by Scott Young
Winning the War Against Forgetting
To retain knowledge is ultimately to combat the inevitable human tendency to forget. This process occurs in all of us, and there’s no way to avoid it completely. However, certain strategies—spacing, proceduralization, overlearning, and mnemonics—can counteract your short- and long-term rates of forgetting and end up making a huge difference in your memorization.
I opened this chapter by discussing Nigel Richards’s mysterious Scrabble mastery. How he is able to recall so many words so quickly and see them in a set of scrambled tiles will likely remain an enigma. What we do know about him fits the picture of other ultralearners who have dominated memory-intensive subjects: active recall, spaced rehearsal, and an obsessive commitment to intense practice. Whether you or I have the will to go as far as Richards does is an open question, but with hard work and a good strategy, it seems likely to me that the battle against forgetting need not be a losing one.
Though Richards’s Scrabble practice may give him the benefit of memorizing words he doesn’t know the meaning of, real life tends to reward a different kind of memory: one that integrates knowledge into a deep understanding of things. In the next principle, we’ll look at going from memory to intuition.
Chapter XI
Principle 8
Intuition
Dig Deep Before Building Up
Do not ask whether a statement is true until you know what it means.
—Errett Bishop, mathematician
To the world, he was an eccentric professor and Nobel Prize–winning physicist; to his biographer, he was a genius; but to those who knew him, Richard Feynman was a magician. His colleague the mathematician Mark Kac once posited that the world holds two types of geniuses. The first are ordinary geniuses: “Once we understand what they have done we feel certain that we, too, could have done it.” The other type are magicians, whose minds work in such inscrutable ways that “Even after we understand what they have done, the process by which they have done it is completely dark.” Feynman, by his reckoning, was “a magician of the highest caliber.”1
Feynman could take problems others had worked on for months and immediately see the solution. In high school, he competed in mathematics tournaments, where he would often get the correct answer while the problem was still being stated. While his competitors had just begun to compute, Feynman already had the answer circled on the page. In his college days, he competed in the Putnam Mathematics Competition, with the winner receiving a paid scholarship to Harvard. This competition is notoriously difficult, requiring clever tricks rather than straightforward application of previously learned principles. Time is also a factor, and some examination sessions have a median score of zero, meaning the typical competitor didn’t get even one right. Feynman walked out of the exam early. He scored first place, with his fraternity brothers later being amazed at the drastic gap between Feynman’s score and the next four on the list. During his work on the Manhattan Project, Niels Bohr, then one of the most famous and important living physicists, asked to speak with Feynman directly, to run his ideas by the young grad student before talking with the other physicists. “He’s the only guy who’s not afraid of me” was Bohr’s explanation. “[He] will say when I’ve got a crazy idea.”2
Nor was Feynman’s magic restricted to physics. As a child he went around fixing people’s radios, in part because paying an adult for repairs in the Depression was too costly but also because the radio owners marveled at his process. Once, while he was lost in thought trying to figure out why a radio was producing an awful noise as it started up, the owner of the radio got impatient. “What are you doing? You come to fix the radio, but you’re only walking back and forth!” “I’m thinking!” came the reply, at which the owner, startled at the boldness for which Feynman would later become famous, laughed. “He fixes radios by thinking!”
As a young man during the construction of the atomic bomb in the Manhattan Project, he occupied his free time picking the locks of his supervisors’ desks and cabinets. He once broke into a senior colleague’s filing cabinet, where the secrets for building a nuclear bomb were kept, as a practical joke. Another time, he demonstrated his technique to a military official, who, instead of fixing the security flaw, decided the proper course was to warn everyone to keep Feynman away from their safes! Later, upon meeting a locksmith, he found that his reputation had grown to the point where the professional said, “God! You’re Feynman—the great safecracker!”
He also created the impression of being a human calculator. On a trip to Brazil, he went toe to toe against an abacus salesman, computing difficult figures such as the cube root of 1,729.03. Not only did Feynman get the right answer, 12.002, but he got it to more decimal places than the abacus salesman, who was still furiously calculating to get to 12 when Feynman displayed his five-digit result. This ability impressed even other professional mathematicians, to whom he argued that he could, within one minute, get the answer to any problem that could be stated in ten seconds to within 10 percent of the correct number. The mathematicians threw questions at him such as “e to the power of 3.3” or “e to the power of 1.4,” and Feynman managed to spit back the correct answer almost immediately.
Demystifying Feynman’s Magic
Feynman was certainly a genius. Many people, including his biographer James Gleick, are satisfied to leave it at that. A magic trick, after all, is most dazzling when you don’t know how it is done. Perhaps this is why many accounts of the man have focused on his magic instead of his method.
Though Feynman was quite smart, his magic had its gaps. He excelled in math and physics but was abysmal in the humanities. His college grades in history were in the bottom fifth of his class, in literature in the bottom sixth, and his fine arts grades were worse than those of 93 percent of his fellow students. At one point, he even resorted to cheating on a test to pass. His intelligence, measured while he was in school, scored 125. The average college graduate has a score of 115, which puts Feynman only modestly higher. Perhaps, as has been argued afterward, Feynman’s genius failed to be captured in his IQ score, or it simply was a poorly administered test. However, for someone so celebrated for a mind beyond comprehension, these facts remind us that Feynman was mortal.
What about Feynman’s mental calculus? In this case, we have Feynman’s words himself for how he could compute so much faster than the abacus salesman or his mathematician colleagues. The cube root of 1,729.03? Feynman explained, “I happened to know that a cubic foot contains 1728 cubic inches, so the answer is a tiny bit more than 12. The excess, 1.03, is only one part in nearly 2000, and I had learned in calculus that for small fractions, the cube root’s excess is one-third of the number’s excess. So all I had to do was find the fraction 1/1728, and multiply by 4.” The constant e to the power of 1.4? Feynman revealed, “because of radioactivity (mean-life and half-life), I knew the log of 2 to the base e, which is .69315 (so I also knew that e to the power of .7 is nearly equal to 2).” To go to the power of 1.4, he’d just have to multiply that number against itself. “[S]heer luck,” he explained.3 The secret was his impressive memory for certain arithmetic results and an intuition with numbers that enabled him to interpolate. However, the lucky picks of his examiners allowed him to leave an impression of a magical ability to calculate.
How about the famous lock picking? Once again, it was magic, in the same sense as a magician performing well-practiced tricks. He obsessed over figuring out how combination locks worked. One day he realized that by fiddling with a lock when it was open, he could figure out the last two numbers on the safe. He would write them down on a note after he left the person’s office and then could sneak back in, crack the remaining number with some patience, and leave ominous notes behind.
Even his magical intuition for physics had its explanation: “I had a scheme, which I still use today when somebody is explaining something that I’m trying to understand: I keep making up examples.” Instead of trying to follow an equation, he woul
d try to imagine the situation it described. As more information was given, he’d work it through on his example. Then whenever his interlocutor made a mistake, he could see it. “As they’re telling me the conditions of the theorem, I construct something which fits all the conditions. You know, you have a set (one ball)—disjoint (two balls). Then the balls turn colors, grow hairs, or whatever, in my head as they put more conditions on. Finally they state the theorem, which is some dumb thing about the ball which isn’t true for my hairy green ball thing, so I say, ‘False!’”4
Magic, perhaps, Feynman did not possess, but an incredible intuition for numbers and physics he certainly did. This might downplay the idea that his mind worked in a fundamentally different way from yours or mine, but it doesn’t negate the impressiveness of his feats. After all, even knowing the logic behind Feynman’s sleight of hand, I’m certain I wouldn’t have been able to calculate the numbers he did so effortlessly or follow some complex theory in my mind’s eye. This explanation doesn’t provide the satisfying “Aha!” that it would have had the magician’s trick been revealed as something trivial. Therefore, we need to dig deeper to an understanding of how someone such as Feynman could develop this incredible intuition in the first place.
Inside the Mind of the Magician
Psychological researchers have investigated the problem of how intuitive experts, such as Feynman, think differently about problems than novices do. In a famous study, advanced PhDs and undergraduate physics students were given sets of physics problems and asked to sort them into categories.5 Immediately, a stark difference became apparent. Whereas beginners tended to look at superficial features of the problem—such as whether the problem was about pulleys or inclined planes—experts focused on the deeper principles at work. “Ah, so it’s a conservation of energy problem,” you can almost hear them saying as they categorized the problem by what principles of physics they represented. This approach is more successful in solving problems because it gets to the core of how the problems work. The surface features of a problem don’t always relate to the correct procedure needed to solve it. The students needed much more trial and error to home in on the correct method, whereas the experts could immediately start with the right approach.
If the principles-first way of thinking of problems is so much more effective, why don’t students start there instead of attending to superficial characteristics? The simple answer may be that they can’t. Only by developing enough experience with problem solving can you build up a deep mental model of how other problems work. Intuition sounds magical, but the reality may be more banal—the product of a large volume of organized experience dealing with the problem.
Another study, this time comparing chess masters and beginners, offered an explanation of why this might be so.6 The memory for chess positions of experts and novices was tested by showing them a particular chess setup and then asking them to re-create it on an empty board. The masters could recall far more than the beginners. The new players needed to put down pieces one by one and were often unable to fully remember all the details of the position. The masters, in contrast, remembered the board in larger “chunks” with several pieces corresponding to a recognizable pattern put down at the same time. Psychologists theorize that the difference between grand masters and novices is not that grand masters can compute many more moves ahead but that they have built up huge libraries of mental representations that come from playing actual games. Researchers have estimated that having around 50,000 of these mental “chunks” stored in long-term memory is necessary to reach expert status.7 These representations allow them to take a complex chess setup and reduce it to a few key patterns that can be worked with intuitively. Beginners, who lack this ability, have to resort to representing each piece as a single unit and are therefore much slower.*
This facility of chess grand masters, however, is limited to the patterns that come from real chess games. Give beginners and experts a randomized chess board (one that doesn’t arise from normal play), and the experts no longer display the same marked advantage. Without the library of memorized patterns at their disposal, they have to resort to the beginner’s method of remembering the board piece by piece.
This research gives us a glimpse into how the mind of a great intuitionist such as Feynman operated. He, too, focused on principles first, building off examples that cut straight to the heart of what the problem represented rather than focusing on superficial features. His ability to do this was also built off an impressive library of stored physics and math patterns. His mental calculation feats seem impressive to us but were trivial to him, because he happened to know so many mathematical patterns. Like chess grand masters, when given real physics problems he excelled because he had built a huge library of patterns from real experiences with physics. However, his intuition, too, would fail him when the subject of his study wasn’t built on those assumptions. Feynman’s mathematician friends would test him on counterintuitive theorems from mathematics. His intuition there would fail when properties of the procedure (such as that an object can be cut into infinitely small pieces) defied the normal physical limitations that aided his intuition elsewhere.
Feynman’s magic was his incredible intuition, coming from years of playing with the patterns of math and physics. Could emulating his approach to learning enable someone else to capture some of that magic? Let’s look at some of Feynman’s hallmark approaches to learning and solving problems and try to reveal some of the magician’s secrets.
How to Build Your Intuition
Simply spending a lot of time studying something isn’t enough to create a deep intuition. Feynman’s own experience demonstrates this. On numerous occasions, he would encounter students who memorized solutions to a particular problem but failed to see how they applied outside the textbook domain. In one story, he tricked some of his classmates into believing that a French curve (a device for drawing curved lines) was special because, no matter how you hold it, the bottom is tangent to a horizontal line. This, however, is true of any smooth shape, and it is an elementary fact of calculus that his fellow classmates should have realized. Feynman saw this as an example of a particularly “brittle” way of learning things, since students didn’t really think about relating what they had learned to problems outside the textbook.
How, then, can someone avoid a similar fate—spending a lot of time learning something without really developing the flexible intuition for it that made Feynman famous? There’s no precise recipe for doing so, and a healthy dose of experience and smarts certainly helps. However, Feynman’s own account of his learning process offers some useful guidelines for how he did things differently.
Rule 1: Don’t Give Up on Hard Problems Easily
Feynman was obsessed with solving problems. Starting in his childhood days of tinkering with radios, he would work stubbornly on a problem until it yielded. Sometimes, when the owner of the radio would get impatient, he recalled, “If [he] had said, ‘Never mind, it’s too much work,’ I’d have blown my top, because I want to beat this damn thing, as long as I’ve gone this far.”8 This tendency carried over into mathematics and physics. He’d often eschew easier methods, such as the Lagrangian technique, forcing himself to painstakingly calculate all the forces by hand, simply because with the latter method he came to understand it better. Feynman was a master at pushing farther on problems than others expected of him, and this itself might have been the source of many of his unorthodox ideas.
One way you can introduce this into your own efforts is to give yourself a “struggle timer” as you work on problems. When you feel like giving up and that you can’t possibly figure out the solution to a difficult problem, try setting a timer for another ten minutes to push yourself a bit further. The first advantage of this struggle period is that very often you can solve the problem you are faced with if you simply apply enough thinking to it. The second advantage is that even if you fail, you’ll be much more likely to remember the way to arrive at the solution when y
ou encounter it. As mentioned on the chapter on retrieval, difficulty in retrieving the correct information—even when the difficulty is caused by the information not being there—can prime you to remember information better later.
Rule 2: Prove Things to Understand Them
Feynman told a story of his first encounter with the work by the physicists T. D. Lee and C. N. Yang.9 “I can’t understand these things that Lee and Yang are saying. It’s all so complicated,” he declared. His sister, lightly teasing him, remarked that the problem wasn’t that he couldn’t understand it but that he hadn’t invented it. Afterward, Feynman decided to read through the papers meticulously, finding that they weren’t actually so difficult but that he had simply been afraid to go through them.
Though this story illustrates one of Feynman’s quirks, it is also revealing because it illustrates a major point in his method. Feynman didn’t master things by following along with other people’s results. Instead, it was by the process of mentally trying to re-create those results that he became so good at physics. This could be a disadvantage at times, since it caused him to repeat work and reinvent processes that already existed in other forms. However, his drive to understand things by virtue of working through the results himself also assisted in building his capacity for deep intuition.