Form (religion)

In academic discussions of organized religion, the term form is sometimes used to describe prescriptions or norms on religious practice.

Christian forms

Forms in Christianity are mostly familiarly dictates of church authority or tradition (e.g. church government, liturgy, doctrine). However, the term is used by some authors to refer to a broader category that includes other patterns of religious practice.

Most notably, Christian scholar D. G. Hart uses this term to compare and contrast the practices of evangelical Protestants and what he calls "confessional Protestants" (for example Anglicans and most Lutherans). He argues that the confessionals follow forms that are dictated by church authority or tradition, and calls these forms churchly forms. On the other hand, noting the resistance to such central authority and tradition among evangelicals, he labels the forms of these denominations parachurchly forms, as they are often dictated by parachurch organizations and other influences beyond the direct control of any particular church.

Religion

Religion is a cultural system of behaviors and practices, world views, ethics, and social organisation that relate humanity to an order of existence. About 84% of the world's population is affiliated with one of the five largest religions, namely Christianity, Islam, Hinduism, Buddhism or forms of folk religion.

With the onset of the modernisation of and the scientific revolution in the western world, some aspects of religion have cumulatively been criticized. Though the religiously unaffliated, including atheism and agnosticism, have grown globally, many of the unaffiliated still have various religious beliefs. About 16% of the world's population is religiously unaffiliated.

The study of religion encompasses a wide variety of academic disciplines, including comparative religion and social scientific studies. Theories of religion offer explanations for the origins and workings of religion.

Etymology

Religion

Religion (from O.Fr. religion "religious community", from L. religionem (nom. religio) "respect for what is sacred, reverence for the gods", "obligation, the bond between man and the gods") is derived from the Latin religiō, the ultimate origins of which are obscure. One possibility is an interpretation traced to Cicero, connecting lego "read", i.e. re (again) + lego in the sense of "choose", "go over again" or "consider carefully". Modern scholars such as Tom Harpur and Joseph Campbell favor the derivation from ligare "bind, connect", probably from a prefixed re-ligare, i.e. re (again) + ligare or "to reconnect", which was made prominent by St. Augustine, following the interpretation of Lactantius. The medieval usage alternates with order in designating bonded communities like those of monastic orders: "we hear of the 'religion' of the Golden Fleece, of a knight 'of the religion of Avys'".

Forma

Forma is a Latin word meaning "form". Both the word "forma" and the word "form" are used interchangeably as informal terms in biology:

Homogeneous polynomial

In mathematics, a homogeneous polynomial is a polynomial whose nonzero terms all have the same degree. For example, is a homogeneous polynomial of degree 5, in two variables; the sum of the exponents in each term is always 5. The polynomial is not homogeneous, because the sum of exponents does not match from term to term. A polynomial is homogeneous if and only if it defines a homogeneous function. An algebraic form, or simply form, is a function defined by a homogeneous polynomial. A binary form is a form in two variables. A form is also a function defined on a vector space, which may be expressed as a homogeneous function of the coordinates over any basis.

A polynomial of degree 0 is always homogeneous; it is simply an element of the field or ring of the coefficients, usually called a constant or a scalar. A form of degree 1 is a linear form. A form of degree 2 is a quadratic form. In geometry, the Euclidean distance is the square root of a quadratic form.

Homogeneous polynomials are ubiquitous in mathematics and physics. They play a fundamental role in algebraic geometry, as a projective algebraic variety is defined as the set of the common zeros of a set of homogeneous polynomials.

Differential form

In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates. Differential forms provide a unified approach to defining integrands over curves, surfaces, volumes, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, especially in geometry, topology and physics.

For instance, the expression f(x) dx from one-variable calculus is called a 1-form, and can be integrated over an interval [a, b] in the domain of f:

and similarly the expression f(x, y, z) dx ∧ dy + g(x, y, z) dx ∧ dz + h(x, y, z) dy ∧ dz is a 2-form that has a surface integral over an oriented surface S:

Likewise, a 3-form f(x, y, z) dx ∧ dy ∧ dz represents a volume element that can be integrated over a region of space.

The algebra of differential forms is organized in a way that naturally reflects the orientation of the domain of integration. There is an operation d on differential forms known as the exterior derivative that, when acting on a k-form, produces a (k + 1)-form. This operation extends the differential of a function, and the divergence and the curl of a vector field in an appropriate sense that makes the fundamental theorem of calculus, the divergence theorem, Green's theorem, and Stokes' theorem special cases of the same general result, known in this context also as the general Stokes' theorem. In a deeper way, this theorem relates the topology of the domain of integration to the structure of the differential forms themselves; the precise connection is known as de Rham's theorem.