Inverting your problems: what a detective, a mathematician and a billionaire have in common.

Invert, always invert (“man muss immer umkehren”) -  Carl Jacob

A rational thought process is difficult and hard to accomplish on a regular basis. In real life there are many variables to evaluate before making choices. That's why guys like Charlie Munger borrowed a highly useful idea from the great 19th Century German mathematician Carl Jacob

Jacob believed that the solution for many difficult problems could be found if the problems were expressed in the inverse – by working backward. As in most cases, we would do well to emulate Charlie here.


in WW2 another mathematician by the name of Abraham Ward was charged with finding a solution to solving the problem of B-17s being destroyed. The goal was to add more armor to the aircraft however, because armor is heavy and restrictive, they thought it best to add it in the most vulnerable locations to insure the pilot and aircraft made it back.

Most specialists who were also charged with answering this question, often looked at the problem from the outlook of where the planes that returned had been hit.

Abraham knew that the more useful data was in the planes that were shot down and unavailable; not the ones that survived. Solutions had to be “gathered” by induction in that instance.  This insight lies behind what we now call survivorship bias – our tendency to include only successes in statistical analysis, skewing or even invalidating the results.

Here is a another small example…

“Gregory (Scotland Yard detective): “Is there any other point to which you would wish to draw my attention?”

Holmes: “To the curious incident of the dog in the night-time.”

Gregory: “The dog did nothing in the night-time.”

Holmes: “That was the curious incident.”

Looking at the problem from the opposite end of the spectrum is how Sherlock, realized that the dog knew the person who had stolen the horse.

By looking at the question like “ why didn’t the dog bark?” instead of “ why would someone steal a horse?” Sherlock, was able to see the answer to the problem that others were not able to see.

Let's apply this to real life:

Imagine for a moment that you want to invest in a company like AT&T.

You have done your research and come to a reasonable value of say 260 billion dollars, you see that it is trading at 240 billion as of this writing. You think the margin of safety is large enough and you feel like you think AT&T has a solid moat ( competitive advantage) as you are about to get on the phone with your broker and order up 10,000 shares. Now before you hit that buy button you stop and think to yourself "How can investing in AT&T cause permanent loss of capital?"

Upon pondering this question you realize that AT&T spends most of its free cash on paying dividends. About 90% give or take. That's a red flag because if one company is paying most of its earnings in dividends then the company will not have much wiggle room to increase dividends if the company has a down year. That will lead to AT&T ensuring that it grows its earnings each and everyday. If not they will need to take on more debt or issue more shares to keep its dividend alive.

AT&T is what they call a dividend aristocrat. A dividend aristocrat is a company that has paid and increased its dividend for over 20 years. If AT&T can not increase its dividend that will spell doom for  the company at least in the short term and depending on if you are looking for a stable and secure dividend, the merits may say pass.

Knowing what can go wrong with this investment is one of the last steps in seeing if AT&T is a worthwhile investment. Once you have inverted the question(s) it's time to compare that worst case scenario to your next best alternative or opportunity cost.

Making sound rational choices is all we are trying to do. Charlie Munger once said, “ all I am trying to do is find out where I am going to die and never go there” Likewise we are trying to find the worst possible outcome, and avoid it at all costs.

Using tools from different schools of thought is the perfect way to solve such problems.

  1. Margin of safety from engineering
  2. Inverting for mathematics
  3. Opportunity cost from economics
  4. Cognitive bias identification form psychology

Using these ‘safety latches' can help us make rational choices. In thinking fast and slow  Daniel Kahneman tells us that we are prone to making quick decisions because we are hardwired to. Making rational choices goes against our DNA. We are designed to make use of biases, and stereotypes (past information) to make sweeping judgements that require little rational thought.

“Think forwards and backwards — invert, always invert.” “Many hard problems are best solved when they are addressed backward.” “The way complex adaptive systems work and the way mental constructs work is that problems frequently get easier, I’d even say usually are easier to solve, if you turn them around in reverse. In other words, if you want to help India, the question you should ask is not “how can I help India,” it’s “what is doing the worst damage in India? What will automatically do the worst damage and how do I avoid it?” “Figure out what you don’t want and avoid it and you’ll get what you do want. How can you best get what you want? The answer: Deserve what you want! How can it be any other way?” - Charlie Munger

“I think part of the popularity of Berkshire Hathaway is that we look like people who have found a trick. It’s not brilliance. It’s just avoiding stupidity.” - Charlie Munger

 “Let me use a little inversion now. What will really fail in life? What do you want to avoid?” “Having a certain kind of temperament is more important than brains. You need to keep raw irrational emotion under control.” “When you have a huge convulsion, like a fire in this auditorium right now, you do get a lot of weird behavior. If you can be wise [during such times, you’ll profit].” - Charlie Munger

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