Communication to the Natural Science & Mathematics Communities
In science a notational system is for communication. We use a highly formalized language designed to support science of knowledge creation, sharing and management. [*]
Differential ontology framework was designed to measure stochastic structure and convert this structure to a collection of discrete elements, in this case a specific graph structure with node values occurring or having been inferred as afforded by the structure of invariance within the data.
The term “affordance” is used first by J.J. Gibson in the foundations of an academic discipline called “ecological physics”. This term is one of those that are essential within an objective discussion about knowledge creation, sharing and management. In the knowledge sciences, one also has to account for the differences between viewpoint and the difference between private experience and shared experiences. One way to approach these differences is in a separate delineation of function and structure. In linguistics this differentiation between descriptions of function and of structure is called double articulation.
We are conjecturing that class:object pairing is the proper way to discuss the relationship between function and structure, and is perhaps optimal in terminological use for modeling complex systems where structure is differentially shaped by the functional needs of an environment.
The indeterminacy seen in function/structure descriptions has not been precisely captured by Hilbert (or “classical”) mathematics. In computer science we find open problems related to the halting conditions. In mathematical biology we find that the more mathematics is used in a strict since, the less biology we study.
For us, it has seemed appropriate to create a new stratified mathematics with the Hilbert space mathematics as the "crisp" expression.
In the non-crisp form we have a tri-level architecture and both differential ontology and formative ontology. But still open problems remain.
Artificial neural networks, of the more advanced form from the Stephen Grossberg school, can be used within each level to create process dynamics governed by first order differential equations, as models providing adaptive selection and categorization, or first order predicate logics.
Here is the question that might be asked and answered by the group, and by leading scholars and policy makers.
“Fundamental question: Do we wish to reinforce the notion that class exists at one level of informational organization and localized informational objects exists at a different level of informational organization?
If the answer to this fundamental question is yes, then we must develop the theory of Human-centric Information Production (HIP) in a way that is consistent with the notions of "cross scale transforms" that
1: creates localized "units" of information from some global measurement, and
2: aggregates collections of these localized units of information into a global organization (or schema) in a formative fashion
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