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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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      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

      More by this author

      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 September 30, 2020

      Effective vs Efficient: What’s the Difference Regarding Productivity?

      Effective vs Efficient: What’s the Difference Regarding Productivity?

      When it comes to being effective vs efficient, there are a lot of similarities, and because of this, they’re often misused and misinterpreted, both in daily use and application.

      Every business should look for new ways to improve employee effectiveness and efficiency to save time and energy in the long term. Just because a company or employee has one, however, doesn’t necessarily mean that the other is equally present.

      Utilizing both an effective and efficient methodology in nearly any capacity of work and life will yield high levels of productivity, while a lack of it will lead to a lack of positive results.

      Before we discuss the various nuances between the word effective and efficient and how they factor into productivity, let’s break things down with a definition of their terms.

      Effective vs Efficient

      Effective is defined as “producing a decided, decisive, or desired effect.” Meanwhile, the word “efficient ” is defined as “capable of producing desired results with little or no waste (as of time or materials).”[1]

      A rather simple way of explaining the differences between the two would be to consider a light bulb. Say that your porch light burned out and you decided that you wanted to replace the incandescent light bulb outside with an LED one. Either light bulb would be effective in accomplishing the goal of providing you with light at night, but the LED one would use less energy and therefore be the more efficient choice.

      Now, if you incorrectly set a timer for the light, and it was turned on throughout the entire day, then you would be wasting energy. While the bulb is still performing the task of creating light in an efficient manner, it’s on during the wrong time of day and therefore not effective.

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      The effective way is focused on accomplishing the goal, while the efficient method is focused on the best way of accomplishing the goal.

      Whether we’re talking about a method, employee, or business, the subject in question can be either effective or efficient, or, in rare instances, they can be both.

      When it comes to effective vs efficient, the goal of achieving maximum productivity is going to be a combination where the subject is effective and as efficient as possible in doing so.

      Effectiveness in Success and Productivity

      Being effective vs efficient is all about doing something that brings about the desired intent or effect[2]. If a pest control company is hired to rid a building’s infestation, and they employ “method A” and successfully completed the job, they’ve been effective at achieving the task.

      The task was performed correctly, to the extent that the pest control company did what they were hired to do. As for how efficient “method A” was in completing the task, that’s another story.

      If the pest control company took longer than expected to complete the job and used more resources than needed, then their efficiency in completing the task wasn’t particularly good. The client may feel that even though the job was completed, the value in the service wasn’t up to par.

      When assessing the effectiveness of any business strategy, it’s wise to ask certain questions before moving forward:

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      • Has a target solution to the problem been identified?
      • What is the ideal response time for achieving the goal?
      • Does the cost balance out with the benefit?

      Looking at these questions, a leader should ask to what extent a method, tool, or resource meets the above criteria and achieve the desired effect. If the subject in question doesn’t hit any of these marks, then productivity will likely suffer.

      Efficiency in Success and Productivity

      Efficiency is going to account for the resources and materials used in relation to the value of achieving the desired effect. Money, people, inventory, and (perhaps most importantly) time, all factor into the equation.

      When it comes to being effective vs efficient, efficiency can be measured in numerous ways[3]. In general, the business that uses fewer materials or that is able to save time is going to be more efficient and have an advantage over the competition. This is assuming that they’re also effective, of course.

      Consider a sales team for example. Let’s say that a company’s sales team is tasked with making 100 calls a week and that the members of that team are hitting their goal each week without any struggle.

      The members on the sales team are effective in hitting their goal. However, the question of efficiency comes into play when management looks at how many of those calls turn into solid connections and closed deals.

      If less than 10 percent of those calls generate a connection, the productivity is relatively low because the efficiency is not adequately balancing out with the effect. Management can either keep the same strategy or take a new approach.

      Perhaps they break up their sales team with certain members handling different parts of the sales process, or they explore a better way of connecting with their customers through a communications company.

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      The goal is ultimately going to be finding the right balance, where they’re being efficient with the resources they have to maximize their sales goals without stretching themselves too thin. Finding this balance is often easier said than done, but it’s incredibly important for any business that is going to thrive.

      Combining Efficiency and Effectiveness to Maximize Productivity

      Being effective vs efficient works best if both are pulled together for the best results.

      If a business is ineffective in accomplishing its overall goal, and the customer doesn’t feel that the service is equated with the cost, then efficiency becomes largely irrelevant. The business may be speedy and use minimal resources, but they struggle to be effective. This may put them at risk of going under.

      It’s for this reason that it’s best to shoot for being effective first, and then work on bringing efficiency into practice.

      Improving productivity starts with taking the initiative to look at how effective a company, employee, or method is through performance reviews. Leaders should make a point to regularly examine performance at all levels on a whole, and take into account the results that are being generated.

      Businesses and employees often succumb to inefficiency because they don’t look for a better way, or they lack the proper tools to be effective in the most efficient manner possible.

      Similar to improving a manager or employee’s level of effectiveness, regularly measuring the resources needed to obtain the desired effect will ensure that efficiency is being accounted for. This involves everything from keeping track of inventory and expenses, to how communication is handled within an organization.

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      By putting in place a baseline value for key metrics and checking them once changes have been made, a company will have a much better idea of the results they’re generating.

      It’s no doubt a step-by-step process. By making concentrated efforts, weakness can be identified and rectified sooner rather than later when the damage is already done.

      Bottom Line

      Understanding the differences between being effective vs efficient is key when it comes to maximizing productivity. It’s simply working smart so that the intended results are achieved in the best way possible. Finding the optimal balance should be the ultimate goal for employees and businesses:

      • Take the steps that result in meeting the solution.
      • Review the process and figure out how to do it better.
      • Repeat the process with what has been learned in a more efficient manner.

      And just like that, effective and efficient productivity is maximized.

      More on How to Improve Productivity

      Featured photo credit: Tim van der Kuip via unsplash.com

      Reference

      [1] Merriam-Webster: effective and efficient
      [2] Mind Tools: Being Effective at Work
      [3] Inc.: 8 Things Really Efficient People Do

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