Breakthroughs are technological advances which change how people think. It's almost a given in popular culture that breakthroughs can't be predicted or characterized. To merely conceive one is to change the world it is born into. That's a very mythological thing to believe about the advancement of human knowledege. Are breakthroughs really immune to analysis?
Suppose that breakthroughs, like the phoenix, do keep their own schedules. We can still examine their nesting sites for clues. Some breakthroughs happen when the demand on a technology overwhelms regular innovation's ability to deliver. This happens in a big way during wartime and on a smaller scale every day. When I discover some new way to look at a program I'm writing, it's only after I've tried to stuff up the cracks with hasty code and deranged notes to myself. Maybe that's a formula: look for vital technologies that seem overly complex and burdened with new words.
"Overly complex" and "burdened with words" are hallmarks of the faux-historical Steampunk style and the predigital technology it cariacatures. I think we are especially fascinated by Steampunk machines because the mechanisms of control are obvious and human-scaled. This lever goes like so, the cable pulls the thingabob thusly, causing the flywheel to spin, etc. Like all cariacatures, Steampunk aesthetic exaggerates the features that make its subject distinctive. Behind the brass fittings and oddly-named components is a portrait of the mind which thought them necessary: ingenious mechanical design combined with astonishing ignorance about the principles of process control those designs embody. There is real tension there, a naive insistence that if something is important it must also be big enough to see.
As a wee lad in the last century I had a job repairing video cassette recording devices. Dozens of parts had to be properly greased, timed, or roughened up to get the right amount of tension and smooth unwinding. They had names like the Reverse/Forward Idler, Flywheel Belt, Pinch Roller, and Flying Erase Head. There was a long coil of wire whose only purpose was to delay the luma signal just enough to sync it with the chroma. Really old VCRs are as Steampunk as they come. 
Over time VCRs became smaller and vastly less complex while performing the same tasks as their ancestors. Very clever people spent decades improving the clockwork of video processing. Now of course we know the real breakthrough lay in getting rid of the clockwork.
It's probably a mistake to feel smug about that. The future isn't measured by years or technology, but by how it disagrees with the past about what is and what is not important. For example, I suspect the future will mock our assumption that computer intelligence will in any way resemble human intelligence, for the same reason we mock brass-handled Victorian contraptions. The idea is so central yet unfounded that it's bound to be wrong somehow. Whatever it is we're grasping toward, it may be "artificial intelligence" only in the sense that a car is an "iron horse".
In the first of the famous SICP lectures Hal Ableson explains that we are as ignorant about the true nature of computing as early Egyptians were about geometry. Those guys did impressive stuff with string and rocks but they didn't really understand why it worked. It took Euclid to distill the axioms and methods we now file under geometry. The misfit name geo-metry, ie earth-measurement, is a fossil of its confused history. Perhaps the jumbled bag of tricks we call "computer science" —not a science, and not about computers— is similarly waiting for something to hatch.
 My father disagrees with this interpretation. He points out that in the 1970s consumer video players were a huge gamble. It was decided that they had to be super reliable, and so were overbuilt. The evolution of VCRs post 1980 is a story of materials science (eg Teflon-coated plastic parts instead of greased metal and rubber belts) and amazing advances in integrated circuits. In short, VCRs became less reliable at roughly the same rate they became cheap enough that it didn't matter.
He has a point. The designers of early VCRs were not confused or stupid. Nevertheless they produced the most complex mechanical devices ever seen in the home, the maintainence of which provided employment for thousands.