Introduction.

The term "B-spline" was coined by Isaac Jacob Schoenberg and is short for basis spline. A spline function of order formula_1 is a piecewise polynomial function of degree formula_2 in a variable formula_3. The places where the pieces meet are known as knots. The key property of spline functions is that they and their derivatives may be continuous, depending on the multiplicities of the knots.  B-splines of order formula_4 are basis functions for spline functions of the same order defined over the same knots, meaning that all possible spline functions can be built from a linear combination of B-splines, and there is only one unique combination for each spline function.

Definition.

A spline of order formula_4 is a piecewise polynomial function of degree formula_6 in a variable formula_7. The values of formula_7 where the pieces of polynomial meet are known as knots, denoted formula_9 and sorted into non-decreasing order. When the knots are distinct, the first formula_10 derivatives of the polynomial pieces are continuous across each knot. When formula_11 knots are coincident, then only the first formula_12 derivatives of the spline are continuous across that knot.  For a given sequence of knots, there is, up to a scaling factor, a unique spline formula_13 satisfying  If we add the additional constraint that formula_15 for all formula_7 between the first and last knot, then the scaling factor of formula_13 becomes fixed. The resulting formula_13 spline functions are called B-splines.  Alternatively, B-splines can be defined by construction by means of the Cox–de Boor recursion formula. Given a knot sequence formula_19, then the B-splines of order 1 are defined by  These satisfy formula_21 for all formula_7 because for any formula_7 exactly one of the formula_24, and all the others are zero.  The higher order B-splines are defined by recursion

Properties.

B-spline function is a combination of flexible bands that passes through the number of points that are called control points and creates smooth curves. These functions enable the creation and management of complex shapes and surfaces using a number of points. B-spline function and Bézier functions are applied extensively in shape optimization methods.  A B-spline of order formula_4 is a piecewise polynomial function of degree formula_6 in a variable formula_7. It is defined over formula_29 locations formula_30, called knots or breakpoints, which must be in non-descending order formula_31. The B-spline contributes only in the range between the first and last of these knots and is zero elsewhere. If each knot is separated by the same distance formula_32 (where formula_33) from its predecessor, the knot vector and the corresponding B-splines are called 'uniform' (see cardinal B-spline below).  For each finite knot interval where it is non-zero, a B-spline is a polynomial of degree formula_2. A B-spline is a continuous function at the knots. When all knots belonging to the B-spline are distinct, its derivatives are also continuous up to the derivative of degree formula_10. If the knots are coincident at a given value of formula_7, the continuity of derivative order is reduced by 1 for each additional coincident knot. B-splines may share a subset of their knots, but two B-splines defined over exactly the same knots are identical. In other words, a B-spline is uniquely defined by its knots.  One distinguishes internal knots and end points. Internal knots cover the formula_7-domain one is interested in. Since a single B-spline already extends over formula_29 knots, it follows that the internal knots need to be extended with formula_6 end points on each side, to give full support to the first and last B-spline which affect the internal knot intervals. The values of the endpoints do not matter, usually the first or last internal knot is just repeated.  The usefulness of B-splines lies in the fact that any spline function of order formula_4 on a given set of knots can be expressed as a linear combination of B-splines: B-splines play the role of basis functions for the spline function space, hence the name. This property follows from the fact that all pieces have the same continuity properties, within their individual range of support, at the knots.  Expressions for the polynomial pieces can be derived by means of the Cox–de Boor recursion formula  That is, formula_44 is piecewise constant one or zero indicating which knot span "x" is in (zero if knot span "j" is repeated). The recursion equation is in two parts: ramps from zero to one as "x" goes from formula_46 to formula_47 and ramps from one to zero as "x" goes from formula_49 to formula_50. The corresponding "B"s are zero outside those respective ranges. For example, formula_51 is a triangular function that is zero below formula_52, ramps to one at formula_53 and back to zero at and beyond formula_54. However, because B-spline basis functions have local support, B-splines are typically computed by algorithms that do not need to evaluate basis functions where they are zero, such as de Boor's algorithm.  This relation leads directly to the FORTRAN-coded algorithm BSPLV which generates values of the B-splines of order "n" at "x". The following scheme illustrates how each piece of order "n" is a linear combination of the pieces of B-splines of order "n"-1 to its left.  Application of the recursion formula with the knots at formula_56 gives the pieces of the uniform B-spline of order 3 These pieces are shown in the diagram. The continuity property of a quadratic spline function and its first derivative at the internal knots are illustrated, as follows The second derivative of a B-spline of degree 2 is discontinuous at the knots:  Faster variants of the de Boor algorithm have been proposed but they suffer from comparatively lower stability.

Cardinal B-spline.

A cardinal B-spline has a constant separation, "h", between knots. The cardinal B-splines for a given order "n" are just shifted copies of each other. They can be obtained from the simpler definition.  The "placeholder" notation is used to indicate that the "n"th divided difference of the function formula_64 of the two variables "t" and "x" is to be taken by fixing "x" and considering formula_65 as a function of "t" alone.  A cardinal B-spline has uniform spaced knots, therefore interpolation between the knots equals convolution with a smoothing kernel.  Example, if we want to interpolate three values in between B-spline nodes (formula_66), we can write the signal as:  formula_67  Convolution of the signal formula_68 with a rectangle function formula_69 gives first order interpolated b-spline values. Second-order B-spline interpolation is convolution with a rectangle function twice formula_70, by iterative filtering with a rectangle function higher order interpolation is obtained.  Fast b-spline interpolation on a uniform sample domain can be done by iterative mean-filtering. Alternatively, a rectangle function equals Sinc in Fourier domain. Therefore, cubic spline interpolation equals multiplying the signal in Fourier domain with Sinc^4.  See Irwin–Hall distribution#Special cases for algebraic expressions for the cardinal B-splines of degree 1-4.

P-spline.

The term P-spline stands for "penalized B-spline". It refers to using the B-spline representation where the coefficients are determined partly by the data to be fitted, and partly by an additional penalty function that aims to impose smoothness to avoid overfitting.

Derivative expressions.

The derivative of a B-spline of degree "k" is simply a function of B-splines of degree "k"-1. This implies that which shows that there is a simple relationship between the derivative of a spline function and the B-splines of degree one less.

Moments of univariate B-splines.

Univariate B-splines, i.e. B-splines where the knot positions lie in a single dimension, can be used to represent 1-d probability density functions formula_73. An example is a weighted sum of formula_74 B-spline basis functions of order formula_4, which each are area-normalized to unity (i.e. not directly evaluated using the standard de-Boor algorithm)  and with normalization constant constraint formula_77. The k-th raw moment formula_78 of a normalized B-spline formula_79 can be written as Carlson's Dirichlet average formula_80, which in turn can be solved exactly via a contour integral and an iterative sum as  with  and formula_83. Here, formula_84 represents a vector with the formula_85 knot positions and formula_86 a vector with the respective knot multiplicities. One can therefore calculate any moment of a probability density function formula_73 represented by a sum of B-spline basis functions exactly, without resorting to numerical techniques.

Relationship to piecewise/composite Bézier.

A Bézier curve is also a polynomial curve definable using a recursion from lower degree curves of the same class and encoded in terms of control points, but a key difference is that all terms in the recursion for a Bézier curve segment have the same domain of definition (usually formula_88) whereas the supports of the two terms in the B-spline recursion are different (the outermost subintervals are not common). This means a Bézier curve of degree formula_4 given by formula_90 control points consists of about formula_91 mostly independent segments, whereas the B-spline with the same parameters smoothly transitions from subinterval to subinterval. To get something comparable from a Bézier curve, one would need to impose a smoothness condition on transitions between segments, resulting in some manner of Bézier spline (for which many control points would determined by the smoothness requirement).  A piecewise/composite Bézier curve is a series of Bézier curves joined with at least C0 continuity (the last point of one curve coincides with the starting point of the next curve). Depending on the application, additional smoothness requirements (such as C1 or C2 continuity) may be added. C1 continuous curves have identical tangents at the breakpoint (where the two curves meet). C2 continuous curves have identical curvature at the breakpoint.  To gain C2 continuity the Bézier curve loses local control, because to enforce C2 continuity the control points are dependent on each other. If a single control point moves, the whole spline needs to be re-evaluated. B-splines have both C2 continuity and local control, but they lose the interpolation property of a piecewise Bézier.

Curve fitting.

Usually in curve fitting, a set of data points is fitted with a curve defined by some mathematical function. For example, common types of curve fitting use a polynomial or a set of exponential functions. When there is no theoretical basis for choosing a fitting function, the curve may be fitted with a spline function composed of a sum of B-splines, using the method of least squares. Thus, the objective function for least squares minimization is, for a spline function of degree "k", "W(x)" is a weight and "y(x)" is the datum value at "x". The coefficients formula_93 are the parameters to be determined. The knot values may be fixed or they too may be treated as parameters.  The main difficulty in applying this process is in determining the number of knots to use and where they should be placed. de Boor suggests various strategies to address this problem. For instance, the spacing between knots is decreased in proportion to the curvature (2nd. derivative) of the data. A few applications have been published. For instance, the use of B-splines for fitting single Lorentzian and Gaussian curves has been investigated. Optimal spline functions of degrees 3-7 inclusive, based on symmetric arrangements of 5, 6, and 7 knots, have been computed and the method was applied for smoothing and differentiation of spectroscopic curves. In a comparable study, the two-dimensional version of the Savitzky-Golay filtering and the spline method produced better results than moving average or Chebyshev filtering.

Computer-aided design and computer graphics.

In computer-aided design and computer graphics applications, a spline curve is sometimes represented as formula_94, a parametric curve of some real parameter formula_95. In this case the curve formula_94 can be treated as two or three separate coordinate functions formula_97, or formula_98. The coordinate functions formula_99, formula_100 and formula_101 are each spline functions, with a common set of knot values formula_102.  Because a B-splines form basis functions, each of the coordinate functions can be expressed as a linear sum of B-splines, so we have  The weights formula_104, formula_105 and formula_106 can be combined to form points formula_107 in 3-d space. These points formula_108 are commonly known as control points.  Working in reverse, a sequence of control points, knot values, and order of the B-spline define a parametric curve. This representation of a curve by control points has a several useful properties:  A less desirable feature is that the parametric curve does not interpolate the control points. Usually the curve does not pass through the control points.

NURBS.

In computer aided design, computer aided manufacturing, and computer graphics, a powerful extension of B-splines is non-uniform rational B-splines (NURBS). NURBS are essentially B-splines in homogeneous coordinates. Like B-splines, they are defined by their order, and a knot vector, and a set of control points, but unlike simple B-splines, the control points each have a weight. When the weight is equal to 1, a NURBS is simply a B-spline and as such NURBS generalizes both B-splines and Bézier curves and surfaces, the primary difference being the weighting of the control points which makes NURBS curves "rational". By evaluating a NURBS at various values of the parameters, the curve can be traced through space; likewise, by evaluating a NURBS surface at various values of the two parameters, the surface can be represented in Cartesian space.  Like B-splines, NURBS control points determine the shape of the curve. Each point of the curve is computed by taking a weighted sum of a number of control points. The weight of each point varies according to the governing parameter. For a curve of degree "d", the influence of any control point is only nonzero in "d"+1 intervals (knot spans) of the parameter space. Within those intervals, the weight changes according to a polynomial function (basis functions) of degree "d". At the boundaries of the intervals, the basis functions go smoothly to zero, the smoothness being determined by the degree of the polynomial.  The knot vector is a sequence of parameter values that determines where and how the control points affect the NURBS curve. The number of knots is always equal to the number of control points plus curve degree plus one. Each time the parameter value enters a new knot span, a new control point becomes active, while an old control point is discarded.  A NURBS curve takes the following form:  Here the notation is as follows. "u" is the independent variable (instead of "x"), "k" is the number of control points, "N" is a B-spline (used instead of "B"), "n" is the polynomial degree, "P" is a control point and "w" is a weight. The denominator is a normalizing factor that evaluates to one if all weights are one.  It is customary to write this as  in which the functions  are known as the rational basis functions.  A NURBS surface is obtained as the tensor product of two NURBS curves, thus using two independent parameters "u" and "v" (with indices "i" and "j" respectively):  with  as rational basis functions.

References.

Works cited

In the mathematical subfield of numerical analysis, a B-spline or basis spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. Any spline function of given degree can be expressed as a linear combination of B-splines of that degree. Cardinal B-splines have knots that are equidistant from each other. B-splines can be used for curve-fitting and numerical differentiation of experimental data.

B-spline křivka je aproximační křivka, která se často používá v CAD/CAM modelování ve 3D. Nejpoužívanější variantou je NURBS (NeUniformní Racionální B-Spline).


Etymology.

The Greek word "ekklēsia", literally "called out" or "called forth" and commonly used to indicate a group of individuals called to gather for some function, in particular an assembly of the citizens of a city, as in, is the New Testament term referring to the Christian Church (either a particular local group or the whole body of the faithful). In the Septuagint, the Greek word "ἐκκλησία" is used to translate the Hebrew "קהל" (qahal). Most Romance and Celtic languages use derivations of this word, either inherited or borrowed from the Latin form "ecclesia".  The English language word "church" is from the

History.

The Christian Church originated in Roman Judea in the first century AD/CE, founded on the teachings of Jesus of Nazareth, who first gathered disciples. Those disciples later became known as "Christians"; according to Scripture, Jesus commanded them to spread his teachings to all the world. For most Christians, the holiday of Pentecost (an event that occurred after Jesus' ascension to Heaven) represents the birthday of the Church, signified by the descent of the Holy Spirit on gathered disciples. The leadership of the Christian Church began with the Apostles.  Springing out of Second Temple Judaism, from Christianity's earliest days, Christians accepted non-Jews (Gentiles) without requiring full adoption of Jewish customs (such as circumcision). The parallels in the Jewish faith are the Proselytes, Godfearers, and Noahide Law; see also Biblical law in Christianity. Some think that conflict with Jewish religious authorities quickly led to the expulsion of Christians from the synagogues in Jerusalem (see also Council of Jamnia and List of events in early Christianity).  The Church gradually spread throughout the Roman Empire and beyond, gaining major establishments in cities such as Jerusalem, Antioch, and Edessa. It also became a widely persecuted religion. It was condemned by the Jewish authorities as a heresy (see also Rejection of Jesus). The Roman authorities persecuted it because, like Judaism, its monotheistic teachings were fundamentally foreign to the polytheistic traditions of the ancient world and a challenge to the imperial cult. The Church grew rapidly until finally legalized and then promoted by Emperors Constantine I and Theodosius I in the 4th century as the State Church of the Roman Empire.  Already in the 2nd century, Christians denounced teachings that they saw as heresies, especially Gnosticism but also Montanism. Ignatius of Antioch at the beginning of that century and Irenaeus at the end saw union with the bishops as the test of correct Christian faith. After legalization of the Church in the 4th century, the debate between Arianism and Trinitarianism, with the emperors favouring now one side now the other, was a major controversy.

Use by early Christians.

In using the word ἐκκλησία ("ekklēsia"), early Christians were employing a term that, while it designated the assembly of a Greek city-state, in which only citizens could participate, was traditionally used by Greek-speaking Jews to speak of Israel, the people of God, and that appeared in the Septuagint in the sense of an assembly gathered for religious reasons, often for a liturgy; in that translation ἐκκλησία stood for the Hebrew word קהל ("qahal"), which however it also rendered as συναγωγή ("synagōgē", "synagogue"), the two Greek words being largely synonymous until Christians distinguished them more clearly.  The term ἐκκλησία appears in only two verses of the Gospels, in both cases in the Gospel of Matthew. When Jesus says to Simon Peter, "You are Peter, and on this rock I will build my church", the church is the community instituted by Christ, but in the other passage the church is the local community to which one belongs: "If he refuses to listen to them, tell it to the church."  The term

Christianity as Roman state religion.

On February 27, 380, the Roman Empire officially adopted the Nicene version of Christianity as its state religion. Prior to this date, Constantius II (337-361) and Valens (364-378) had personally favored Arian or Semi-Arian forms of Christianity, but Valens' successor Theodosius I supported the more Athanasian or Trinitarian doctrine as expounded in the Nicene Creed from the 1st Council of Nicaea.  On this date, Theodosius I decreed that only the followers of Trinitarian Christianity were entitled to be referred to as Catholic Christians, while

Great Schism of 1054.

Although there had long been frictions between the Bishop of Rome (e.g. the patriarch of the Catholic Church proper) and the eastern patriarchs within the Byzantine Empire, Rome's changing allegiance from Constantinople to the Frankish king Charlemagne set the Church on a course towards separation. The political and theological divisions would grow until Rome and the East excommunicated each other in the 11th century, ultimately leading to the division of the Church into the Western (Catholic) and Eastern

Protestant Reformation.

The changes brought on by the Renaissance eventually led to the Protestant Reformation during which the Protestant Lutheran and the Reformed followers of Calvin, Hus, Zwingli, Melancthon, Knox, and others split from the Catholic Church. At this time, a series of

Catholic tradition.

The Catholic Church teaches in its doctrine that it is the original church founded by Christ on the Apostles in the 1st century AD. The papal encyclical "Mystici corporis" (Pope Pius XII, 1943), expresses the dogmatic ecclesiology of the Catholic Church thus: "If we would define and describe this true Church of Jesus Christ—which is the One, Holy, Catholic, Apostolic, Roman Church–we shall find no expression more noble, more sublime, or more divine, than the phrase which calls it 'the Mystical Body of Jesus Christ'." The Second Vatican Council's dogmatic constitution, "Lumen gentium" (1964), further declares that "the one Church of Christ which in the Creed is professed as one, holy, catholic and apostolic,... constituted and organized in the world as a society, subsists in the Catholic Church, which is governed by the successor of Peter and by the Bishops in communion with him". Likewise, the encyclical of Pope Pius IX, "Singulari Quidem", states in a similar vein, "There is only one true, holy, Catholic

Orthodox tradition.

The term "orthodox" is generally used to distinguish the faith or beliefs of the "true Church" from other doctrines which disagree, traditionally referred to as heresy.  The Eastern Orthodox Church and Oriental Orthodox Churches each claim to be the original Christian Church. The Eastern Orthodox Church bases its claim primarily on its assertion that it holds to traditions and beliefs of the original Christian Church. It also states that four out of the five sees of the Pentarchy (excluding Rome) are still a part of it.

Lutheran tradition.

The Lutheran churches traditionally hold that their tradition represents the true visible Church. The Augsburg Confession found within the Book of Concord, a compendium of belief of the Lutheran Churches, teaches that "the faith as confessed by Luther and his followers is nothing new, but the true catholic faith, and that their churches represent the true catholic or universal church". When the

Anglican tradition.

Anglicans generally understand their tradition as a branch of the historical ""Catholic Church""

Reformed tradition.

Reformed theology defines the Church as being invisible and visible—the former includes the entire communion of saints and the latter is the "institution that God provides as an agency for God's saving,

Methodist tradition.

Methodists affirm belief in "the one true Church, Apostolic and Universal", viewing their churches as constituting a "privileged branch of this true church". With regard to the position of Methodism within Christendom, the founder of the movement "John Wesley once noted that what

Evangelical tradition.

The local Evangelical Church is the organization that represents the universal Church and is seen by evangelicals as the body of Jesus Christ. It is responsible for teaching and ordinances, mainly the believer's baptism and the Lord's Supper. Many churches are members of Evangelical Christian denominations and adhere to a common confession of faith and regulations, despite the autonomy of the church. Some denominations are

Related concepts.

The term "orthodoxy" or "orthodox faith", with a lower-case "O" and thus distinguished from the term Orthodox Church, have been used to distinguish the "true church" from supposedly heretical groups. The term became especially prominent in referring to the doctrine of the Nicene Creed and, in historical contexts, is often still used to distinguish this first "official" doctrine from others.  The "Body of Christ" (cf. ) and "Bride of Christ" (cf. ; ). These terms are used to refer to the whole community of Christians seen as interdependent in a single entity headed by Jesus Christ.  The terms "Churches Militant, Penitent, and Triumphant" (Latin: "Ecclesia Militans" and "Ecclesia Triumphans"), taken together, are used to express the concept of a united Church that extends beyond the earthly realm into Heaven. The term "Church Militant" comprises all living Christians while "Church Triumphant" comprises those in Heaven. Related is the "Church Suffering" or "Church Expectant", a Catholic concept encompassing those Christians in Purgatory, no longer part of the Church Militant and not yet part of the Church Triumphant.  The communion of saints (Latin: "communio sanctorum") is the spiritual union of the members of the Christian Church, living and the dead. It is a union in faith and prayer that binds all Christians regardless of geographical distance or separation by death. In Catholic theology, this union encompasses the Church Militant, the Church Triumphant, and the Church Suffering.

Apostolic succession.

Apostolic succession is a doctrine of the Catholic Church, the Eastern Orthodox Church, the Oriental Orthodox Churches, the Moravian Church, the Scandinavian Lutheran Churches, Anglican Communion, and others. The doctrine asserts that the bishops of the "true Church" enjoy the favor or grace of God as a result of legitimate and unbroken sacramental succession from Jesus' apostles. According to this

One true church.

The phrase "One, holy, catholic, and apostolic Church" appears in the Nicene Creed () and, in part, in the Apostles' Creed ("the holy catholic church", "sanctam Ecclesiam catholicam", which in Greek would be: ). The phrase is intended to set forth the four marks, or identifying signs, of the Christian Church—unity, holiness, universality, and apostolicity—and is based on the premise that all true Christians form a single united group founded by the apostles.  The word "catholic" is derived from the Greek adjective "καθολικός" pronounced "katholikos", which means "general" or "universal". Applied to the Church, it implies a calling to spread the faith throughout the whole world and to all ages. It is also thought of as implying that the Church is endowed with all the means of salvation for its members. In this sense the Church is taken by Christian theology to refer to the single, universal community of faithful. Baptism and communion

Visible and invisible church.

Many Protestants believe that the Christian Church, as described in the Bible, has a twofold character that can be described as the visible and invisible church.  In this view, the church invisible consists of all those from every time and place who are vitally united to Christ through regeneration and salvation and who will be eternally united to Jesus Christ in eternal life. The universal, invisible church refers to the "invisible" body of the elect who are known only to God, and contrasts with the "visible church"—that is, the institutional body on earth which preaches the gospel and administers the sacraments. Every member of the invisible church is considered saved, while the visible church contains some individuals who are saved and others who are unsaved. This concept has been attributed to St Augustine of Hippo as part of his refutation of the Donatist sect, but others question whether Augustine really held to some form of an "invisible true Church" concept.

Church government.

Major forms of church government include episcopal governance (Anglican, Catholic, Eastern Orthodoxy, Oriental Orthodoxy), presbyterian governance, and congregational governance (Baptist,

Metaphors.

Christian scriptures use a wide range

Divisions and controversies.

Today there is a wide diversity of Christian groups, with a variety of different doctrines and traditions. These controversies between the various branches of Christianity naturally include significant differences in their respective ecclesiologies.

Christian denominations.

A denomination in Christianity is a generic term for a distinct religious body identified by traits such as a common name, structure, leadership, or doctrine. Individual bodies, however, may use alternative terms to describe themselves, such as "church" or "fellowship". Divisions between one group and another are defined by doctrine and church authority; issues such as the nature of Jesus, the authority of apostolic succession, eschatology, and papal primacy often separate one denomination from another. Groups of denominations often sharing broadly similar beliefs, practices, and historical ties are known as branches of Christianity.  Individual Christian groups vary widely in the degree to which they recognize one another. Several groups claim to be the direct and sole authentic successor the church founded by Jesus Christ in the 1st century AD. Others, however, believe in denominationalism, where some or all Christian groups are legitimate churches of the same religion regardless of their distinguishing labels, beliefs, and practices. Because of this concept, some Christian bodies reject the term "denomination" to describe themselves, to avoid implying equivalency with other churches or denominations.  The Catholic Church and Eastern Orthodox Church believe that the term "one" in the Nicene Creed describes and prescribes a "visible" institutional and doctrinal unity, not only geographically throughout the world, but also historically

World Christianity.

A number of historians have noted a twentieth-century "global shift" in Christianity, from a religion largely found in Europe and the Americas to one which is found in the global south. Described as "World Christianity" or

Other debates.

Other debates

Christian Church is a Protestant ecclesiological term referring to the church invisible comprising all Christians, used since the Protestant Reformation in the 16th century. In this understanding, "Christian Church" (or "catholic church") does not refer to a particular Christian denomination but to the "body" or "group" of believers, both defined in various ways. A prominent example of this is the branch theory maintained by some Anglicans. This is in contrast to the one true church applied to a specific concrete Christian institution, a majority Christian ecclesiological position maintained by the Catholic Church, the Eastern Orthodox Church, the Oriental Orthodox churches, Assyrian Church of the East and the Ancient Church of the East.

Výraz církev výlučně přísluší náboženskému společenství křesťanskému. Pojem církev pochází z řeckého KYRIAKÉ, tj. Pánova. (v řečtině Kyrios – Pán). Církev se řecky označuje EKKLÉSIA TOY KYRIOY (výslovnost "eklesia tú kyriú"), tj. shromáždění Pánovo. Výraz ekklésia je znám z řeckých právních dějin, jako název sněmu všech plnoprávných občanů demokratické polis. Církev je společenství, není to označení pro nějakou vybranou kněžskou kastu, ale všech, kdo se ke Kristu jako svému Pánu hlásí. Členové společenství nesou právem eschatologický titul „vyvolení“, „svatí“. Tvoří společenství, které smí plným právem převzít velké tituly starozákonního a současně i eschatologického společenství Božího: kehal Jahve, „společenství Boží“.


Origin.

The Gartner Group first used the acronym ERP in the 1990s to include the capabilities of material requirements planning (MRP), and the later manufacturing resource planning (MRP II), as well as computer-integrated manufacturing. Without replacing these terms, ERP came to represent a larger whole that reflected the evolution of application integration beyond manufacturing.  Not all ERP packages are developed from a manufacturing core; ERP vendors variously began assembling their packages with finance-and-accounting, maintenance, and human-resource components. By the mid-1990s ERP systems addressed all core enterprise functions. Governments and non–profit organizations also began to use ERP systems.

Expansion.

ERP systems experienced rapid growth in the 1990s. Because of the year 2000 problem many companies took the opportunity to replace their old systems with ERP.  ERP systems initially focused on automating back office functions that did not directly affect customers and the public. Front office functions, such as customer relationship management (CRM), dealt directly with customers, or e-business systems such as e-commerce, e-government, e-telecom, and e-finance—or supplier relationship management (SRM) became integrated later, when the internet simplified communicating with external parties.  "ERP II" was coined in 2000 in an article by Gartner Publications entitled "ERP Is Dead—Long Live ERP II". It describes web–based software that provides real–time access to ERP systems to employees and partners (such as suppliers and customers). The ERP II role expands traditional ERP resource optimization and transaction processing. Rather than just manage buying, selling, etc.—ERP II leverages information in the resources under its management to help the enterprise collaborate with other enterprises. ERP II is more flexible than the first generation ERP. Rather than confine ERP system capabilities within the organization, it goes beyond the corporate walls to interact with other systems. Enterprise application suite is an alternate name for such systems. ERP II systems are typically used to enable collaborative initiatives such as supply chain management (SCM), customer relationship management (CRM), and business intelligence (BI) among business partner organizations through the use of various e-business technologies.  Developers now make more effort to integrate mobile devices with the ERP system. ERP vendors are extending ERP to these devices, along with other business applications. Technical stakes of modern ERP concern integration—hardware, applications, networking, supply chains. ERP now covers more functions and roles—including decision making, stakeholders' relationships, standardization, transparency, globalization, etc.

Characteristics.

ERP systems typically include the following characteristics:

Functional areas.

An ERP system covers the following common functional areas. In many ERP systems, these are called and grouped together as ERP modules:

GRP.

Government resource planning (GRP) is the equivalent of an ERP for the public sector and an integrated office automation system for government bodies. The software structure, modularization, core algorithms and main interfaces do not differ from other ERPs, and ERP software suppliers manage to adapt their systems to government agencies.  Both system implementations, in private and public organizations, are adopted to improve productivity and overall business performance in organizations, but comparisons (private vs. public) of implementations shows that the main factors influencing ERP implementation success in the public sector are cultural.

Best practices.

Most ERP systems incorporate best practices. This means the software reflects the vendor's interpretation of the most effective way to perform each business process. Systems vary in how conveniently the customer can modify these practices. In addition, best practices reduced risk by 71% compared to other software implementations.  Use of best practices eases compliance with requirements such as IFRS, Sarbanes-Oxley, or Basel II. They can also help comply with de facto industry standards, such as electronic funds transfer. This is because the procedure can be readily codified within the ERP software and replicated with confidence across multiple businesses that share that business requirement.

Connectivity to plant floor information.

ERP systems connect to real–time data and transaction data in a variety of ways. These systems are typically configured by systems integrators, who bring unique knowledge on process, equipment, and vendor solutions.  Direct integration—ERP systems have connectivity (communications to plant floor equipment) as part of their product offering. This requires that the vendors offer specific support for the plant floor equipment their customers operate.  Database integration—ERP systems connect to plant floor data sources through staging tables in a database. Plant floor systems deposit the necessary information into the database. The ERP system reads the information in the table. The benefit of staging is that ERP vendors do not need to master the complexities of equipment integration. Connectivity becomes the responsibility of the systems integrator.  Enterprise appliance transaction modules (EATM)—These devices communicate directly with plant floor equipment and with the ERP system via methods supported by the ERP system. EATM can employ a staging table, web services, or system–specific program interfaces (APIs). An EATM offers the benefit of being an off–the–shelf solution.  Custom–integration solutions—Many system integrators offer custom solutions. These systems tend to have the highest level of initial integration cost, and can have a higher long term maintenance and reliability costs. Long term costs can be minimized through careful system testing and thorough documentation. Custom–integrated solutions typically run on workstation or server-class computers.

Implementation.

ERP's scope usually implies significant changes to staff work processes and practices. Generally, three types of services are available to help implement such changes—consulting, customization, and support. Implementation time depends on business size, number of modules, customization, the scope of process changes, and the readiness of the customer to take ownership for the project. Modular ERP systems can be implemented in stages. The typical project for a large enterprise takes about 14 months and requires around 150 consultants. Small projects can require months; multinational and other large implementations can take years. Customization can substantially increase implementation times.  Besides that, information processing influences various business functions e.g. some large corporations like Wal-Mart use a just in time inventory system. This reduces inventory storage and increases delivery efficiency, and requires up-to-date data. Before 2014, Walmart used a system called Inforem developed by IBM to manage replenishment.

Process preparation.

Implementing ERP typically requires changes in existing business processes. Poor understanding of needed process changes prior to starting implementation is a main reason for project failure. The difficulties could be related to the system, business process, infrastructure, training, or lack of motivation.  It is therefore crucial that organizations thoroughly analyze business processes before they implement ERP software. Analysis can identify opportunities for process modernization. It also enables an assessment of the alignment of current processes with those provided by the ERP system. Research indicates that risk of business process mismatch is decreased by:  ERP implementation is considerably more difficult (and politically charged) in decentralized organizations, because they often have different processes, business rules, data semantics, authorization hierarchies, and decision centers. This may require migrating some business units before others, delaying implementation to work through the necessary changes for each unit, possibly reducing integration (e.g., linking via Master data management) or customizing the system to meet specific needs.  A potential disadvantage is that adopting "standard" processes can lead to a loss of competitive advantage. While this has happened, losses in one area are often offset by gains in other areas, increasing overall competitive advantage.

Configuration.

Configuring an ERP system is largely a matter of balancing the way the organization wants the system to work with the way it was designed to work. ERP systems typically include many settings that modify system operations. For example, an organization can select the type of inventory accounting—FIFO or LIFO—to use; whether to recognize revenue by geographical unit, product line, or distribution channel; and whether to pay for shipping costs on customer returns.

Two-tier enterprise resource planning.

Two-tier ERP software and hardware lets companies run the equivalent of two ERP systems at once: one at the corporate level and one at the division or subsidiary level. For example, a manufacturing company could use an ERP system to manage across the organization using independent global or regional distribution, production or sales centers, and service providers to support the main company's customers. Each independent center (or) subsidiary may have its own business models, workflows, and business processes.  Given the realities of globalization, enterprises continuously evaluate how to optimize their regional, divisional, and product or manufacturing strategies to support strategic goals and reduce time-to-market while increasing profitability and delivering value. With two-tier ERP, the regional distribution, production, or sales centers and service providers continue operating under their own business model—separate from the main company, using their own ERP systems. Since these smaller companies' processes and workflows are not tied to main company's processes and workflows, they can respond to local business requirements in multiple locations.  Factors that affect enterprises' adoption of two-tier ERP systems include:

Customization.

ERP systems are theoretically based on industry best practices, and their makers intend that organizations deploy them "as is". ERP vendors do offer customers configuration options that let organizations incorporate their own business rules, but gaps in features often remain even after configuration is complete.  ERP customers have several options to reconcile feature gaps, each with their own pros/cons. Technical solutions include rewriting part of the delivered software, writing a homegrown module to work within the ERP system, or interfacing to an external system. These three options constitute varying degrees of system customization—with the first being the most invasive and costly to maintain. Alternatively, there are non-technical options such as changing business practices or organizational policies to better match the delivered ERP feature set. Key differences between customization and configuration include:  Customization advantages include that it:  Customization disadvantages include that it may:

Extensions.

ERP systems can be extended with third–party software, often via vendor-supplied interfaces. Extensions offer features such as:

Data migration.

Data migration is the process of moving, copying, and restructuring data from an existing system to the ERP system. Migration is critical to implementation success and requires significant planning. Unfortunately, since migration is one of the final activities before the production phase, it often receives insufficient attention. The following steps can structure migration planning:  Often, data migration is incomplete because some of the data in the existing system is either incompatible or not needed in the new system. As such, the existing system may need to be kept as an archived database to refer back to once the new ERP system is in place.

Advantages.

The most fundamental advantage of ERP is that the integration of a myriad of business processes saves time and expense. Management can make decisions faster and with fewer errors. Data becomes visible across the organization. Tasks that benefit from this integration include:  ERP systems centralize business data, which:

Postmodern ERP.

The term "postmodern ERP" was coined by Gartner in 2013, when it first appeared in the paper series "Predicts 2014". According to Gartner's definition of the postmodern ERP strategy, legacy, monolithic and highly customized ERP suites, in which all parts are heavily reliant on each other, should sooner or later be replaced by a mixture of both cloud-based and on-premises applications, which are more loosely coupled and can be easily exchanged if needed.  The basic idea is that there should still be a core ERP solution that would cover most important business functions, while other functions will be covered by specialist software solutions that merely extend the core ERP. This concept is similar to the so-called best-of-breed approach to software execution, but it shouldn't be confused with it. While in both cases, applications that make up the whole are relatively loosely connected and quite easily interchangeable, in the case of the latter there is no ERP solution whatsoever. Instead, every business function is covered by a separate software solution.  There is, however, no golden rule as to what business functions should be part of the core ERP, and what should be covered by supplementary solutions. According to Gartner, every company must define their own postmodern ERP strategy, based on company's internal and external needs, operations and processes. For example, a company may define that the core ERP solution should cover those business processes that must stay behind the firewall, and therefore, choose to leave their core ERP on-premises. At the same time, another company may decide to host the core ERP solution in the cloud and move only a few ERP modules as supplementary solutions to on-premises.  The main benefits that companies will gain from implementing postmodern ERP strategy are speed and flexibility when reacting to unexpected changes in business processes or on the organizational level. With the majority of applications having a relatively loose connection, it is fairly easy to replace or upgrade them whenever necessary. In addition to that, following the examples above, companies can select and combine cloud-based and on-premises solutions that are most suited for their ERP needs. The downside of postmodern ERP is that it will most likely lead to an increased number of software vendors that companies will have to manage, as well as pose additional integration challenges for the central IT.

Enterprise resource planning (ERP) is the integrated management of main business processes, often in real time and mediated by software and technology.

Plánování podnikových zdrojů (ve zkratce ERP z anglického Enterprise Resource Planning, žádná česká zkratka se neujala) nebo někdy též podnikový informační systém je označení systému, jímž podnik (nebo jiná organizace) za pomoci počítače řídí a integruje všechny nebo většinu oblastí své činnosti, jako jsou plánování, zásoby, nákup, prodej, marketing, finance, personalistika, atd. Každý organizační útvar (oddělení) typicky potřebuje svou vlastní aplikaci schopnou plnit jeho potřeby. S ERP každý útvar takovou vlastní aplikaci dostane, ale je to navíc aplikace, která umí komunikovat a sdílet informace se všemi ostatními v rámci celé organizace. Pojmem ERP se současně označuje i software, který toto vše zajišťuje.


History.

Peter Koestenbaum at San Jose State University in California was an early figure in Philosophical Counseling. His 1978 book "The New Image of the Person: The Theory and Practice of Clinical Philosophy" set out the essential contributions of philosophy to counseling. His own practice was augmented by extensive training of mental health professionals in applications of philosophical principles.  Gerd B. Achenbach and Ad Hoogendijk are two, German and Dutch philosophers who established themselves as consultant philosophers in the 1980s and led the way to a number of other developments all over the world. They proposed an alternative to psychotherapeutic culture by working exclusively within the field of existential investigation with clients or patients, whom they called 'visitors.'  The world's oldest association of philosophical counseling and practice appears to be the German Society for Philosophical Practice and Counseling, which was founded in 1982 by Achenbach. In the United States, the oldest association of philosophical counseling and practice appears to be the National Philosophical Counseling Association (NPCA), formerly called the American Society for Philosophy, Counseling, and Psychotherapy, which was co-founded in 1992 by three American philosophers, Elliot D. Cohen, Paul Sharkey, and Thomas Magnell. The NPCA offers a primary certificate in logic-based therapy (LBT) through the Institute of Critical Thinking. Achenbach and Ad Hoogendijk are two, German and Dutch philosophers who established themselves as consultant philosophers in the 1980s (Achenbach 1984, 2002; Hoogendijk 1988) and led the way to a number of other developments all over the world. They proposed an alternative to psychotherapeutic culture by working exclusively within the field of existential investigation with clients or patients, whom they called 'visitors.' Achenbach argues that it is life that calls to thinking, rather than thinking that informs life. The act of philosophising can, therefore, give direction in its own right, as living precedes thinking and practice precedes theory.  The movement is also connected with and related to Existential Therapy, which has thrived in the United Kingdom since the establishment of the Society for Existential Analysis (SEA) in London in 1988. This was based on the work of Emmy van Deurzen, also a philosopher who has applied philosophical thinking to the practice of psychotherapy. Philosophical consultancy is often applied to business consultancy as well as to individuals, as it frequently involves a rethinking of values and beliefs and is also a method for rational conflict resolution.  Pierre Grimes, PhD founded the Noetic Society in 1967 for the study of dialogue and dialectic. He became the head of the Philosophical Midwifery Program when the Noetic Society was incorporated in 1978. The American Philosophical Practitioners Association (APPA) was founded in 1998 in New York City by Lou Marinoff. APPA offers a certification program in client counseling for those with advanced degrees in philosophy who wish to practice philosophical counseling. It also publishes a professional Journal and has a membership list of those certified as philosophical counselors on its website. Marinoff was at the center of a 2004 controversy when his philosophical counseling practice at City College of New York was temporarily shuttered by college officials who feared he was offering mental health advice without proper training and licensing; Marinoff responded by suing for what he described as his freedom of speech being stifled.  Philosophical practice has continued to expand and is attractive as an alternative to counselling and psychotherapy for those who prefer to avoid a medicalization of life-problems. Numerous philosophical consultants have emerged and there is a strong international interest and a bi-annual international conference. There are a number of important publications in the field (Lahav and Tillmans 1995, Grimes, 1998, Curnow 2001, Herrestad et al. 2002, Marinoff 1999, Rochelle 2008, 2011, Weiss 2015). There are presently a number of professional associations for philosophical counseling throughout the world, including India,France, Belgium, Germany, Austria, Switzerland, Great Britain, Italy, Spain, Greece, the Netherlands, Norway, Denmark, Poland, Finland, Luxembourg, Israel, Canada, South Africa, Australia, Brazil, Portugal, Korea, Turkey, Japan, Taiwan, Singapore and the United States.In India currently, Department of Philosophy, Panjab University, Chandigarh is offering Philosophical Counseling and Therapy courses as part of MA Philosophy degree, with its integration with both Western and Indian Philosophy.

Goals and methods.

Philosophical consultancy is a relatively new movement in philosophy which applies philosophical thinking and debating to the resolution of a person's problem. Achenbach argues that it is life that calls to thinking, rather than thinking that informs life. The act of philosophising can, therefore, give direction in its own right, as living precedes thinking and practice precedes theory.  According to the Preamble of the NPCA Standards of Practice, Activities common to philosophical practice include:  The methods and orientations of philosophical counselors vary greatly. Some practitioners, such as Gerd B. Achenbach (Germany), Michel Weber (Belgium) and Shlomit C. Schuster (Israel) are dialogical and dialective engaged, while confessing to a "beyond method" approach. They hold that philosophical counseling has the aim to empower clients' philosophical abilities, which additionally may have therapeutic implications. "Others are directive oriented and view philosophical counseling as a form of mental health intervention". Some philosophical practitioners, notably Louis Marinoff (U.S.) and Guenther Witzany (Austria), view philosophical practice as a separate practice area distinct from mental health practices such as psychology and mental health counseling; while others, notably Elliot D. Cohen (U.S.), think they are necessarily intertwined. Some philosophical counselors draw inspiration from the anti-psychiatry movement, arguing that widespread mental health diagnostic criteria as outlined in DSM IV have unfairly or inaccurately pathologized humanity.  According to a "New York Times" article on philosophical counseling, "only Cohen and Marinoff have branded easily comprehended techniques. Cohen's logic-based therapy builds on the work of his mentor Albert Ellis, who invented rational emotive behavior therapy."

Philosophical consultancy, also sometimes called philosophical practice or philosophical counseling or clinical philosophy, is a contemporary movement in practical philosophy. Developing since the 1980s as a profession but since 1950’s as a practice (see Pierre Grimes or Philosophical Midwifery), practitioners of philosophical counseling ordinarily have a doctorate or minimally a master's degree in philosophy and offer their philosophical counseling or consultation services to clients who look for a philosophical understanding of their lives, social problems, or even mental problems. In the last case philosophical counseling might be in lieu of, or in conjunction with, traditional psychotherapy. The movement has often been said to be rooted in the Socratic tradition, which viewed philosophy as a search for the Good and the good life. A life without philosophy was not worth living for Socrates.

Stále oblíbenější aplikací filozofie je poradenství. Běžně se má za to, že takzvané filosofické poradenství vzniklo v roce 1981, když Dr. Gerd Achenbach otevřel svoji praxi poblíž Kolína nad Rýnem v Německu a v roce 1987 zveřejnil svůj manifest „Philosophische Praxis.“ Dnes existují filozofičtí poradci, profesní sdružení a certifikované programy v Rakouska (1985, Guenther Witzany, Salzburg), Holandsku, Kanadě, Norsku, Rakousku, Francii, Švýcarsku, Izraeli, Velké Británii, Spojených státech amerických a dalších zemích.


Background.

Emigration restrictions, the Inner German border and Berlin.

By the early 1950s, the Soviet method of restricting emigration was emulated by most of the rest of the Eastern Bloc, including East Germany. However, in occupied Germany, until 1952, the lines between East Germany and the western occupied zones remained easily crossed in most places. Subsequently, the inner German border between the two German states was closed and a barbed-wire fence erected.  Even after closing of the inner German border officially in 1952, the city sector border in between East Berlin and West Berlin remained considerably more accessible than the rest of the border because it was administered by all four occupying powers. Accordingly, Berlin became the main route by which East Germans left for the West. Hence the Berlin sector border was essentially a "loophole" through which Eastern Bloc citizens could still escape.  The 3.5 million East Germans who had left by 1961 totaled approximately 20% of the entire East German population. The emigrants tended to be young and well educated. The loss was disproportionately great among professionals — engineers, technicians, physicians, teachers, lawyers and skilled workers.

Berlin Wall constructed.

The brain drain of professionals had become so damaging to the political credibility and economic viability of East Germany that the re-securing of the Soviet imperial frontier was imperative. Between 1949 and 1961, over 21⁄2 million East Germans fled to the West. The numbers increased during the three years before the Berlin Wall was erected, with 144,000 in 1959, 199,000 in 1960 and 207,000 in the first seven months of 1961 alone. The East German economy suffered accordingly.  On 13 August 1961, a barbed-wire barrier that would become the Berlin Wall separating East and West Berlin was erected by the East Germans. Two days later, police and army engineers began to construct a more permanent concrete wall. Along with the wall, the 830 mile zonal border became 3.5 miles wide on its East German side in some parts of Germany with a tall steel-mesh fence running along a "death strip" bordered by mines, as well as channels of ploughed earth, to slow escapees and more easily reveal their footprints.

Checkpoint.

Checkpoint Charlie was a crossing point in the Berlin Wall located at the junction of with and (which for older historical reasons coincidentally means 'Wall Street'). It is in the Friedrichstadt neighborhood. Checkpoint Charlie was designated as the single crossing point (on foot or by car) for foreigners and members of the Allied forces. (Members of the Allied forces were not allowed to use the other sector crossing point designated for use by foreigners, the Friedrichstraße railway station).  The name Charlie came from the letter C in the NATO phonetic alphabet; similarly for other Allied checkpoints on the "Autobahn" from the West: Checkpoint Alpha at and its counterpart Checkpoint Bravo at Dreilinden, Wannsee in the south-west corner of Berlin. The Soviets simply called it the " Crossing Point" (, ). The East Germans referred officially to Checkpoint Charlie as the ("Border Crossing Point").  As the most visible Berlin Wall checkpoint, Checkpoint Charlie was featured in movies and books. A famous cafe and viewing place for Allied officials, armed forces and visitors alike, ("Eagle Café"), is situated right on the checkpoint. It was an excellent viewing point to look into East Berlin while having something to eat and drink.  The checkpoint was curiously asymmetrical. During its 28-year active life, the infrastructure on the Eastern side was expanded to include not only the wall, watchtower and zig-zag barriers, but a multi-lane shed where cars and their occupants were checked. However, the Allied authority never erected any permanent buildings, and made do with the well-known wooden shed, which was replaced during the 1980s by a larger metal structure, now displayed at the Allied Museum in western Berlin. Their reason was that they did not consider the inner Berlin sector boundary an international border and did not treat it as such.

Related incidents.

Stand-off between Soviet and U.S. tanks in October 1961.

Soon after the construction of the Berlin Wall in August 1961, a stand-off occurred between US and Soviet tanks on either side of Checkpoint Charlie. It began on 22 October as a dispute over whether East German border guards were authorized to examine the travel documents of a US diplomat based in West Berlin named Allan Lightner heading to East Berlin to watch an opera show there, since according to the agreement between all four Allied powers occupying Germany, there was to be free movement for Allied forces in Berlin and that no German military forces from either West Germany or East Germany were to be based in the city, and moreover the USA did not (initially) recognise the East German state and its right to remain in its self-declared capital of East Berlin. Instead, the Americans only recognised the authority of the Soviets over East Berlin rather than their East German allies. By 27 October, ten Soviet and an equal number of American tanks stood 100 yards apart on either side of the checkpoint. This stand-off ended peacefully on 28 October following a US-Soviet understanding to withdraw tanks and reduce tensions. Discussions between US Attorney General Robert F. Kennedy and KGB spy Georgi Bolshakov played a vital role in realizing this tacit agreement.

Early escapes.

The Berlin Wall was erected with great speed by the East German government in 1961, but there were many means of escape that had not been anticipated. For example, Checkpoint Charlie was initially blocked only by a gate, and a citizen of the DDR (East Germany) smashed a car through it to escape, so a strong pole was erected. Another escapee approached the barrier in a convertible, the windscreen removed prior to the event, and slipped under the barrier. This was repeated two weeks later, so the East Germans duly lowered the barrier and added uprights.

Death of Peter Fechter.

On 17 August 1962, a teenaged East German, Peter Fechter, was shot in the pelvis by East German guards while trying to escape from East Berlin. His body lay tangled in a barbed wire fence as he bled to death in full view of the world's media. American soldiers could not rescue him because he was a few metres inside the Soviet sector. East German border guards were reluctant to approach him for fear of provoking Western soldiers, one of whom had shot an East German border guard just days earlier. More than an hour later, Fechter's body was removed by the East German guards. A spontaneous demonstration formed on the American side of the checkpoint, protesting against the action of the East and the inaction of the West.  A few days later, a crowd threw stones at Soviet buses driving towards the Soviet War Memorial, located in the Tiergarten in the British sector; the Soviets tried to escort the buses with armoured personnel carriers (APCs). Thereafter, the Soviets were only allowed to cross via the Sandkrug Bridge crossing (which was the nearest to Tiergarten) and were prohibited from bringing APCs. Western units were deployed in the middle of the night in early September with live armaments and vehicles, in order to enforce the ban.

Today: Tourist and memorial site.

Although the wall was opened in November 1989 and the checkpoint booth removed on 22 June 1990, the checkpoint remained an official crossing for foreigners and diplomats until German reunification during October 1990.  Checkpoint Charlie has since become one of Berlin's primary tourist attractions, where some original remnants of the border crossing blend with reconstructed parts, memorial and tourist facilities.  The guard house on the American side was removed in 1990; it is now on display in the open-air museum of the Allied Museum in Berlin-Zehlendorf. A copy of the guard house and the sign that once marked the border crossing was reconstructed later on roughly the same site. It resembles the first guard house erected during 1961, behind a sandbag barrier toward the border. Over the years this had been replaced several times by guard houses of different sizes and layouts (see photographs). The one removed during 1990 was considerably larger than the first one and did not have sandbags. Tourists used to be able to have their photographs taken for a fee with actors dressed as allied military policemen standing in front of the guard house but Berlin authorities banned the practice in November 2019 stating the actors had been exploiting tourists by demanding money for photos at the attraction.  The course of the former wall and border is now marked in the street with a line of cobblestones. An open-air exhibit was opened during the summer of 2006. Gallery walls along Friedrichstraße and Zimmerstraße give information about escape attempts, how the checkpoint was expanded, and its significance during the Cold War, in particular the confrontation of Soviet and American tanks in 1961. Also an overview of other important memorial sites and museums about the division of Germany and the wall is presented.  Developers demolished the East German checkpoint watchtower in 2000, to make way for offices and shops. The watchtower was the last surviving major original Checkpoint Charlie structure. The city tried to save the tower but failed, as it was not classified as a historic landmark. Yet, that development project was never realised. To this day, the area between Zimmerstraße and Mauerstraße/Schützenstraße (the East German side of the border crossing) remains vacant, providing space for a number of temporary tourist and memorial uses. New plans since 2017 for a hotel on the site stirred a professional and political debate about an appropriate development of the area. After the final listing of the site as a protected heritage area in 2018, plans were changed towards a more heritage-friendly approach.

Exhibition BlackBox Cold War.

Since 2012 the exhibition “BlackBox Cold War” illuminates the division of Germany and Berlin. The free open-air exhibit offers original Berlin Wall segments and informations about the historic sight. However the indoor exhibit illustrates Berlin's contemporary history with 16 media stations, a movie theater as well as original objects and documents (liable to pay costs). It is run by the NGO "Berliner Forum fuer Geschichte und Gegenwart e.V.."

Checkpoint Charlie Museum.

Near the location of the guard house is the "Haus am Checkpoint Charlie". The "Mauermuseum - Museum Haus am Checkpoint Charlie" was opened on 14 June 1963, in the immediate vicinity of the Berlin Wall. It shows photographs and fragments of the separation of Germany. The border fortifications and the "assistance of the protecting powers" are illustrated. In addition to photos and documentation of successful escape attempts, the exhibition also showcases escape devices including a hot-air balloon, escape cars, chair lifts, and a mini-submarine.  From October 2004 until July 2005, the Freedom Memorial, consisting of original wall segments and 1,067 commemorative crosses, stood on a leased site.  The museum is operated by the "Arbeitsgemeinschaft 13. August e. V.", a registered association founded by Dr. Rainer Hildebrandt. The director is Alexandra Hildebrandt, the founder's widow. The museum is housed in part in the "House at Checkpoint Charlie" building by architect Peter Eisenman.  With 850,000 visitors in 2007, the Wall Museum is one of the most visited museums in Berlin and in Germany.

In popular culture.

James Bond (played by Roger Moore) passed through Checkpoint Charlie in the film "Octopussy" (1983) from West to East.  Checkpoint Charlie is featured in the opening scene of the 1965 Martin Ritt film "The Spy Who Came in from the Cold" (starring Richard Burton and Claire Bloom), based on the John le Carré novel of the same name.

Checkpoint Charlie (or "Checkpoint C") was the name given by the Western Allies to the best-known Berlin Wall crossing point between East Berlin and West Berlin during the Cold War (1947–1991).

Checkpoint Charlie byl hraniční přechod v Berlíně. Patří k nejznámějším přechodům rozděleného Berlína. Checkpoint Charlie se nachází na křižovatce ulic Friedrichstraße a Kochstraße a spojoval americký sektor města se sovětským.


Life.

In general, the details of Aristotle's life are not well-established. The biographies written in ancient times are often speculative and historians only agree on a few salient points.  Aristotle, whose name means "the best purpose" in Ancient Greek, was born in 384 BC in Stagira, Chalcidice, about 55 km (34 miles) east of modern-day Thessaloniki. His father Nicomachus was the personal physician to King Amyntas of Macedon. Both of Aristotle's parents died when he was about thirteen, and Proxenus of Atarneus became his guardian. Although little information about Aristotle's childhood has survived, he probably spent some time within the Macedonian palace, making his first connections with the Macedonian monarchy.  At the age of seventeen or eighteen, Aristotle moved to Athens to continue his education at Plato's Academy. He probably experienced the Eleusinian Mysteries as he wrote when describing the sights one viewed at the Eleusinian Mysteries, "to experience is to learn" [παθείν μαθεĩν]. Aristotle remained in Athens for nearly twenty years before leaving in 348/47 BC. The traditional story about his departure records that he was disappointed with the Academy's direction after control passed to Plato's nephew Speusippus, although it is possible that he feared the anti-Macedonian sentiments in Athens at that time and left before Plato died. Aristotle then accompanied Xenocrates to the court of his friend Hermias of Atarneus in Asia Minor. After the death of Hermias, Aristotle travelled with his pupil Theophrastus to the island of Lesbos, where together they researched the botany and zoology of the island and its sheltered lagoon. While in Lesbos, Aristotle married Pythias, either Hermias's adoptive daughter or niece. She bore him a daughter, whom they also named Pythias. In 343 BC,

Speculative philosophy.

Logic.

With the "Prior Analytics", Aristotle is credited with the earliest study of formal logic, and his conception of it was the dominant form of Western logic until 19th-century advances in mathematical logic. Kant stated in the "Critique of Pure Reason" that with Aristotle logic reached its completion.

"Organon".

What we today call "Aristotelian logic" with its types of syllogism (methods of logical argument), Aristotle himself would have labelled "analytics". The term "logic" he reserved to mean "dialectics". Most of Aristotle's work is probably not in its original form, because it was most likely edited by students and later lecturers. The logical works of Aristotle were compiled into a set of six books called the "Organon" around 40 BC by Andronicus of Rhodes or others among his followers. The books are:  The order of the books (or the teachings from which they are composed) is not certain, but this list was derived from analysis of Aristotle's writings. It goes from the basics, the analysis of simple terms in the "Categories," the analysis of propositions and their elementary relations in "On Interpretation", to the study of more complex forms, namely, syllogisms (in the "Analytics") and dialectics (in the "Topics" and "Sophistical Refutations"). The first three treatises form the core of the logical theory "stricto sensu": the grammar of the language of logic and the correct rules of reasoning. The "Rhetoric" is not conventionally included, but it states that it relies on the "Topics".

Metaphysics.

The word "metaphysics" appears to have been coined by the first century AD editor who assembled various small selections of Aristotle's works to the treatise we know by the name "Metaphysics". Aristotle called it "first philosophy", and distinguished it from mathematics and natural science (physics) as the contemplative ("theoretikē") philosophy which is "theological" and studies the divine. He wrote in his "Metaphysics" (1026a16):

Substance.

Aristotle examines the concepts of substance ("ousia") and essence ("to ti ên einai", "the what it was to be") in his "Metaphysics" (Book VII), and he concludes that a particular substance is a combination of both matter and form, a philosophical theory called hylomorphism. In Book VIII, he distinguishes the matter of the substance as the substratum, or the stuff of which it is composed. For example, the matter of a house is the bricks, stones, timbers etc., or whatever constitutes the "potential" house, while the form of the substance is the "actual" house, namely 'covering for bodies and chattels' or any other differentia that let us define something as a house. The formula that gives the components is the account of the matter, and the formula that gives the differentia is the account of the form.

Epistemology.

Aristotle's immanent realism means his epistemology is based on the study of things that exist or happen in the world, and rises to knowledge of the

Natural philosophy.

Aristotle's "natural philosophy" spans a wide range of natural phenomena including those now covered by physics, biology and other natural sciences. In Aristotle's terminology, "natural philosophy" is a branch of philosophy examining the phenomena of the natural world, and includes fields that would be regarded today as physics, biology and other natural sciences. Aristotle's work encompassed virtually all facets of intellectual inquiry. Aristotle makes philosophy in the broad sense coextensive with reasoning, which he also would describe as "science". Note, however, that his use of the term "science" carries a different meaning than that covered by the term "scientific method". For Aristotle, "all science ("dianoia") is either practical, poetical or theoretical" ("Metaphysics" 1025b25). His practical science includes ethics and politics; his poetical science means the study of fine arts including poetry; his theoretical science covers physics, mathematics and metaphysics.

Physics.

Five elements.

In his "On Generation and Corruption", Aristotle related each of the four elements proposed earlier by Empedocles, Earth, Water, Air, and Fire, to two of the

Motion.

Aristotle describes two kinds of motion: "violent" or "unnatural motion", such as that of a thrown stone, in the "Physics" (254b10), and "natural motion", such as of a falling object, in "On the Heavens" (300a20). In violent motion, as soon as the agent stops causing it, the motion stops also; in other words, the natural state of an object is to be at rest, since Aristotle does not address friction. With this understanding, it can be observed that, as Aristotle stated, heavy objects (on the ground, say) require more force to make them move; and objects pushed with greater force move faster. This would imply the equation  incorrect in modern physics.  Natural motion depends on the element concerned: the aether naturally moves in a circle around the heavens, while the 4 Empedoclean elements move vertically up (like fire, as is observed) or down (like earth) towards their natural resting places.  In the "Physics" (215a25), Aristotle effectively states a quantitative law, that the speed, v, of a falling body is proportional (say, with constant c) to its weight, W, and inversely proportional to the density, ρ, of the

Four causes.

Aristotle suggested that the reason for anything coming about can be attributed to four different types of simultaneously active factors. His

Optics.

Aristotle describes experiments in optics using a camera obscura in "Problems", book 15. The apparatus consisted of a dark chamber with a small aperture that

Chance and spontaneity.

According to Aristotle, spontaneity and chance are causes of some things, distinguishable from other types of cause such as simple necessity. Chance as an incidental cause lies in the realm of accidental things, "from what is spontaneous". There is also more a specific kind of chance, which Aristotle names "luck", that only applies to people's moral choices.

Astronomy.

In astronomy, Aristotle refuted Democritus's claim that the Milky Way was made up of "those stars which are shaded by the earth from the sun's rays," pointing out correctly that

Geology.

Aristotle was one of the first people to record any geological observations. He stated that geological change was too slow to be observed in one person's lifetime. The geologist Charles Lyell noted

Biology.

Empirical research.

Aristotle was the first person to study biology systematically, and biology forms a large part of his writings. He spent two years observing and describing the zoology of Lesbos and the surrounding seas, including in particular the Pyrrha lagoon in the centre of Lesbos. His data in "History of Animals", "Generation of Animals", "Movement of Animals", and "Parts of Animals" are assembled from his own observations, statements given by people with specialized knowledge such as beekeepers and fishermen, and less accurate accounts provided by travellers from overseas. His apparent emphasis on animals rather than plants is a historical accident: his works on botany have been lost, but two books on plants by his pupil Theophrastus have survived.  Aristotle reports on the sea-life visible from observation on Lesbos and the catches of fishermen. He describes the catfish, electric ray, and frogfish in detail, as well as cephalopods such as the octopus

Scientific style.

Aristotle did not do experiments in the modern sense. He used the ancient Greek term "pepeiramenoi" to mean observations, or at most investigative procedures like dissection. In "Generation of Animals", he finds a fertilized hen's egg of a suitable stage and opens it to see the embryo's heart beating inside.  Instead, he practiced a different style of science: systematically gathering data, discovering patterns common to whole groups of animals, and inferring possible causal explanations from these. This style is common in modern biology when large amounts of data become available in a new field,

Classification of living things.

Aristotle distinguished about 500 species of animals, arranging these in the "History of Animals" in a graded scale of perfection, a "scala naturae", with man at the top. His system had eleven grades of animal, from highest potential to lowest, expressed in their form at birth: the highest gave live birth to hot and wet creatures, the lowest laid cold, dry mineral-like eggs. Animals came above plants, and these in turn were above minerals. see also: He grouped what the modern zoologist would call vertebrates as the hotter "animals with blood", and below them the colder invertebrates as "animals without blood". Those with blood were divided into the live-bearing (mammals), and the egg-laying (birds, reptiles, fish). Those without blood were insects, crustacea (non-shelled – cephalopods, and shelled) and the hard-shelled molluscs (bivalves and gastropods). He recognised that animals did not exactly fit into a linear scale, and noted various exceptions, such as that sharks had a placenta like the tetrapods. To a modern biologist, the explanation, not available to Aristotle, is convergent evolution. He believed that purposive final causes guided all natural processes; this teleological view justified his observed data as an expression of formal design.

Psychology.

Soul.

Aristotle's psychology, given in his treatise "On the Soul" ("peri psychēs"), posits three kinds of soul ("psyches"): the vegetative soul, the sensitive soul, and the rational soul. Humans have a rational soul. The human soul incorporates the powers of the other kinds: Like the vegetative soul it can grow and nourish itself; like the sensitive soul it can experience sensations and move locally. The unique part of the human, rational soul is its ability to receive forms of

Memory.

According to Aristotle in "On the Soul", memory is the ability to hold a perceived experience in the mind and to distinguish between the internal "appearance" and an occurrence in the past. In other words, a memory is a mental picture (phantasm) that can be recovered. Aristotle believed an impression is left on a semi-fluid bodily organ that undergoes several changes in order to make a memory. A memory occurs when stimuli such as sights or sounds are so complex that the nervous system cannot receive all the impressions at once. These changes are the same as those involved in the operations of sensation, Aristotelian 'common sense', and thinking.  Aristotle uses the term'memory' for the actual retaining of an experience in the impression that can develop from sensation, and for the intellectual anxiety that comes with the impression because it is formed at a particular time and processing specific contents. Memory is of the past, prediction is of the future, and sensation is of the present. Retrieval of impressions cannot be

Dreams.

Aristotle describes sleep in "On Sleep and Wakefulness". Sleep takes place as a result of overuse of the senses or of digestion, so it is vital to the body. While a person is asleep, the critical activities, which include thinking, sensing, recalling and remembering, do not function as they do during wakefulness. Since a person cannot sense during sleep they can not have desire, which is the result of sensation. However, the senses are able to work during sleep, albeit differently, unless they are weary.  Dreams do not involve actually sensing a stimulus. In dreams, sensation is still involved, but in an altered manner. Aristotle explains that when a person stares at a moving stimulus such as the waves in a body of water, and then look away, the next thing they look at appears to have a wavelike motion. When a person perceives a stimulus and the stimulus is no longer the focus of their attention, it leaves an impression. When the body is awake and the senses are functioning properly, a person constantly encounters new stimuli to sense and so the impressions of previously perceived stimuli are ignored. However, during sleep the impressions made throughout the day are noticed as there are no new distracting sensory experiences. So, dreams

Practical philosophy.

Aristotle's practical philosophy covers areas such as ethics, politics, economics, and rhetoric.

Just war theory.

Aristotelian just war theory is not well regarded in the present day, especially his view that warfare was justified to enslave "natural slaves". In Aristotelian philosophy, the abolition of what he considers "natural slavery" would undermine civic freedom. The pursuit of freedom is inseparable from pursuing mastery over "those who deserve to be slaves". According to "The Cambridge Companion to Aristotle's Politics" the targets

Ethics.

Aristotle considered ethics to be a practical rather than theoretical study, i.e., one aimed at becoming good and doing good rather than knowing for its own sake. He wrote several treatises on ethics, including most notably, the "Nicomachean Ethics".  Aristotle taught that virtue has to do with the proper function ("ergon") of a thing. An eye is only a good eye in so much as it can see, because the proper function of an eye is sight. Aristotle reasoned that humans must have a function specific to humans, and that this function must be an activity of the "psuchē" ("soul") in accordance with

Politics.

In addition to his works on ethics, which address the individual, Aristotle addressed the city in his work titled "Politics". Aristotle considered the city to be a natural community. Moreover, he considered the city to be prior in importance to the family which in turn is prior to the individual, "for the whole must of necessity be prior to the part". He also famously stated that "man is by nature a political animal" and also arguing that humanity's defining factor among others in the animal kingdom is its rationality. Aristotle conceived of politics as being like an organism rather than like a machine, and as a collection of parts none of which can

Economics.

Aristotle made substantial contributions to economic thought, especially to thought in the Middle Ages. In "Politics", Aristotle addresses the city, property, and trade. His response to criticisms of private property, in Lionel Robbins's view, anticipated later proponents of private property among philosophers and economists, as it related to the overall utility of social arrangements. Aristotle believed that although communal arrangements may seem beneficial to society, and that although private property is often blamed for social strife, such evils in fact come from human nature. In "Politics", Aristotle offers one of the earliest accounts of the origin of money. Money came into use because people became dependent on one another, importing what they needed and exporting the surplus. For the sake of convenience, people then agreed to deal in something that is intrinsically useful and easily applicable, such as iron

Rhetoric and poetics.

Aristotle's "Rhetoric" proposes that a speaker can use three basic kinds of appeals to persuade his audience: "ethos" (an appeal to the speaker's character), "pathos" (an appeal to the audience's emotion), and "logos" (an appeal to logical reasoning). He also categorizes rhetoric into three genres: epideictic (ceremonial speeches dealing with praise or blame), forensic (judicial speeches over guilt or innocence), and deliberative (speeches calling on an audience to make a decision on an issue). Aristotle also outlines two kinds of rhetorical proofs: "enthymeme" (proof by syllogism) and "paradeigma" (proof by example).  Aristotle writes in his "Poetics" that epic poetry, tragedy, comedy, dithyrambic poetry, painting, sculpture, music, and dance are all fundamentally acts of "mimesis" ("imitation"), each varying in imitation by medium, object, and manner. He applies the term "mimesis" both as a property of a work of art and also as the product of the artist's intention and contends that the audience's realisation of the "mimesis" is vital to understanding the work itself. Aristotle states that "mimesis" is a natural instinct of humanity that separates humans from animals and that all human artistry "follows the pattern of

Views on women.

Aristotle's analysis of procreation describes an active, ensouling masculine element bringing life to an inert, passive female element. On this ground, proponents of feminist metaphysics have

Influence.

More than 2300 years after his death, Aristotle remains one of the most influential people who ever lived. He contributed to almost every field of human knowledge then in existence, and he was the founder of many new fields. According to the philosopher Bryan Magee, "it is doubtful whether any human being has ever known as much as he did". Among countless other achievements, Aristotle was the founder of formal logic, pioneered the study of zoology, and left every future scientist and philosopher in his debt through his contributions to the scientific method. Taneli Kukkonen, writing in "The Classical Tradition", observes that his achievement in founding two sciences is unmatched, and his reach in influencing "every branch of intellectual enterprise" including Western ethical and political theory, theology, rhetoric and literary analysis is equally long. As a result, Kukkonen argues, any analysis of reality today "will almost certainly carry Aristotelian overtones... evidence of an exceptionally forceful mind." Jonathan Barnes wrote that "an account of Aristotle's intellectual afterlife would be little less than a history of European thought".

On his successor, Theophrastus.

Aristotle's pupil and successor, Theophrastus, wrote the "History of Plants", a pioneering work in botany. Some of his technical terms remain

On later Greek philosophers.

The immediate influence of Aristotle's work was felt as the Lyceum grew into the Peripatetic school. Aristotle's notable students included Aristoxenus, Dicaearchus, Demetrius of Phalerum, Eudemos of Rhodes, Harpalus, Hephaestion, Mnason of Phocis, Nicomachus, and Theophrastus. Aristotle's influence over Alexander the Great is seen in the latter's bringing with him on his expedition a host of

On Hellenistic science.

After Theophrastus, the Lyceum failed to produce any original work. Though interest in Aristotle's ideas survived, they were generally taken unquestioningly. It is not until the age of Alexandria under the Ptolemies that advances in biology can be again found.  The first medical teacher at Alexandria, Herophilus of Chalcedon, corrected Aristotle, placing intelligence in the brain,

On Byzantine scholars.

Greek Christian scribes played a crucial role in the preservation of Aristotle by copying all the extant Greek language manuscripts of the corpus. The first Greek Christians to comment extensively on Aristotle were Philoponus, Elias, and David in the sixth century, and Stephen of Alexandria in the early seventh century.

On the medieval Islamic world.

Aristotle was one of the most revered Western thinkers in early Islamic theology. Most of the still extant works of Aristotle, as well as a number of the original Greek commentaries, were translated into Arabic and studied by Muslim philosophers, scientists and scholars. Averroes, Avicenna and Alpharabius, who wrote on

On medieval Europe.

With the loss of the study of ancient Greek in the early medieval Latin West, Aristotle was practically unknown there from c. AD 600 to c. 1100 except through the Latin translation of the "Organon" made by Boethius. In the twelfth and thirteenth centuries, interest in Aristotle revived and Latin Christians had translations made, both from Arabic translations, such as those by Gerard of Cremona, and from the original Greek, such as those by James of Venice and William of Moerbeke. After the Scholastic Thomas Aquinas wrote his "Summa Theologica", working from Moerbeke's translations and calling Aristotle "The Philosopher", the

On Early Modern scientists.

In the Early Modern period, scientists such as William Harvey in England and Galileo Galilei in Italy reacted against the theories of Aristotle and other classical era thinkers like Galen, establishing new theories based to some degree on

On 19th-century thinkers.

The 19th-century German philosopher Friedrich Nietzsche has been said to have taken nearly all of his political philosophy from Aristotle. Aristotle rigidly separated action from production, and argued for the deserved subservience of some people ("natural slaves"), and the natural superiority (virtue, "arete") of others. It was Martin Heidegger, not Nietzsche, who elaborated a new interpretation

Modern rejection and rehabilitation.

During the 20th century, Aristotle's work was widely criticized. The philosopher Bertrand Russell argued that "almost every serious intellectual advance has had to begin with an attack on some Aristotelian doctrine". Russell called Aristotle's ethics "repulsive", and labelled his logic "as definitely antiquated as Ptolemaic astronomy". Russell stated that these errors made it difficult to do historical justice to Aristotle, until one remembered what an advance he made upon all of his predecessors.  The Dutch historian of science Eduard Jan Dijksterhuis wrote that Aristotle and his predecessors showed the difficulty of science by "proceed[ing] so readily to frame a theory of such a general character" on limited evidence from their senses. In 1985, the biologist Peter Medawar could still state in "pure seventeenth century" tones that Aristotle

Surviving works.

Corpus Aristotelicum.

The works of Aristotle that have survived from antiquity through medieval manuscript transmission are collected in the Corpus Aristotelicum. These texts, as opposed to Aristotle's lost works, are

Loss and preservation.

Aristotle wrote his works on papyrus scrolls, the common writing medium of that era. His writings are divisible into two groups: the "exoteric", intended for the public, and the "esoteric", for use within the Lyceum school. Aristotle's "lost" works stray considerably in characterization from the surviving Aristotelian corpus. Whereas the lost works appear to have been originally written with a view to subsequent publication, the surviving works mostly resemble

Legacy.

Depictions.

Aristotle has been depicted by major artists including Lucas Cranach the Elder, Justus van Gent, Raphael, Paolo Veronese, Jusepe de Ribera, Rembrandt, and Francesco Hayez over the centuries. Among the best-known is Raphael's fresco "The School of Athens", in the Vatican's Apostolic Palace, where the figures of Plato

Eponyms.

The Aristotle Mountains in Antarctica are named after Aristotle. He was the first person known to conjecture, in his book

Educational establishments.

Thessaloniki named the university within the city

Further reading.

The secondary literature on Aristotle is vast. The following is only a small selection.

Aristotle (; "Aristotélēs", ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Lyceum, the Peripatetic school of philosophy, and the Aristotelian tradition. His writings cover many subjects including physics, biology, zoology, metaphysics, logic, ethics, esthetics, poetry, theatre, music, rhetoric, psychology, linguistics, economics, politics, and government. Aristotle provided a complex synthesis of the various philosophies existing prior to him. It was above all from his teachings that the West inherited its intellectual lexicon, as well as problems and methods of inquiry. As a result, his philosophy has exerted a unique influence on almost every form of knowledge in the West and it continues to be a subject of contemporary philosophical discussion.

Aristoteles ze Stageiry () byl filosof vrcholného období řecké filosofie, nejvýznamnější žák Platonův a vychovatel Alexandra Makedonského. Jeho rozsáhlé encyklopedické dílo položilo základy mnoha věd. Narodil se 384 př. n. l. v osadě Stageira na poloostrově Chalkidiki v dnešní řecké Makedonii, asi 80 km východně od Soluně - Thessalonike (proto se někdy nazývá Stagirita), zemřel v roce 322 př. n. l. v Chalkidě, asi 60 km SV od Athén.