Computability

Computability is the ability for a computer to perform work within a system. In order to make certain we are on the same page; we want to define several specific terms very clearly.

A system is a set of elements, structures, connections, types, conditions, boundaries, observations, measurements, algorithms, and interaction patterns between the different parts and boundaries of the system which serves a specific purpose. A system is created by a group of stakeholders that have a shared understanding.

Complexity is the degree or level to which a system’s elements, structures, conditions, observations, measurements, and behavior depends on interactions that may, or may not, be cleanly decomposed into it understandable independent parts.

There tends to be three levels of complexity which have an impact on computability of a system: simple, complicated, and complex.

  • Simple system (a.k.a. non-complex): Predictable and deterministic. The system is “simple” or "non-complex" and therefore computable; clear and obvious for a pretty much anyone  including non-subject matter experts to understand, and the set of elements, connections, types/categories, conditions, boundaries, and interaction patterns are fully understandable and understood.  Easy to understand control techniques can be used to eliminate all risk errors from the system.
  • Complicated system (a.k.a. not simple, but still non-complex): Predictable and deterministic. The system is "non-complex" and therefore computable; clear and obvious for a skilled and experienced subject matter expert in the area of knowledge to which the system relates to understand, and the set of elements, connections, types/categories, conditions, boundaries, and interaction patterns are still fully understood. Control techniques can still be used to eliminate all risk of errors from the system.
  • Complex system: Not entirely predictable or unpredictable and therefore not deterministic. The system is "complex" and therefore NOT computable; tend to lack clear boundaries, tend to be constantly changing and evolving, there tend to be large numbers of elements, connections, structures, types/categories, conditions, observations, measurements, and interaction patterns which are not completely understood, the system seems to contradict itself on occasion, and the number of forces impacting the system tends to be large and the dynamics are not well understood. Control techniques cannot be used to fully eliminate all risk of errors from the system.

Note that some complex systems can have specific subsystems which are simple systems or complicated systems and if these systems can be separated then some aspects of a complex system can be made computable.

A complex system which can be "dumbed down" (a.k.a. simplistic) to a degree to enable the system to be computable but also adequately meet the goals and objectives of system stakeholders can be make both computable and perhaps useful/adequate to its stakeholders.


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