Boundary

1. A line or area which determines inclusion in and exclusion from a system.

2. Any system as an entity which can be investigated in its own right must have boundaries, either spatial or dynamic. Strictly speaking, spatial boundaries exist only in naive observation, and all boundaries are ultimately dynamic.

3. Systems, described as bounded regions in space-time, involving energy interchange among their parts, possess boundaries which may be clearcut and simple or non-material. An individual's self-identity and self-direction may be considered intimately linked to the role of boundaries in the conceptualizing process. In organizing sensory phenomena, the individual responds to stimuli in terms of patterns, and it is the segregation of circumscribed wholes which enables the sensory world to appear imbued with meaning.

4. A sub-system in a nearly-decomposable system in n dimensions will have boundary surfaces of n minus 1 dimensions between a high-interaction region and a low-interaction region. The surface may be taken as passing through a family of points where some parameter such as interaction-density has a maximum density. The boundary-surface for one property will tend to coincide with the boundary-surfaces for many other properties because the surfaces are mutually reinforcing. All gradients and flows in the region very near the boundary will tend to be either parallel or perpendicular to the boundary.

5. Indicates or fixes a limit on, or the extent of, the phase space (namely the particular area of the universe of numbers defined by a particular set of mathematical equations) which has to be searched in order to find the answer to a particular problem. Limiting conditions which restrict the range of possible solutions.

6. The extent of a field measured statistically and probabilistically in terms of incidence of the field's properties, e.g., the bounds of the gravitational field of the solar system or the bounds of the human (individual) energy field or the bounds of the noosphere.