How to Solve Problems Successfully Using the Power of Inversion

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When you outscore your opponent in football, you win. In the quest to win English footballs biggest prize, managers have chased the glory of goals to succeed. Teams have gone all out to keep hitting the back of the net. It drives the game forward, as managers seek to adopt smarter ways to create and score goals.

Twenty-five years ago, Kevin Keegan managed a Newcastle team utterly focused on scoring goals. Attack, attack, attack. Scoring freely, they were still outgunned by Manchester Utd, who scored more goals and won more games.

Newcastle came second that season.

There is always another team who will outplay you and outscore you. What could Newcastle have done differently? Conventional wisdom tells us to win, teams must score more than the opponent.

But what if you did the opposite?

What, instead of asking how to win, you asked how not to lose?

In football, the answer is to not concede goals. If you can stop your opponent from scoring, they can’t win. It doesn’t guarantee you winning, but it does guarantee you won’t lose.

This concept is how inversion works.


Defeating conventional wisdom

Inversion is a glorious problem-solving technique, but it goes against the grain of how we think. We are forward-looking, forward-thinking, and forward planning. Subsequently, we attempt to solve problems in much the same way.

“We’ve always done it like this.”

What follows is an ethos of repeating patterns.

We do what we’ve done before. Processes stay rigidly firm as our brains fail to lead us past the structures we’ve previously created. “We’ve always done it like this” is a quote that supports the limitations of our creative thinking.

It stops us from solving problems, it stops businesses from improving and it stops football teams from winning championships.  

We even have a name for it, conventional wisdom.

The world stands still though if we keep following conventional wisdom. Nothing gets better, and although we accept what’s gone before, we all have an urge to do better. Our challenge is we don’t know how to do better.

Thankfully, people don’t want to accept conventional wisdom. They want to solve problems and move the world forward. As we have evolved and learnt from our forefathers, so we have come to understand mental models.

Mental models are methods of thinking which explain how the world works. First-principles thinking is one such concept.

Another is inversion; the art of doing the opposite.  


Inversion: The art of doing the opposite

Winning isn’t losing. In hindsight it seems such an obvious statement, but one we can’t readily accept. We are so focused on winning, we forget about not losing, but the first step to winning is to not lose.

We are now inverting. Using inversion to ask not how to win, but how not to lose. The distinction is clear, we are doing the opposite. Of course, by focusing on not losing you are also preventing your opponent from winning.

Now, how you defend matters. Is your goalkeeper world-class? Do you play with a back three or back four? How defensive should your midfield be? Do you defend from the front – pressing their defenders when they have the ball?

Liverpool tackled these during the 2019/2020 season.

They scored fewer goals than the team who came second but conceded fewer goals and won the league by a margin of eighteen points. Player investments brought in terms of a goalkeeper, central defender, full back, and a central defensive midfielder made the difference.

Never has a team better demonstrated the meaning of winning isn’t losing than Liverpool did during the 2019/2020 season.

But that’s football. What about real life?


Inversion in life

My example comes from seeking a job promotion. I wanted to get noticed, so I chased the big deals, all to catch the eye of my boss. I believed if I could get noticed for good things, I would get promoted.

I failed to think about the bad things I would get noticed for.

I didn’t think about the sick days, the late starts, and the failure to submit my expense reports on time. These, to my boss, carried the same weight as achieving the big deal, but in a negative light.

I didn’t get the promotion, and through frustration, I left.

Six months later I was back. The grass wasn’t greener on the other side. During those six months, I learnt about inversion. Now, armed with this knowledge, my approach to work changed.

This meant returning my expense reports on time, it meant not being late, it meant no more sick days. By ensuring these bad behaviours didn’t happen, I was being noticed for the good behaviours. The sales kept coming and after a year, so did a promotion. I went on to have six promotions in eight years – all because of what I wasn’t doing.


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How to solve problems using Inversion

When we think of inversion or inverting, we think of working backwards or turning something upside down. There is nothing wrong with working backwards; reverse engineering is a powerful mental model for solving problems as well.

But inversion is more nuanced.

The mental model of inversion calls for asking the opposite.

  • Instead of winning, how do you not lose?
  • Instead of being brilliant, how do you not look stupid?
  • Instead of making gains on the stock market, how do you not make losses?

As I mentioned earlier, this approach is at odds with normal life. We work forwards. Often, we only look back at past events. Then hindsight kicks in and we become experts at seeing the wood from the trees. This is a mental bias we all have. The skill is using it, not on events that have occurred, but events or problems ahead.

Inversion helps you overcome conventional wisdom.


Concluding thoughts

Inversion is a great mental model. It’s a tool that helps with critical thinking and stretching your mind. Solving problems is a mental exercise where you need creative imagination to picture what’s happening. Then, you need to invert; come at the problem from an opposite viewpoint.

Thinking like this takes concentration and a clear mind to unpick what you’re seeing. Fascination unrolls into fantasy as different scenarios play out in your mind; solutions come into focus as you work through the problem.

For some, it’s knowing where to start.

Start simple. Start with something that isn’t working for you and ask yourself the opposite. Of course, you will find some ugly truths – they’re hidden in plain sight – within the context of conventional wisdom, but that’s okay.

Now, you’re using the power of inversion.


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