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Mental Models: How Intelligent People Solve Unsolvable Problems

Mental Models: How Intelligent People Solve Unsolvable Problems

Richard Feynman won the Nobel Prize in Physics in 1965. He is widely regarded as one of the greatest physicists of all-time. (He was a pretty solid bongo player as well). [1]

Feynman received his undergraduate degree from MIT and his Ph.D. from Princeton. During those years, he became known for waltzing into the math department at each school and solving problems that the brilliant math Ph.D. students couldn’t solve.

Feynman describes why he was able to do this in his fantastic book, Surely You’re Joking Mr. Feynman! (one of my favorite books that I read last year).

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)

 
richard-feynman
    Richard Feynman (Image Source: California Institute of Technology)

    Mental Models

    Point of View is worth 80 IQ points.
    –Alan Kay

    A mental model is a way of looking at the world.

    Put simply, mental models are the set of tools that you use to think. Each mental model offers a different framework that you can use to look at life (or at an individual problem). Feynman’s strategy of differentiating under the integral sign was a unique mental model that he could pull out of his intellectual toolbox and use to solve difficult problems that eluded his peers. Feynman wasn’t necessarily smarter than the math Ph.D. students, he just saw the problem from a different perspective.

    I have written about mental models before. For example, you can use the Inversion Technique to view situations in a different way and solve difficult problems.

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    Where mental models really shine, however, is when you develop multiple ways of looking at the same problem. For example, let’s say that you’d like to avoid procrastination and have a productive day. If you understand the 2-Minute Rulethe Eisenhower Box, and Warren Buffett’s 25-5 Rule, then you have a range of options for determining your priorities and getting something important done.

    There is no one best way to manage your schedule and get something done. When you have a variety of mental models at your disposal, you can pick the one that works best for your current situation.

    The Law of the Instrument

    In Abraham Kaplan’s book, The Conduct of Inquiry, he explains a concept called The Law of the Instrument.

    Kaplan says, “I call it the law of the instrument, and it may be formulated as follows: Give a small boy a hammer, and he will find that everything he encounters needs pounding.” (p.28)

    Kaplan’s law is similar to a common proverb you have likely heard before: “If all you have is a hammer, everything looks like a nail.” If you only have one framework for thinking about the world, then you’ll try to fit every problem you face into that framework. When your set of mental models is limited, so is your potential for finding a solution.

    Interestingly, this problem can become more pronounced as your expertise in a particular area grows. If you’re quite smart and talented in one area, you have a tendency to believe that your skill set is the answer to most problems you face. The more you master a single mental model, the more likely it becomes that this mental model will be your downfall because you’ll start applying it indiscriminately to every problem. Smart people can easily develop a confirmation bias that leaves them stumped in difficult situations.

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    However, if you develop a bigger toolbox of mental models, you’ll improve your ability to solve problems because you’ll have more options for getting to the right answer. This is one of the primary ways that truly brilliant people separate themselves from the masses of smart individuals out there. Brilliant people like Richard Feynman have more mental models at their disposal.

    This is why having a wide range of mental models is important. You can only choose the best tool for the situation if you have a full toolbox.

    How to Develop New Mental Models

    In my experience, there are two good ways to build new mental models.

    1. Read books outside the norm. If you read the same material as everyone else, then you’ll think in the same way as everyone else. You can’t expect to see problems in a new way if you’re reading all the same things as your classmates, co-workers, or peers. So, either read books that are seldom read by the rest of your group (like Feynman did with his Calculus book) or read books that are outside your area of interest, but can overlap with it in some way. In other words, look for answers in unexpected places. [2]

    2. Create a web of ideas that shows how seemingly unrelated ideas connect. Whenever you are reading a new book or listening to someone lecture, write down the various ways that this new information connects to information you already understand. We tend to view knowledge as separated into different silos. We think that a certain set of ideas have to do with economics and another set have to do with medicine and a third set have to do with art history. This is mostly a product of how schools teach subjects, but in the real world information is not separated like this.

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    unrelated-intersection-700x466

      For example, I was watching a documentary the other day that connected the design of the Great Pyramids in Egypt with the fighting rituals of animals. According to the historians on the show, when animals are battling one another they will often rise up on their back feet to increase their height and show their dominance. Similarly, when a new Pharaoh took power in Egypt, he wanted to assert his dominance over the culture and so he built very tall structures as a symbol of power. This explanation links seemingly unrelated areas (architecture, ancient history, and animal behavior) in a way that results in a deeper understanding of the topic.

      In a similar way, mental models from outside areas can reveal a deeper level of understanding about issues in your primary field of interest.

      Don’t try to tighten a screw with a hammer. The problems of life and work are much easier to solve when you have the right tools.

      This article was originally published on JamesClear.com.

      Notes

      1. Feynman was famously eccentric and varied in his hobbies. Among other things, he played the bongos, spent years as an artist drawing nude models, and cracked a safe with top secret information about the atomic bomb inside.
      2. This isn’t to say that you should avoid reading the books your peers are reading. You should probably read those too, so that you have the same baseline of knowledge.

      Thanks to Shane Parrish for sending me down the rabbit hole of mental models.

      Featured photo credit: Christian Weidinger via flickr.com

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      James Clear

      James Clear is the author of Atomic Habits. He shares self-improvement tips based on proven scientific research.

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      Last Updated on March 31, 2020

      How To Break the Procrastination Cycle

      How To Break the Procrastination Cycle

      How often do you find yourself procrastinating? Do you wish you could procrastinate less? We all know how debilitating procrastination can make us feel, and it seems to be a challenge we all share. Procrastination is one of the biggest hindrances to moving forward and doing the things that we want to in life.

      There are many reasons why you might be procrastinating, and sometimes, it is really difficult to pinpoint why. You might be procrastinating because of something related to the past, present, or future (they are all intertwined), or it could be as simple as biological factors. Whatever the reason, most of us follow a cycle when we procrastinate, from the moment we decide to do something to actually getting it done, or in this case, not getting it done.

      The Vicious Procrastination Cycle

      For some reason, it helps to understand that we all go through the same thing, even though we often feel like the only person in the world who struggles with this. Do you resonate with the cycle below?

      1. Feeling Eager and Energized

      This is when you commit to taking a new action or getting something done. You are feeling confident and optimistic that, this time round, you will do it!

      2. Apprehension Starts to Come Up

      The beginning stages of optimism are starting to fade. There is still time, but you haven’t done anything yet, and you start to feel uneasy. You realize that you actually have to do something to get it done, and that good intentions are not enough.

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      3. Still No Action

      More time has passed. You still haven’t taken any action and probably have a lot of excuses why. You start to panic a little and wish you had started sooner. Your panic starts to turn into frustration and perhaps even irritability.

      4. Flicker of Hope Left

      You can still make it; there is a little time left and you ponder how you are going to get it done. The rush you get from leaving your task until the last minute gives you a flicker of hope. There is still time; you can do this!

      5. Fading Quickly

      Your hope starts to quickly fade as you try desperately to understand why you just can’t do this. You may feel desperate and have thoughts like, “What is wrong with me?” and “Why do I ALWAYS do this?” You feel discouraged, or perhaps angry and resentful at yourself.

      6. Vow to Yourself

      Once the feeling of anger or disappointment disappears, you most likely swear to yourself that this will never happen again; that this was the last time and next time will be different.

      Does this sound like you? Is the next time different? I understand the devastating effect that procrastination has on many lives, and for some, it is a really serious problem. You also have, on the other hand, those who procrastinate but it doesn’t affect them in any way. You know whether it is affecting you or not and whether it undermines your results.

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      How to Break the Procrastination Cycle

      Unless you break the cycle, you will keep reinforcing it!

      To break the cycle, you need to change the sequence of events. Here is my suggestion on how you can effectively break the vicious cycle you are in!

      1. Feeling Eager and Energized

      This is when you commit to taking a new action or getting something done. You are feeling confident and optimistic that, this time round, you will do it! The first stage is always the same.

      2. Plan

      Thinking alone will not help; you need to plan your actions. I always put my deadlines one or two days in advance because you know Murphy’s Law! Take into consideration everything that you need to do, how long it will take you, and what you will need to get it done, then plan the individual steps.

      3. Resistance

      Just because you planned doesn’t mean that this time is guaranteed to be different. You will most likely still feel the resistance so expect this. This stage is key to identifying why you are procrastinating, so when you feel the resistance, try to identify it immediately.

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      What is causing you to hesitate in this moment? What do you feel?  Write them down if it helps.

      4. Confront Those Feelings

      Once you have identified what could possibly be holding you back, for example, fear of failure, lack of motivation, etc. You need to work on lessening the resistance.

      Ask yourself, “What do I need to do to move forward? What would make it easier?” If you find that you fear something, overcoming that fear is not something that will happen overnight — keep this in mind.

      5. Put Results Before Comfort

      You need to keep moving forward and put results before comfort. Take action, even if it is only for 10 minutes. The key is to break the cycle and not reinforce it. You have more control that you think.

      6. Repeat

      Repeat steps 3-5 until you achieve what you first set out to do.

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      Final Thoughts

      Change doesn’t happen overnight, and if you have some deeper underlying reasons why you procrastinate, it may take longer to finally break the cycle.

      If procrastination is holding you back in life, it is better to deal with it now than to deal with the negative consequences later on. It is not a question of comfort anymore; it is a question of results. What is more important to you?

      Learn more about how to stop procrastinating here: What Is Procrastination and How to Stop It (The Complete Guide)

      Featured photo credit: Luke Chesser via unsplash.com

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