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Related to a project I'm working on:

Sit down before fact like a little child, and be prepared to give up every preconceived notion, follow humbly wherever and to whatever abyss Nature leads, or you shall learn nothing.

—T. H. Huxley

Or, in other words, problem solving through serendipity. It doesn't sound very reliable, but it has always worked for me.

(knock on wood)