Season 2

S.2 RT6 – Understand Deeply


He never did a thing so very bad.
He don’t know why he isn’t quite as good
As anyone.
—From “The Death of the Hired Man” by Robert Frost

Silas felt the nervous excitement that all students feel as their professor returns graded exams. When Silas saw the red “58%” on the top of his test paper, he was frustrated, annoyed, and bewildered. “I really knew the stuff on the test. I just made a bunch of stupid little mistakes. I really knew it. Really.” And he really believed he knew it. Really. Sadly, such unpleasant surprises do not necessarily end after we receive our diplomas. Many people spend their entire careers confidently (and erroneously) thinking they know more and deserve more than their yearly evaluations, salaries, and success seem to reflect.

Understanding is not a yes-or-no proposition; it’s not an on-or-off switch. Silas spent hours studying for his test. But he spent that time memorizing facts rather than building a deep understanding. He would have earned a higher grade had he invested the same amount of time mastering the fundamentals, identifying essential themes, attaching each idea to that core structure, and, finally, imagining what surrounds or extends the material he was studying. Instead, Silas’s strategy was like that of a well-intentioned elementary school student who meticulously memorizes the mechanics of adding two-digit numbers but has no idea why the process works, and, as a result, finds adding three-digit numbers as alien as visiting another planet. Silas’s understanding was, at best, thin and fragile. Even tiny variations threw him, because he viewed his job as pinning down a certain number of isolated facts rather than understanding the meaning and connections of the ideas.

When you learn anything, go for depth and make it rock solid. If you learn a piece of music for the piano, then, instead of just memorizing finger movements, learn to hear each note and understand the structure of the piece. Ask yourself, “Can I play the notes of the right hand while just humming the notes of the left hand?” If you study the Civil War, rather than memorizing some highlights—Lincoln was president; Lee was a general; slavery played a role—you can try to understand the background, competing forces, and evolving social values that ignited the bloody conflict. When you make political decisions, instead of focusing on a candidate’s good looks and fifteen-second sound bites, you can objectively learn about the issues and develop your own reasoned opinions.

You can understand anything better than you currently do. Setting a higher standard for yourself for what you mean by understanding can revolutionize how you perceive the world. The following steps illustrate why a deep understanding is essential to a solid foundation for future thinking and learning.

Understand simple things deeply

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.

Trumpeting understanding through a note-worthy lesson.

Tony Plog is an internationally acclaimed trumpet virtuoso, composer, and teacher. A few years ago we had the opportunity to observe him conducting a master class for accomplished soloists. During the class, each student played a portion of his or her selected virtuosic piece. They played wonderfully. Tony listened politely and always started his comments, “Very good, very good. That is a challenging piece, isn’t it?” As expected, he proceeded to give the students advice about how the piece could be played more beautifully, offering suggestions about physical technique and musicality. No surprise. But then he shifted gears.

He asked the students to play a very easy warm-up exercise that any beginning trumpet player might be given. They played the handful of simple notes, which sounded childish compared to the dramatically fast, high notes from the earlier, more sophisticated pieces. After they played the simple phrase, Tony, for the first time during the lesson, picked up the trumpet. He played that same phrase, but when he played it, it was not childish. It was exquisite. Each note was a rich, delightful sound. He gave the small phrase a delicate shape, revealing a flowing sense of dynamics that enabled us to hear meaning in those simple notes. The students’ attempts did not come close—the contrast was astounding. 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.

The lesson was simple. The master teacher suggested that the advanced students focus more of their time on practicing simple pieces intensely—learning to perform them with technical efficiency and beautiful elegance. Deep work on simple, basic ideas helps to build true virtuosity—not just in music but in everything.

What is deep understanding?

How can you realize when you don’t know something deeply? When the advanced trumpet students played the simple phrase, they played every note and it sounded good to them. Before hearing the contrast between their renditions and the true virtuoso’s performance, the students might not have realized that it was possible to play that phrase far, far better.

In everything you do, refine your skills and knowledge about fundamental concepts and simple cases. Once is never enough. As you revisit fundamentals, you will find new insights. It may appear that returning to basics is a step backward and requires additional time and effort; however, by building on firm foundations you will soon see your true abilities soar higher and faster.

The whole of science is merely a refinement of everyday thinking.
—Albert Einstein

A commonsense approach leads to the core.

Many of the most complicated, subtle, and profound ideas arise from looking unmercifully clearly at simple, everyday experiences. Calculus is one of the most influential concepts in history. It has fundamentally changed the way we experience life today—a wide range of technological innovations, from space exploration to plasma TVs, computers, and cell phones, would not exist without calculus. And calculus is based on thinking deeply about simple, everyday motion—like an apple falling from a tree.

In 1665, England suffered an epidemic of bubonic plague. Cambridge University was closed to stem the dreaded disease’s spread, so Isaac Newton and the other students were sent home. Newton spent the next two years on his aunt’s farm, during which time he formulated the fundamental ideas of calculus and the laws of physics. The famous story about Newton sitting under an apple tree when an apple fell on his head, giving him the idea of universal gravitation and calculus, may be almost literally true. Thinking about the speed of a falling apple can generate the idea of the derivative—the profound extension of the basic notion that speed equals distance divided by time. Thinking about how far the apple would fall if you knew its speed at each instant leads to the idea of the integral—the abstraction that distance equals speed multiplied by time.

The grandest, most cosmic ideas, such as how the planets move, arise from thinking deeply about an apple hitting Newton. Newton described the universe—the behavior of the sun, planets, and distant stars—using the same laws that describe everyday occurrences like apples falling from trees. The simple and familiar hold the secrets of the complex and unknown. The depth with which you master the basics influences how well you understand everything you learn after that.

Today, when math teachers are asked what makes calculus so difficult to teach, most reply, “My students don’t know the basic mathematics that they saw in the eighth or ninth grade.” One secret to mastering calculus is to truly master basic algebra. In any class, when preparing for your next exam, make sure you can earn a 100% on all the previous exams—if you can’t, then you’re not ready for the test looming in your future. Instructors should also embrace this fundamental reality and help their students have a firmer grasp of the basics that preceded the material currently being explored.

To learn any subject well and to create ideas beyond those that have existed before, return to the basics repeatedly. When you look back after learning a complicated subject, the basics seem far simpler; however, those simple basics are a moving target. As you learn more, the fundamentals become at once simpler but also subtler, deeper, more nuanced, and more meaningful. The trumpet virtuoso found limitless beauty in a simple exercise and, in turn, found deep insights into the more interesting difficult pieces.

When faced with a difficult challenge—don’t do it!

In a speech delivered to Congress on May 25, 1961, John F. Kennedy challenged the country with the words “I believe that this nation should commit itself to achieving the goal, before this decade is out, of landing a man on the Moon and returning him safely to the Earth.” On May 26, the National Space Council didn’t suit up an astronaut. Instead their first goal was to hit the moon—literally. And just over three years later, NASA successfully smashed Ranger 7 into the moon at an impact velocity of 5,861 miles per hour (after the unmanned spacecraft transmitted over four thousand photographs of the lunar surface). It took fifteen ever-evolving iterations before the July 16, 1969, gentle moon landing and subsequent moon walk by the crew of the Apollo 11 spacecraft.

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

When the going gets tough, creative problem solvers create an easier, simpler problem that they can solve. They resolve that easier issue thoroughly and then study that simple scenario with laser focus. Those insights often point the way to a resolution of the original difficult problem.

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.

Adapted from "The 5 Elements of Effective Thinking" by Edward B. Burger and Michael Starbird.

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