How to Create Your Own Mental Model
Learning a method that colleagues seldom use can give you another way to approach a difficult problem. Feynman’s account of differentiating under the integral sign illustrates the value of adding tools to your repertoire and recognizing when they fit.
THE IDEA
How to Create Your Own Mental Model
“One day [my high school physics teacher, Mr. Bader,] told me to stay after class. ‘Feynman,’ he said, ‘you talk too much and you make too much noise. I know why. You’re bored. So I’m going to give you a book. You go up there in the back, in the corner, and study this book, and when you know everything that’s in this book, you can talk again.’
So every physics class, I paid no attention to what was going on with Pascal’s Law, or whatever they were doing. I was up in the back with this book: Advanced Calculus, by Woods. Bader knew I had studied Calculus for the Practical Man a little bit, so he gave me the real works–it was for a junior or senior course in college. It had Fourier series, Bessel functions, determinants, elliptic functions—all kinds of wonderful stuff that I didn’t know anything about.
That book also showed how to differentiate parameters under the integral sign—it’s a certain operation. It turns out that’s not taught very much in the universities; they don’t emphasize it. But I caught on how to use that method, and I used that one damn tool again and again. So because I was self-taught using that book, I had peculiar methods of doing integrals.
The result was, when the guys at MIT or Princeton had trouble doing a certain integral, it was because they couldn’t do it with the standard methods they had learned in school. If it was a contour integration, they would have found it; if it was a simple series expansion, they would have found it. Then I come along and try differentiating under the integral sign, and often it worked. So I got a great reputation for doing integrals, only because my box of tools was different from everybody else’s, and they had tried all their tools on it before giving the problem to me.”
—Richard Feynman, Surely You’re Joking, Mr. Feynman! (pages 86–87)
A model represents selected features of something more complex. A map leaves out much of a landscape while helping us navigate it. A familiar diagram of an atom may draw on Niels Bohr’s model; it is a representation, not a literal picture. Computer simulations and mathematical descriptions can serve a similar purpose.
Feynman’s story illustrates a related point about methods. He learned an existing technique that his peers used less often, so he could try it after their usual approaches had failed. You can build a broader repertoire in the same way: learn how an unfamiliar method works, practice it, and look for problems where its assumptions fit. The story offers a way to develop your approach, rather than a recipe for inventing a new model.
When to use it
When faced with a complex problem, try approaching it from a perspective outside your field of expertise.
In a team setting, encourage members to share their unique mental models to solve problems more creatively.
When learning a new subject, focus on understanding the underlying models rather than memorizing facts.
In decision-making, consciously consider if your current mental model is appropriate or if you need to switch to a different one.
When learning a new subject, deliberately seek out less common frameworks or perspectives to build a unique mental toolbox.
In a brainstorming session, encourage team members to share and apply different mental models (e.g., first principles, inversion, systems thinking) to generate diverse solutions.
When stuck on a problem, choose a few methods whose assumptions fit and examine what each lets you try.
FROM THEORY TO EVERYDAY LIFE
In practice
Feynman's Integral Trick
Feynman reports trying differentiation under the integral sign after colleagues had exhausted their standard methods. It sometimes solved an integral they had brought to him, showing the value of an additional method.
Feynman's Differentiating Under the Integral Sign
Feynman learned the technique while studying an advanced calculus book on his own. His account emphasizes repeated practice with a method that was less prominent in his peers’ training.
Applying a Unique Mental Model in Business
A product manager at a tech company might use the 'Inversion' mental model (thinking backward from a desired outcome) to identify risks and opportunities that colleagues using traditional forward-planning models miss. By switching to this less common perspective, the manager can propose innovative solutions that others overlooked.
A MOMENT TO REFLECT
Put it to work.
What unique mental models do you have that others may not?
How can you deliberately learn new perspectives to expand your toolbox?
Think of a problem you recently solved. What mental model did you use? Could a different model have been more effective?
What is one mental model you currently use that is different from the ‘standard’ approach in your field? How did you acquire it?
Think of a recent problem you faced. What mental models did you apply? How might switching to a different model have changed your approach or outcome?
Identify a skill or domain you want to master. What unconventional mental models could you deliberately learn to gain a unique advantage?
References
- Surely You're Joking, Mr. Feynman! — Richard Feynman (1985)
- Surely You’re Joking, Mr. Feynman! — Richard Feynman
CONTINUE THE CONVERSATION
Source texts
- Richard Feynmans Mental Models by Peter Hollins
- Richard Feynmans Mental Models by Peter Hollins