Aha! The moments of insight that shape our world

Great ideas often develop gradually after studying a problem at length - but not always. Sometimes, an insight hits like a bolt from the blue. For Archimedes, clarity struck while he was taking a bath. For Gustav Mahler, it came as the blades of his oars touched the water. And for Albert Einstein, it emerged while he was talking to a friend. Why do these moments of insight strike so suddenly? Why do they so often come to us when we are focused on something completely unrelated? And when great ideas "come to" us, where do they come from?