What’s the similarity between Andy Warhol and the GPS system?

USSR launched the Sputnik on 4 October 1957. And it took the world by storm! A man made satellite was orbiting the earth! But it spooked the Americans who thought that they were losing the space war. The Americans invested a lot of effort into tracking the orbit of Sputnik and any other satellites the USSR would launch.

Two researchers from the John Hopkins University found a novel solution to track the orbits. William Guier and George Weiffenbach figured out a way with which they could predict the position of Sputnik using doppler data from a single pass of the satellite! This meant that they didn’t have to follow and observe the satellite from multiple points. They could simply measure the doppler effect – the shifts in the radio signal of the passing satellite – to predict its orbit. It was a very hard problem to solve that required mathematical genius.

But it was an insight after their work that was the real genius. Frank McClure – the deputy director of the John Hopkins lab asked a question: can we invert the equation? If we can use doppler data from a stationary receiver to predict the orbit of a moving satellite, can we do the reverse too? Knowing the position and orbit of a satellite, could it locate any object on earth?

That question led to the discovery and development of the GPS system!

Andy Warhol’s strategy to make his art stand out

And apparently it’s the same strategy that Andy Warhol used to become a famous artist. What do you do to create art that stands out from the crowd? Invert. Do the opposite. “When you do something exactly wrong, you always turn up something.”

Warhol became the leader of “Pop Art”. Where everyday mundane objects like the Campbell soup cans became pieces of art! 

And then he repeated the feat. He took pictures of famous people and asked: how can I make them look different? He just inverted the colours! The same pictures in very weird colours became really famous!

Niels Bohr famously said: “The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth.” But it was a century before him when another mathematician showed us how to actually use profound truth for success.

Carl Jacobi is a German mathematician and a professor in the 1850s. When his students ask him what topics they should research for their thesis, his answer is: “Invert. Always invert.”

Inverting known results can open new fields of research.

What does this mean actually?

• Jacobi took a math problem. 
• And wrote its opposite – its inverse form. 
• And then tried to solve for the inverse.

Sometimes he would find that solving the inverse opens up a whole new field. And if the inverse led to a dead end, it would at least clarify the original problem a lot more in his mind! 

That’s how Jacobi discovered many of the properties of the theta functions and made huge advances in the field of elliptic functions!

How can you use this inverse strategy in non-math related subjects? 

Take a cue from Marie Kondo. She created a huge empire out of helping people declutter their homes. 

Before Kondo, decluttering meant discarding unwanted things. Kondo subtly but powerfully changed that. “We should be choosing what we want to keep, not what we want to get rid of.” Ask if something sparks joy. Retain it if it does, otherwise discard it. 

It’s such a subtle difference. You are still discarding and decluttering. But the change in focus made it a fun activity! Inversion helped Kondo become a phenomenon and enabled millions to declutter their homes without frustration.

Inversion means asking: what if the opposite is also true?

What if freedom does not require violence? What if work does not require an office space? What if you don’t require a 1000 fans to succeed? What if paintings don’t require an eye soothing colour palette? Everytime people have gone to find what lies on the opposite of an assumed truth, they’ve found a new way to grow.

Inversion doesn’t necessarily mean that the opposite will always be true. But it does mean that you’ll always be pushing the envelope.

When you chase the opposite, you’ll either find something true or novel. Or you will find more clarity on your existing path.

Action Summary:

• Make a list of your assumptions. Something you believe to be true. Then chase the opposite. There are two ways to do that. 
• Ask what if the assumption is wrong?
• Or make an opposite assumption and see if that could be true.