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.
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“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.
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.
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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.”
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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.
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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!
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