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unlock your potential

Richard Feynman, the bongo-playing, Nobel Prize–winning physicist, was a happy-go-lucky guy. But there were a few years—the best and worst of his life—when his exuberance was challenged.

In the early 1940s, Feynman’s beloved wife, Arlene, lay in a distant hospital, deathly ill with tuberculosis. He only rarely could get away to see her because he was in the isolated New Mexico town of Los Alamos, working on one of the most important projects of World War II—the top-secret Manhattan Project. Back then, Feynman was nobody famous. No special privileges were afforded him.

To help keep his mind occupied when his workday ended and anxiety or boredom reared its head, Feynman began a focused effort to peer into people’s deepest, darkest secrets: He began figuring out how to open safes.

Becoming an accomplished safecracker isn’t easy. Feynman developed his intuition, mastering the internal structures of the locks, practicing like a concert pianist so his fingers could swiftly run through remaining permutations if he could discover the first numbers of a combination.

Eventually, Feynman happened to learn of a professional locksmith who had recently been hired at Los Alamos—a real expert who could open a safe in seconds.

An expert, right at hand! Feynman realized if only he could befriend this man, the deepest secrets of safecracking would be his.

IN THIS BOOK we’ve explored new ways of looking at how you learn. Sometimes, as we’ve discovered, your desire to figure things out right now is what prevents you from being able to figure things out. It’s almost as if, when you reach too quickly with your right hand, your left hand automatically latches on and holds you back.

Great artists, scientists, engineers, and chess masters like Magnus Carlsen tap into the natural rhythm of their brains by first intently focusing their attention, working hard to get the problem well in mind. Then they switch their attention elsewhere. This alternation between focused and diffuse methods of thinking allows thought clouds to drift more easily into new areas of the brain. Eventually, snippets of these clouds—refined, refluffed—can return with useful parts of a solution.

Reshaping your brain is under your control. The key is patient persistence—working knowledgeably with your brain’s strengths and weaknesses.

You can improve your focusing ability by gently redirecting your responses to interrupting cues like your phone’s ring or the beep of a text message. The Pomodoro—a brief, timed period of focused attention—is a powerful tool in diverting the well-meaning zombies of your habitual responses. Once you’ve done a bout of hard, focused work, you can then really savor the mental relaxation that follows.

The result of weeks and months of gradual effort? Sturdy neural structures with well-cured mortar laid between each new learning period. Learning in this way, with regular periods of relaxation between times of focused attention, not only allows us to have more fun, but also allows us to learn more deeply. The relaxation periods provide time to gain perspective—to synthesize both the context and the big picture of what we are doing.

Be mindful that parts of our brain are wired to believe that whatever we’ve done, no matter how glaringly wrong it might be, is just fine, thank you very much. Indeed, our ability to fool ourselves is part of why we check back—Does this really make sense?—before turning in an examination. By ensuring that we step back and take fresh perspectives on our work, by testing ourselves through recall, and by allowing our friends to question us, we can better catch our illusions of competence in learning. It is these illusions, as much as any real lack of understanding, that can trip us up en route to success in studying math and science.

Rote memorization, often at the last minute, has given many lower-level learners the illusory sense that they understand math and science. As they climb to higher levels, their weak understanding eventually crumbles. But our growing understanding of how the mind truly learns is helping us move past the simplistic idea that memorization is always bad. We now know that deep, practiced internalization of well-understood chunks is essential to mastering math and science. We also know that, just as athletes can’t properly develop their muscles if they train in last-minute cramming sessions, students in math and science can’t develop solid neural chunks if they procrastinate in their studies.

No matter what our age and degree of sophistication, parts of our brain remain childlike. This means that we sometimes can become frustrated, a signal to us to take a breather. But our ever-present inner child also gives us the potential to let go and use our creativity to help us visualize, remember, make friends with, and truly understand concepts in math and science that at first can seem terribly difficult.

In a similar way, we’ve found that persistence can sometimes be misplaced—that relentless focus on a problem blocks our ability to solve that problem. At the same time, big-picture, long-term persistence is key to success in virtually any domain. This kind of long-term stick-to-it-iveness is what can help get us past the inevitable naysayers or unfortunate vicissitudes of life that can temporarily make our goals and dreams seem too far to grasp.

A central theme of this book is the paradoxical nature of learning. Focused attention is indispensable for problem solving—yet it can also block our ability to solve problems. Persistence is key—but it can also leave us unnecessarily pounding our heads. Memorization is a critical aspect of acquiring expertise—but it can also keep us focused on the trees instead of the forest. Metaphor allows us to acquire new concepts—but it can also keep us wedded to faulty conceptions.

Study in groups or alone, start hard or start easy, learn concretely or in abstract, success or failure . . . In the end, integrating the many paradoxes of learning adds value and meaning to everything we do.

Part of the magic long used by the world’s best thinkers has been to simplify—to put things into terms that even a kid brother or sister can understand. This, indeed, was Richard Feynman’s approach; he challenged some of the most esoteric theoretical mathematicians he knew to put their complicated theories in simple terms.

It turned out they could. You can, too. And like both Feynman and Santiago Ramón y Cajal, you can use the strengths of learning to help reach your dreams.

AS FEYNMAN CONTINUED to refine his safecracking skills, he befriended the professional locksmith. Through time and talk, Feynman gradually swept away superficial pleasantries, digging deeper and deeper so that he could understand the nuance behind what he saw to be the locksmith’s utter mastery.

Late one night, at long last, that most valuable of arcane knowledge became clear.

The locksmith’s secret was that he was privy to the manufacturers’ default settings.

By knowing the default settings, the locksmith was often able to slip into safes that had been left unchanged since they’d arrived from the manufacturer. Whereas everyone thought that safecracking wizardry was involved, it was a simple understanding of how the device arrived from the manufacturer that was fundamental.

Like Feynman, you can achieve startling insights into how to understand more simply, easily, and with less frustration. By understanding your brain’s default settings—the natural way it learns and thinks—and taking advantage of this knowledge, you, too, can become an expert.

In the beginning of the book, I mentioned that there are simple mental tricks that can bring math and science into focus, tricks that are helpful not only for people who are bad at math and science but also for those who already good at it. You’ve walked through all these tricks in the course of reading this book. But, as you now know, nothing beats grasping the chunked and simplified essence. So what follows sums up my final thoughts—the chunked essence of some of the central ideas in this book, distilled into the ten best and worst rules of studying.

Remember—Lady Luck favors the one who tries. A little insight into learning how to learn best doesn’t hurt, either.

TEN RULES OF GOOD STUDYING

1. Use recall. After you read a page, look away and recall the main ideas. Highlight very little, and never highlight anything you haven’t put in your mind first by recalling. Try recalling main ideas when you are walking to class or in a different room from where you originally learned it. An ability to recall—to generate the ideas from inside yourself—is one of the key indicators of good learning.

2. Test yourself. On everything. All the time. Flash cards are your friend.

3. Chunk your problems. Chunking is understanding and practicing with a problem solution so that it can all come to mind in a flash. After you solve a problem, rehearse it. Make sure you can solve it cold—every step. Pretend it’s a song and learn to play it over and over again in your mind, so the information combines into one smooth chunk you can pull up whenever you want.

4. Space your repetition. Spread out your learning in any subject a little every day, just like an athlete. Your brain is like a muscle—it can handle only a limited amount of exercise on one subject at a time.

5. Alternate different problem-solving techniques during your practice. Never practice too long at any one session using only one problem-solving technique—after a while, you are just mimicking what you did on the previous problem. Mix it up and work on different types of problems. This teaches you both how and when to use a technique. (Books generally are not set up this way, so you’ll need to do this on your own.) After every assignment and test, go over your errors, make sure you understand why you made them, and then rework your solutions. To study most effectively, handwrite (don’t type) a problem on one side of a flash card and the solution on the other. (Handwriting builds stronger neural structures in memory than typing.) You might also photograph the card if you want to load it into a study app on your smartphone. Quiz yourself randomly on different types of problems. Another way to do this is to randomly flip through your book, pick out a problem, and see whether you can solve it cold.

6. Take breaks. It is common to be unable to solve problems or figure out concepts in math or science the first time you encounter them. This is why a little study every day is much better than a lot of studying all at once. When you get frustrated with a math or science problem, take a break so that another part of your mind can take over and work in the background.

7. Use explanatory questioning and simple analogies. Whenever you are struggling with a concept, think to yourself, How can I explain this so that a ten-year-old could understand it? Using an analogy really helps, like saying that the flow of electricity is like the flow of water. Don’t just think your explanation—say it out loud or put it in writing. The additional effort of speaking and writing allows you to more deeply encode (that is, convert into neural memory structures) what you are learning.

8. Focus. Turn off all interrupting beeps and alarms on your phone and computer, and then turn on a timer for twenty-five minutes. Focus intently for those twenty-five minutes and try to work as diligently as you can. After the timer goes off, give yourself a small, fun reward. A few of these sessions in a day can really move your studies forward. Try to set up times and places where studying—not glancing at your computer or phone—is just something you naturally do.

9. Eat your frogs first. Do the hardest thing earliest in the day, when you are fresh.

10. Make a mental contrast. Imagine where you’ve come from and contrast that with the dream of where your studies will take you. Post a picture or words in your workspace to remind you of your dream. Look at that when you find your motivation lagging. This work will pay off both for you and those you love!

TEN RULES OF BAD STUDYING

Avoid these techniques—they can waste your time even while they fool you into thinking you’re learning!

1. Passive rereading—sitting passively and running your eyes back over a page. Unless you can prove that the material is moving into your brain by recalling the main ideas without looking at the page, rereading is a waste of time.

2. Letting highlights overwhelm you. Highlighting your text can fool your mind into thinking you are putting something in your brain, when all you’re really doing is moving your hand. A little highlighting here and there is okay—sometimes it can be helpful in flagging important points. But if you are using highlighting as a memory tool, make sure that what you mark is also going into your brain.

3. Merely glancing at a problem’s solution and thinking you know how to do it. This is one of the worst errors students make while studying. You need to be able to solve a problem step-by-step, without looking at the solution.

4. Waiting until the last minute to study. Would you cram at the last minute if you were practicing for a track meet? Your brain is like a muscle—it can handle only a limited amount of exercise on one subject at a time.

5. Repeatedly solving problems of the same type that you already know how to solve. If you just sit around solving similar problems during your practice, you’re not actually preparing for a test—it’s like preparing for a big basketball game by just practicing your dribbling.

6. Letting study sessions with friends turn into chat sessions. Checking your problem solving with friends, and quizzing one another on what you know, can make learning more enjoyable, expose flaws in your thinking, and deepen your learning. But if your joint study sessions turn to fun before the work is done, you’re wasting your time and should find another study group.

7. Neglecting to read the textbook before you start working problems. Would you dive into a pool before you knew how to swim? The textbook is your swimming instructor—it guides you toward the answers. You will flounder and waste your time if you don’t bother to read it. Before you begin to read, however, take a quick glance over the chapter or section to get a sense of what it’s about.

8. Not checking with your instructors or classmates to clear up points of confusion. Professors are used to lost students coming in for guidance—it’s our job to help you. The students we worry about are the ones who don’t come in. Don’t be one of those students.

9. Thinking you can learn deeply when you are being constantly distracted. Every tiny pull toward an instant message or conversation means you have less brain power to devote to learning. Every tug of interrupted attention pulls out tiny neural roots before they can grow.

10. Not getting enough sleep. Your brain pieces together problem-solving techniques when you sleep, and it also practices and repeats whatever you put in mind before you go to sleep. Prolonged fatigue allows toxins to build up in the brain that disrupt the neural connections you need to think quickly and well. If you don’t get a good sleep before a test, NOTHING ELSE YOU HAVE DONE WILL MATTER.

PAUSE AND RECALL

Pause the recording. What were the most important ideas in this book? As you reflect, consider also how you will use these ideas to help reshape your learning.