by Scott Young
Feynman was not alone in this approach. Albert Einstein, as a child, built his intuitive powers by trying to prove propositions in math and physics. One of Einstein’s earliest mathematical forays was trying to prove the Pythagorean Theorem on the basis of similar triangles.10 What this approach indicates is that both men had a tendency to dig much deeper before they considered something to be “understood.” Feynman’s scoffing at not understanding Lee and Yang wasn’t because there was no understanding; indeed, he was familiar with much of the background work on the problem. Instead, it was probably because his notion of understanding was much deeper and more based on demonstrating results himself, rather than merely nodding along while reading.
The challenge of thinking you understand something you don’t is unfortunately a common one. Researcher Rebecca Lawson calls this the “illusion of explanatory depth.”11 At issue here is the notion that we judge our own learning competency, not directly but through various signals. Assessing whether or not we know a factual matter, such as what is the capital of France, is quite easy—either the word “Paris” comes up in your mind, or it doesn’t. Asking whether you understand a concept is a lot harder because you may understand it a little, but not enough for the purposes at hand.
Here’s a perfect thought experiment to help you understand the problem. Get out a piece of paper, and try, briefly, to sketch how a bicycle looks. It doesn’t need to be a work of art; just try to place the seat, handles, tires, pedals, and bike chain in the right place. Can you do it?
Don’t cheat by just trying to visualize the bicycle. Actually see if you can draw it. If you don’t have a pencil or paper handy, you can simulate it by saying which things connect to what. Have you tried it?
Interestingly, Rebecca Lawson’s study asked participants to do exactly this. As the illustrations clearly show, most participants had no idea how the machines were assembled, even though they used them all the time and believed they understood them quite well. The illusion of understanding is very often the barrier to deeper knowledge, because unless that competency is actually tested, it’s easy to mislead yourself into thinking you understand more than you do. Feynman’s and Einstein’s approach to understanding propositions by demonstrating them prevents this problem in a way that’s hard to do otherwise.12
Were you one of the lucky ones who managed to put the chains on correctly? Try the exercise again, except this time with a can opener. Can you explain how it works? How many gears are there? How does it cut the lid open? This one is much harder, yet most of us would say we understand can openers!
Rule 3: Always Start with a Concrete Example
Human beings don’t learn things very well in the abstract. As the research on transfer demonstrates, most people learn abstract, general rules only after being exposed to many concrete examples. It’s not possible to simply present a general principle and expect that you can apply it to concrete situations. As if presaging this observation, Feynman himself would supply concrete examples even when they were not given. Working through an explicit example in his mind’s eye, he could follow along and see what the math was trying to demonstrate.
This process of following along with one’s own example forces a deeper level of processing the material as it is being presented. A finding from the literature on memory, known as the levels-of-processing effect, suggests that it isn’t simply how much time you spend paying attention to information that determines what you retain but, crucially, how you think about that information while you pay attention to it. In one study of this effect, participants were asked to review a list of words; half of them were told it would be for a test (and thus they were motivated to learn it), while the others were simply told to review the list.13 Within each group, participants were again split by what orienting technique they used to review the list. Half were asked to notice whether or not the words contained the letter e, a relatively shallow level of processing, while the others were asked if the word was pleasant or not, a deeper processing of the meaning of the word, not merely its spelling. The result was that motivation played no difference; telling students to study for a test didn’t impact how much they retained. However, the orienting technique did make a large difference. Those who processed the words deeply remembered almost twice as much as those who simply scanned their spelling.14
Feynman’s habit of developing a concrete instance of a problem can be seen as an example of this deeper form of processing, which not only enhances later retention but also fosters an intuitive understanding. This technique also enables some feedback, because when it’s not possible to imagine an appropriate example, that’s evidence that you don’t understand something well enough and would benefit from going back a few steps and learning the material better before continuing. Using feedback-rich processes to test whether or not he knew something was a hallmark of Feynman’s learning style.
Rule 4: Don’t Fool Yourself
“Don’t fool yourself” was one of Feynman’s most popular aphorisms, to which he added, “and you’re the easiest person to fool.” He was deeply skeptical of his own understanding. He presaged the current replication crisis in psychology, attacking what he perceived as many social scientists fooling themselves into believing they had discovered something they had not. I suspect that part of this insight arose from the fact that he had cultivated such rigorous standards for what he counted as knowing.
The Dunning-Kruger effect occurs when someone with inadequate understanding of a subject nonetheless believes he or she possesses more knowledge about the subject than the people who actually do.15 This can occur because when you lack knowledge about a subject, you also tend to lack the ability to assess your own abilities. It is true that the more you learn about a subject, the more questions arise. The reverse also seems to be true, in that the fewer questions you ask, the more likely you are to know less about the subject.
One way to avoid this problem of fooling yourself is simply to ask lots of questions. Feynman took this approach himself: “Some people think in the beginning that I’m kind of slow and I don’t understand the problem, because I ask a lot of these ‘dumb’ questions: ‘Is a cathode plus or minus? Is an an-ion this way, or that way?’”*16 How many of us lack the confidence to ask “dumb” questions? Feynman knew he was smart and had no problem asking them. The irony is that by asking questions with seemingly obvious answers, he also noticed the not-so-obvious implications of the things he studied.
The opposite tendency, to avoid asking questions in the vain attempt to appear knowledgeable, has considerable costs. While lecturing in Brazil, Feynman’s students would often complain when he asked simple questions that they knew the answers to already, instead of just lecturing. Why waste valuable classroom time on such exercises? The answer, Feynman eventually realized, was that they didn’t know the answers but didn’t want to admit it in front of everyone else in the class, wrongly assuming that they were the only ones who didn’t know it. Explaining things clearly and asking “dumb” questions can keep you from fooling yourself into thinking you know something you don’t.
The Feynman Technique
When I first read about Feynman, I was inspired to try to formulate many of these different observations into a concrete method I could apply to my own studies. What resulted was something I named the Feynman Technique and applied extensively during my MIT Challenge. The purpose of using this technique is to help develop intuition about the ideas you are learning. It can be used when you don’t understand an idea at all or simply when you understand something a little but really want to turn it into a deep intuition.
The method is quite simple:
Write down the concept or problem you want to understand at the top of a piece of paper.
In the space below, explain the idea as if you had to teach it to someone else.
If it’s a concept, ask yourself how you would convey the idea to someone who has never heard of it before.
If it’s a problem, explain how to solve it
and—crucially—why that solution procedure makes sense to you.
When you get stuck, meaning your understanding fails to provide a clear answer, go back to your book, notes, teacher, or reference material to find the answer.
The crux of this method is that it tries to dispel the illusion of explanatory depth. Since many of our understandings are never articulated, it’s easy to think you understand something you don’t. The Feynman Technique bypasses this problem by forcing you to articulate the idea you want to understand in detail. Just as drawing a bicycle quickly confirms whether you have a basic grasp of how it is put together, using this technique will quickly reveal how much you really understand of your subject. Now any gaps in your understanding will become obvious as you struggle to explain key parts of the idea.
The technique itself has some nuances and can be applied in a few different ways that might be helpful, depending on your specific intuitive deficit.
Application 1: For Things You Don’t Understand at All
The first way to use this approach is when you don’t understand something at all. In this case, the easiest way is to do it with the book in hand and go back and forth between your explanation and the one in the book. This lacks the benefits of retrieval practice, but it can often be essential when the explanation you’ve been given baffles you. Feynman himself did something similar when presented with what he saw to be philosophical gobbledygook:
I had this uneasy feeling of “I’m not adequate,” until finally I said to myself, “I’m going to stop, and read one sentence slowly, so I can figure out what the hell it means.”
So I stopped—at random—and read the next sentence very carefully. I can’t remember it precisely, but it was very close to this: “The individual member of the social community often receives his information via visual, symbolic channels.” I went back and forth over it, and translated. You know what it means? “People read.”17
Although Feynman’s method was aimed more at illustrating the deliberately confusing nature of the prose rather than trying to understand a nuanced meaning, the same method can help whenever you’re learning anything that goes over your head.
I used this technique when taking a class on machine vision during the MIT Challenge. I didn’t understand photogrammetry, a technique of determining the 3D shape of an object based on a series of 2D pictures taken under different lighting conditions. It involved some tricky concepts, so I wasn’t quite sure how it worked. With my textbook at my side, I wrote a few pages of notes, trying to sketch out the broad strokes of the idea so I could get the general gist of it.18
Application 2: For Problems You Can’t Seem to Solve
A second way to apply this is for solving a difficult problem or mastering a technique. In this instance, it’s very important to go through the problem step by step alongside the explanation you generate, rather than simply summarizing it. Summarizing may end up skipping over the core difficulties of the problem. Going deeper may take time, but it can help you get a strong grasp over a new method in one go, rather than needing numerous repetitions to memorize the steps.
I applied this to a class in computer graphics for a technique I was struggling with called grid acceleration. This is a method of speeding up the performance of ray-traced rendering systems by avoiding analyzing objects that “obviously” won’t be on the part of the screen you’re drawing. To get a better handle on this, I walked through the problem with the technique, drawing a little snowman that I imagined rendering, with lines shooting out of an eyeball representing the camera.19
Application 3: For Expanding Your Intuition
A final way to apply this method is to ideas that are so important that it would really help if you had a great intuition about them. In this application of the method, instead of focusing on explaining every detail or going along with the source material, you should try to focus on generating illustrative examples, analogies, or visualizations that would make the idea comprehensible to someone who has learned far less than you have. Imagine that instead of trying to teach the idea, you are being paid to write a magazine article explaining the idea. What visual intuitions would you use to pin down the abstractions? Which examples would flesh out a general principle? How could you make something confusing feel obvious?
I applied this to understanding the concept of voltage in an early class on electromagnetism during the MIT Challenge. Though I was comfortable using the concept in problems, I didn’t feel that I had a good intuition of what it was. It’s obviously not energy, electrons, or flows of things. Still, it was hard to get a mental image of an abstract concept on a wire. Going through this technique and comparing the equations to the ones for gravity, it’s clear that voltage is to the electrical force as height is to the gravitational force. Now I could form a visual image. The wires were like troughs of water at different heights. Batteries were like pumps, moving the water up. Resistors were like hoses dropping down, of various widths to impede the flow of water draining down. Although this picture of troughs and hoses wasn’t necessary for solving the equations, it stuck with me and helped me reason my way out of new situations more easily than if voltage had just been an abstract quantity.
Demystifying Intuition
When many people look at a genius like Richard Feynman, they’re inclined to focus on his seemingly effortless intuitive leaps. In his playful style and rebellious impulses, he may seem to defy the stereotype that learning requires hard work. However, as we go beneath the surface, it becomes clear that he shared much in common with the other ultralearners I’ve studied. He worked hard on understanding things, and he put incredible amounts of his spare time into mastering the methods that made his intuition work. In his early days in college, he and a friend went back and forth over the early books on quantum mechanics, racing ahead of their classmates to understand it. He even made a meticulous timetable to allocate hours to his many intellectual pursuits. Even in his trivial obsessions, he displayed a streak for aggressive methods; while learning lock picking, for example, he trained himself to go through all the possible combinations, practicing them repeatedly: “I got it down to an absolute rhythm so I could try the 400 possible back numbers in less than half an hour. That meant I could open a safe in a maximum of eight hours—with an average time of four hours.”20
When people hear about geniuses, especially the iconoclastic ones such as Feynman, there’s a tendency to focus on their gifts and not their efforts. I have no doubt that Feynman possessed gifts. But perhaps his greatest one was his ability to merge tenacious practice and play. He approached picking locks with the same enthusiasm for solving puzzles that he did for unraveling the secrets of quantum electrodynamics. It’s this spirit of playful exploration that I want to turn to in the final principle of ultralearning: experimentation.
Chapter XII
Principle 9
Experimentation
Explore Outside Your Comfort Zone
Results? Why, I have gotten lots of results! I know several thousand things that won’t work.
—Thomas Edison
If you were to read his story without seeing his art, Vincent van Gogh would be the last person you would expect to become one of the most famous painters of all time. He started at a late age, twenty-six. Art is a field of precocity, and famous masters typically display their gifts early. Pablo Picasso’s cubist style, for example, came out of his already being able to paint realistically as a child, allowing him to boldly declare that it had taken him “four years to paint as Rafael, but a lifetime to paint like a child.” Leonardo da Vinci was apprenticed as a painter in his teens. One story has him, as a youth, painting a monster on a peasant’s shield only to have it resold to the duke of Milan. Salvador Dalí had his first exhibit before his fourteenth birthday, already showcasing the talent that would make him famous. Van Gogh, in contrast, was delayed and did not possess any obvious signs of ability. It was only after failing as an art dealer and minister that he picked up the brush. An art sell
er and family friend, H. G. Tersteeg, believed his artistic aspirations were put on to mask his laziness. “You started too late,” he declared. “Of one thing I am sure, you are no artist. . . . This painting of yours will be like all the other things you started, it will come to nothing.”1
Worse than the fact that he started late, however, was that van Gogh simply wasn’t very good at drawing. His drafting was crude and childlike. When he finally convinced models to sit for portraits—no small task in light of the Dutchman’s famously difficult personality—it took him many attempts to get anything resembling a likeness. While in a brief stint at a Parisian atelier, he even studied next to future leaders of the Post-Impressionist movement, such as Henri de Toulouse-Lautrec. However, unlike the effortless quality with which Toulouse-Lautrec captured the likeness of a scene with a few flicks of his wrist, van Gogh struggled. “We considered his work too unskillful,” one classmate recalled. “His drawings had nothing remarkable about them.”2 In the end, his inability to fit in with his classmates, lack of talent, and off-putting manners had him leaving the studio after less than three months.
His late start and lack of obvious talent were compounded by his temperament. Nearly everyone who entered his life would eventually reject him, as his manic enthusiasm and fraternal solidarity would inevitably sour into bitter fights with nearly every person he met. Near the end of his life, he was routinely placed in mental asylums, varyingly diagnosed with disorders from “acute mania with generalized delirium” to “a kind of epilepsy.” His outbursts, or “attacks,” as he referred to them, alienated him from people who could potentially serve as his peers, mentors, and teachers. As a result, despite having attempted formal schooling, van Gogh was largely self-taught, capturing only brief moments of more traditional education in the moments during which he could hold on to friendships before pushing people away.
