The laws of evolution of complexity of systems vs complexity of their controllers

Y. B. Karasik,
Thoughts Guiding Systems Corp.,
Ottawa, Canada.
e-mail:karasik@sympatico.ca

The first law: Let Cs(t) be the complexity of system S at a time t and Cc(t) be the complexity of its controller. Then

Cs(t)/Cc(t) 0

In other words, complexity of controller grows faster than the complexity of system that it controls. Eventually controller becomes infinitely more complex than the system.

The second law: The speed of deceleration of Cs(t) / Cc(t) reaches a local maximum when old principle of operation exhausts itself and system transitions to a new principle of operation:

max     d(Cs(t) / Cc(t))     =     d(Cs(t) / Cc(t))  
dt dt   t = ttransition

The transition time coincides with the time of transition from one S-curve to another.

For example, piston aircraft engines were pretty complex mechanically but their automatics was almost non existent. With transition to jet engines the role of automatics increased significantly. The ratio Cs(t) / Cc(t) experienced the biggest drop at that time. Neither before nor after the drop was as dramatic as during the transition time.