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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 23, 2021

      Manage Your Energy so You Can Manage Your Time

      Manage Your Energy so You Can Manage Your Time

      One of the greatest ironies of this age is that while various gadgets like smartphones and netbooks allow you to multitask, it seems that you never manage to get things done. You are caught in the busyness trap. There’s just too much work to do in one day that sometimes you end up exhausted with half-finished tasks.

      The problem lies in how to keep our energy level high to ensure that you finish at least one of your most important tasks for the day. There’s just not enough hours in a day and it’s not possible to be productive the whole time.

      You need more than time management. You need energy management

      1. Dispel the idea that you need to be a “morning person” to be productive

      How many times have you heard (or read) this advice – wake up early so that you can do all the tasks at hand. There’s nothing wrong with that advice. It’s actually reeks of good common sense – start early, finish early. The thing is that technique alone won’t work with everyone. Especially not with people who are not morning larks.

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      I should know because I was once deluded with the idea that I will be more productive if I get out of bed by 6 a.m. Like most of you Lifehackers, I’m always on the lookout for productivity hacks because I have a lot of things in my plate. I’m working full time as an editor for a news agency, while at the same time tending to my side business as a content marketing strategist. I’m also a travel blogger and oh yeah, I forgot, I also have a life.

      I read a lot of productivity books and blogs looking for ways to make the most of my 24 hours. Most stories on productivity stress waking up early. So I did – and I was a major failure in that department – both in waking up early and finishing early.

      2. Determine your “peak hours”

      Energy management begins with looking for your most productive hours in a day. Getting attuned to your body clock won’t happen instantly but there’s a way around it.

      Monitor your working habits for one week and list down the time when you managed to do the most work. Take note also of what you feel during those hours – do you feel energized or lethargic? Monitor this and you will find a pattern later on.

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      My experiment with being a morning lark proved that ignoring my body clock and just doing it by disciplining myself to wake up before 8 a.m. will push me to be more productive. I thought that by writing blog posts and other reports in the morning that I would be finished by noon and use my lunch break for a quick gym session. That never happened. I was sleepy, distracted and couldn’t write jack before 10 a.m.

      In fact that was one experiment that I shouldn’t have tried because I should know better. After all, I’ve been writing for a living for the last 15 years, and I have observed time and again that I write more –and better – in the afternoon and in evenings after supper. I’m a night owl. I might as well, accept it and work around it.

      Just recently, I was so fired up by a certain idea that – even if I’m back home tired from work – I took out my netbook, wrote and published a 600-word blog post by 11 p.m. This is a bit extreme and one of my rare outbursts of energy, but it works for me.

      3. Block those high-energy hours

      Once you have a sense of that high-energy time, you can then mold your schedule so that your other less important tasks will be scheduled either before or after this designated productive time.

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      Block them out in your calendar and use the high-energy hours for your high priority tasks – especially those that require more of your mental energy and focus. You also need to use these hours to any task that will bring you closer to you life’s goal.

      If you are a morning person, you might want to schedule most business meetings before lunch time as it’s important to keep your mind sharp and focused. But nothing is set in stone. Sometimes you have to sacrifice those productive hours to attend to other personal stuff – like if you or your family members are sick or if you have to attend your son’s graduation.

      That said, just remember to keep those productive times on your calendar. You may allow for some exemptions but stick to that schedule as much as possible.

      There’s no right or wrong way of using this energy management technique because everything depends on your own personal circumstances. What you need to remember is that you have to accept what works for you – and not what other productivity gurus say you should do.

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      Understanding your own body clock is the key to time management. Without it, you end up exhausted chasing a never-ending cycle of tasks and frustrations.

      Featured photo credit: Collin Hardy via unsplash.com

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