Popular culture, on average, has been growing more cognitively challenging over the past thirty years, not less. Despite everything you hear about declining standards and dumbing-down, you have to do more intellectual work to make sense of today's television or games - much less the internet - than you did a few decades ago.

It may not be possible to 'win the future,' in President Obama's words, but if we're going to encourage more innovation, it's not enough for us to just dig in and work harder. We also need to encourage surprise and serendipity. We need to play each other's instruments.

What you end up seeing when you look at history is that people who have been good at pushing the boundaries of possibility, and exploring those frontiers of good ideas and innovations, have rarely done it in moments of great inspiration. They don't just have a brilliant breakthrough idea out of nowhere and leap ahead of everyone else.

Calculus, the electrical battery, the telephone, the steam engine, the radio - all these groundbreaking innovations were hit upon by multiple inventors working in parallel with no knowledge of one another.

Silicon-based life may be impossible for one other reason: silicon bonds readily dissolve in water.

How could so many intelligent people be so grievously wrong for such an extended period of time? How could they ignore so much overwhelming evidence that contradicted their most basic theories? These questions, too, deserve their own discipline: the sociology of error.

This is how great intellectual breakthroughs usually happen in practice. It is rarely the isolated genius having a eureka moment alone in the lab. Nor is it merely a question of building on precedent, of standing on the shoulders of giants, in Newton's famous phrase. Great breakthroughs are closer to what happens in a flood plain: a dozen separate tributaries converge, and the rising waters lift the genius high enough that he or she can see around the conceptual obstructions of the age.