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"Coefficient of Restitution" mind matters
November 18, 2002
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When a something flexible is dropped, it bounces.

How high it bounces is dependent upon the coefficient of restitution. This is a mathematical property which allows us to predict how far an object will rebound. The formula isn't complicated mathematically -- the coefficient is equal to the square root of the ratio of bounce height to drop height -- but it's a number determined only through experimentation. The coefficient of restitution is always less than one. If it were exactly one, then the object would bounce all the way back up (and never stop bouncing).

A regulation tennis ball, for example, is required to bounce at least 53 inches when dropped from the height of 100 inches. The coefficient of restitution is therefore equal to the square root of 0.53, or approximately 0.728. In comparison, a wet wad of paper has a coefficient of restitution equal to zero. It just goes plop.

This idea got me wondering about the idiom "bouncing back." It's a phrase used in response to defeat or loss. A company's stock price might drop 20 points, but if it "bounces back" it should regain the entire loss. When a couple breaks up, we hope they'll bounce back over time, recovering their emotional well-being. The problem with how we use this expression is that the coefficient of restitution can't be equal to one. We expect things to go back to their original state.

This is psychologically (and mathematically) impossible. Changes in our lives are responsible for changes within us. We become different people. We grow. Conflict and failure educate us, granting us strength and wisdom. To bounce back entirely -- to maintain a coefficient of one -- is to stagnate and deny our feelings. Life is challenging enough without insisting on mathematically perfect recovery.

Remember, the coefficient of restitution doesn't depend on external forces. Regardless of how high the tennis ball is when it drops, its bounciness is the same. Drop it from a greater height and it will bounce more. At extreme heights there are other forces at play, like the wind resistance on the tennis ball's nap, but these are external forces.

The "bounciness" of people is part of their nature. Some recover well, and some are sore losers. Our inherent qualities of emotional strength, sense of humor, and sense of reason contribute to our recoverability. Recovery may be difficult, but it's always just as likely. This means that we are going to recover from a death in the family just as often as we can for a failed investment, or a bad golf game. In other words, if you can survive a bad hair day, you can survive anything. Hard to believe, isn't it?

But our coefficients of restitution are entirely within our control. We can train ourselves to bounce back better when the small stuff goes wrong. We can become better losers and to take criticism less personally. We can accept our failures by simply trying again, and soon. Why be a depressing wet blanket when you can be a strong, whole human being?

Have you ever seen a wet blanket bounce?

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Copyright 2002 Seth Maislin


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