The first law: Let C_{s}(t) be the complexity of system S at a time t and C_{c}(t) be the complexity of its controller. Then
C_{s}(t)/C_{c}(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 C_{s}(t) / C_{c}(t) reaches a local maximum when old principle of operation exhausts itself and system transitions to a new principle of operation:
max | d(C_{s}(t) / C_{c}(t)) | = | d(C_{s}(t) / C_{c}(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 C_{s}(t) / C_{c}(t) experienced the biggest drop at that time. Neither before nor after the drop was as dramatic as during the transition time.