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Two fun thoughts to ponder:
1. A common view of the schema or DTD is as a means
to validate the instance for acceptance. However,
it is perfectly useful as a means to validate an
instance for rejection. You can have anti-schemas,
anti-anti-schemas and so forth given some dynamic
exchange such as messages which are themselves,
evolving (the schema is a kind of message).
2. A URI as a namespace identifier takes a single
value from an infinite space and uses it to
label an instance from a potentially infinite
space (vocabularies are dynamic in time as
expressed by a schema signature). If we think
of that variation as motion, then the equations
evolve in time. If the DTD or schema for a
vocabulary is considered a classifier, then
as noted by Farmer and Packard, "in typical
studies in dynamical systems theory the dimension
and the components of the state vector are fixed.
In contrast while the list of variables in the
immune or classifier systems is always finite,
its composition varies with time. As components
are created or destroyed the differential
equations describing the dynamics change
and both the dimension N and composition of
the state vector changes... Of course it is
possible to embed such a system in an infinite
dimensional space and view the dynamics as fixed
in time. We find it more useful though to
construct an algorithm that generates the
appropriate dynamical equations in the lowest
possible dimensional state space and study the
dynamics in this context." (1)
(1) J.D. Farmer et al./The Immune System, Adaptation and Machine Learning
len
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