The idea of inversion was introduced to me by a guy named Carl Jacobi. I heard the quote "invert, always invert" and thought it was a great concept so I dug around to find out who said it.
For a great article on using inversion to solve real problems, you can read this post. If you don't want to bother the summary is that the problem of trying to keep B17s from being shot down during WWII was looking at bullet patters on the planes that returned and then extrapolating that where there were NO bullet holes must be where the planes are weak (because the weak planes didn't return).
This is classic inverted thinking. You look at information from the opposite point of view. The absence of data can be more meaningful than the presence of data.
Why is this hard?
Many things work against this kind of thinking. The most obvious one is that we have WAY too much information around us... so it's unlikely that we will get through this information and find our way to the non-information.
Another reason is that it's much more difficult mentally. If I show you a pretty graph with nice pictures and well stated text your natural thinking process attempts to understand what is being said. Only afterwards and with much deliberation will you consider what is NOT being said. What we can see overwhelms our mental processes making it very difficult to contemplate what can not be seen.
Why is inversion valuable?
I am a firm believer that value and difficulty tend to be related. Inverted thinking is valuable because it is hard. Because it is hard, less people do it less frequently and thus the insights it can provide are discovered with less frequency. Therefore it pays to practice it on things that aren't that important, just to get the knack.
I also think it's valuable because it forces you to look at things in a much clearer way. It tends to be "unnatural" and a bit ridiculous to invert some things... sort of like a child constantly asking why. And yet. It can be really enlightening.
OK. How can I practice?
Well... it's actually not that hard to do. I'll take a few contemporary examples.
1) It believe Donald Trump is a self-serving bigot who should never be president.
OK. That's a sentiment I hear a lot these days. Let's invert it... and see what happens.
Step 1: Inversion: Assume I believe that Donald Trump is a giving uniter who wants what's best for people and would be a great president.
Step 2: What would have to be true for that statement to hold? What would I have to believe that I don't? What would I have to assume is true that I believe is false?
This forces me to take a position I don't hold and then imagine myself believing something completely different. That's the first step to understanding an opposing point of view which is one of the benefits of inverted thinking!
Inversion can be used in goals as well!
2) I want to lose weight and get in shape.
This is a pretty popular and valuable goal that few people attain. Let's invert
Step 1: I want to get really fat and out of shape.
Step 2: What do I need to do to accomplish that goal? Eat all the unhealthy food I want. Lead a sedentary lifestyle. Avoid the discomforts of physical activity.
That gives me a nice list of things that I would do if I wanted to get fat. That may seem obvious, but I think that when I make that list I find that a lot of it is about delayed gratification and discomfort. Thus, I could conclude that if I want to lose weight and get in shape, I must embrace discomfort and instant gratification.
That's quite different than buying exercise programs, a gym membership and fancy workout clothes.
So next time you find yourself thinking something that is obvious or seeing something that you are trying to understand, practice inverting it. Why is there rush hour traffic? Why do we pay $5 for coffee? What causes cancer (Mole rats never get cancer)?
Those are all questions that you can practice inversion on.