Rethinking Thinking

Dimensional Thinking

By David Jiles, Ph.D.

Imagine what the weightlessness of space travel may someday allow dancers to do. No longer imprisoned on a surface by gravity, they will truly be free to move in three dimensions. However they will have to contend with spatial inertia — a completely different physical problem, as astronauts and cosmonauts have already discovered. Twist a wrench and it twists back. Newton’s principle that every action has an equal but opposite reaction reigns supreme, unmitigated by the gravity and friction that governs us here on Earth. If you move your hand one way in space, your body wants to go the other way to keep the center of gravity where it was. No floor to counteract the movement. No up, no down. The spatial limitations for dance, sports, arts, games, and sciences are almost unimaginable. Simple games like billiards, when translated from two to three dimensions, may become so esoteric that only the best mathematicians can play it. Does that sound crazy?

Dimensional thinking involves moving from 2-D to 3-D or vice versa; mapping, or transforming information provided in one set of dimensions to another set; scaling, or altering the proportions of an object or process within one set of dimensions; and conceptualizing dimensions beyond space and time as we know them. Every time we make a paper airplane from a flat piece of paper and send it flying or draw a map of the neighborhood with directions to our house we are using dimensional thinking. We scale things when we convert a recipe for two into a recipe for twenty. Dimensional thinking pervades our lives.

We have all seen footprints in the mud, snow, or concrete and inferred what a person or creature left them there. We have all noticed how our shadow follows us around like some misshapen ghost. These phenomena are all projections, or maps of some or all of a body onto a relatively flat plane, representations of a 3-D object in 2-D. Such representations are of major importance to a number of professions. Archeologists and forensic experts must reconstruct the size, weight, and height of an individual from footprints or other indentations left by bodies in the ground. Intelligence analysts must draw three-dimensional inferences from two-dimensional photographs taken by reconnaissance aircraft and “spy satellites.” Physicians analyzing x-ray photographs, CAT (computerized axial tomography) scans, or MRI (Magnetic resonance imaging) results see only static slices through their patients’ bodies, but they have to interpret what they see in terms of dynamic living beings. The medical literature is now full of articles discussing three-, four-, five-, and even six-dimensional analyses of techniques ranging from calculation of proper corrections for visual defects such as myopia to facial reconstruction during plastic surgery. Sonograms and positron emission tomography (PET) scans allow us to view the body and its functions not only in space but over time.

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© David Jiles, Ph.D. All rights reserved.

About the Author | More by David Jiles
David Jiles, Ph.D. latest book is Creativity and the Secret Language of the Mind (LuLu Press, 2007). In an effort to re-think thinking, he has examined the best creative thinkers e.g. Einstein, Hemingway, Picasso, Tesla, Beethoven and countless others to find common secrets towards creative thinking.

07/12/08