The principle of inversion is a common trick used by mathematicians but rarely practiced outside the discipline of mathematics. Reversing how you look at a situation can open up new possibilities and dislodge assumptions. 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.
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 isn’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 writes:
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.
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.
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 pre-mortem 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 pre-mortem, 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.
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.