[Inquiry] Re: Prospects for Inquiry Driven Systems

[Jon Awbrey]

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PRO.  Note 8

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1.1.2.2.  Fields of Information and Fields of Knowledge

Successive extensions of the vector field concept can be achieved
by generalizing the form of pointwise information that is 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 it 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", gives rise
to the subject of stochastic differential geometry and to the investigation
of the associated dynamic systems.  An alternative development in this same
spirit might embody pointwise information about tangent vectors in the form
of linguistic expressions and ultimately in the form of knowledge bases that
enjoy the characters of empirical summaries or full-fledged logical theories
attaching themselves to each point of a phase space.

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 "distributed" a manner of information storage are extremely
well documented (cf. Hansel & Gretel), but there are times when it affords
the only means available.

Jon Awbrey

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