The three muses of scientific discovery

How much of a great new idea is supposed to come from sheer inspiration? The related questions are how much should be coming from brute-force experimentation (these days generally machine-aided) and how much from sheer accident and coincidence? Those are, I would submit, three of the main sources for what looks, from a distance, like a single spring of knowledge. So when we triumphantly dip a cup into it, what’s the blend we’re drinking?