In The Evolution of Physics, Einstein described the collapse of the mechanical world-view, leaving an intellectual vacuum before the radically new "field" theory could emerge. A field describes the behaviour of a dynamic system that is extended in space, through kinetics (interaction in time) and relational order (in space). It is a function of space and time coordinates that assigns a value of the field for each of the coordinates. Jackson Pollock, Number IIA, 1948
In current physics, several kinds of fundamental fields are recognized: the gravitational and electro-magnetic fields and the matter fields of quantum physics. Physicists talk about two kinds of fields: classical fields and quantum fields, although, for the most part, they believe that all fields in nature are quantum fields, and that a classical field is just a large-scale manifestation of a quantum field.
"A classical field is a kind of tension or stress that can exist in empty space in the absence of matter. It reveals itself by producing forces, which act on material objects that happen to lie in the space the field occupies." (Freeman Dyson, "Field Theory," in From Eros to Gaia, p. 93)
Fields are not a form of matter. Instead, matter is energy bound within fields. For classical physics, force is really only explainable in terms of bodies in contact. "Action at a distance", which is also a feature of gravity, seems "occult." Yet from the work of Kepler and Newton, particles had a dual nature: on the one hand, a highly localized object, and on the other an influence extending through the whole of space. In What is Matter?, Hermann Weyl gives a detailed outline of the displacement of the old "substance theory" by the modern "field theory." He locates the essential and epistemologically important difference between the two in the fact that the field can no longer be understood as a merely additive whole, as an aggregate of parts. The field is not a thing-concept but a relation-concept; it is not composed of pieces but is a system, a totality of lines of force. "For field theory, a material particle, such as the electron, is merely a small area of the electrical field in which the strength of the field assumes enormously high values and where there is, consequently, an intense concentration of field force in a small space. This conception of the world reposes entirely on the continuum; even atoms and electrons are not ultimate unchanging elements shoved around by the bombarding forces of nature but are themselves subject to continuously extended and delicately flowing changes." (quoted in Ernst Cassirer, The Problem of Form and the Problem of Cause , in The Logic of the Cultural Sciences, p. 92)
The modern concept of a field does not require a bodily medium, such as the ether, although objects can register the properties of the field. James Clerk Maxwell demonstrated that an insubstantial magnetic field could move matter held in its sway. Maxwell was the first to realize that electric and magnetic fields can exist not only near charges and magnets but also in free space disconnected from objects. From his equations he deduced that in empty space such fields would travel with the velocity of light. Hence, he made the epoch-making guess that light consists of travelling electro-magnetic fields.
Although modern physicists do not try to visualize the objects they discuss, Freeman Dyson suggests that we can think of a field as a flowing liquid which fills a given space and has at each point a certain velocity and direction of flow. This model must be imagined as an ideal liquid, not composed of atoms, since it is characteristic of a classical field that its strength at a given point varies smoothly as the point moves about in space. Dyson compares a quantum field to a turbulent flow. Superimposed on the steady average motion there is a tremendous confusion of eddies, of all sizes, overlapping and mingling with one another. Again, the limits of fluctuation imposed by real liquids must be ignored. Viscosity, or stickiness, damps out turbulence in liquids, and the atomic structure of the liquid sets a minimum size for eddies. In the quantum model, there is no dissipation of energy by viscosity, nor any minimum size of eddies. The velocity in a given region can continue to grow without diminution forever, and the fluctuations grow more intense without limit as the size of the region is reduced.
In 1922, Alexander Gurwitch employed the term "field" to describe, for example, the regular forms exhibited by the flowers of certain varieties of mushrooms, and distinguished them from the relatively undifferentiated organic structures from which they emerge. Hans Spemann used the concept of a morphogenetic field in 1921 in describing the localized embryonic "organizer." Paul Weiss in 1923 introduced the concept of field for the study of regeneration and extended it to include ontogeny. see morphic fields see also morphogenesis
An important characteristic of fields is their ability to exhibit gradients, or "lines of force." D'Arcy Thompson describes the trabeculae in bones as diagrams of stress fields. Like straw dispersed in the wind, iron filings in a magnetic field, and spin glasses. the location and orientation of objects can describe a field.
Futurist artists followed Boccioni's field-theory of space, with objects distributing lines of force through their surroundings.... Field is also a term in Gestalt psychology. (see also figure / ground.) Gestalt psychologists explicitly connected their theories with contemporary physics. Wolfgang Köhler connected psychology to physics through the concepts of closed / open systems, and elaborated Gestalt theory's position in response to Hans Driesch's vitalist interpretations of fields in embryology. Following the Gestalt psychologists, Michael Polanyi describes a parallelism between comprehension and morphogenesis, describing the lines of force of thought, whose gradients arise from proximity to possible achievement.
Deleuze and Guattari describe " Smooth space" as a field without conduits or channels. A field, a heterogeneous smooth space, is wedded to a very particular type of multiplicity: nonmetric, acentered, rhizomatic multiplicities that occupy space without 'counting' it and can 'be explored only by legwork.'" (Thousand Plateaus, p.371) Proponents of architecture "after geometry" describe "texture fields" as the forms of an emerging visuality. Stan Allen points out the aesthetics of fields in Mondrian's paintings of the 1920's, minimalist and postminimalist art that moved "from object to field," and in the clouds of sounds of Iannis Xenakis.
According to Stuart Kaufman, " self-organization is the capacity of a field to generate patterns spontaneously, without any specific instructions. What exists in the field is a set of relationships among the components of the system such that the dynamically stable state into which it goes naturally -- what mathematicians call the generic (typical)) state of the system has spatial and temporal patterns. Fields of this type are now called excitable media.