1 H. Poincaré, ‘Mathematical creation’, in H. Poincaré, The Foundations of Science (New York: Science Press, 1913).
2 Paul Hindemith, A Composer’s World: Horizons and Limitations (Cambridge, MA: Harvard University Press, 1953), p. 50; online at <http://www.alejandrocasales.com/teoria/sound/composers_world.pdf>.
3 I challenge the reader to listen to a short piano piece such as Hindemith’s fascinating Piano Sonata No. 3 (Fugue) and to believe that its astonishing intricacies could have been conceived, except in the vaguest and most general terms, in any sudden flash of insight. Indeed, it seems mysterious how Hindemith could have convinced himself that this dazzling web of notes, extending over several minutes, arose fully formed in his consciousness in a single moment. We shall see later that Hindemith did not intend to be taken entirely literally.
4 Left image: R. L. Gregory (2001), The Medawar Lecture 2001: ‘Knowledge for vision: vision for knowledge’, Philosophical Transactions of the Royal Society Lond B, 360: 1231–51; the right image is by psychologist Karl Dallenbach.
5 U. N. Sio and T. C. Ormerod (2009), ‘Does incubation enhance problem solving? A meta-analytic review’, Psychological Bulletin, 135(1): 94.
6 But might unconscious mental work occur when we are asleep, when the brain is otherwise unoccupied? This is very unlikely: the coherent, flowing brain waves that overtake our brains through most of the night are utterly unlike the brainwaves indicative of intensive mental activity – the brain is, after all, resting. And the short bursts of dream sleep, though much more similar to waking brain activity, are taken up with other things: namely, creating the strange and jumbled images and stories of our dreams.
7 Hindemith, A Composer’s World: Horizons and Limitations, p. 51.
8 J. Levy, H. Pashler and E. Boer (2006), ‘Central interference in driving: Is there any stopping the psychological refractory period?’ Psychological Science, 17(3): 228–35.
9 Psychologists typically use ‘detection’ for tasks which require determining whether a ‘signal’ (a flash, a beep, or an aircraft on a radar screen) is present or not. This task is marginally more complex, requiring categorization into one or two categories (one event or two).
10 J. Levy and H. Pashler (2008), ‘Task prioritization in multitasking during driving: Opportunity to abort a concurrent task does not insulate braking responses from dual-task slowing’, Applied Cognitive Psychology, 22: 507–25.
11 E. A. Maylor, N. Chater and G. V. Jones (2001), ‘Searching for two things at once: Evidence of exclusivity in semantic and autobiographical memory retrieval’, Memory & Cognition, 29(8): 1185–95.