for me. There is not only the will, there is also the feelings, and I must take a personal decision so that it will become a truth which is mine. This truth is totally separated from the scientific truth which is really more concrete and objective. So a true truth is always bond to someone. But, we can say that every woman loves her husband. Then, this truth can be generalised.

1.4 . THE truth.

Several true truths can exist and a well-determined person must choose his. There is also different truths but then for different people.

1.5 . “The truth is true” if and only if the truth is true.

It is the “if and only if” that says the truth can’t be true. It is only true for a given space-time. One of the goals of man is to reach the truth but it’s impossible, he can only approach it.

Chapter 2: introduction Man needs knowledge. The scientific look for the origin of human instead of worrying about his future. The philosophers who we will analyse try to explain the origins and the conceptions of the reality and the truth.

In the texts we read, we find two kinds of beliefs: those who are for the correspondent reality (Tarski and the Circle of Vienna): a “subject” world would be bond to an “object” world. And those against this correspondent reality (Rorty and Putnam). According to them, we must try to approach, by different visions of the truth, an objective reality which escapes from all kinds of prejudices,… Lots of people are looking for an absolute truth? Does it exist? It’s difficult to answer this question, some people say “yes”, the others say “no”. It’s like the question of god, does he exist? To offer the truth, we must prepare people to receive it. The information that earth is spherical took a long time to spread. We also must spread the concepts of truth progressively.

In this analyse, we will try to show that man is just human and that he has imagined everything he thinks. We will speak about the concept of truth and its origin. To conclude, we will propose you the notion of truth that, according to us, seems to be the most plausible.

Chapter 3: all our concepts are human.

Truth was born with man and evolved with him. In each human mind, the truth would be the same for all of us. The problem is to define what are the criteria to say that something is true or false. After that, it’s possible to give a definition of the truth. These criteria depend of our values. Indeed, “the real world depends on our values” wrote Putnam. Then we can say that facts and values are bond. Every person has got his own valour, so the truth is different for each of us. Another reason to say that, is our perception by senses. The absolute truth is unreachable because we try to find it by our senses, which are distorting. Rorty is against the correspondent-truth and we agree with him. According to him, the postulate of truth is inside each man and is his own one.

Chapter 4: why was the truth born? Which false ideas have we got about it?

All the things that make the concept of man were only born of what we felt of the world that surrounded us. Actually all our concepts come from or imagination and we represented them into our mind because we needed to at a moment in the history of mankind. What do the truth represent exactly for man and what did he do with it? His notion of truth became bigger each time he found an answer to his questions. When man wanted to share his knowledge, he created the language. However, the different peoples didn’t have the same explanation for one phenomenon, so they couldn’t be all true. To explain the world, several people invented gods, and the others invented an absolute energy. Their beliefs were their truth. According to Platon, we shouldn’t explain the world but find it. He said that the search after the truth was to find the supreme cause. After that, we would be able to explain everything.

Chapter 5: “p is true” if and only if.

The theory of metalanguage allows us to understand our problematic. This theory maintains that, if a proposition isn’t true in the language, it is in the metalanguage. Now we can have an idea on the truth by correspondence: it supposes a dualism, a subject and an object. The object is human because we must think it to refer to it, and thought is bond to subject. Then we can’t separate subject and object. Another problematic is that every thing we call truth is only an appearance. We do agree with the materialists, the concept of truth was born of human will and is not the shadow of another world. Here is why we chose this point of view: -the theory saying that the notion of truth would be born of human will, is really more         plausible that the one saying that the truth forced itself upon us -we are against those who believe too much in the existence of an absolute. -only someone who tackle this problem with materialists eyes is able to find a 	solution -science can exist and be useful only if we establish criteria to say that one thing is true or not. However, we must be careful and distinguish the problem of knowing what is true and the problem of truth itself. What can be qualified of true? According to Rorty, knowing which affirmations are true is not a question of usefulness in what we maintain. The society considers two truths: science and all the things which are bond to ethics. Now, we can't hope to find a metaphysic truth, an absolutely true truth. So we must create a new concept based on a usefulness criterion. But Rorty omitted to define what was useful for scientific truth. The circle of Vienna approach science with an empiric point of view. According to them, a proposition is only accepted if it can be justified rationally. We think that we must tackle the question of «what is true» like the pragmatics (Rorty and Putnam),But it is very theoretic. At a practical point of view, we must do like the circle of Vienna and consider their methods like a set of values, which represent something very useful for the need of our society.

Chapter 6: what is the relation between this report and the profession of the engineer?

The main gaol of the engineer is to develop high technologies for the society. He must satisfy the request of his customers and use technological tools to create a practical product that could be directly used by them. We can say that the truth of the engineer is the set of his technological tools. It is with a practical product that the engineer answers to a practical request. Then, which aspects of the truth interest the engineer but the practice? What we wrote in this report can help the engineer to see how he must consider and manage his knowledge.

Chapter 7: conclusion

To answer the question : “Is the truth true if and only if the truth is true ?”, we had to define the notion of truth. So we tried to approach it by the best way. We looked for ideas near several philosophers and to be honest, all their versions seemed to us to be incoherent. It proves that it is impossible to find an absolute truth. But, how must we prove that the truth is true if and only if the truth is true? We just can’t, so our answer is : “no”. Then, we decided to use the ideas of Putnam, Rorty and also of the circle of Vienna to find a human truth, relative but not absolute. According to us, human truth is a variable notion. It depends on the society. The truth is a practical issue.

El Mohor Mehdi

title: User:Melmohor


text:
Sunday roast

A Sunday roast or roast dinner is a traditional meal of British origin. Although it can be consumed throughout the week, it is traditionally consumed on Sunday. It consists of roasted meat, roasted potatoes or mashed potatoes, and accompaniments such as Yorkshire pudding, stuffing, gravy, and condiments such as apple sauce, mint sauce, or redcurrant sauce. A wide range of vegetables can be served as part of a roast dinner, such as broccoli, Brussels sprouts, cabbage, carrots, cauliflower, parsnips, or peas, which can be boiled, steamed, or roasted alongside the meat and potatoes.

The Sunday roast's prominence in British culture is such that in a UK poll in 2012 it was ranked second in a list of things people love about Britain. Other names for this meal include Sunday lunch, Sunday dinner, roast dinner, and full roast. The meal is often described as a less grand version of a traditional Christmas dinner.

Besides being served in its original homelands, the tradition of a Sunday roast lunch or dinner has been a major influence on food cultures in the English-speaking world, particularly in Australia, Canada, South Africa, the United States, and New Zealand. A South African Sunday roast normally comprises roast pork, beef, lamb or chicken, roast potatoes or mashed potatoes, and various vegetables like cauliflower-broccoli cheese, creamed spinach, green beans, carrots, peas, beetroot, and sweet potato. It is also fairly common to serve rice and gravy or pap and tomato gravy in South Africa instead of Yorkshire pudding.

Origin
The Sunday roast originated in the British Isles, particularly Yorkshire, as a meal to be eaten after the church service on Sunday. Eating a large meal following church services is common to most of Europe, but the Sunday roast variant developed unique to the British Isles. On Sundays, all types of meat and dairy produce are allowed to be eaten; this is unlike Fridays, where many Christians of the Roman Catholic, Anglican and Methodist denominations traditionally abstain from eating meats and instead eat fish. Likewise, it is traditional for Anglicans and English Catholics to fast before Sunday services, with a larger meal to break the fast afterwards. These Christian religious rules created several traditional dishes in the United Kingdom.
 * Only eating fish on Friday resulted in a British tradition of 'fish Fridays', which is still common in fish and chip shops and restaurants across the United Kingdom on Fridays; particularly during Lent.
 * To mark the end of not being able to eat meat, the Sunday roast was created as a mark of celebration.

There are two historical points on the origins of the modern Sunday roast.

 * In the late 1700s, during the industrial revolution in the United Kingdom, families would place a cut of meat into the oven as they got ready for church. They would then add in vegetables such as potatoes, turnips and parsnips before going to church on a Sunday morning. When they returned from the church, the dinner was all but ready. The juices from the meat and vegetables were used to make a stock or gravy to pour on top of the dinner.

 * The second opinion holds that the Sunday roast dates back to medieval times, when the village serfs served the squire for six days a week. Then, on the Sunday, after the morning church service, serfs would assemble in a field and practise their battle techniques and were rewarded with a feast of oxen roasted on a spit.

Meat
Typical meats used for a Sunday roast are chicken, lamb, pork, or roast beef, although seasonally duck, goose, gammon, turkey, or (rarely) other game birds may be used.

Vegetables
Sunday roasts can be served with a range of boiled, steamed and/or roasted vegetables. The vegetables served vary seasonally and regionally, but will usually include roast potatoes, roasted in meat dripping or vegetable oil, and also gravy made from juices released by the roasting meat, perhaps supplemented by one or more stock cubes, gravy browning/thickening, roux or corn flour.

The potatoes can be cooked around the meat itself, absorbing the juices and fat directly (as in a traditional Cornish under-roast). However, many cooks prefer to cook the potatoes and the Yorkshire pudding in a hotter oven than that used for the joint and so remove the meat beforehand to rest and "settle" in a warm place.

Other vegetable dishes served with roast dinner can include mashed swede or turnips, roast parsnips, cabbage, boiled or steamed cabbage, broccoli, green beans, and boiled carrots and peas. It is also not uncommon for vegetable dishes—such as cauliflower cheese and stewed red cabbage to be served alongside the more usual assortment of plainly-cooked seasonal vegetables.

Accompaniments
Common traditional accompaniments include:

 * beef: Yorkshire pudding, suet pudding; English mustard, gravy sauce or horseradish sauce. Roast beef with Yorkshire pudding accompanied by "roast potatoes, vegetables, and horseradish sauce" is considered by National Geographic as the national dish of England.
 * pork: crackling and sage-and-onion stuffing; apple sauce or English mustard.
 * lamb: mint sauce or jelly or redcurrant jelly.
 * chicken: sausages or sausage meat, stuffing, bread sauce, apple sauce, cranberry sauce or redcurrant jelly.

title: Sunday roast