Watch this one minute video  and when you’re done smiling, think about the problem in a rational way.
At first, the problem seemed that the kid had his head stuck between the iron bars. Although nobody saw how the kid’s head really got trapped in the first place – they just assumed that he somehow managed to slide his head through the narrow bars. Naturally, the intuitive solution was to pull the head in the same way it got stuck – which obviously didn’t seem to work.
But the right solution appeared when people stood the problem on its head (no pun intended) i.e., instead of trying to pull the head they pushed in the body through the trap. They inverted the problem and voila! Problem solved.
That’s called principle of inversion. It’s a common trick used by mathematicians but rarely practiced outside the discipline of mathematics. Carl Jacobi, a German mathematician, said, “Invert, always invert”, expressing his belief that the solution of many hard problems can be clarified by re-expressing them in inverse form.
Charlie Munger, the business partner of Warren Buffett and Vice Chairman at Berkshire Hathaway, came up with his own version of Jacobi’s maxim –
All I want to know is where I am going to die so that I’ll never go there.
Munger is 91 years now so I guess his strategy has worked out pretty darn well so far.
It is not enough to think about difficult problems one way. You need to think about them forwards and backwards. “Indeed,” says Munger, “many problems can’t be solved forward.” You should read how inversion was used by one of Munger’s family members to guess the correct answer to a trivia question .
Roger von Oech’s Creative Whack Pack is a great tool to instil Munger’s way of thinking – combining various ideas from different spheres of life and joining them to create a process of thinking creatively. Here is what the Inversion card says –
Reversing how you look at a situation can open up new possibilities and dislodge assumptions. Example: When everyone else is gazing at a glorious sunset, why not turn around to see the blues and violets behind you? What do you notice when you look at a coffee cup? Its design or color? Reverse your focus and look at the space inside – that’s what gives it its functional value.
Inversion and Proofreading
In this short video , a chess grandmaster walks us through retrograde analysis, which is a method to solve game positions in chess by working backwards from known outcomes. Even if you don’t play chess, you should watch it because it has interesting insights about problem solving.
As mentioned in the video, reading a text backwards reveals glaring errors which aren’t normally caught while you’re reading forward.
The reason this trick works is because when you are proofreading, especially your own work, your brain has a tendency to start skimming through the material and jumping from one sentence to the next. When it does this, it is very difficult to catch mistakes because you can very easily look past them as you are reading. When you go through your essay or article backwards you will catch more mistakes because each sentence is taken out of context so that you can focus on it by itself. Also, it’s easier to spot errors when you view words in a different order.
This cool inversion hack tricks your brain into looking at everything in a different way.
Another useful way to think about forward vs backward thinking is to model them as additive vs subtractive measures. Additive measures manifest in form of an urge to do something about a problem which may not need any intervention . Subtractive measures adhere to the philosophy of “don’t try to fix something which ain’t broken.”
Nassim Taleb calls this ‘subtractive epistemology’. He argues that the greatest and most robust contribution to knowledge consists in removing what we think is wrong. According to him we know a lot more about what is wrong than what is right. What does not work, that is negative knowledge, is more robust than positive knowledge. This is because it’s a lot easier for something we know to fail than it is for something we know that isn’t so to succeed. He dubs this philosophy as Via Negativa.
Taleb has written a whole book, The Black Swan , based on this idea that the absence of evidence doesn’t qualify as the evidence of absence. In other words, just because all the swans, that have been observed so far, are white doesn’t prove that all swans are white. Since one small observation (spotting a black swan) can conclusively disprove a statement – all swans are white – while millions can hardly confirm it, disconfirmation is more rigorous than confirmation.
Inverting the problem not just helps you in solving the problem, but it will also help you in avoiding trouble.
So how does this idea translate into practice? It’s a choice between avoiding stupidity and seeking brilliance.
A lot of success in life and success in business, says Munger, “comes from knowing what you really want to avoid-like early death and a bad marriage.” He continues –
What will really fail in life? What do we want to avoid? Some answers are easy. For example, sloth and unreliability will fail. If you’re unreliable it doesn’t matter what your virtues are, you’re going to crater immediately. So, faithfully doing what you’ve engaged to do should be an automatic part of your conduct. Of course you want to avoid sloth and unreliability.
It’s a common knowledge that to succeed you should find role models and follow them. But it would be equally effective, and perhaps even more, to find anti-models – people you don’t want to resemble when you grow up. And then avoid the path they took.
In Business and Decision Making
John Paul Getty, an American business tycoon, said –
In every business deal or transaction, identify the worst thing that can possibly go wrong, and then make sure it doesn’t happen.
Donald Keough in his book The Ten Commandments for Business Failure  (a book recommended by Warren Buffett) used the inversion principle by showing the direct paths to failure. He talks about things like – not taking risks, being inflexible, playing the game too close to the foul line, etc. These are precisely the things that one can do to ensure a failure in business. Hence avoid them like a plague.
Jeff Bezos, founder and CEO of Amazon, used the inversion principle to break his dilemma about leaving a high paying job and starting Amazon. He recounts –
When you are in the thick of things, you can get confused by small stuff. I knew when I was eighty that I would never, for example, think about why I walked away from my 1994 Wall Street bonus right in the middle of the year at the worst possible time. That kind of thing just isn’t something you worry about when you’re eighty years old. At the same time, I knew that I might sincerely regret not having participated in this thing called the Internet that I thought was going to be a revolutionizing event. When I thought about it that way … it was incredibly easy to make the decision.
Have you heard of post-mortem technique? When a project fails, typically the stakeholders get together and do the root cause analysis trying to figure out the reason for failure and possible learnings from the mistake. It’s a good practice but it’s not sufficient. You need to again apply the inversion principle here. How?
Instead of doing post-mortem at the end, why not do a premortem at the beginning. Sounds confusing? Here is how it’s done.
Before getting started, assume that the project has failed (or in case of a personal decision, assume that it has backfired) one year down the line. That done, run your imagination wild and come with possible reasons for failure. So in a premortem, you think of ways in which the project in its current form is destined for failure before the launch . It’s not easy but if you want to exploit the inversion mental model, it’s something which you should definitely give a try.
In his Art of Investing workshops, Vishal talks about the concept of reverse DCF. The idea is that instead of asking what’s the present value of future cash flows, ask what growth rate market is assuming to justify the present value of future cash flows. Valuation, being an imprecise art, is a good candidate for inversion.
By thinking forward (i.e. by estimating present value of future cash flows), we are prone to making mistakes. By thinking backward, we create a sanity check on thinking forward.
From perspectives on floats to risk arbitrage – everything can be investigated using the lens of inversion. And there is only one place where you can find truck loads of such insights about how to use inversion for stock analysis. That’s Prof. Sanjay Bakshi’s blog . Just go and search for the word “inversion” on his blog – the results would keep you busy for weeks.
Remember Warren Buffett’s rules of investing?
Notice the core message here. It’s not focussing on how to make money, instead it asks you to invert the problem and ensure that you don’t lose money. Put simply, to implement the inversion principle in stock picking, you need to focus less on –
- How to earn great returns, and more on how to avoid permanent capital loss;
- How to pick the great stocks, and more on how to avoid the dangerous ones;
- Things to do for investing success, and more on things to avoid for investing failure.
The inversion trick is a very powerful idea because it de-biases us. Backward thinking makes us more objective. And in business and life, just as in algebra, inversion will help you solve problems that you can’t otherwise handle.
Every time you learn a new mental model your scaffolding, to retain information in useful way, becomes stronger. A wise man once said – A man’s mind stretched to a new idea never goes back to its original dimensions.
I hope that practicing inversion will stretch your mind and build stronger thinking muscles which will make you a better decision maker.
Take care and keep learning.