6 ideas
A system can be studied entirely through the relation between its inputs and outputs without opening it, and two systems are functionally identical if they respond identically to all inputs regardless of internal construction. Understanding is built by systematically perturbing the box and recording how its outputs change, not by inspecting its hidden parts.
A system's behavior can be fully described as a transformation that maps each present state to a determinate next state, so its entire trajectory is fixed once the operator and initial state are known. Treating dynamics as repeated application of a transformation lets you analyze any process — physical, biological, or social — using the same abstract machinery of states and operands.
Variety is the number of distinguishable elements or states in a set, and it is the fundamental quantity governing what any regulator or communication channel can handle. Counting variety, often in logarithmic (bit) form, turns vague notions of complexity into a precise budget that constrains what control is possible.
Only variety can destroy variety: to keep an outcome within acceptable bounds against a set of disturbances, the regulator must command at least as many distinct responses as there are distinct disturbances. No amount of effort overcomes this limit — if the disturbances have more variety than the regulator can match, some disturbances will inevitably get through to the output.
A system maintains its essential variables within survivable limits by absorbing disturbances through feedback, and when ordinary feedback fails it reorganizes its own internal parameters until a stable configuration is found. Adaptation is thus a search across possible internal organizations driven by the threat of essential variables leaving their viable range.
A regulator works by intercepting the flow of variety from disturbances before it can reach and corrupt the protected outcome, so good regulation is equivalent to preventing information about disturbances from appearing in the essential variables. Viewing control this way reveals that every effective regulator must contain a model or correlate of the system it regulates.