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Focused-mode thinking is essential for studying math and science. It involves a direct approach to solving problems using rational, sequential, analytical approaches. The focused mode is associated with the concentrating abilities of the brain’s prefrontal cortex, located right behind your forehead.
Diffuse-mode thinking is also essential for learning math and science. It allows us to suddenly gain a new insight on a problem we’ve been struggling with and is associated with “big-picture” perspectives. Diffuse-mode thinking is what happens when you relax your attention and just let your mind wander.
If you are trying to understand or figure out something new, your best bet is to turn off your precision-focused thinking and turn on your “big picture” diffuse mode,
now follow the rule of thumb that is basically: The harder you push your brain to come up with something creative, the less creative your ideas will be. So
But as long as we are consciously focusing on a problem, we are blocking the diffuse mode.
Articulating your question is 80 percent of the battle. By the time you’ve figured out what’s confusing, you’re likely to have answered the question yourself!”
If you want to apply a more advanced version of this approach, imagine that at the end of the day, you are reflecting on the one most important task that you accomplished that day. What would that task be? Write it down. Then work on it. Try to complete at least three of these twenty-five-minute sessions that day, on whatever task or tasks you think are most important. At the end of your workday, look at what you crossed off your list and savor the feeling of accomplishment. Then write a few key things that you would like to work on the next day. This early preparation will help your diffuse
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For most people, shifting from focused to diffuse mode happens naturally if you distract yourself and then allow a little time to pass. You can go for a walk, take a nap, or go to the gym. Or you can work on something that occupies other parts of your brain: listening to music, conjugating Spanish verbs, or cleaning your gerbil cage.1 The key is to do something else until your brain is consciously free of any thought of the problem.
Creativity expert Howard Gruber has suggested that one of the three B’s usually seems to do the trick: the bed, the bath, or the bus.
One remarkably inventive chemist of the mid-1800s, Alexander Williamson, observed that a solitary walk was worth a week in the laboratory in helping him progress in his work.3 (Lucky for him there were no smartphones then.)
Once you are distracted from the problem at hand, the diffuse mode has access and can begin pinging about in its big-picture way to settle on a solution.
That twilight, disconnected feeling one experiences while drifting off to sleep was, it seems, part of the magic behind Edison’s extraordinary creativity. When faced with a difficult problem, instead of focusing intently on it, Edison, according to legend, took a nap.
Wild surrealist painter Salvador Dalí, like Thomas Edison, also used a nap and the clatter of an object falling from his hand to tap into his diffuse-mode creative perspectives. (Dalí called this “sleeping without sleeping.”
Mistakes are inevitable. To work past them, start early on your assignments and, unless you are really enjoying what you are doing, keep your working sessions short. Remember, when you take breaks, your diffuse mode is still working away in the background.
You may want your learning to progress more quickly—to somehow command your diffuse mode to assimilate new ideas faster. But compare it to exercise. Constantly lifting weights won’t make your muscles any bigger—your muscles need time to rest and grow before you use them again. Taking time off between weight sessions helps build strong muscles in the long run. Consistency over time is key!
USE THESE DIFFUSE-MODE TOOLS AS REWARDS AFTER FIRM FOCUSED-MODE WORK14 General Diffuse-Mode Activators Go to the gym Play a sport like soccer or basketball Jog, walk, or swim Dance Go for a drive (or tag along for the ride) Draw or paint Take a bath or shower Listen to music, especially without words Play songs you know well on a musical instrument Meditate or pray Sleep (the ultimate diffuse mode!)
You may be surprised to discover that learning slowly can mean you learn more deeply than your fast-thinking classmates. One of the most important tricks that helped me retool my brain was learning to avoid the temptation to take too many math and science classes at once.
Remember, accepting the first idea that comes to mind when you are working on an assignment or test problem can prevent you from finding a better solution.
According to recent research, blinking is a vital activity that provides another means of reevaluating a situation.
When Carlsen stood and turned his glance—and his attention—toward other chess boards, he may have been helping his mind leap momentarily out of focused mode. Turning his eyes and attention elsewhere likely was critical in allowing his diffuse intuition to go to work on his game with Kasparov.
This is a hint that you, too, may be able to develop ways to quickly toggle between the focused and diffuse modes as you develop your expertise in a subject.
Figuring out a difficult problem or learning a new concept almost always requires one or more periods when you aren’t consciously working on the problem.
“As a piano player for a decade and a half, I sometimes found myself facing a particularly difficult run. I just couldn’t get it, so I would force my fingers to do it over and over again (albeit very slowly or incorrectly), and then I’d take a break. The next day when I tried it again, I would be able to play it perfectly, as if by magic.
The resting times between your focused-mode efforts should be long enough to get your conscious mind completely off the problem you’re working on.
A good rule of thumb, when you are first learning new concepts, is not to let things go untouched for longer than a day.
The diffuse mode not only allows you to look at the material in new ways but also appears to allow you to synthesize and incorporate the new ideas in relation to what you already know.
Working in the focused mode is like providing the bricks, while working in the diffuse mode is like gradually joining the bricks together with mortar.
Introduction to Working and Long-Term Memory
Working memory is the part of memory that has to do with what you are immediately and consciously processing in your mind. It used to be thought that our working memory could hold around seven items, or “chunks,” but it’s now widely believed that the working memory holds only about four chunks of information.
In contrast, long-term memory might be thought of as a storage warehouse.
Research has shown that when your brain first puts an item of information in long-term memory, you need to revisit it a few times to increase the chances you’ll later be able to find it when you need it.21
Long-term memory is important for learning math and science because it is where you store the fundamental concepts and techniques that you need to use in problem solving. It takes time to move information from working memory to long-term memory.
To help with this process, use a technique called spaced repetition. As you may have guessed, this technique involves repeating what you are trying to retain, like a new vocabulary word or a new problem-solving technique, but spacing this repetition out over a number of days.
Putting a day between bouts of repetition—extending your practice over a number of da...
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The next time you are tackling a tough problem, work on it for a few minutes. When you get stuck, move on to another problem. Your diffuse mode can continue working on the tougher problem in the background. When you later return to the tougher problem, you will often be pleasantly surprised by the progress you’ve made.
When you get too little sleep, the buildup of these toxic products is believed to explain why you can’t think very clearly.
Part of what this special sleep-time tidying does is erase trivial aspects of memories and simultaneously strengthen areas of importance.
During sleep, your brain also rehearses some of the tougher parts of whatever you are trying to learn—going over and over neural patterns to deepen and strengthen them.
It seems that if you go over the material right before taking a nap or going to sleep for the evening, you have an increased chance of dreaming about it. If
Dreaming about what you are studying can substantially enhance your ability to understand—it somehow consolidates your memories into easier-to-grasp chunks.28
Experienced learners will attest to the fact that reading for one hour with a well-rested brain is better than reading for three hours with a tired brain.
It’s best to work at math and science in small doses—a little every day. This gives both the focused and diffuse modes the time they need to do their thing so you can understand what you are learning. That’s how solid neural structures are built.
When you are learning new concepts, you want to review the material within a day so that the initial changes you made in your brain don’t fade away. But your mind often becomes preoccupied with other matters—it’s easy to let several days or more pass before you get around to looking at the material. What kind of action plan could you develop to ensure that you review important new material in a timely fashion?
Creativity is a numbers game: The best predictor of how many creative works we produce in our lifetime is . . . the number of works we produce. I sometimes find it excruciating to pull the trigger and expose my work to other people, but every time I do, it turns out for the best.
Redos come with the territory: If you don’t like the way it turned out—do it again!
Criticism makes us better: By exposing our work to others, and by externalizing it so we can inspect it ourselves, we gain unique perspective and insight and develop new and improved plans for the next version.
What Solomon found surprising was that he thought everyone had a memory like his. Perfect. Indelible.1 Wouldn’t you love to have the gift of such a memory? Actually, you probably wouldn’t. Because hand-in-hand with his extraordinary memory, Solomon had a problem.
Your neurons fire and wire together in a shimmering mental loop, cementing the relationship in your mind between the sound mama and your mother’s smiling face. That scintillating neural loop is one memory trace—connected, of course, to many other related memory traces.
The best language programs—such as those at the Defense Language Institute, where I learned Russian—incorporate structured practice that includes plenty of repetition and rote, focused-mode learning of the language, along with more diffuse-like free speech with native speakers. The goal is to embed the basic words and patterns so you can speak as freely and creatively in your new language as you do in English.
