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   Schemas As Anti-bodies and Dynamical Systems

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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



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