The history of radio astronomy has been a series of discoveries, mostly serendipitous, using a new instrument, or using an old instrument in a new unintended way. Theoretical predictions have had little influence, and in some cases actually delayed the discovery by discouraging observers. Many of the key transformational discoveries were made while investigating other areas of astronomy; others came as a result of commercial and military pursuits unrelated to astronomy. We discuss how the transformational serendipitous discoveries in radio astronomy depended on luck, age, education, and the institutional affiliation of the scientists involved, and we comment on the effect of peer review in the selection of research grants, observing time, and the funding of new telescopes, and speculate on its constraint to new discoveries. We discuss the decrease in the rate of new discoveries since the Golden Years of the 1960s and 1970s and the evolution of radio astronomy to a big science user oriented discipline. We conclude with a discussion of the impact of computers in radio astronomy and speculations on the potential for future discoveries in radio astronomy – the unknown unknowns.

The Rumsfeld knowledge matrix – which spans the knowledge categories “known knowns,” “known unknowns,” and “unknown unknowns” – is used to illustrate the process of model improvement. Two new knowledge subcategories – “poorly known unknowns” and “well-known unknowns” – are introduced to distinguish between accuracy of parameterizations. A distinction is made between “downstream benefits” of parameterizations, which improve prediction skill, and “upstream benefits,” which improve understanding of the phenomenon being parameterized but not necessarily the prediction skill. Since new or improved parameterizations add to the complexity of models, it may be important to distinguish between essential and nonessential complexity. The fourth knowledge category in the Rumsfeld matrix is “unknown knowns” or willful ignorance, which can be used to describe contrarian views on climate change. Contrarians dismiss climate models for their limitations, but typically only offer alternatives born of unconstrained ideation.

Each of the three challenges introduced in Part I sets up a specific cognitive illusion for the learner. Together they conspire to block our learning. The first trap arises from the tactical paradox: It is tempting to see only one side of the coin and overlook the other, as in an optical illusion. The task appears to be more coherent than it really is, thereby preventing learners from seeing the full picture and fully understanding the task in hand.