At Renaissance Weekend a few months ago, I heard a phenomenal lecture by Michael Starbird, a mathematician at the University of Texas. Afterwards, I bought his book, co-authored with Williams College professor Edward Burger, called The 5 Elements of Effective Thinking.
It’s a very short, lively book that persuasively makes the case that there are learnable general skills that contribute to clear thinking and effective problem solving. The four elements they highlight are:
Understand deeply: Don’t face complex issues head-on; first understand simple ideas deeply. Clear the clutter and expose what is really important. Be brutally honest about what you know and don’t know. Then see what’s missing, identify the gaps, and fill them in. Let go of bias, prejudice, and preconceived notions. There are degrees to understanding (it’s not just a yes-or-no proposition) and you can always heighten yours. Rock-solid understanding is the foundation for success. Make mistakes: Fail to succeed. Intentionally get it wrong to inevitably get it even more right.
Make mistakes: Fail to succeed. Intentionally get it wrong to inevitably get it even more right. Mistakes are great teachers— they highlight unforeseen opportunities and holes in your understanding. They also show you which way to turn next, and they ignite your imagination.
Raise questions: Constantly create questions to clarify and extend your understanding. What’s the real question? Working on the wrong questions can waste a lifetime. Ideas are in the air— the right questions will bring them out and help you see connections that otherwise would have been invisible.
Follow the flow of ideas: Look back to see where ideas came from and then look ahead to discover where those ideas may lead. A new idea is a beginning, not an end. Ideas are rare— milk them. Following the consequences of small ideas can result in big payoffs.
(The fifth element is change.)
To remember these, they associate each of the four habits with a classic element of nature: Earth (understand deeply), Fire (make mistakes), Air (ask questions), Water (follow the flow).
I found many good points on each front, especially on the importance of depth of understanding. Kindle highlights below. All direct quotes from the book; bolded sentences my own addition.
The most fundamental ideas in any subject can be understood with ever-increasing depth. Professional tennis players watch the ball; mathematicians understand a nuanced notion of number; successful students continue to improve their mastery of the concepts from previous chapters and courses as they move toward the more advanced material on the horizon; successful people regularly focus on the core purpose of their profession or life. True experts continually deepen their mastery of the basics.
The fundamental difference between the true master and the talented students clearly occurred at a far more basic level than in the intricacies of complex pieces. Tony explained that mastering an efficient, nuanced performance of simple pieces allows one to play spectacularly difficult pieces with greater control and artistry.
Consider a subject you think you know or a subject you are trying to master. Open up a blank document on your computer. Without referring to any outside sources, write a detailed outline of the fundamentals of the subject. Can you write a coherent, accurate, and comprehensive description of the foundations of the subject, or does your knowledge have gaps? Do you struggle to think of core examples? Do you fail to see the overall big picture that puts the pieces together? Now compare your effort to external sources (texts, Internet, experts, your boss). When you discover weaknesses in your own understanding of the basics, take action.
Great scientists, creative thinkers, and problem solvers do not solve hard problems head-on. When they are faced with a daunting question, they immediately and prudently admit defeat. They realize that there is no sense in wasting energy vainly grappling with complexity when, instead, they can productively grapple with simpler cases that will teach them how to deal with the complexity to come. If you can’t solve a problem, then there is an easier problem you can’t solve: find it. —George Polya
Apply this mind-set to your work: when faced with a difficult issue or challenge, do something else. Focus entirely on solving a subproblem that you know you can successfully resolve. Be completely confident that the extraordinarily thorough work that you invest on the subproblem will later be the guide that allows you to navigate through the complexities of the larger issue. But don’t jump to that more complex step while you’re at work on the subissue. First just try to hit the moon … walking on its surface is for another day.
I simply asked the artist, “Tell me one insight into painting.” The artist, a bit surprised by the out-of-the-blue request, thought for several moments and then responded, “Shadows are the color of the sky.” I didn’t really believe him at first. Like most people, I thought shadows were gray or black, but if you look closely, you will see that indeed shadows in the great outdoors do have color—albeit subtle. I had seen shadows every day of my life, but I was wrong about what they really look like. Those colorful shadows gave me a whole new view of the world—a fresh perspective that transcends the art of painting.
Let’s return to a time in which photographs were not in living color. During that period, people referred to pictures as “photographs” rather than “black-and-white photographs” as we do today. The possibility of color did not exist, so it was unnecessary to insert the adjective “black-and-white.” However, suppose we did include the phrase “black-and-white” before the existence of color photography. By highlighting that reality, we become conscious of current limitations and thus open our minds to new possibilities and potential opportunities. World War I was given that name only after we were deeply embattled in World War II. Before that horrific period of the 1940s, World War I was simply called “The Great War” or, even worse, “The War to End All Wars.” What if we had called it “World War I” back in 1918? Such a label might have made the possibility of a second worldwide conflict a greater reality for governments and individuals, and might have led to better international policy decisions. We become conscious of issues when we explicitly identify and articulate them.
From the physical world to society, academics, personal relations, business, abstract ideas, and even sports, a deep examination of the simple and familiar is a potent first step for learning, thinking, creating, and problem solving.
instead extract a new insight from that misstep and correctly think, “Great: one down, nine to go—I’m making forward progress!” And indeed you are. After your first failure, think, “Terrific, I’m 10% done!” Mistakes, loss, and failure are all flashing lights clearly pointing the way to deeper understanding and creative solutions.
Success is not about almost always succeeding. How would you feel if you were failing about 60% of the time? Sounds like a solid “F.” Well, in certain contexts you’d be a superstar. A major league baseball player who failed 60% of the time—that is, who had a batting average of .400—would be phenomenal. No
A transformative but challenging personal policy is to never pretend to know more than you do. Don’t build on ambiguity and ignorance. When you don’t know something, admit it as quickly as possible and immediately take action—ask a question.
If you are a teacher or a manager, instead of asking, “Are there any questions?” assume there are, and say, “Talk to your neighbor for sixty seconds and write down two questions.” Then randomly call on pairs to read their questions. That is, instead of asking whether there are questions, tell your listeners that they are to create questions—an important habit to develop for lifelong learning and curiosity.
…recognize that each new idea extends a line that started in the past and travels through the present into the future. Successful and effective learners and innovators harness the power of the flow of ideas, which suggests the element Water.
When you learn a new concept or master a skill, think about what extensions, variations, and applications are possible. It’s natural to think of the moment when you’ve solved a problem or mastered a new idea as a time to party and rest on your laurels—as if you’ve arrived at the final chapter of some great story. In fact, a bed of laurels will never offer a satisfying rest, and a new idea or solution should always be viewed as a beginning. Effective students and creative innovators regularly strive to uncover the unintended consequences of a lesson learned or a new idea. The time to work on a problem is after you’ve solved it. —R. H. Bing
I begin with an idea and then it becomes something else. —Pablo Picasso
Consider an issue or problem and now exaggerate some feature of it to a ridiculous extreme. If you are arguing one side of an issue, support the side you truly believe; then make the argument so exaggerated that you realize that it’s way over the top. Now study your exaggerated description and discover some underlying defect. Does that defect also exist in a nonexaggerated perspective?