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.

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.

If you look at history, innovation doesn't come just from giving people incentives; it comes from creating environments where their ideas can connect.

As much as we sometimes roll our eyes at the ivory-tower isolation of universities, they continue to serve as remarkable engines of innovation.

The patterns are simple, but followed together, they make for a whole that is wiser than the sum of its parts. Go for a walk; cultivate hunches; write everything down, but keep your folders messy; embrace serendipity; make generative mistakes; take on multiple hobbies; frequent coffeehouses and other liquid networks; follow the links; let others build on your ideas; borrow, recycle; reinvent. Build a tangled bank.

When you don't have to ask for permission innovation thrives.

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.