What's the point of √2; Being irrational and a mental model

Invert, invert and invert.

Hey

Welcome to another fresh edition of Atomic Ideas newsletter, where I bring you atomic idea curated from the world’s best books.

Talking about square root √2, the story goes that Hippasus, a follower of Pythagoras spent a lot of time and effort solving for √2.

Frustrated after many futile attempts, Hippasus decided to take the reverse route, thinking about what the square root of 2 might imply, and started working backwards from there.

If he couldn’t find it the way he had expected to, he’d start by proving what the number couldn’t be.

And this process led to the discovery of irrational numbers, which changed mathematics forever!

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Talking about mathematics, one of the core framework in proving any theorem is to invert. That is, look for all possible non-answers, till you have figured out the right one.

And that leads us to a mental model widely used by successful people, inversion.

Ideas from the book, The Great Mental Models by Shane Parrish.

“He wins his battles by making no mistakes” Sun Tzu

Inversion Mental Model

Inversion is a powerful tool to improve your thinking because it helps you identify and remove obstacles to success.

The root of inversion is “invert,” which means to upend or turn upside down. As a thinking tool it means approaching a situation from the opposite end of the natural starting point.

Most of us tend to think one way about a problem: forward. Inversion allows us to flip the problem around and think backward. Sometimes it’s good to start at the beginning, but it can be more useful to start at the end.

Think of it this way: Avoiding stupidity is easier than seeking brilliance. Combining the ability to think forward and backward allows you to see reality from multiple angles.

Inversion is counterintuitive. It forces you to treat your decisions like a court of law. In court, the jury has to listen to both sides of the argument before making up their mind. Inversion helps you do something similar.

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How do I apply inversion in my life?

There are two approaches to applying inversion in your life.

1. Start by assuming that what you’re trying to prove is either true or false, then show what else would have to be true.

2. Instead of aiming directly for your goal, think deeply about what you want to avoid and then see what options are left over.

We frequently employ optimistic objectives, such "I want to be wealthy," to direct our efforts. We choose our careers and investments based on our desire to amass wealth. We seek out mystical answers, such as trying to outwit the stock market. These eventually lead nowhere, and in the process, we frequently take awful risks that make us worse off.

We can try flipping the goal as an alternative. It turns into avoiding poverty rather than being wealthy. Instead of attempting to predict the choices that will increase wealth, we first attempt to stop the actions that are certain to deplete it. Of course, there are a few that are rather evident!

When to use inversion?

When you are stuck.

Psychologist Kurt Lewin shares 5 step process to start your inversion journey.

1. Identify the problem

2. Define your objective

3. Identify the forces that support change towards your objective

4. Identify the forces that impede change towards the objective

5. Strategize a solution! This may involve both augmenting or adding to the forces in step 3, and reducing or eliminating the forces in step 4.

I hope this was useful.

If you wanna brainstorm on a specific problem you are trying to solve and explore where you can use inversion, just hit the reply button.

Till next week.

Sinha