Topologists know that the shape of a doughnut can transform into the shape of a coffee mug. The two forms are homotopic or isotopic. For many of us, the transformation seems a stretch, especially when we dunk our doughnuts into our coffee. We think, “These don’t look alike. How can they be the same?”
But the reality is that the shape of a doughnut can be transformed into the shape of a mug, and the opposite transformation is just as easy. We can with a little practice visualize the change, and there are plenty of diagrams, drawings, and videos to help us see how one can become the other.*
The difficulty we might have in visualizing the change is related to another change we find difficult to perceive: That a troubled person can change into an untroubled person. We think the shape of a life that we know is the only shape it can take. Lives, like coffee mugs and doughnuts, can be altered.
“No, I can’t believe he’s (she’s) changed. Once an/a (addict, criminal, liar, uneducated person, etc.), always an/a (________). People don’t change,” you might hear or say.
All of us can take a lesson from topology. Every mug is a potential doughnut, and every doughnut is a potential mug. Transformation is possible with imagination, mental manipulation, and practical application of a psychological topology.
When we look on our lives to see the many transformations we have undergone, we realize that transformation is built into the geometry of life. Become a topologist. Look for the hidden shape in the lives in need of transformation.
* https://en.wikipedia.org/wiki/Homotopy
http://www.bing.com/videos/search?q=video+on+topology+doughnut+to+mug&&view=detail&mid=65DDE6EF2751207E685365DDE6EF2751207E6853&rvsmid=10BD1E3736A280E247BB10BD1E3736A280E247BB&fsscr=0&FORM=VDQVAP
But the reality is that the shape of a doughnut can be transformed into the shape of a mug, and the opposite transformation is just as easy. We can with a little practice visualize the change, and there are plenty of diagrams, drawings, and videos to help us see how one can become the other.*
The difficulty we might have in visualizing the change is related to another change we find difficult to perceive: That a troubled person can change into an untroubled person. We think the shape of a life that we know is the only shape it can take. Lives, like coffee mugs and doughnuts, can be altered.
“No, I can’t believe he’s (she’s) changed. Once an/a (addict, criminal, liar, uneducated person, etc.), always an/a (________). People don’t change,” you might hear or say.
All of us can take a lesson from topology. Every mug is a potential doughnut, and every doughnut is a potential mug. Transformation is possible with imagination, mental manipulation, and practical application of a psychological topology.
When we look on our lives to see the many transformations we have undergone, we realize that transformation is built into the geometry of life. Become a topologist. Look for the hidden shape in the lives in need of transformation.
* https://en.wikipedia.org/wiki/Homotopy
http://www.bing.com/videos/search?q=video+on+topology+doughnut+to+mug&&view=detail&mid=65DDE6EF2751207E685365DDE6EF2751207E6853&rvsmid=10BD1E3736A280E247BB10BD1E3736A280E247BB&fsscr=0&FORM=VDQVAP
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