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Homogeneity
to axiomatic systems
Simple explanation:
There are two fundamentally
different types of systems, the finite state machine, an abstraction,
and the natural system. Natural systems interact in the real
world to
produce what we know as ecosystems. Ecosystems are stratified
organizationally and have both local and non-local causality.
Finite
state machines interact to produce "larger" finite state
machines.
There is no non-locality due to design principles, all finite state
machine entailment is local. The ecosystem is embedded in other
natural ecosystems and has behavior that bubbles up from within.
This
"bubbling up" involves emergence, and in emergence we may have
non-deterministic behavior. This is an open question, of
course. A
cybernetic interface to natural ecosystems applies engineering to the
behavior of the ecosystem using a class of mechanisms while being open
to changes induced by internal or external causality. The
cybernetic
interface has both properties of natural systems and properties of
formal systems.
History:
Nature of first principles:
Functions provided by axiomatic
systems: