@oristarA,
I think the context of the sentence would really help anyone understand it better!
Baconfield was on the verge of understanding
randomness when
chaos swept into his life.
Randomness and chaos are really the same thing so Baconfield wasn't on the verge of understanding anything -- he only thought he was.
I would take the sentence to mean that Baconfield was a man who had steadily built himself a certain kind of life, that he thought he had everything figured out and that made him feel very powerful. That he had laid down a certain kind of order to his life and that made him feel that he understood life.
Then something happened that set that world spinning and he realized that what he thought he had been building wasn't what he ended up with.