Those "coincidences" in Connections are really no coincidence at all, but path dependence. Breakthrough advance A is impossible or useless without prerequisites B and C and economic conditions D, but once B and C and D are in place, A becomes obvious next step.

Some of those really are coincidences, like "Person A couldn't find their left shoe and ended up in London at a coffee house, where Person B accidentally ended up when their carriage hit a wall, which lead to them eventually coming up with Invention C" for example.

Although from what I remember from the TV show, most of what he investigates/talks about is indeed path dependence in one way or another, although not everything was like that.

That’s why I’ve put the word in parentheses :)