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Computational complexity theory

In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm.

A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computational complexity theory is to determine the practical limits on what computers can and cannot do. The P versus NP problem, one of the seven Millennium Prize Problems, is part of the field of computational complexity.

Closely related fields in theoretical computer science are analysis of algorithms and computability theory. A key distinction between analysis of algorithms and computational complexity theory is that the former is devoted to analyzing the amount of resources needed by a particular algorithm to solve a problem, whereas the latter asks a more general question about all possible algorithms that could be used to solve the same problem. More precisely, computational complexity theory tries to classify problems that can or cannot be solved with appropriately restricted resources. In turn, imposing restrictions on the available resources is what distinguishes computational complexity from computability theory: the latter theory asks what kinds of problems can, in principle, be solved algorithmically.

Problem instances
A computational problem can be viewed as an infinite collection of instances together with a set (possibly empty) of solutions for every instance. The input string for a computational problem is referred to as a problem instance, and should not be confused with the problem itself. In computational complexity theory, a problem refers to the abstract question to be solved. In contrast, an instance of this problem is a rather concrete utterance, which can serve as the input for a decision problem. For example, consider the problem of primality testing. The instance is a number (e.g., 15) and the solution is "yes" if the number is prime and "no" otherwise (in this case, 15 is not prime and the answer is "no"). Stated another way, the instance is a particular input to the problem, and the solution is the output corresponding to the given input.

To further highlight the difference between a problem and an instance, consider the following instance of the decision version of the travelling salesman problem: Is there a route of at most 2000 kilometres passing through all of Germany's 15 largest cities? The quantitative answer to this particular problem instance is of little use for solving other instances of the problem, such as asking for a round trip through all sites in Milan whose total length is at most 10 km. For this reason, complexity theory addresses computational problems and not particular problem instances.

Representing problem instances
When considering computational problems, a problem instance is a string over an alphabet. Usually, the alphabet is taken to be the binary alphabet (i.e., the set {0,1}), and thus the strings are bitstrings. As in a real-world computer, mathematical objects other than bitstrings must be suitably encoded. For example, integers can be represented in binary notation, and graphs can be encoded directly via their adjacency matrices, or by encoding their adjacency lists in binary.

Even though some proofs of complexity-theoretic theorems regularly assume some concrete choice of input encoding, one tries to keep the discussion abstract enough to be independent of the choice of encoding. This can be achieved by ensuring that different representations can be transformed into each other efficiently.

Decision problems as formal languages
Decision problems are one of the central objects of study in computational complexity theory. A decision problem is a special type of computational problem whose answer is either yes or no, or alternately either 1 or 0. A decision problem can be viewed as a formal language, where the members of the language are instances whose output is yes, and the non-members are those instances whose output is no. The objective is to decide, with the aid of an algorithm, whether a given input string is a member of the formal language under consideration. If the algorithm deciding this problem returns the answer yes, the algorithm is said to accept the input string, otherwise it is said to reject the input.

An example of a decision problem is the following. The input is an arbitrary graph. The problem consists in deciding whether the given graph is connected or not. The formal language associated with this decision problem is then the set of all connected graphs — to obtain a precise definition of this language, one has to decide how graphs are encoded as binary strings.

Function problems
A function problem is a computational problem where a single output (of a total function) is expected for every input, but the output is more complex than that of a decision problem—that is, the output is not just yes or no. Notable examples include the traveling salesman problem and the integer factorization problem.

It is tempting to think that the notion of function problems is much richer than the notion of decision problems. However, this is not really the case, since function problems can be recast as decision problems. For example, the multiplication of two integers can be expressed as the set of triples (a, b, c) such that the relation a × b = c holds. Deciding whether a given triple is a member of this set corresponds to solving the problem of multiplying two numbers.

Measuring the size of an instance
To measure the difficulty of solving a computational problem, one may wish to see how much time the best algorithm requires to solve the problem. However, the running time may, in general, depend on the instance. In particular, larger instances will require more time to solve. Thus the time required to solve a problem (or the space required, or any measure of complexity) is calculated as a function of the size of the instance. This is usually taken to be the size of the input in bits. Complexity theory is interested in how algorithms scale with an increase in the input size. For instance, in the problem of finding whether a graph is connected, how much more time does it take to solve a problem for a graph with 2n vertices compared to the time taken for a graph with n vertices?

If the input size is n, the time taken can be expressed as a function of n. Since the time taken on different inputs of the same size can be different, the worst-case time complexity T(n) is defined to be the maximum time taken over all inputs of size n. If T(n) is a polynomial in n, then the algorithm is said to be a polynomial time algorithm. Cobham's thesis argues that a problem can be solved with a feasible amount of resources if it admits a polynomial-time algorithm.

Turing machine
A Turing machine is a mathematical model of a general computing machine. It is a theoretical device that manipulates symbols contained on a strip of tape. Turing machines are not intended as a practical computing technology, but rather as a general model of a computing machine—anything from an advanced supercomputer to a mathematician with a pencil and paper. It is believed that if a problem can be solved by an algorithm, there exists a Turing machine that solves the problem. Indeed, this is the statement of the Church–Turing thesis. Furthermore, it is known that everything that can be computed on other models of computation known to us today, such as a RAM machine, Conway's Game of Life, cellular automata, lambda calculus or any programming language can be computed on a Turing machine. Since Turing machines are easy to analyze mathematically, and are believed to be as powerful as any other model of computation, the Turing machine is the most commonly used model in complexity theory.

Many types of Turing machines are used to define complexity classes, such as deterministic Turing machines, probabilistic Turing machines, non-deterministic Turing machines, quantum Turing machines, symmetric Turing machines and alternating Turing machines. They are all equally powerful in principle, but when resources (such as time or space) are bounded, some of these may be more powerful than others.

A deterministic Turing machine is the most basic Turing machine, which uses a fixed set of rules to determine its future actions. A probabilistic Turing machine is a deterministic Turing machine with an extra supply of random bits. The ability to make probabilistic decisions often helps algorithms solve problems more efficiently. Algorithms that use random bits are called randomized algorithms. A non-deterministic Turing machine is a deterministic Turing machine with an added feature of non-determinism, which allows a Turing machine to have multiple possible future actions from a given state. One way to view non-determinism is that the Turing machine branches into many possible computational paths at each step, and if it solves the problem in any of these branches, it is said to have solved the problem. Clearly, this model is not meant to be a physically realizable model, it is just a theoretically interesting abstract machine that gives rise to particularly interesting complexity classes. For examples, see non-deterministic algorithm.

Other machine models
Many machine models different from the standard multi-tape Turing machines have been proposed in the literature, for example random-access machines. Perhaps surprisingly, each of these models can be converted to another without providing any extra computational power. The time and memory consumption of these alternate models may vary. What all these models have in common is that the machines operate deterministically.

However, some computational problems are easier to analyze in terms of more unusual resources. For example, a non-deterministic Turing machine is a computational model that is allowed to branch out to check many different possibilities at once. The non-deterministic Turing machine has very little to do with how we physically want to compute algorithms, but its branching exactly captures many of the mathematical models we want to analyze, so that non-deterministic time is a very important resource in analyzing computational problems.

Complexity measures
For a precise definition of what it means to solve a problem using a given amount of time and space, a computational model such as the deterministic Turing machine is used. The time required by a deterministic Turing machine M on input x is the total number of state transitions, or steps, the machine makes before it halts and outputs the answer ("yes" or "no"). A Turing machine M is said to operate within time f(n) if the time required by M on each input of length n is at most f(n). A decision problem A can be solved in time f(n) if there exists a Turing machine operating in time f(n) that solves the problem. Since complexity theory is interested in classifying problems based on their difficulty, one defines sets of problems based on some criteria. For instance, the set of problems solvable within time f(n) on a deterministic Turing machine is then denoted by DTIME(f(n)).

Analogous definitions can be made for space requirements. Although time and space are the most well-known complexity resources, any complexity measure can be viewed as a computational resource. Complexity measures are very generally defined by the Blum complexity axioms. Other complexity measures used in complexity theory include communication complexity, circuit complexity, and decision tree complexity.

The complexity of an algorithm is often expressed using big O notation.

Best, worst and average case complexity
The best, worst and average case complexity refer to three different ways of measuring the time complexity (or any other complexity measure) of different inputs of the same size. Since some inputs of size n may be faster to solve than others, we define the following complexities: The order from cheap to costly is: Best, average (of discrete uniform distribution), amortized, worst.
 * 1) Best-case complexity: This is the complexity of solving the problem for the best input of size n.
 * 2) Average-case complexity: This is the complexity of solving the problem on an average. This complexity is only defined with respect to a probability distribution over the inputs. For instance, if all inputs of the same size are assumed to be equally likely to appear, the average case complexity can be defined with respect to the uniform distribution over all inputs of size n.
 * 3) Amortized analysis: Amortized analysis considers both the costly and less costly operations together over the whole series of operations of the algorithm.
 * 4) Worst-case complexity: This is the complexity of solving the problem for the worst input of size n.

For example, consider the deterministic sorting algorithm quicksort. This solves the problem of sorting a list of integers that is given as the input. The worst-case is when the pivot is always the largest or smallest value in the list (so the list is never divided). In this case the algorithm takes time O(n2). If we assume that all possible permutations of the input list are equally likely, the average time taken for sorting is O(n log n). The best case occurs when each pivoting divides the list in half, also needing O(n log n) time.

Upper and lower bounds on the complexity of problems
To classify the computation time (or similar resources, such as space consumption), it is helpful to demonstrate upper and lower bounds on the maximum amount of time required by the most efficient algorithm to solve a given problem. The complexity of an algorithm is usually taken to be its worst-case complexity unless specified otherwise. Analyzing a particular algorithm falls under the field of analysis of algorithms. To show an upper bound T(n) on the time complexity of a problem, one needs to show only that there is a particular algorithm with running time at most T(n). However, proving lower bounds is much more difficult, since lower bounds make a statement about all possible algorithms that solve a given problem. The phrase "all possible algorithms" includes not just the algorithms known today, but any algorithm that might be discovered in the future. To show a lower bound of T(n) for a problem requires showing that no algorithm can have time complexity lower than T(n).

Upper and lower bounds are usually stated using the big O notation, which hides constant factors and smaller terms. This makes the bounds independent of the specific details of the computational model used. For instance, if T(n) = 7n2 + 15n + 40, in big O notation one would write T(n) = O(n2).

Defining complexity classes
A complexity class is a set of problems of related complexity. Simpler complexity classes are defined by the following factors:
 * The type of computational problem: The most commonly used problems are decision problems. However, complexity classes can be defined based on function problems, counting problems, optimization problems, promise problems, etc.
 * The model of computation: The most common model of computation is the deterministic Turing machine, but many complexity classes are based on non-deterministic Turing machines, Boolean circuits, quantum Turing machines, monotone circuits, etc.
 * The resource (or resources) that is being bounded and the bound: These two properties are usually stated together, such as "polynomial time", "logarithmic space", "constant depth", etc.

Some complexity classes have complicated definitions that do not fit into this framework. Thus, a typical complexity class has a definition like the following:

 * The set of decision problems solvable by a deterministic Turing machine within time f(n). (This complexity class is known as DTIME(f(n)).)

But bounding the computation time above by some concrete function f(n) often yields complexity classes that depend on the chosen machine model. For instance, the language {xx | x is any binary string} can be solved in linear time on a multi-tape Turing machine, but necessarily requires quadratic time in the model of single-tape Turing machines. If we allow polynomial variations in running time, Cobham-Edmonds thesis states that "the time complexities in any two reasonable and general models of computation are polynomially related". This forms the basis for the complexity class P, which is the set of decision problems solvable by a deterministic Turing machine within polynomial time. The corresponding set of function problems is FP.

Important complexity classes
Many important complexity classes can be defined by bounding the time or space used by the algorithm. Some important complexity classes of decision problems defined in this manner are the following:

The logarithmic-space classes (necessarily) do not take into account the space needed to represent the problem.

It turns out that PSPACE = NPSPACE and EXPSPACE = NEXPSPACE by Savitch's theorem.

Other important complexity classes include BPP, ZPP and RP, which are defined using probabilistic Turing machines; AC and NC, which are defined using Boolean circuits; and BQP and QMA, which are defined using quantum Turing machines. #P is an important complexity class of counting problems (not decision problems). Classes like IP and AM are defined using Interactive proof systems. ALL is the class of all decision problems.

Hierarchy theorems
For the complexity classes defined in this way, it is desirable to prove that relaxing the requirements on (say) computation time indeed defines a bigger set of problems. In particular, although DTIME(n) is contained in DTIME(n2), it would be interesting to know if the inclusion is strict. For time and space requirements, the answer to such questions is given by the time and space hierarchy theorems respectively. They are called hierarchy theorems because they induce a proper hierarchy on the classes defined by constraining the respective resources. Thus there are pairs of complexity classes such that one is properly included in the other. Having deduced such proper set inclusions, we can proceed to make quantitative statements about how much more additional time or space is needed in order to increase the number of problems that can be solved.

More precisely, the time hierarchy theorem states that
 * $$\mathsf{DTIME}\big(o(f(n)) \big) \subsetneq \mathsf{DTIME} \big(f(n) \sdot \log(f(n)) \big)$$.

The space hierarchy theorem states that
 * $$\mathsf{DSPACE}\big(o(f(n))\big) \subsetneq \mathsf{DSPACE} \big(f(n) \big)$$.

The time and space hierarchy theorems form the basis for most separation results of complexity classes. For instance, the time hierarchy theorem tells us that P is strictly contained in EXPTIME, and the space hierarchy theorem tells us that L is strictly contained in PSPACE.

Reduction
Many complexity classes are defined using the concept of a reduction. A reduction is a transformation of one problem into another problem. It captures the informal notion of a problem being at most as difficult as another problem. For instance, if a problem X can be solved using an algorithm for Y, X is no more difficult than Y, and we say that X reduces to Y. There are many different types of reductions, based on the method of reduction, such as Cook reductions, Karp reductions and Levin reductions, and the bound on the complexity of reductions, such as polynomial-time reductions or log-space reductions.

The most commonly used reduction is a polynomial-time reduction. This means that the reduction process takes polynomial time. For example, the problem of squaring an integer can be reduced to the problem of multiplying two integers. This means an algorithm for multiplying two integers can be used to square an integer. Indeed, this can be done by giving the same input to both inputs of the multiplication algorithm. Thus we see that squaring is not more difficult than multiplication, since squaring can be reduced to multiplication.

This motivates the concept of a problem being hard for a complexity class. A problem X is hard for a class of problems C if every problem in C can be reduced to X. Thus no problem in C is harder than X, since an algorithm for X allows us to solve any problem in C. The notion of hard problems depends on the type of reduction being used. For complexity classes larger than P, polynomial-time reductions are commonly used. In particular, the set of problems that are hard for NP is the set of NP-hard problems.

If a problem X is in C and hard for C, then X is said to be complete for C. This means that X is the hardest problem in C. (Since many problems could be equally hard, one might say that X is one of the hardest problems in C.) Thus the class of NP-complete problems contains the most difficult problems in NP, in the sense that they are the ones most likely not to be in P. Because the problem P = NP is not solved, being able to reduce a known NP-complete problem, Π2, to another problem, Π1, would indicate that there is no known polynomial-time solution for Π1. This is because a polynomial-time solution to Π1 would yield a polynomial-time solution to Π2. Similarly, because all NP problems can be reduced to the set, finding an NP-complete problem that can be solved in polynomial time would mean that P = NP.

P versus NP problem
The complexity class P is often seen as a mathematical abstraction modeling those computational tasks that admit an efficient algorithm. This hypothesis is called the Cobham–Edmonds thesis. The complexity class NP, on the other hand, contains many problems that people would like to solve efficiently, but for which no efficient algorithm is known, such as the Boolean satisfiability problem, the Hamiltonian path problem and the vertex cover problem. Since deterministic Turing machines are special non-deterministic Turing machines, it is easily observed that each problem in P is also member of the class NP.

The question of whether P equals NP is one of the most important open questions in theoretical computer science because of the wide implications of a solution. If the answer is yes, many important problems can be shown to have more efficient solutions. These include various types of integer programming problems in operations research, many problems in logistics, protein structure prediction in biology, and the ability to find formal proofs of pure mathematics theorems. The P versus NP problem is one of the Millennium Prize Problems proposed by the Clay Mathematics Institute. There is a US$1,000,000 prize for resolving the problem.

Problems in NP not known to be in P or NP-complete
It was shown by Ladner that if P ≠ NP then there exist problems in NP that are neither in P nor NP-complete. Such problems are called NP-intermediate problems. The graph isomorphism problem, the discrete logarithm problem and the integer factorization problem are examples of problems believed to be NP-intermediate. They are some of the very few NP problems not known to be in P or to be NP-complete.

The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic. An important unsolved problem in complexity theory is whether the graph isomorphism problem is in P, NP-complete, or NP-intermediate. The answer is not known, but it is believed that the problem is at least not NP-complete. If graph isomorphism is NP-complete, the polynomial time hierarchy collapses to its second level. Since it is widely believed that the polynomial hierarchy does not collapse to any finite level, it is believed that graph isomorphism is not NP-complete. The best algorithm for this problem, due to László Babai and Eugene Luks has run time $$O(2^{\sqrt{n \log n}})$$ for graphs with n vertices, although some recent work by Babai offers some potentially new perspectives on this.

The integer factorization problem is the computational problem of determining the prime factorization of a given integer. Phrased as a decision problem, it is the problem of deciding whether the input has a prime factor less than k. No efficient integer factorization algorithm is known, and this fact forms the basis of several modern cryptographic systems, such as the RSA algorithm. The integer factorization problem is in NP and in co-NP (and even in UP and co-UP ). If the problem is NP-complete, the polynomial time hierarchy will collapse to its first level (i.e., NP will equal co-NP). The best known algorithm for integer factorization is the general number field sieve, which takes time $$O(e^{\left(\sqrt[3]{\frac{64}{9}}\right)\sqrt[3]{(\log n)}\sqrt[3]{(\log \log n)^2}})$$ to factor an odd integer n. However, the best known quantum algorithm for this problem, Shor's algorithm, does run in polynomial time. Unfortunately, this fact doesn't say much about where the problem lies with respect to non-quantum complexity classes.

Separations between other complexity classes
Many known complexity classes are suspected to be unequal, but this has not been proved. For instance P ⊆ NP ⊆ PP ⊆ PSPACE, but it is possible that P = PSPACE. If P is not equal to NP, then P is not equal to PSPACE either. Since there are many known complexity classes between P and PSPACE, such as RP, BPP, PP, BQP, MA, PH, etc., it is possible that all these complexity classes collapse to one class. Proving that any of these classes are unequal would be a major breakthrough in complexity theory.

Along the same lines, co-NP is the class containing the complement problems (i.e. problems with the yes/no answers reversed) of NP problems. It is believed that NP is not equal to co-NP; however, it has not yet been proven. It is clear that if these two complexity classes are not equal then P is not equal to NP, since P=co-P. Thus if P=NP we would have co-P=co-NP whence NP=P=co-P=co-NP.

Similarly, it is not known if L (the set of all problems that can be solved in logarithmic space) is strictly contained in P or equal to P. Again, there are many complexity classes between the two, such as NL and NC, and it is not known if they are distinct or equal classes.

It is suspected that P and BPP are equal. However, it is currently open if BPP = NEXP.

Intractability
A problem that can be solved in theory (e.g. given large but finite resources, especially time), but for which in practice any solution takes too many resources to be useful, is known as an . Conversely, a problem that can be solved in practice is called a , literally "a problem that can be handled". The term infeasible (literally "cannot be done") is sometimes used interchangeably with intractable, though this risks confusion with a feasible solution in mathematical optimization.

Tractable problems are frequently identified with problems that have polynomial-time solutions (P, PTIME); this is known as the Cobham–Edmonds thesis. Problems that are known to be intractable in this sense include those that are EXPTIME-hard. If NP is not the same as P, then NP-hard problems are also intractable in this sense.

However, this identification is inexact: a polynomial-time solution with large degree or large leading coefficient grows quickly, and may be impractical for practical size problems; conversely, an exponential-time solution that grows slowly may be practical on realistic input, or a solution that takes a long time in the worst case may take a short time in most cases or the average case, and thus still be practical. Saying that a problem is not in P does not imply that all large cases of the problem are hard or even that most of them are. For example, the decision problem in Presburger arithmetic has been shown not to be in P, yet algorithms have been written that solve the problem in reasonable times in most cases. Similarly, algorithms can solve the NP-complete knapsack problem over a wide range of sizes in less than quadratic time and SAT solvers routinely handle large instances of the NP-complete Boolean satisfiability problem.

To see why exponential-time algorithms are generally unusable in practice, consider a program that makes 2n operations before halting. For small n, say 100, and assuming for the sake of example that the computer does 1012 operations each second, the program would run for about 4 × 1010 years, which is the same order of magnitude as the age of the universe. Even with a much faster computer, the program would only be useful for very small instances and in that sense the intractability of a problem is somewhat independent of technological progress. However, an exponential-time algorithm that takes 1.0001n operations is practical until n gets relatively large.

Similarly, a polynomial time algorithm is not always practical. If its running time is, say, n15, it is unreasonable to consider it efficient and it is still useless except on small instances. Indeed, in practice even n3 or n2 algorithms are often impractical on realistic sizes of problems.

Continuous complexity theory
Continuous complexity theory can refer to complexity theory of problems that involve continuous functions that are approximated by discretizations, as studied in numerical analysis. One approach to complexity theory of numerical analysis is information based complexity.

Continuous complexity theory can also refer to complexity theory of the use of analog computation, which uses continuous dynamical systems and differential equations. Control theory can be considered a form of computation and differential equations are used in the modelling of continuous-time and hybrid discrete-continuous-time systems.

History
An early example of algorithm complexity analysis is the running time analysis of the Euclidean algorithm done by Gabriel Lamé in 1844.

Before the actual research explicitly devoted to the complexity of algorithmic problems started off, numerous foundations were laid out by various researchers. Most influential among these was the definition of Turing machines by Alan Turing in 1936, which turned out to be a very robust and flexible simplification of a computer.

The beginning of systematic studies in computational complexity is attributed to the seminal 1965 paper "On the Computational Complexity of Algorithms" by Juris Hartmanis and Richard E. Stearns, which laid out the definitions of time complexity and space complexity, and proved the hierarchy theorems. In addition, in 1965 Edmonds suggested to consider a "good" algorithm to be one with running time bounded by a polynomial of the input size.

Earlier papers studying problems solvable by Turing machines with specific bounded resources include John Myhill's definition of linear bounded automata (Myhill 1960), Raymond Smullyan's study of rudimentary sets (1961), as well as Hisao Yamada's paper on real-time computations (1962). Somewhat earlier, Boris Trakhtenbrot (1956), a pioneer in the field from the USSR, studied another specific complexity measure. As he remembers:

"However, [my] initial interest [in automata theory] was increasingly set aside in favor of computational complexity, an exciting fusion of combinatorial methods, inherited from switching theory, with the conceptual arsenal of the theory of algorithms. These ideas had occurred to me earlier in 1955 when I coined the term 'signalizing function', which is nowadays commonly known as 'complexity measure'."

In 1967, Manuel Blum formulated a set of axioms (now known as Blum axioms) specifying desirable properties of complexity measures on the set of computable functions and proved an important result, the so-called speed-up theorem. The field began to flourish in 1971 when Stephen Cook and Leonid Levin proved the existence of practically relevant problems that are NP-complete. In 1972, Richard Karp took this idea a leap forward with his landmark paper, "Reducibility Among Combinatorial Problems", in which he showed that 21 diverse combinatorial and graph theoretical problems, each infamous for its computational intractability, are NP-complete.

title: Computational complexity theory


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Cadence (disambiguation)

A cadence is a melodic or harmonic configuration that creates a sense of resolution.

Cadence may also refer to:

Music

 * Cadence (vocal group), a Canadian a cappella quartet
 * Drum cadence, played exclusively by the percussion section of a marching band
 * Military cadence, a marching chant
 * Cadence, the high school band of Chris Daughtry

Record labels

 * Cadence Jazz Records, a record label associated with Cadence magazine
 * Cadence Records, a 1940s/1950s American record label during the
 * Cadence Music Group, formerly MapleMusic Recordings, a Canadian record label

Other uses in arts and entertainment

 * Cadence (film), a 1990 film by Martin Sheen
 * Cadence (magazine), a quarterly review of jazz, blues and improvised music
 * Cadence (poetry), the fall in pitch of the intonation of the voice
 * Cadance, a character in My Little Pony: Friendship is Magic

Businesses

 * Cadence Bank, an American bank
 * Cadence Bank (1887–2021), a former company merged into this bank
 * Cadence Biomedical, an American medical device company
 * Cadence Design Systems, an American company
 * Cadence Industries, an American conglomerate

People

 * Cadence (given name)

Other uses

 * Cadence (cycling), a measure of cycling pedalling rate (r/min)
 * Cadence (gait), a measure of athletic performance

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Cadence (disambiguation)


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Camelot

Camelot is a legendary castle and court associated with King Arthur. Absent in the early Arthurian material, Camelot first appeared in 12th-century French romances and, since the Lancelot-Grail cycle, eventually came to be described as the fantastic capital of Arthur's realm and a symbol of the Arthurian world.

Medieval texts locate it somewhere in Great Britain and sometimes associate it with real cities, though more usually its precise location is not revealed. Most scholars regard it as being entirely fictional, its unspecified geography being perfect for chivalric romance writers. Nevertheless, arguments about the location of the "real Camelot" have occurred since the 15th century and continue today in popular works and for tourism purposes.

Etymology
The name's derivation is uncertain. It has numerous different spellings in medieval French Arthurian romances, including Camaalot, Camalot, Chamalot, Camehelot (sometimes read as Camchilot), Camaaloth, Caamalot, Camahaloth, Camaelot, Kamaalot, Kamaaloth, Kaamalot, Kamahaloth, Kameloth, Kamaelot, Kamelot, Kaamelot, Cameloth, and Gamalaot. Arthurian scholar Ernst Brugger suggested that it was a corruption of the site of Arthur's final battle, the Battle of Camlann, in Welsh tradition. Roger Sherman Loomis believed it was derived from Cavalon, a place name that he suggested was a corruption of Avalon (under the influence of the Breton place name Cavallon). He further suggested that Cavalon became Arthur's capital due to confusion with Arthur's other traditional court at Caerleon (Caer Lleon in Welsh).

Others have suggested a derivation from the British Iron Age and Romano-British place name Camulodunum, one of the first capitals of Roman Britain and which would have significance in Romano-British culture. Indeed, John Morris, the English historian who specialized in the study of the institutions of the Roman Empire and the history of Sub-Roman Britain, suggested in his book The Age of Arthur that as the descendants of Romanized Britons looked back to a golden age of peace and prosperity under Rome, the name "Camelot" of Arthurian legend may have referred to the capital of Britannia (Camulodunum) in Roman times. It is unclear, however, where Chrétien de Troyes would have encountered the name Camulodunum, or why he would render it as Camaalot, though Urban T. Holmes argued Chrétien could have had access to Book 2 of Pliny's Natural History, where it is rendered as Camaloduno.

Medieval literature
Arthur's court at Camelot is mentioned for the first time in Chrétien's poem Lancelot, the Knight of the Cart, dating to the 1170s, though it does not appear in all the manuscripts. In the C manuscript (Paris, Bibliothèque Nationale de France, fonds français 794, folio 27r), which might in fact contain the proper reading of Chretien's original text, instead of the place name there is the Old French phrase con lui plot, meaning "as he pleased". The other manuscripts spell the name variously as Chamalot (MS A, f. f. 196r), Camehelot (MS E, f. 1r), Chamaalot (MS G, f. 34f), and Camalot (MS T, f. 41v); the name is missing, along with the rest of the passage containing it, in MS V (Vatican, Biblioteca Vaticana, Regina 1725). Camelot is mentioned only in passing and is not described:

"A un jor d'une Acenssion / Fu venuz de vers Carlion / Li rois Artus et tenu ot / Cort molt riche a Camaalot, / Si riche com au jor estut. King Arthur, one Ascension Day, had left Caerleon and held a most magnificent court at Camelot with all the splendour appropriate to the day."

Nothing in Chrétien's poem suggests the level of importance Camelot would have in later romances. For Chrétien, Arthur's chief court was in Caerleon in Wales; this was the king's primary base in Geoffrey of Monmouth's Historia Regum Britanniae and subsequent literature. Chrétien depicts Arthur, like a typical medieval monarch, holding court at a number of cities and castles.

It is not until the 13th-century French prose romances, including the Vulgate and Post-Vulgate cycles, that Camelot began to supersede Caerleon, and even then, many descriptive details applied to Camelot derive from Geoffrey's earlier grand depiction of the Welsh town. Most Arthurian romances of this period produced in English or Welsh did not follow this trend; Camelot was referred to infrequently, and usually in translations from French. One exception is Sir Gawain and the Green Knight, which locates Arthur's court at "Camelot"; however, in Britain, Arthur's court was generally located at Caerleon, or at Carlisle, which is usually identified with the "Carduel" of the French romances.

The Lancelot-Grail cycle and the texts it influenced depict the city of Camelot as standing along a river, downstream from Astolat. It is surrounded by plains and forests, and its magnificent cathedral, St. Stephen's, originally established by Josephus, the son of Joseph of Arimathea, is the religious centre for Arthur's Knights of the Round Table. There, Arthur and Guinevere are married and there are the tombs of many kings and knights. In a mighty castle stands the Round Table, created by Merlin and Uther Pendragon; it is here that Galahad conquers the Siege Perilous, and where the knights see a vision of the Holy Grail and swear to find it. Jousts are often held in a meadow outside the city.

Its imprecise geography serves the romances well, as Camelot becomes less a literal place than a powerful symbol of Arthur's court and universe. There is also a Kamaalot featured as the home of Percival's mother in the romance Perlesvaus. In Palamedes and some other works, including the Post-Vulgate cycle, King Arthur's Camelot is eventually razed to the ground by the treacherous King Mark of Cornwall (who had besieged it earlier) in his invasion of Logres after the Battle of Camlann. In the Tavola Ritonda, Camelot is abandoned and falls to ruin after the death of Arthur.

From Geoffrey's grand description of Caerleon, Camelot gains its impressive architecture, its many churches and the chivalry and courtesy of its inhabitants. Geoffrey's description in turn drew on an already established tradition in Welsh oral tradition of the grandeur of Arthur's court. The tale Culhwch and Olwen, associated with the Mabinogion and perhaps first written in the 11th century, draws a dramatic picture of Arthur's hall and his many powerful warriors who go from there on great adventures, placing it in Celliwig, an uncertain locale in Cornwall.

Although the court at Celliwig is the most prominent in remaining early Welsh manuscripts, the various versions of the Welsh Triads agree in giving Arthur multiple courts, one in each of the areas inhabited by the Celtic Britons: Cornwall, Wales and the Hen Ogledd. This perhaps reflects the influence of widespread oral traditions common by the 9th century which are recorded in various place names and features such as Arthur's Seat, indicating Arthur was a hero known and associated with many locations across Brittonic areas of Britain as well as Brittany. Even at this stage Arthur could not be tied to one location. Many other places are listed as a location where Arthur holds court in the later romances, Carlisle and London perhaps being the most prominent.

In the 15th century, the English writer Thomas Malory created the image of Camelot most familiar today in his Le Morte d'Arthur, a work based mostly on the French romances. He firmly identifies Camelot with Winchester in England, an identification that remained popular over the centuries, though it was rejected by Malory's own editor, William Caxton, who preferred a Welsh location.

Identifications

Arthurian scholar Norris J. Lacy commented that "Camelot, located no where in particular, can be anywhere." The romancers' versions of Camelot draw on earlier traditions of Arthur's fabulous court. The Celliwig of Culhwch and Olwen appears in the Welsh Triads as well; this early Welsh material places Wales' greatest leader outside its national boundaries. Geoffrey's description of Caerleon is probably based on his personal familiarity with the town and its Roman ruins; it is less clear that Caerleon was associated with Arthur before Geoffrey. Several French romances (Perlesvaus, the Didot Perceval attributed to Robert de Boron, and even the early romances of Chrétien such as Erec and Enide and Yvain, the Knight of the Lion) have Arthur hold court at "Carduel in Wales", a northern city based on the real Carlisle. Malory's identification of Camelot as Winchester was probably partially inspired by the latter city's history: it had been the capital of Wessex under Alfred the Great, and boasted the Winchester Round Table, an artefact constructed in the 13th century but widely believed to be the original by Malory's time. Caxton rejected the association, saying Camelot was in Wales and that its ruins could still be seen; this is a likely reference to the Roman ruins at Caerwent.

In 1542, John Leland reported that the locals around Cadbury Castle (formerly known as Camalet) in Somerset considered it to be the original Camelot. This theory, which was repeated by later antiquaries, is bolstered, or may have derived from, Cadbury's proximity to the River Cam and the villages of Queen Camel and West Camel, and remained popular enough to help inspire a large-scale archaeological dig in the 20th century. These excavations, led by archaeologist Leslie Alcock from 1966 to 1970, were titled "Cadbury-Camelot" and won much media attention. The dig revealed that the site seems to have been occupied as early as the 4th millennium BC and to have been refortified and occupied by a major Brittonic ruler and his war band from c. 470. This early medieval settlement continued until around 580. The works were by far the largest known fortification of the period, double the size of comparative caers and with Mediterranean artefacts representing extensive trade  and Saxon ones showing possible conquest. The use of the name Camelot and the support of Geoffrey Ashe helped ensure much publicity for the finds, but Alcock himself later grew embarrassed by the supposed Arthurian connection to the site. Following the arguments of David Dumville, Alcock felt the site was too late and too uncertain to be a tenable Camelot. Modern archaeologists follow him in rejecting the name, calling it instead Cadbury Castle hill fort. Despite this, Cadbury remains widely associated with Camelot.

The name of the Romano-British town of Camulodunum (modern Colchester) was derived from the Celtic god Camulus. However, it was located well within territory usually thought to have been conquered early in the 5th century by Saxons, so it is unlikely to have been the location of any "true" Camelot, as Arthur is traditionally dated to the late 5th and early 6th century. The town was definitely known as Colchester as early as the Anglo-Saxon Chronicle in 917. Even Colchester Museum argues strongly regarding the historical Arthur: "It would be impossible and inconceivable to link him to the Colchester area, or to Essex more generally," pointing out that the connection between the name Camulodunum and Colchester was unknown until the 18th century. Arthurian scholar Peter Field has suggested that another Camulodunum, a former Roman fort, is a likely location of King Arthur's Camelot and that "Slack, on the outskirts of Huddersfield in West Yorkshire," is where Arthur would have held court. This is because of the name, and also regarding its strategic location: it is but a few miles from the extreme south-west of Hen Ogledd (also making close to North Wales), and would have been a flagship point in staving off attacks to the Celtic kingdoms from the Angles and others.

Other places in Britain with names related to "Camel" have also been suggested, such as Camelford in Cornwall, located down the River Camel from where Geoffrey places Camlann, the scene of Arthur's final battle. The area's connections with Camelot and Camlann are merely speculative. Further north, Camelon and its connections with Arthur's O'on have been mentioned in relation to Camelot, but Camelon may be an antiquarian neologism coined after the 15th century, with its earlier name being Carmore or Carmure. Graham Phillips rejected the word "Camelot" entirely as just Chrétien's invention and instead proposed the old Roman city of Viroconium (near Shrewsbury in modern England) as Arthur's capital, citing archaeological evidence of a grand palace having been in use around 500 AD. Alistair Moffat identified Camelot with Roxburgh in Scotland.

Modern culture
Camelot has become a permanent fixture in modern interpretations of the Arthurian legend. The symbolism of Camelot so impressed Alfred, Lord Tennyson that he wrote up a prose sketch on the castle as one of his earliest attempts to treat the legend. Modern stories typically retain Camelot's lack of precise location and its status as a symbol of the Arthurian world, though they typically transform the castle itself into romantically lavish visions of a High Middle Ages palace. Some writers of the "realist" strain of modern Arthurian fiction have attempted a more sensible Camelot. Inspired by Alcock's Cadbury-Camelot excavation, some authors such as Marion Zimmer Bradley and Mary Stewart place their Camelots in that place and describe it accordingly.

Camelot lends its name to the musical Camelot, which was adapted into a film of the same title, featuring the Castle of Coca, Segovia as Camelot. An Arthurian television series Camelot was also named after the castle, as were some other works including the video game Camelot and the comic book series Camelot 3000. French television series Kaamelott presents a humorous alternative version of the Arthurian legend; Camelot Theme Park is a now-abandoned Arthurian theme park resort located in the English county of Lancashire. The Camelot Group was the first operator of the UK National Lottery with lottery machines named after characters, places, and objects in Arthurian legend.

In American contexts, Camelot era refers to the presidency of John F. Kennedy. In a 1963 Life interview, Jacqueline, his widow, referenced a line from the Lerner and Loewe musical to describe the Kennedy era White House: "Don't let it be forgot, that once there was a spot, for one brief shining moment, that was known as Camelot." She indicated that it was one of Kennedy's favourite lyrics from the musical and added, "there'll be great Presidents again [...] but there'll never be another Camelot again."

title: Camelot


text:
Talk:Crucifix

query
What exactly IS a crucifix? I'm not Christian, sorry for my ignorance. But is it the cross WITH the body of Christ? That's what I thought. --Dmerrill

Yep, in the technical usage of the Roman CAtholic church a cross is a cross, while a crucifix has a corpus (Latin, 'body') fixed to it. The entry needs to be disambiguated. --MichaelTinkler.

 * Have you noticed that Cross has a link to Christian cross, which redirects to this article? There should probably be some actual text at the Christian cross article, instead of redirecting straight here. I didn't set up the redirects, but I've been wondering when someone would notice and object. Guess that would be me now.... --Wesley

Just out of curiousity, if someone wants to make their own crucifix is there any place where a corpus may be obtained? I ask because I had a hard time finding one when I went to make a crucifix last year, only one store had one and it was about three feet tall and was several hundred dollars. I couldn't find any on the internet either in the size or cost range I wanted. I wound up carving the corpus myself - easier said than done because at the time I had very little experience carving stuff. JesseG 19:58, Apr 22, 2005 (UTC)

Irish Penal Cross
I have a replica of what is called, in Ireland, a Penal Cross, the word "cross" being used, rather than "crucifix." This cross takes its name from the days of the Penal Laws (at their worst in the early 18th century). The Penal Laws was the name given to a body of extremely harsh repressive legislation, aimed at reducing the Catholic Irish to abject misery. In practice, even if the niceties of legal terminology put it otherwise, the Catholic Church was outlawed. Priests found in Ireland faced death as did Bishop (now Blessed) Oliver Plunkett.

My carved bog-oak replica is about 9 inches long, the crossbeam 3 inches wide and the upright, which is slightly curved, varying from 1 and a half to 2 inches wide. Note that it bears no resemblance to Celtic Crosses, although an expert in the field might point out similarities in carving styles. Irish lore has it that its peculiar elongated shape allowed the carrier to slip it up his sleeve when necessary.

The Cross, which is representative, or stylized, rather than realistic, is carved with:
 * the letters INRI at the top
 * a hammer and 3 nails below the letters
 * the sun, moon and stars, presumably referring to the unusual meteorological events reported at the time of the Crucifixion
 * the crucified Jesus
 * under Jesus's right arm is what I take--perhaps wrongly--to be a fish
 * under His left arm are two streaks, which I take--again, perhaps wrongly--to represent a flow of blood
 * to Jesus's right, roughly parallel with the legs of the victim, are a spear and a whip, the whip curling around below his feet--4 curved cords
 * to Jesus's left, again roughly parallel, is a primitive ladder
 * below the feet (and the curled whip) is a stylized representation of a cock, poised just above a cooking pot--perhaps a little irony in this grim representation.

I wish to stress that:
 * 1) I am no art historian, I am unfamiliar with the technical terms of this discipline and I make no claims to any specialized knowledge in this field
 * 2) This item is sold as a replica and is available in many Irish shops for tourists.

If anyone can correct my errors, or give more detailed explanations, I will be happy to read it!--PeadarMaguidhir 20:10, 4 August 2006 (UTC)

A little addendum: In the Irish language, a cross is generally called a "cros," whereas a crucifix is generally called a "cros céasta."--PeadarMaguidhir 21:08, 4 August 2006 (UTC) Hi Peadar, The cock and pot were symbols for the resurrection, probably a secret symbol? See my Penal Cross at http:// www.killylissstudio.com for illustration. Colm Mc Cann. —Preceding unsigned comment added by 80.42.62.233 (talk) 11:06, 14 September 2009 (UTC)

when did this happen?
In the beginning of the second section, it says "Also, in the Old Testament, Moses lifted up a snake crucified on a pole-- a kind of symbolic crucifix". This didn't happen in the Torah, which is the original old testament. Could someone please clarify how they got this from the old testament? It's obviously Christian, but which version of the bible is it? Could someone please clarify this for me? thanks. Ilikefood 23:38, 21 December 2006 (UTC)

It is from the Torah -- Numbers 21:9. 71.206.186.34 (talk) 06:17, 27 October 2008 (UTC)

Is the Crucifix a Catholic Thing?
I am just wondering why were references to Oriental Orthodox (and Anglican churches) have been removed. A large Crucifix is used in all Coptic Orthodox Churches above the altar. Furthermore the Crucifix is used in processions on various major feasts. I am just trying to make a point that it is used extensively in the Oriental Orthodox Church. (Mike Morgan 21:16, 26 August 2007 (UTC))

 * It is used in most of the European protestant churches, as well. See http://www.dorfkirche-bentwisch.de/?page_id=14 for a reference. --62.224.194.7 (talk) 22:20, 19 November 2008 (UTC)

 * The quote at the top of the article says "It is primarily used...", that doesn't mean exclusively used. In addition to orthodox, many "high-order" protestant denominations use the crucifix. If varies denomination to denomination, but many protestant denominations prefer just the cross. By the way I reverted the edit dealing with atheists using the upside down cross as a protest. It was actually added by an atheist based on a cite. Not a church going "hate monger"  Please refrain from attacks.  Marauder40 (talk) 03:34, 20 November 2008 (UTC)

Random comment
Anyway -- it should be mentioned that they used to have daggers embedded in their crucifixes. I'd like to know if that was for self-defense, forceable conversion, both, or neither :) ClintJCL (talk) 18:22, 18 April 2008 (UTC)
 * Nonsense, I have never heard that. References please?Tarheelz123 (talk) 23:28, 1 June 2009 (UTC)

Controversies in other religions
I gather that many other religions find the crucifix to be offensive, especially among muslims, jews, seculars and evangelicals, who claim it to be an idol. There should be information on this, since in many occasions crucifixes have been banned in public because of controversies surrounding them. ADM (talk) 18:07, 3 January 2009 (UTC)

which is the essential bit?

 * A crucifix (from Latin cruci fixus meaning "(one) fixed to a cross") is a cross with a representation of Jesus' body....

Given the etymology, might it not be a bit more more accurate to say a crucifix is a representation of Jesus' body (on a cross)? When Jesus is displayed in the same position but without an explicit image of the cross itself, wouldn't that also be a crucifix? —Tamfang (talk) 16:30, 7 July 2009 (UTC)
 * In order to qualify as a crucifix there must be both a cross and the image of the crucified Christ. If either is missing then it isn't a crucifix, it is just a cross or a picture of the Risen Christ.  Marauder40 (talk) 20:18, 7 July 2009 (UTC)
 * Um, I wouldn't think it represents "Risen" if he has his arms out in cross position. —Tamfang (talk) 15:57, 12 July 2009 (UTC)
 * Actually it depends on what the artist of the image intended. If you have seen the San Damiano cross, it is called a cross as opposed to a crucifix because of the fact that Jesus is not actually attached to the cross in the image.  It is because of the fact the artist wanted to represent that Jesus had risen.  When the term crucifix is used, both Jesus (in a crucified image) and the cross must be present. Marauder40 (talk) 17:53, 13 July 2009 (UTC)

Stil Suffering?
The article states, "depictions of the still-suffering Jesus ... are more typical of Western churches". While there are many famous Western crucifixes which show Christ still suffering, I think the majority show him with his eyes closed and his head down to the right (inclined towards St. Dismas). MishaPan (talk) 04:37, 25 January 2010 (UTC)
 * Yes, I have rewritten this. It has varied over the centuries, & many larger paintings show the moment of death (with the spear), but not crucifixes normally of course. The presence or absence of the spear wound would traditionally be the mark of whether he is alive or dead, though I wonder how many Catholics today, or artists, are aware of that (now added). "Popular culture" depictions generally show him alive, I think, as did early Western ones (before about 1000). The Baroque, following Michelangelo, often showed him alive too. Johnbod (talk) 05:22, 25 January 2010 (UTC)

Roman Catholic vs Orthodox use of "Crucifix"
The use of three dimentional religious figures is of ROMAN CATHOLIC origin. Although Rome claims Apostolic Succession from the early Church, the ROMAN CATHOLIC CHURCH started after the http://en.wikipedia.org/wiki/East-West_Schism in 1054 AD, when Rome split from THE CHURCH in Constantinople, now Instanbul. The Eastern Orthodox Church uses only an "image" of Jesus on the cross, and an image of Jesus and Saints on icons. That image may be raised like the "profile" on a coin, usually only on metal crosses or icons, but never three dimensional, thereby eliminating any claims of practicing IDOLTRY.

Treckoj (talk) 20:37, 18 March 2010 (UTC)
 * Yes, thats what the article says. Johnbod (talk) 20:41, 18 March 2010 (UTC)

Early history of this page
The early history of this page from December 2001 is at the article cross. Graham 87 11:00, 26 May 2010 (UTC)

Veneration
Any items on the veneration of the Crucifix? Seems missing. History2007 (talk) 20:36, 16 June 2010 (UTC)
 * The Good Friday article has the following quote with references. It could be put here. "The Veneration of the Cross, has a crucifix, not necessarily the one that is normally on or near the altar at other times, solemnly displayed to the congregation and then venerated by them, individually if possible and usually by kissing the feet of the Corpus, while hymns and the Improperia ("Reproaches") with the Trisagion hymn are chanted.[24]"  Maybe add something about the fact it is done on Good Friday throughout the Catholic Church and other times as local custom dictates. It's up to you. Marauder40 (talk) 20:44, 16 June 2010 (UTC)

 * I just did not do enough of a search, hoping someone knew. The question was, is there an official Crucifix version of Eucharistic Adoration, even without a ceremony? History2007 (talk) 21:21, 16 June 2010 (UTC)

 * Haven't heard of anything official outside of the Good Friday service. But that doesn't mean there isn't one.  If you are talking is there a Church-wide one in the rubrics, I don't think so.  Is there a local devotion that has been approved, probably. Marauder40 (talk) 12:58, 17 June 2010 (UTC)

 * Thanks, I will have to do more searching. Alas Google books seems to be cutting back on free material, so life on that front will be less easy. History2007 (talk) 14:28, 17 June 2010 (UTC)

What about the bent crucifix?
This is a very odd motive, and I would like to see it explained and discussed somewhere. __meco (talk) 16:24, 19 November 2010 (UTC)
 * It's a crucifix that the artist who created it decided to create bent. What is there to explain and discuss?Farsight001 (talk) 01:30, 9 December 2010 (UTC)
 * As you said not much to discuss for the article, but the reasoning I have heard for the reasoning behing the bent crucifix is the implication that nothing could hold the "spiritual" weight of Jesus without bending.Marauder40 (talk) 14:37, 9 December 2010 (UTC)

Terminology in "Usage" section
Just need to point out that the initial phrase stating "Roman Catholic (Eastern and Western Rite Catholics)" is a hideous error. The logical and proper terminology for referring to the Church at large, particularly when specifying both East and West is simply the Catholic Church, as Wikipedia does. For a period in history RCC and CC were interchangeable due to the East(Greek)-West Schism where the ROMAN or Western section was considered to be the lone remnant of the Catholic Church.[Albiet Italo Greek and Maronite Eastern Catholics never broke union with the Holy See] However it should be understood and respected that if not all Catholics belong simply to the "Roman" Latin Rite- there are now reunified co-equal representative Eastern Catholic churches per every post-Schismatic orthodox church -  then you should not refer to Eastern or Greek Rite Catholics as "Roman". Thus it is factual, liturgical, and historically erroneous to make such a statement as "Roman Catholic (Eastern and Western Rite Catholics)" and may implicate a pejorative against Eastern Catholics.

Please make the appropriate changes: Catholic (Eastern and Western Rite Catholics). Thank you. Micael (talk) 23:32, 2 April 2011 (UTC)

 * Please see Roman Catholic (term)... If I had an electron for every time I have said that the world's energy problems would be over. I will link to in in the article now. History2007 (talk) 00:27, 3 April 2011 (UTC)

History'07 that is a terrible alibi (wonder why it is a recurrent theme?), the article is about the Crucifix, not about the historical reasons for variations in terminology.

The article referenced says it all:
 * "The term Roman Catholic appeared in the English language at the beginning of the 17th century, to differentiate specific groups of Christians in communion with the Pope from others... It has continued to be widely used in the English language ever since, although its usage has changed over the centuries. The church widely known as the Catholic Church consists of 23 autonomous churches... "

The article is not about historical nuances within the English language (and consequently the convoluted misnomers it creates) or English theological-socio-political changes introduced by the English Reformation. This is a generic article about an ancient Christian symbol, the Crucifix. The more this "less than widely known" and particularly its awkward use within the article is rammed upon wikipedia readers - the more evidence there must me some subliminal ulterior motive behind its stubborn inclusion. Additionally, I don't know why "Roman Catholic" must be used when to refering to the widely known Catholic Church (Eastern and Western..) when you never see Eastern Churches refered to as the "Easterm Roman Catholic" Church : Because its a laughably ridiculous and silly statement. Hence  Roman Catholic (Eastern and Western Rite Catholics) should be made history, History!!!

Lastly, the use of a link does not help it only serves the ulterior motive to attempt to substantiate the obtuse use of such a term. Micael (talk) 05:41, 6 April 2011 (UTC)

 * Ooooh, are we not getting upset now. Actually, you were right about one usage, now that I have read the page more carefully, and I changed that. However, if you read the RC term page, you will see that popes have used that term in the 20th century, etc. But let us let that be the cause of a heart attack another day, not today. Cheers. History2007 (talk) 06:36, 6 April 2011 (UTC)
 * The "Roman Catholic (term)" article says the first known occurrence in English of the term "Roman Catholic" was at the beginning of the 17th century. (A slightly inaccurate statement, since some instances of its use in English have been found in the late 16th century.)  It was in use in Latin and other languages earlier, even, it seems, before the Protestant Reformation: according to section 423 of this source, the Church "outside which we believe no one is saved" (and so the Catholic Church as a whole) was called Roman at latest by the year 1208.  This church, "widely known as the Catholic Church" - nobody denies that - is also widely known as the "Roman Catholic Church".  The Popes repeatedly call it by this name, as well as by the name "Catholic Church".  Are they laughable, ridiculous, silly and obtuse?  As for the application of "Roman Catholic" to Eastern Catholic Churches, search the Internet with Google or any other search application, and you will find thousands of instances of the use of "Maronite Roman Catholic".  Esoglou (talk) 07:45, 6 April 2011 (UTC)

 * Yes, I agree with Esoglou. The term "Maronite Roman Catholic" says a lot. Now, in order not to let this page become the site of the new debate I will say no more. I am however, thinking of calling the Pope to issue an encyclical on this, because this issue just does not want to die. History2007 (talk) 12:07, 6 April 2011 (UTC)

Esoglou/History it IS a ridiculous, silly and obtuse statement...you just don't find such a phrase as "Roman Catholic Eastern and Western Rite" in any respectable literature, period. Cherry picking the rare Eastern Catholic church that might advertise itself as "Roman Catholic- Maronite Rite" to help many ignorant Latin Rite Catholics understand that they are welcome and are in union with the Holy See does not help your argumentation. But, this issue is not merely a religious argument, it is self evident that phrase sounds awkward regardless and the more you all try to deny it the more it is apparent you have a hidden agenda. The phrase plain and simply flows much better and is understood without any problem by just stating "Catholicism (Eastern and Western Rites) or just "Catholicism". What is the problem with that? What irks you so much about keeping it simple!!! Micael (talk) 19:23, 6 April 2011 (UTC)

 * I should say no more so that my hidden agenda about the use of that term on the Grassy knoll may become apparent here - just kidding. But Micael, please do calm down. It is just a term. Thanks. History2007 (talk) 19:44, 6 April 2011 (UTC)

I'm just trying to help out...I do not understand why you all get so worked up about keeping things on the simplest terms. If it is sincerely "just a term" then keeping things straighforward should be the matter here and would certainly be greatly appreciated. Micael (talk) 22:17, 7 April 2011 (UTC)

I reiterate to the benefit of Wikpedia readers, can we end this terminology issue and just keep things to the simplest of terms? Thanks. Micael (talk) 18:22, 14 April 2011 (UTC)

 * I was trying not to prolong this discussion, but I will give some examples. Esoglou knows a lot about this issue and his opinion will also be appreciated. But the fact is that there are many differences with the Eastern Catholics anyway, so the distinction needs to be maintained at that level, e.g. the Wiki-article on Sacred Heart correctly states:

 * Devotion to the Sacred Heart is sometimes seen in the Eastern Catholic Churches, where it remains a point of controversy and is seen as an example of Liturgical Latinisation.

 * Moreover, as the case for many scapular shows, there are many devotional differences, so the term "Roman" needs to be maintained to avoid errors when making statements. One can not just say: "Catholics follow the devotion to TopicA" because the Eastern may not follow it. On another front, as the examples on the Roman Catholic (term) page show, the popes have used the term Roman Catholic Church to refer to the whole Church. So who am I to disagree? I assure you that I have almost no hope of getting elected as the next pope, so I will not second guess their usage. History2007 (talk) 19:20, 14 April 2011 (UTC)

Sorry History'07, what are you talking about? ... "  the term "Roman" needs to be maintained to avoid errors when making statements. One can not just say: Catholics follow the devotion to TopicA because the Eastern may not follow it. "  You need not express this as "errors" but points of view and regardless the words E."Catholic" and E."Orthodox" clearly differentiate the two. In claiming that Eastern implicates strictly an Eastern Orthodox definition and that all else is "error" you make a clear and unfortunate presumption. You need to respect that Eastern Christianity contains various POV including Eastern Catholics.

Because of such bias, you and others fail to recognize that devotionals, though initiated in particular churches are not restrained to liturgical rites. Even within Latins! You see though I am a Latin RITE Catholic it does not exclude me from expressing my Catholicity (in addition to the Latin Rite) in my devotions or prayers. For example: I frequently pray the Jesus prayer, an Eastern devotion, before receiving communion and am avid devotee of certain Eastern saints as St. Nickolas regardless of RITE...as ultimately we are united in the same faith: Catholicism.

Lastly just because in the past the Church has refered to itself as the Roman Catholic Church in a general sense (albeit rare) does not mean that NON-Catholics use it or understand the term in the same sense []... in fact some use the ROMAN term PEJORATIVELY emphasizing the ROME, thus mis-characterizing the church in a highly insultive manner.[]  Since, many if not most here are not Catholic and some show significant resistance to such a simple term as just Catholic it can be presumed that some though not all may use this additional and unnecessary term to apply (even in an incorrect and inappropriate sense)to belittle Eastern Catholics and Catholics in general just to get their point across. NOTE:You will never see such a silly term as RC Eastern Church in any official church document...which I remind you is required by proper Wiki standards.

Similarly, the church allows all Catholics to satisfy the Sunday obligation -Divine Liturgy/Mass regardless of Rite (Roman, Byzantine, Chaldean) without making one any less Catholic regardless of rite...actually its what makes us Katholic(greek) for UNIVERSAL. we are not restricted by liturgical rite in our devotionals whether Eastern or Western.[][] Micael (talk) 07:57, 24 April 2011 (UTC)

 * So is the devotion to Sacred heart a Catholic or Roman Catholic devotion? History2007 (talk) 08:15, 24 April 2011 (UTC)

Excellent question History'07! The Sacred Heart devotion is a Catholic devotion developed via the Western Church (aka, Roman Catholic/Latin Rite - small "c"- church), but to myopically focus on the region of development really diminishes its Universal character, its very Catholicity{Katholic=Greek for universal} For example, the concept and devotion to iconography though developed in the East is a venerable practice of the entire Catholic Church, regardless of liturgical rite. With icons being displayed on alters of many Latin Rite Churches despite of whether it is an eastern or western devotion (ie, my own local parish church).

A precise example of this open practice of Catholic devotion is exemplified in the late Blessed Pope John Paul the Great's apostolic letter Orientale Lumen (Light of the East), as follows:

 * Since, in fact, we believe that the venerable and ancient tradition of the Eastern Churches is an integral part of the heritage of Christ's Church, the first need for Catholics is to be familiar with that tradition, so as to be nourished by it and to encourage the process of unity in the best way possible for each.

 * Our Eastern Catholic brothers and sisters are very conscious of being the living bearers of this tradition, together with our Orthodox brothers and sisters. The members of the Catholic Church of the Latin tradition must also be fully acquainted with this treasure and thus feel, with the Pope, a passionate longing that the full manifestation of the Church's catholicity be restored to the Church and to the world, expressed not by a single tradition, and still less by one community in opposition to the other; and that we too may be granted a full taste of the divinely revealed and undivided heritage of the universal Church which is preserved and grows in the life of the Churches of the East as in those of the West.

This Dominican order has a particular devotion to iconography, DominICON. Thus likewise Eastern Catholics also may be great devotees of such other Catholic devotions as the Sacred Heart as it also forms an integral part of the heritage of Christ's Church! Thus please, I reiterate, clarify the statement to simply say: " Catholic (Eastern and Western Rite Catholics)". Thanks and may God bless you! Micael (talk) 05:07, 13 May 2011 (UTC)

 * But the question still remains: Are all devotions shared among Eastern and Western Catholics? Are there no devotions that take place within one and not the other? Are there no differences whatsoever between Western and Eastern Catholics? History2007 (talk) 07:00, 13 May 2011 (UTC)

Merge the article "Christian cross" into this article
The article Christian cross is largely a duplication of this article. As the term "Christian cross" is referring to the crucifix that Jesus was put on, I believe that "Christian cross" should redirect to this article as the single article on the topic of Christian crucifix symbol.--R-41 (talk) 23:23, 15 October 2011 (UTC)
 * The content seems totally different to me - just in case you haven't read the first sentence of this article, it reads: "A crucifix (from Latin cruci fixus meaning "(one) fixed to a cross") is a usually three-dimensional cross with a representation of Jesus' body", Johnbod (talk) 23:28, 15 October 2011 (UTC)

 * Agree with John, it is not going to work at all, please see: Coptic ankh Maltese-Cross, Cross crosslet etc. etc. etc. which are not Crucifixes. A Crucifix is a WP:Notable item in its own right and must have a separate article, as does Christian Cross. The issue of any possible overlap in current article texts is in any case a separate issue which may need a separate remedy. History2007 (talk) 23:33, 15 October 2011 (UTC)

 * This is about the premier Christian symbol that is the crucifix - a cross shaped device of connected wooden boards used in the form of execution utilized by the Romans called crucifixion, Jesus was executed by crucifiction as were other people including other Christians such as Saint Peter. Many images displayed on the Christian cross article are almost all crucifixes, the Coptic ankh has its own article for the symbol of Coptic Christianity - and it has ancient Egyptian origins and appears very different from the standard Christian cross that is a crucifix.--R-41 (talk) 23:40, 15 October 2011 (UTC)

 * No, in any case you need WP:RS sources to support your assertions, which are, as is personal commentary, and not correct in any case. History2007 (talk) 23:48, 15 October 2011 (UTC)
 * Let's spell it out very clearly: if there's no figure it's not a crucfifix. A crucifix is a religious image, it is not an "execution device".  Jesus was not put on a crucifix (as you say above), but a cross, and a crucifix is not  "a cross shaped device of connected wooden boards used in the form of execution utilized by the Romans called crucifixion" - that's a cross.  There's no point continuing the discussion until you're clear on that.  I suggest you look at a dictionary.   Most of the images in the cross article are not crucifixes, though the ones in the text near the top are - which should probably be changed. Johnbod (talk) 02:34, 16 October 2011 (UTC)
 * Alright I end my proposal to merge the two articles. Howevever I do have a question for Johnbod. What would you call the form of execution that Jesus and other people went through via being nailed to a cross-shaped device? You say that crucifix exclusively means the specific symbol of Jesus on a cross, but the term crucifixion is a term used for that form of execution existing at back at earliest to the 6th century BC, see here: . The crucifix has been referred to as connection of a body to a cross execution device not only for Jesus, but also including others such as the bishop Geno in the 10th century, see here .--R-41 (talk) 18:34, 16 October 2011 (UTC)
 * As I'm sure the article explains, crucifixion is derived from a Latin word made up of "crux, crucis" meaning cross and "fix-" meaning fix, so fixed to a cross. In English crucifixion is a method, that uses a cross, and a crucifix is an image of the crucifixion of Jseus taking place. The Gero Cross is a sculpted crucifixion image (of Jesus) commissioned by Bishop Gero, who died in his bed. Hope that helps. Johnbod (talk) 19:11, 16 October 2011 (UTC)
 * Actually there is no historical record that a cross was used in Calvary. Some people (and I am not among them) argue that it was a straight pole, but they are in a minority. History2007 (talk) 18:57, 16 October 2011 (UTC)

Róðukross
The new language editing system is not cooperating. So I'll just put this information here in case an experienced editor sees it. The Icelandic Wikipedia page for Róðukross should be language linked to the page for Crucifix. https://is.wikipedia.org/wiki/Róðukross — Preceding unsigned comment added by 130.243.173.224 (talk) 19:52, 3 August 2015 (UTC)
 * Yes check.svg Done Elizium23 (talk) 01:25, 4 August 2015 (UTC)

title: Talk:Crucifix