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Both create insight. Rather than leading us along a plodding route from one incremental step to the next, the ideas give us a sudden, dramatic glimpse of how the world might unfold. And not just how but why.

Both create knowledge gaps. Loewenstein, the author of the gap theory, says it’s important to remember that knowledge gaps are painful. ā€œIf people like curiosity, why do they work to resolve it?ā€ he asks. ā€œWhy don’t they put mystery novels down before the last chapter, or turn off the television before the final inning of a close ball game?ā€

Both of these unexpected ideas set up big knowledge gaps—but not so big that they seemed insurmountable. Kennedy didn’t propose a ā€œman on Mercury,ā€ and Ibuka didn’t propose an ā€œimplantable radio.ā€ Each goal was audacious and provocative, but not paralyzing. Any engineer who heard the ā€œman on the moonā€ speech must have begun brainstorming immediately: ā€œWell, first we’d need to solve this problem, then we’d need to develop this technology, then …