This made me think of engines as computers- the crank shaft connected to the timing belt goes up to the camshafts to instantly calculate the positions of the valves.
The solenoids control which pair of clutches in the transmission engage, which in turn, determines the gear the transmission is in.
Driveability wise, they were awful, and their overall efficiency was pretty bad. But the fact that it could automatically select the correct gear out of three or four with just one user input (throttle) is still marvelous.
They could also handle insane amounts of power for the era. The GM 3L series came out in 1964 and was the transmission people would reach for when they were putting WWII era plane engines into crazy automobiles.
Whereas modern 6+ speed transmissions are very different in design and control.