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Consider the classic teaser of the mirror: why does a mirror seem to invert left and right but not top and bottom? That is, why are the letters of a book backward but not upside down, and why is your left hand the double’s right and your right the double’s left?

When we look into a mirror, we imagine ourselves turned left to right, as if we walked around a pane of glass to look the other way. This conventional perspective is why we cannot explain what is happening with a mirror. To understand a mirror’s image, you have to psychologically reverse the way you perceive your image. Imagine your nose and the back of your head reversed: if your nose points north, your double’s nose points south. The problem is on the axis running through the mirror. You have to imagine yourself reversed, “squashed” back to front. Stand in front of the mirror with one hand pointing east and the other west. Wave the east hand. The mirror image waves its east hand. Its west hand lies to the west. Its head is up and the feet are down. Once you look at a mirror with this perspective, you gain an understanding about the axis of the mirror.

Psychologically reversing the way, we perceive our image helps us understand a mirror. In the same way, reversing your perspective about problems sometimes will lead to a different insight or a quicker, easier solution to a problem. Add up the numbers 1 to 100. The task is not difficult, but it takes time and eventually we arrive at 5050 as the answer. Now imagine the numbers 1 to 100 written in a row. Now reverse the numbers and write them beneath the first row as follows:

Writing 1 to 100 you always increase by one. Reversing this to listing 100 to 1 you always decrease by one. Adding up each pair of numbers always gives you 101. So, the total is 100 X 101 = 10100. We’ve used two sets of numbers, so we divide by 2 to give us 5050. Reversing the numbers allows you to visualize the rows of numbers and to understand the sequence. You can then multiply and divide in your head and arrive at the answer quickly and with little chance of error as compared to the conventional method of addition.

Reversals generate a lot of provocative ideas in a short period of time. In one example, a manager for a major copier company reversed her company’s attitude toward the competition from non-cooperation to cooperation. The conventional thinking in the copier business is not to cooperate with your competitor in any way. Consequently, her company refused to service the competitors’ machines. She reversed this to a policy which publicly stated that the company would not only service the competition’s machines but would honor their service warranties as well. The policy was tremendously successful. It allowed the company to establish relationships with the competitor’s customers that eventually led to new sales.

When Henry Ford went into the automobile business, the conventional thinking was that you had to “bring people to the work.” He reversed this to “bring the work to the people” and accomplished this by inventing the assembly line. When Al Sloan became CEO of General Motors, the common assumption was that people had to pay for a car before they drove it. He reversed this to you can drive the car before you pay for it and, to accomplish this, he pioneered the idea of installment buying.

Years back, chemists had great difficulty putting a pleasant-tasting coating on aspirin tablets. Dipping tablets led to uneven and lumpy coats. They were stumped until they reversed their thinking. Instead of looking for ways to put something “on” the aspirin, they looked for ways to take something “off” the aspirin. This reversal led to one of the newer techniques for coating pills. The pills are immersed in a liquid which is passed onto a spinning disk. The centrifugal force on the fluid and the pills causes the two to separate, leaving a nice, even coating around the pill.

Physicist and philosopher David Bohm believed geniuses were able to think different thoughts because they could tolerate ambivalence between opposites or two incompatible subjects. Thomas Edison’s breakthrough invention of a practical system of lighting involved wiring his circuits in parallel and of using high-resistance filaments in his bulbs, two things that were not considered possible by conventional thinkers, in fact were not considered at all because of an assumed incompatibility. Because Edison could tolerate the ambivalence between the two incompatible things, he could see the relationship that led to his breakthrough.

In recent years, scientists have started looking through the other end of the telescope to find a different perspective about life. Instead of attempting to explain how the universe gave rise to life, they reversed this thinking and, now, start with life as a given and work the other way. Given that we are here, the initial conditions must have been a certain way. Reversing your problem helps you focus in a different way on the problem. If someone has been promoted ahead of you, you might define it as “This happened because the boss dislikes me.” Reversed, it becomes “It happened because I dislike the boss.” Does this way of looking at the problem change your perspective?

Michael Michalko is the author of the highly acclaimed Thinkertoys: A Handbook of Creative Thinking Techniques; Cracking Creativity: The Secrets of Creative Genius; ThinkPak: A Brainstorming Card Deck and Creative Thinkering: Putting Your Imagination to Work.

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