It’s rare that you can solve a problem by operating at the level of the problem. You are more likely to find a solution by going “up” one level of abstraction/organization, or “down” a level to wrestle with more detail.
Leaders and managers in every organization should study and understand Kurt Godel’s Incompleteness Theorems, because leaders must think outside the circle.
Kurt Godel was an Austrian mathematician and logician who proved in 1931 (at age 25!) that no system can prove its own assumptions; you must have information from outside the system to prove its base assumptions. The information inside the system is incomplete. Think of it this way: If you can draw a circle around something, you need information from outside the circle to understand everything inside the circle.
What does this mean for leaders and managers? When you face organizational challenges, you need information from outside your regular working system to appreciate what’s going on, and make improvements. You must get outside the trees in order to understand the forest. Solutions are rarely found by working exclusively within the existing system. That’s why outsiders can often spot problems or leverage points that insiders have missed.
The Incompleteness Theorems help keep us humble, teachable, and open to outside information.
I strongly recommend leaders investigate multiple fields outside of their professional work, and cultivate learning in several disciplines. Business leaders have much to learn from music, quantum mechanics, ecology, neurobiology, linguistics, architecture, textiles, politics, and astrophysics. Some people call this cross-fertilization of ideas, but in Godel’s terms any one system is incomplete. This is a lifetime adventure of learning and growing.
I wish Godel’s Incompleteness Theorems were taught in every high school. His work is one of the greatest contributions in the 20th century. I suspect that the reason they are not taught is that understanding them has a tendency to cause people to doubt that the teachers and leaders are right about everything they want you to believe, and this makes it more difficult to keep sheeple in line. But, that is a conversation for another time…
Recommended resources if you’d like to learn more about Kurt Godel and his incompleteness theorems:
The best biography of Kurt Godel I’ve read is Incompleteness: The Proof and Paradox of Kurt Gödel — excellent. The sections on his interactions with Albert Einstein and Bertrand Russell are fantastic. (Bertrand Russell was close to finishing his magnum opus, a mathematical “theory of everything”, but switched to writing popular philosophy after Godel’s proofs demolished his dream.)
If you want to appreciate the math, the Wikipedia article on the 2 incompleteness theorems is worth reviewing.
I first learned about Godel’s work when I read Douglas Hofstadter’s Pulitizer Prize winning book, Godel, Escher, Bach: An Eternal Golden Braid in 1985 while working on my Ph.D. in Molecular Biology; the concepts were hugely influential on me at the time. Hofstadter puts Godel’s work in context with art, computer science, music theory, and psychology.