Complexity and the Systems Approach

Systems definition of complexity:
sub-definition: ample: statistically significant in number
sub-definition: trivial: easily or simply characterized
1. an ample supply of distinctly different component types
2. a non-trivial arrangement of components for nominal system operation
3. typically exhibits synergy
4. a non-trivial interface to external systems

4 is not strictly required for complexity but is typically found in natural / human made systems.
Synergy is difficult to quantify and is difficult for a Western mind to appreciate. Because Western science was historically based on reduction, admittedly a very expedient approach to problem solving, Western scientists and engineers have had trouble understanding, appreciating, and integrating the concept. Reduction works amazingly well on simple non-systemic problems. But for precisely this reason, Westerners have over-applied reduction - attempting to 'divide and conquer' problems which are systemic in nature or problems associated with complex systems. If indeed reduction works with some of these mis-applications, it is likely chance or a result of ill-framing the problem in the first place. The general rule-of-thumb for applying the systems-reliability approach to solving a problem is: if you suspect a problem is complex, it probably is; when in doubt, apply the systems approach.

Purpose of definition:
Complexity is a modern concept. Many approaches are ambiguous / ill defined / overly specific in application. Many, if not most, modern problems require the systems-reliability approach. This is specifically required because of the level of complexity involved. To reiterate, modern problems are complex; complexity requires explicit definition; complex problems require the systems-reliability approach.

Illustrations:
a simple system: a ball rolling down a hill
a simple dynamical system: a speed governor in an operating school-bus
a complex natural system: dolphin sonar
a complex human-made system: the American defense system

Dynamical system: past inputs affect current outputs.

Unstable system: inputs or state trajectory result in catastrophic failure.
Examples: long tension bridges under sheer wind stress, an insane human mind, a speeding vehicle on black-ice over uneven terrain, a poorly maintained/designed space shuttle during takeoff or reentry, a poorly operated nuclear reactor such as Chernobyl, the Earth's climate system subject to unregulated human pollutants, the modern global unregulated economic system,..

Reliability: basically entails dependability. If a component/subsystem has a particular failure rate independent of other components, if the entire system has a particular calculable dependency on that component, if we know the cost of catastrophic failure, then we can calculate the relative cost of loss for failure of that particular component.

A linear system is explicitly and completely characterized by a set of linear differential equations describing system state. Linear systems are well understood. Observability and controllability are linear system concerns. Non-linear systems are characterized by a set of non-linear differential equations governing system state. Non-linear systems are less well understood and typically, we can do stability analysis of these types. The Lorenz equations are the 'classic example' for non-linear systems.

Stochastic systems are those with random inputs or random components. Do not confuse stochastic systems with chaotic systems. Many non-linear systems exhibit chaotic behavior but are completely deterministic in characterization. Again, it is easy to confuse the two. System identification refers to the part of the systems approach devoted to determining system structure and attributes. For instance, determining whether a natural/human system is stochastic, non-linear, or linear is part of system identification. Parameter estimation is part of system identification once system type is determined. This is essentially an attempt to statistically determine coefficients in a transfer function or system of differential equations.

Please do not let this brief overview/introduction confuse you. The systems approach is actually very simple. It is in the details or conscientious application that things get 'hairy'.

There are four views/aspects of the systems approach:
boundary
scope
maintenance
reliability
..they can be understood by recursive application. In Humanity Thrive!, i encourage students / those new to systems-design to apply those main views to various scenarios. However, this essay is not primarily about the systems approach - it's about the systems definition of complexity.

..There is a general apathy about the systems approach for mixed reasons. For one, it's an engineering domain which typically interests only engineers or like minded individuals. Second, it demands a kind of holistic thinking or way of looking at things which requires broad / open minded individuals. Third, there must be a genuine desire to learn about it which usually comes from the heart - inspired individuals. Rare indeed are: inspired open-minded engineers. So when i call for the establishment of an American systems society, it should not be surprising i receive no interest whatsoever..

It doesn't help that American Systems Society reduces to ASS. ;)
Maybe if we prefix it with nice-ASS we can get some attention. ;)
..sigh..