Inversion : A useful Thinking Tool

All I wanted to know where I'm going to die and then I'd never go there. Charlie Munger

Let's draw an analogy to understand what inversion means. Assume you were sleeping, in your dreams you were thrown in a forest. It's very haunting place and you desperately wanted to go home. Suddenly, sky starts thundering and raining. To go to your home you need to cross a river which starts overflowing because of heavy rain. Unfortunately, you don't know how to swim. Since you desperately wanted to go home but the problem is how to cross a river?

In your mind you have inverted the problem i.e You already crossed the river.How? With the help of a bridge. How to build a bridge? With a help of woods. Where does the woods come? From the forest. Indeed, there are plenty of woods in the forest. Wow!!! in your mind you have solved this problem. Now you need to execute your plan by reversing your thought process.

Search for woods-->Build a bridge-->Cross the river-->Go to your home.(You saved yourself by using the inversion principle)

Someone asked the 19th century German mathematician What's the secret of your mathematical discoveries. He replied "You must always invert."

G Polya in "How to Solve it" defined Inversion as

In Inversion, we start from what is required, we take it for granted, and we draw consequences from it, and consequences from the consequences, till we reach at a point that we can use a starting point in synthesis. For inversion we assume what is required to be done as already done (what is sought as already found, what we have to prove as true). We inquire from what antecedent the desired result could be derived; then we inquire again what could be the antecedent of that antecedent, and so on until passing from antecedent to antecedent, we come eventually upon something already known or admittedly true. This procedure we call inversion.

Can we use this principle across multiple disciplines? Yes, of course we can.

LIFE

When we were born we also carried the seed of death along with ourselves. Life and death are the two opposite sides of the same coin. I came across this beautiful anecdote in the book " Seven Habits of Highly Effective people" where Stephen Covey writes:

In your mind's eye, see yourself going to the funeral of a loved one. Picture yourself driving to the funeral parlor, parking the car, and getting out. As you walk inside the building, you notice the flowers. You see the faces of friends and family pass along the way. You feel the shared sorrow of losing, the joy of having known, that radiates from the hearts of the people there. As you walk down to the front of the room and look inside the casket, you suddenly come face to face with yourself. This is your funeral, unknown years from today. All these people have come to honor you, to express feeling of love and appreciation for your life. As you take a seat and wait for the services to begin, you look at the program in your hand. There are to be four speakers. The first is from your family, immediate and also extended. The second speaker is one of your friends, someone who can give a sense of what you were as a person. The third speaker is from your work or profession. And the fourth is from some community organization where you have been involved as a person.

Now think deeply. What would you like each of these speakers to say about you and your life? What kind of husband, wife, father or mother would you like their words to reflect? What kind of son or daughter or cousin? What kind of friend? What kind of working associate?

What characters would you like them to have seen in you? What achievements, what contributions would you want them to remember? Look carefully at the people around you. What difference would you like to have made in their lives?

In this anecdote Stephen Covey have inverted the entire process. He started with death, move backwards and reached at present situation. Answer those questions honestly, start taking actions in specific direction so that you don't have any regret when you will die.

High Stake Decisions

Most of us heard about postmortem. It means doctors convene to examine the causes of an unexpected death of a patient so that they can learn and improve themselves if they encounter similar circumstances in future. Inversion of Postmortem is premortem a term defined by psychologist Gary Klein. Suppose you have to take a high stake decision, organize a meeting invite all the knowledgeable people who have expertise in that field. Ask them we have taken the decision and it failed spectacularly. What are the possible reasons? List them. Use them as a checklist while taking decision. It doesn't ensure success but chances of failure would be reduced drastically.

Productivity

Wanna increase your productivity. Ask yourself How can I decrease my productivity?

1. By watching too much television.

2. Using Social media.

3. Playing too much video games.

.......

Don't do them. Hence productivity will increase

Avoiding Stupidity is better than seeking brilliance. Shane Parish

RELATIONSHIPS

Relationships: Wanna foster your relations with your loved ones. Ask yourself How can I destroy relations with my loved ones?

1. Getting angry on trivial things.

2. Not being loyal to them.

3. Backstabbing.

4. Using them as a thing.

5. Don't care about their feelings.

.....

Don't do them. Hence relationships will foster.

Mathematics

There is a river and you have 4 litres and 9 litres bottle at your disposal. Can you bring 6 litre water with the help of 4 litre and 9 litre bottles?

Invert, my dear invert. Assume 6L water is already present in 9L bottle. What are its consequences?

Using 4L bottle fill 9L bottle. We get 1L water in 4L bottle.

We got new problem 1L water in 4L bottle. What are its consequences?

Add 1L water from 4L bottle into 9L bottle. Can we reach at out initial condition. Let's see.

Add 4L water from 4l bottle into 9L bottle. We get 5L water in 9L bottle.

We got another new problem 5L water in 9L bottle. Can we reach at initial condition. Let's see.

Again, add 4L water into 9L bottle. We got 9L water in 9L bottle. Wow!!! we reach at initial condition. Reverse the process and problem is solved.

Conclusion: First get 5L water then 1L water. We got 6L water.

Are prime numbers finite or infinite?

Invert, my dear Invert. Assume prime numbers are finite. As we know prime numbers are atomic number i.e every number is written as the sum of two prime numbers. Total prime numbers are 2,3,5,......,q. q is the largest prime number.

Let's define r = (2*3*5*.....*q)+1. It's the multiplication of all prime numbers plus 1.

It means r is also a prime number.Why? Because r is not divisible by any number except 1 and itself. Hence we got a prime number greater than q which contradicts our assumption. Hence prime numbers are infinite.

Watch this wonderful video on Inversion.

Cosmology

How did universe began?

Scientist think that universe began because of Big Bang. What is Big Bang?

Big Bang suggested that the universe began at a definite moment in time, in a strange kind of explosion. Do we have any evidence to support it?

In "The Magic of Reality" Richard Dawkin explains:

A spectroscopy is a rainbow machine. If it is attached to a telescope, it takes the light from one particular star or galaxy and spreads it out as a spectrum....

When starlight is splayed out by a spectroscope, strange pattern of thin black lines appear in a very particular places along the spectrum. These lines are known as Bar codes. And what makes these bar codes, it turns out its different elements. For eg: Sodium has prominent lines in the yellow part of the spectrum....

If you look at the sodium spectrum from a star in a different galaxy. You get a fascinatingly different pictures. Sodium light from a distant galaxy has the same pattern of bars spaced at the same distance from each other but the whole pattern is shifted towards the red end of the spectrum. The same thing happened with not only sodium but with every other element. This shift towards the red end of spectrum is known as Hubble shift or Red shift.

Why does it shift towards the red direction? Because of doppler effect. Doppler effect means if the source of the wave and the person(who is looking or listening the wave) is moving towards each other the wavelength of the wave decreases. Hence shifted towards blue side. If the source and the listener is moving away from each other, wavelength increases. Hence shifting towards red direction.

What it has to do with inversion?

Dawkin explains if an astronomer is looking at a star in different galaxy and the bar code is shifted towards red direction. It means galaxy is moving away from us at a very high speed which means whole universe is expanding. Why aren't you and me rushing away from each other? The reason is the things which are very close to each other like everything in a galaxy. They feel the strongest pull of gravity from their neighbors. This holds them together while the distant objects recede away from each other.

Astronomers used inversion, looked at expansion and work backward through time. It is as if they constructed a movie of expanding universe with the galaxy rushing apart and they ran the film in reverse. Instead of hurtling away from each other in backward film the galaxies converge which eventually reach at a moment when the expansion of universe must have begun. Hence Big Bang.

We can use this principle in almost every part of our life. Keeping this model in mind will definitely help us in improving the quality of our life.