System Complexity and Computability

A system is a set of elements, categories or sets into which the elements fall, and interaction patterns that describe the interactions between the different types of elements within a system. (a.k.a. formal system)

A system has a level of  complexity.  There are two groups of complexity: complex and non-complex.  Non-complex systems are computable, they have computability. Complex systems are not computable.

A system can be simple, complicated, or complex. (See this explanation of system theory.)

  • Non-complex
    • Simple system: The system is "non-complex" and therefore computable; clear and obvious for a non-subject matter expert to understand, and the set of elements, categories, and interaction patterns are fully understood.  Control techniques can be used to eliminate all risk from the system.
    • Complicated system: The system is "non-complex" and therefore computable; clear and obvious for a subject matter expert in the area of knowledge to which the system relates to understand, and the set of elements, categories, and interaction patterns are fully understood. Control techniques can be used to eliminate all risk from the system.
  • Complex
    • Complex system: 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, categories, 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 from the system.
    • Complex systems with non-complex subsystems: A complex system with some simple or complicated subsystems which can be separated and some aspects made computable.
    • Complex systems which can be simplified to simulate non-complex systems: A complex system which can be "dumbed down" to a degree to enable the system to be computable but also adequately meet the goals and objectives of system stakeholders.
What makes a system complex? The following are things that contribute to system complexity or make a system non-complex:
  • System evolution: Rapid evolution of the set of elements, categories, and interaction patterns of the pieces of a system contributes to system complexity.  Slow system evolution or unchanging systems make systems non-complex.
  • System boundaries: Unclear or unknown system boundaries contribute to making systems complex. Fixed and well understood system boundaries make a system non-complex.
  • System elements and interactions: The larger the number of elements a system has, the categories of elements, and interaction patterns between elements and categories contribute to complexity.  Unknown elements, categories, and interaction patterns also contribute to complexity.  Complete and well understood sets of elements, categories, and interaction patterns contribute to  non-complexity.
  • System forces: The more different forces acting on a system the more complex the system.  Even if the number of forces are low but the forces are not well understood can make a system complex.  A low number of well understood forces which act upon a system contribute to making a system non-complex.
  • System predictability: An inability to predict system behavior contributes to system complexity.  If the behavior of a system is predictable, the predictability contributes to non-complexity.
  • System equilibrium: A system that is never in equilibrium is complex.  A system that is always in equilibrium is non-complex.
There is a difference between real complexity (a.k.a. inherent complexity, essential complexity, irreducible complexity) and accidental complexity.  Accidental complexity is always removable from a system.  Ignorance of how to remove accidental complexity is not complexity; it is a lack of understanding of the system.

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