The Power of Reframing Problems Through Inversion

In the whirl of our day-to-day interactions, it’s all too easy to forget the nuances that distinguish great teams, great cultures, and great products/services.

52-Foibles brings together 52 mental models from psychology into an easy reference and brainstorming tool. Each card describes one mental model into human behavior and suggests ways to apply this to your teams as well as the design of your products and services.

For more context and a complete list of mental models, click here.

CARD Inversion
An approach to problem-solving that starts with imagining worst-case scenarios – and then using those scenarios as the basis for developing solutions.
How might this apply to great teams and cultures?
One of the methods used in creative ideation sessions is reverse thinking. Instead of following the ‘normal, logical’ direction of a challenge, you turn it around (or an important element in the challenge) and look for opposite ideas.How might this apply to great products?
For instance,  when designing a chair, you can list the assumptions of a chair (it needs to have legs)  and think its opposite (no legs?!) to trigger additional ideas: what if chairs were hanging from the ceiling? or be built as part of the table? or….

The concept of Inversion is often interpreted in two different ways, both are valuable to consider.

The first is the idea of considering the opposite. In particular, envision the negative things that could happen in life. The Stoic philosophers like Marcus Aurelius, Seneca, and Epictetus regularly conducted an exercise known as a premeditatio malorum, which translates to a “premeditation of evils.”

The second is the idea of working with the end in mind. German mathematician Carl Gustav Jacob Jacobi was famous for some work on elliptic functions that eludes me. Jacobi often solved difficult problems by following a simple strategy: “man muss immer umkehren” (or loosely translated, “invert, always invert.”).

Both approaches look at the end result uniquely. Considering an opposite asks you to hold your ideal result loosely, and to consider the opposite of your desired result. Working with the end in mind assumes you are keeping the same goal but approaching the solution from a different direction, by backing into it.

Very few problems can be solved directly. The most wicked, intractable problems must be dealt with indirectly. As such, the Inversion model is one of the most powerful mental models in our toolkit as human beings.

If you are always inverting a problem, like the way you play with a Rubik’s cube, you experience them from multiple perspectives. Multiple vantage points challenges your certainty. It can shake your beliefs.

Let’s take a look at some examples.

Let’s start with the positive-negative notion. When I coach clients, I get many people at major points of transition in their lives and careers. Some are facing big promotions, others are considering leaving their jobs for a second chapter.

Often I’ll ask: what is it you want? Seems like a simple enough question, but it’s really hard to answer. Specifically, what do you really want to happen?

Many people have a very hard time imagining the life, career, or outcome we want because we’ve been conditioned for such long periods of our life (at home, in school, at work) to think a certain way or to embrace a certain idea of success.

However, when asked to consider what would guarantee our unhappiness…and few are at a lack of words.

Let’s move on to the positive-negative notion. I teach an EMBA class called Managing Innovation. Most people take the class to learn how to improve and manage innovation in their organizations.

The course is guided by the central question: What can be done to foster innovation? The answers are pretty standard: engage small teams, enable autonomy, consider the tension of deliberate and emergent strategies, etc. And, by the way, implementing any one of those things in a culture that doesn’t naturally gravitate toward those qualities is really hard. 

But if we invert the problem to: How do we avoid becoming traditional or unoriginal? we consider all the things we can do to discourage innovation: reduce feedback loops, increase top-down decision making, enable homogeneous thinking, foster resistance to risk. Generally speaking, we would want to avoid these things, right?

And, it sounds so easy, doesn’t it? If we were to follow our own council we would have to take our own advice: “Just stop doing these things and do less of these other things instead.” Behavior change of any kind is no small thing.

Moving indirectly gains more ground than directly. 

Thinking forward/backward or negative/positive about a problem results in some action, you can also think of adding vs. subtracting.

Despite our best intentions, thinking forward increases the odds that you’ll cause harm (through unintended consequences). For example, drugs designed eradicate one disease might also have adverse effects, become harmful if overused, or cause antibiotic resistance in bacteria.

Thinking backward, call it subtractive avoidance or inversion, you are less likely to cause harm. Inverting the problem won’t always solve it, but it will help you avoid trouble and thinking through some of the undesirable and unintended consequences. You can think of it as the avoiding negativity filter. It’s not sexy but it’s a very easy way to improve.

So what does this mean in practice?

Thinking about what you don’t want isn’t necessarily inspiring, but it does bring clarity and can aid decision making to a problem or question that brings nothing but overwhelm. Many of the smartest people in history have done this naturally.

Inversion helps improve understanding of the problem on which you are focused. By using this method, you are forcing yourself toward doing the work of having an opinion that considers multiple perspectives.

The key takeaway: Spend less time trying seeking the right answer and more time avoiding the wrong answer. Avoiding loss is an easier starting point than seeking gain.


Higher Order Thinking

Howard Marks, the chairman and co-founder of Oaktree Capital Management, is renowned for his insightful assessments of market opportunity and risk. After four decades spent ascending to the top of the investment management profession, today he is sought out by the world’s leading value investors, and his client memos brim with insightful commentary and a time-tested, fundamental philosophy.

In his book, The Most Important Thing, Howard Marks explains the concept of first and second-order thinking, which he calls second-level thinking.

First-level thinking is simplistic and superficial, and just about everyone can do it (a bad sign for anything involving an attempt at superiority). All the first-level thinker needs is an opinion about the future, as in “The outlook for the company is favorable, meaning the stock will go up.” Second-level thinking is deep, complex and convoluted.

First-level thinking says, “I think the company’s earnings will fall; sell.” Second-level thinking says, “I think the company’s earnings will fall less than people expect, and the pleasant surprise will lift the stock; buy.”

First level thinking is simplistic.  It occurs when we want a fast fix. It does not take consequences into consideration. If you are hungry, you eat.

Second level thinking is more considered. It considers context, alternatives, and unintended consequences. Second order thinkers ask themselves the question “Why?” or “Then what?” to deepen their understanding of an issue. If they are hungry, they consider the consequences of eating when they are hungry versus the time of day or circumstance in which their hunger strikes. They make connections, draw correlations, and notice nuance. Doing this, they are likely to make healthier choices when addressing their hunger.

Remember here that consequences are not always negative. Positive outcomes are consequences too.

Short term bias and negativity bias are actually first-order-thinking biases

Humans don’t have a negativity bias. We miss long term trends regardless of whether they’re good or bad. The root cause that makes us miss them is not that we are biased towards short-term choices (that’s a byproduct). Our negativity bias and short-term biases are byproducts of a first-order-thinking bias. Our brain is wired to be unable to perform second-order-thinking while thinking intuitively: therefore, the bias. –via Luca Dellana

With first-level thinking, everyone reaches the same answer. This is where quick fixes and easy answers abound. With second-order thinking, we are all deeply interpreting the same situation uniquely. We apply our unique perspective. We see what others cannot.

Example excerpt from “It’s Not Easy: Memo To Oaktree Clients” by Howard Marks

Improve Your Thinking, as a skill

Now that you know this kind of thinking exists, what will you do differently today? Here’s how you can practice it now:

  1. Ask yourself “Why?” “What’s It For?” or “Then What?
  2. Think through time — What will the situation be in 1 hour, 1 day, 1 month, 1 year? How will that impact the consequences?
  3. Identify your problem-solution-decision. Consider the pros-cons. Think through the consequences. Reviewing these on a regular basis will help you calibrate your thinking more nimbly.
  4. (Bonus) If you’re using this concept to think about business decisions, consider how it impacts other areas of your ecosystem. How will key players respond? What meaning will employees make of it? How will stakeholders deal with it? How will competitors respond? How will suppliers react? What regulations are we likely to incur?

Often the answer will be little to no impact, but you want to understand the immediate and second-order consequences before you make the decision.

The difference of a second-level thinker is effort:

The difference in workload between first-level and second-level thinking is clearly massive, and the number of people capable of the latter is tiny compared to the number capable of the former…

First-level thinkers think the same way other first-level thinkers do about the same things, and they generally reach the same conclusions…To outperform the average investor, you have to be able to outthink the consensus.

Getting to the next level, in anything, is the result of things that are first-order negative, second order positive. A situation might appear to have no immediate benefit or payoff, but that doesn’t mean that’s the case.  What it indicates is that there is less competition if deeper thinking yields positive outcomes because everyone who simplistically won’t think things through.

Second-order thinking takes effort, effort most people will not invest. It takes effort to think in terms of systems, interactions, and time. But investing this kind of effort sets you apart from everyone else.

The Map is not the Territory

In the whirl of our day-to-day interactions, it’s all too easy to forget the nuances that distinguish great teams, great cultures, and great products/services.

This is part of a series on mental models from psychology. Use as an easy reference and brainstorming tool. Each model describes one bias into human behavior and suggests ways to apply this to your teams as well as the design of your products and services.

For more context and a complete list of mental models, click here.

CARD Map v Territory
A metaphor illustrating the differences between belief and reality.
How might this apply to great teams and cultures?
Our perception of the world is being generated by our brain and can be considered as a ‘map’ of reality written in neural patterns. Reality exists outside our mind but we can construct models of this ‘territory’ based on what we glimpse through our senses.
How might this apply to great products?
There are times when an old map, one that worked in a particular context, does not apply to a new context.
Even the best maps are imperfect because they are reductions of what they represent. If a map were to represent the territory with perfect fidelity, it would no longer be a reduction and thus would no longer be useful to us. Scribbling on the map does not change the territory: If you change what you believe about an object, that is a change in the pattern of neurons in your brain. The real object will not change because of this edit. A map can also be a snapshot of a point in time, representing something that no longer exists. This is important to keep in mind as we think through problems and make better decisions.

Case Study: JC Penny

Every day, leaders make decisions about maximizing current cash flow and profits or reinvesting and building for the long term. But if decisions were as easy as moving money around from budget A to budget B, there would be a lot more successful businesses. A substantial portion of business failures–from the costly to the catastrophic–can be attributed to not paying attention to the right balance between maximizing current performance and building future potential.

Photo: Andrew Burton/Reuters Ron Johnson, chief executive of J.C. Penney, says the store renovation plan is a success.

Apple’s Ron Johnson made the radar in 2011. Handpicked by Steve Jobs to build the Apple Stores, he is also credited with playing a major role in turning Target from a K-Mart look-alike into the trendy-but-cheap Tar-zhey by the late 1990s and early 2000s.

By 2011, Apple stores the most productive retail per-square-foot basis, leaving Tiffany’s in the dust. The gleaming glass cube on Fifth Avenue became a more popular tourist attraction than the Statue of Liberty.

Asked to apply his success from Apply and Target to J.C.Penny’s, Johnson was hired by Bill Ackman, Steven Roth, and other luminaries to turn around the tired old department store. The chain was attempting to reinvent themselves, leaving behind the core customer in an attempt to gain new ones. This was a much different proposition.

Johnson pitched his idea in with standard Apple suspense and fanfare. JC Penney’s stock price went from $26 in the summer of 2011 to $42 in early 2012 on the strength of the pitch.

The idea failed almost immediately. His new pricing model (eliminating discounting) was a flop. The coupon-hunters rebelled. Much of his new product was deemed too trendy. His new store model was wildly expensive for a middling department store chain – including operating losses purposefully endured, he’d spent several billion dollars trying to affect the physical transformation of the stores. JC Penney customers had no idea what was going on, and by 2013, Johnson was sacked. The stock price sank into the single digits, where it remains two years later.

What went wrong in the quest to build America’s Favorite Store? It turned out that Johnson was using a map of Portland Maine to navigate Portland Oregon. Apple’s products, customers, and history had far too little in common with JC Penney’s. Apple had a rabid, young, affluent fan-base before they built stores; JC Penney’s was not associated with youth or affluence. Apple had shiny products, and needed a shiny store; JC Penney was known for its affordable sweaters. Apple had never relied on discounting in the first place; JC Penney was taking away discounts given prior, triggering massive deprival super-reaction.

“All models are wrong but some are useful.”

— George Box

In other words, the old map was not very useful. Even his success at Target, which seems like a closer analog, was misleading in the context of JC Penney. Target had made small, incremental changes over many years, to which Johnson had made a meaningful contribution. JC Penney was attempting to reinvent the concept of the department store in a year or two, leaving behind the core customer in an attempt to gain new ones. This was a much different proposition.

The main issue was not that Johnson was incompetent. He wasn’t. He wouldn’t have gotten the job if he was. He was extremely competent. But it was exactly his competence and past success that got him into trouble. He was like a great swimmer that tried to tackle a grand rapid, and the model he used successfully in the past, the map that had navigated a lot of difficult terrain, was not the map he needed anymore. He had an excellent theory about retailing that applied in some circumstances, but not in others. The terrain had changed, but the old idea stuck.

Relevant Books:

Mental Models: An Overview

Understanding Our Foibles Helps Us Make Better Decisions

Photo by Danielle MacInnes

mental model is an explanation of someone’s thought process about how something works in the real world. It is a representation of the surrounding world, the relationships between its various parts and a person’s intuitive perception about his or her own acts and their consequences.

If used responsibly, mental models can inform marketing, product design, and influence technology. If left unchecked, mental models can turn into foibles or minor weaknesses or eccentricities in our character.

Artificial intelligence and predictive data will continue to advance, enabling exponential growth. In AI and machine learning programs, discrimination is caused by data. This “algorithmic bias” occurs when AI and computing systems act not in objective fairness, but according to the prejudices that exist with the people who formulated, cleaned and structured their data. This is not inherently harmful – human bias can be as simple as preferring red to blue – but warning signs have started to appear.

A research team at the University of California Berkeley distinguished pre-existing biases in training data from the technical biases that arise from the tools and algorithms that power these AI systems and from the emergent biases that result from human interactions with them.

Ultimately, the solutions we embrace (whether technically or process-oriented) are only as good as the data it is trained to analyze. How we assess problems includes pre-existing (human) biases. These impact us on an individual and societal level. This kind of bias was found in a risk assessment software known as COMPAS. Courtroom judges used it to forecast which criminals were most likely to offend. When news organization ProPublica compared COMPAS risk assessments for 10,000 people arrested in one county in Florida with data showing which ones went on to re-offend, it discovered that when the algorithm was right, its decision making was fair. But when the algorithm was wrong, people of color were almost twice as likely to be labeled a higher risk, yet they did not re-offend.

Gaining insight to our mental models are how we understand the world. Not only do they shape what we think and how we understand but they shape the connections and opportunities that we see. Mental models help make the complex simple. complexity, why we consider some things more relevant than others, and how we reason.

A mental model is just that…a model. It’s a tool that enables us to make an abstract representation of a complex issue. Models help our brains filter the details of the world so we can focus on the relevant details of an issue.

Photo by Todd Quackenbush

A path toward better thinking

The quality of our thinking is proportional to the models we are aware of, and our ability to apply them correctly in a situation. The more models you know, the bigger your toolbox. The more models you apply, the more likely you are to see reality with greater clarity and make better decisions. When it comes to improving your ability to make decisions variety (and volume) matters.

Most of us, however, are specialists. Instead of a latticework of mental models, we have a few from our discipline–a few “rules of thumb.” Each specialist sees something different.

When you look at a forest, do you focus on:

  • the ecosystem? You might be a botanist.
  • the impact of climate change? You might be an environmentalist.
  • the state of the tree growth? You might be forestry engineer.
  • the value of the land? You might be a business person.

None of these perspectives are wrong. And, none of them see the forest in its entirety. That is the value of cross-disciplinary thinking. Understanding the basics of the other perspectives leads to a more well-rounded understanding of the forest allowing for better initial decisions about managing it. That’s latticework.

By putting these disciplines together in our head, we can gain greater proximity to the problem at hand by seeing it in a three dimensional way. If consider the problem merely from one angle, we’ve got a blind spot. And blind spots can kill you.

Photo by Nicolas Picard

A Network of Mental Models for “good humaning”

Building your repertoire of mental models will help you make better decisions. Once you know a few, you will start to make connections between them, helping you create a networked understanding of how you operate as a human being. I’ve collected and summarized the ones I’ve found the most useful. You can use them almost like a deck of cards.

One of the reasons I refer to them as “Foibles” is because these biases are universal to us all. They are what make us human. Succumbing to them clouds our view of the world and contributes to making costly mistakes in our relationships, our businesses, and as a society.

I refer to “good humaning” because between learning and integration lies “the journey”, “the struggle”, “the gap.”  Part of our work is learning and re-learning what it means to be a good human or to do “humaning” well, by making better decisions in our relationships, business, and society at large.

Remember: Developing this level of self-awareness about how you and others operate is a lifelong project. Stick with it, and you’ll find that you will see reality more clearly, make better decisions more consistently, and help those you love and care with greater your increased presence.

Mental Models Explained


General Concepts Map v Territory
Higher-Order Thinking
More to come!
Systems Thinking Law of Diminishing Returns
Feedback Loops
Pareto Principle
Chaos Dynamics/Butterfly Effect
Tragedy of the Commons
Gresham’s Law
Network Effects
Complex Adaptive Systems
Biological Concepts Incentives
Red Queen Effect
Natural Selection
Dunbar’s Number
Physics Concepts here
Psychological Concepts Social Proof
Confirmation Bias
Fundamental Attribution Error
Pavlovian Association
Narrative Instinct
First-conclusion bias
Hindsight Bias
Bias toward action
Biases that influence marketing and product design Value Effect
Value Attribution
Peak-End Rule
Serial Position Effect
Variable Reward
Commitment and Consistency
Set Consistency
Appropriate Challenges
Collection Bias
Visual Imagery
Aesthetic-Usability Effect
Authority Principle
Certainty Bias
Familiarity Bias
Humor Effect
Limited Choice
Limited Access
Contrast Effect
Anchoring & Adjustment
Status Quo
Microeconomic Concepts Opportunity (sunk) costs
Creative destruction
Supply / Demand
Seizing the middle
Military Concepts Counterinsurgency
Seeing the front
Mutually assured destruction
Two-front war


1. The Map is not the Territory metaphorically illustrates the differences between belief and reality. The phrase was coined by Alfred Korzybski. Our perception of the world is being generated by our brain and can be considered as a ‘map’ of reality written in neural patterns. Reality exists outside our mind but we can construct models of this ‘territory’ based on what we glimpse through our senses.

2. Higher Order Thinking moves from the easier and safer anticipation of the immediate results of our actions, to thinking farther ahead and thinking holistically. The first approach ensures we get the same results as everyone else. Second-order thinking requires us to not only consider our actions and their immediate consequences but consider the long game. Failing to think through long term effects can invite crisis and disaster.

3. Inversion is a common method used in creative ideation sessions, also known as reverse thinking. Instead of following the ‘normal, logical’ direction of a challenge, you turn it around (or an important element in the challenge) and look for opposite ideas.


52 Foibles: Story

In the whirl of our day-to-day interactions, it’s all too easy to forget the nuances that distinguish great teams, great cultures, and great products/services.

52-Foibles brings together 52 insights from psychology into an easy reference and brainstorming tool. Each card describes one insight into human behavior and suggests ways to apply this to your teams as well as the design of your products and services.

CARD Story
All our decisions are filtered through a story—real or imagined—that we believe.
How might this apply to great teams and cultures?
We tell a lot of stories in organizations:

How might this apply to your business?
Are you creating a story that includes your stakeholders? Stories can be explicit—simple, episodic narratives. Or a story can be implied, using words that suggest conflict, a hero or other narrative elements. The most powerful stories are well-crafted visions that give significance to mundane tasks.

What story did you tell yourself about the last person you just met or came into contact with?
See Also
Commitment & Consistency, Autonomy, Authority, Affect Heuristic, Conceptual Metaphor, Priming, Framing, Periodic Events, Task Significance


Story Bias: War Stories

War stories in organizations are not literal stories of international military conflict, although they do tell of trials and troubles and how people survived and overcame the events that afflicted them.

War stories are typically told at meetings, conferences, and social settings, where old and young corporate warriors swap tales of what trials they survived and how hard it was, much as their military counterparts may tell and re-tell of their exploits.

Bill Gates and Steve Jobs never quite got along. Over the course of 30-plus years, the two went from cautious allies to bitter rivals to something almost approaching friends — sometimes, they were all three at the same time. It seems unlikely that Apple would be where it is today without Microsoft, or Microsoft without Apple. Their story here.

But when we reminisce, it’s more about how life felt “in those days.” We worked long hours, didn’t get paid well, there were public arguments, backstabbing, sabotage–and through it all there were foxhole buddies that helped us through.

War stories are typically told as ways of nostalgic invocation of past trials. When told with old colleagues, they re-affirm bonds of friendship and shared experience. When told to younger colleagues, they may demonstrate authority or other superiority, giving evidence of their prowess. When a younger person tells the story, perhaps they are saying ‘Hey, I’m a tough guy too!’

By re-telling the stories, the teller also re-experiences them, gaining again the sense of excitement and danger, though now within a safe present.

War stories may also be told as a form of bragging, and competitions may arise as the warriors try to out-do each other with increasingly amazing stories (and maybe increasing elaboration).

Story Bias: Visionary Stories

Visionary stories tell about a desirable future that inspires and motivates people to work towards that future.

They are usually couched in very positive terms and may well be told from the viewpoint of the future, where the desirable state has been reached.


Steve Jobs is often referred to as one of the most visionary leaders of our time. He is credited with:

  • Igniting the personal computer revolution. …
  • Introducing the mouse and graphical user interface. …
  • Bringing portable music players to the masses. …
  • Revolutionizing the sale of music. …
  • Shepherding the age of computer animation. …
  • Opening Apple stores. …
  • Making personal computers stylish. …
  • Launching the smartphone revolution.

But vision seldom makes sense in the beginning. Pay attention to how it feels to hear something new. An example of vision might look something like this: Imagine it is five years from now. Imagine dry toilets being sold worldwide. Imagine them in every home from New York to New Delhi. In the midst of a worldwide water crisis, this is not fanciful. The greatest research and the greatest product exist for this to occur. It’s now up to a visionary leader to make this a reality regionally, then nationally, to make those products known and desired around the world.

Stories about the future motivate by giving hope and meaning, setting clear goals and giving people reason to work together.

Visionary stories also say much about the person who is telling the tale, showing them to be imaginative and positive.

Visionary stories are a common tool of leaders (and indeed the term ‘visionary leader’ is quite common) who use them to motivate people to work together towards a common goal that extends beyond the everyday ‘doing the business’.