You should also check out Bronowski's Ascent of Man, it was made with many of the same people, before Connections. Later, they again worked on Carl Sagan's Cosmos.
I have a bias against Bronowski from years ago, when I heard him say that man is unique among animals because only man plays, and science is his play. I remember thinking - good lord, man, have you never seen a cat?
I had a lot of problems with him in the documentary, especially his dismissals of certain cultures based on extremely sparse data from archeological records. But it was still good overall.