When things "all hang together," you have either gotten the joke, solved the puzzle, argued in a circle, focused your chain of logic so narrowly that you will be blindsided—or discovered a hidden pattern in nature. Science, in large part, consists of imagining coherent solutions and then making sure that you weren't fooled by a false coherence as in astrology.
To arrive at the edge of the world's knowledge, seek out the most complex and sophisticated minds,
put them in a room together, and have them ask each other the questions they are asking themselves.