For your personal development, I just finished and highly recommend a rather big (530 pages), but readable, book on thinking–Surfaces and Essences: Analogy As The Fuel and Fire of Thinking. The authors are Douglas Hofstadter and Emmanuel Sander. You may remember Hofstadter from an earlier book, Gödel, Escher, Bach: An Eternal Golden Braid.
Don’t let the size scare you off. It is quite an enjoyable read packed with everyday examples and ending with the fascinating examples of mathematicians pursuit of solving quadratic equations and the development of Einstein’s thinking as he came up with his many theories that explained gravitation and mass-energy unity.
Analogy is the selective exploitation of past experiences to shed light on new and unfamiliar things belonging to another domain. Analogy-making is the lifeblood of cognition. It is also is the wellspring of creativity. As they explore analogy making, they touch on the education establishment’s tendency to believe in teaching things–especially science and math–with formal logic rather than analogy. This latter is ironic because so many advances in math are accomplished through analogy and not through formal logic.
This book’s summary of research and story of stories added to my knowledge and experience about how importance of story over lists of facts. Even in science and technology. Partly because sometimes what we take as facts really aren’t. I am betting that you all have developed new technologies or applications because you’ve visualized them first and then proceeded to search for the appropriate solution.
Go dive into the story. It’s fascinating…and life-changing.