The "Eureka moment" came one evening after work when we first realized that--in the simplest possible sense--any given aircraft maneuver could be defined as one unique setting of the aircraft autopilot.
This unique setting has 3 numbers, one for heading, one for altitude, one for speed.
Defined that way, we immediately realized it should be possible to construct a 3D volume--a "state space"--determined by 3 coordinate axes of heading, altitude, and speed. Individual aircraft maneuvers could then be defined as unique points within that space.
Suddenly, what had once been very hard now became very simple.
Now, every possible maneuver could be classified into one of two states. Eiither it (1) leads to future conflict or (2) does not.
Conflict maneuvers could be then drawn out as colored regions in a 3D display. Theoretically, this should make it possible to resolve all possible conflicts with all possible objects in a matter of seconds.
This led directly to the theory of the maneuver space and the development of 4CAS, the world's first navaid based upon it.