Changes

=====1.1.2.2.  Fields of Information and Knowledge=====

=====1.1.2.2.  Fields of Information and Knowledge=====

Successive extensions of the vector field concept can be achieved by generalizing the form of pointwise information defined on a phase space. A subset of a tangent space at a point can be viewed as a boolean-valued function there, and as such can be generalized to a probability distribution that is defined on the tangent space at that point.  This type of probabilistic vector field or "information field" founds the subject of stochastic differential geometry and its associated dynamic systems.  An alternate development in this spirit might embody pointwise information about tangent vectors in the form of linguistic expressions and ultimately in knowledge bases with the character of empirical summaries or logical theories attached to each point of a phase space.

Successive extensions of the vector field concept can be achieved by  

generalizing the form of pointwise information defined on a phase space.

A subset of a tangent space at a point can be viewed as a boolean-valued

function there, and as such can be generalized to a probability distribution

that is defined on the tangent space at that point.  This type of probabilistic

vector field or "information field" founds the subject of stochastic differential

geometry and its associated dynamic systems.  An alternate development in this

spirit might embody pointwise information about tangent vectors in the form of

linguistic expressions and ultimately in knowledge bases with the character of

empirical summaries or logical theories attached to each point of a phase space.

It is convenient to bring together under the heading of a "knowledge field" any

It is convenient to bring together under the heading of a "knowledge field" any form of pointwise information, symbolic or numerical, concrete or theoretical, that constrains the set of pointwise tangent vectors defined on a phase space. In computational settings this information can be procedural and declarative program code augmented by statistical and qualitative data.  In computing applications a knowledge field acquires an aptly suggestive visual image: bits and pieces of code and data elements sprinkled on a dynamic surface, like bread crumbs to be followed through a forest.  The rewards and dangers of so literally a "distributed" manner of information storage are extremely well-documented (Hansel & Gretel, n.d.), but there are times when it provides the only means available.

form of pointwise information, symbolic or numerical, concrete or theoretical,

that constrains the set of pointwise tangent vectors defined on a phase space.

In computational settings this information can be procedural and declarative

program code augmented by statistical and qualitative data.  In computing

applications a knowledge field acquires an aptly suggestive visual image:

bits and pieces of code and data elements sprinkled on a dynamic surface,

like bread crumbs to be followed through a forest.  The rewards and dangers

of so literally a "distributed" manner of information storage are extremely

well-documented (Hansel & Gretel, n.d.), but there are times when it provides

the only means available.

=====1.1.2.3.  The Trees, The Forest=====

=====1.1.2.3.  The Trees, The Forest=====