Rethinking Thinking

Creative Abstracting

By David Jiles, Ph.D.

(con't from page 1)

Abstracting, by simplifying, yields the common links, the nexuses, in the fabric of perception and nature. But seeing through the complexity of reality to discover these simple principles often takes the greatest genius. As Picasso said, “Whatever is most abstract may perhaps be the summit of reality,” (9) and as Werner Heisenberg wrote, “The step toward greater generality is always itself a step into abstraction — or more precisely, into the next highest level of abstraction; for the more general unites the wealth of diverse individual things.” (10) Nobelist Richard Feynman put it more simply still in one of his notebooks: “Phenomena complex — laws simple…. Know what to leave out.” (11)

Knowing what to abstract is and why it is so important, though, is only half the problem. The other half is learning how to find the simple concepts hiding among complex expressions. How do you do it? Fortunately, many creative people have left detailed records of how they invented their abstractions. One mistake many people make is to begin by ignoring reality. Bridget Riley, an artist famous for her nonrepresentational and op-art paintings, tells us that abstractions must evolve from something real. Observing that natural view is a first and important step for any artist. Even for someone like Riley, whose purpose in painting is to awaken “recognition of the sensation without the actual incident that prompted it,” the sensation must be experienced and understood and purified.

Picasso also cautioned other painters, “To arrive at abstraction, it is always necessary to begin with a concrete reality…. You must always start with something. Afterward you can remove all traces of reality. There’s no danger then, anyway, because the idea of the object will have left and indelible mark. It is what started the artist off, excited his ideas, and stirred his emotions.” (12) True to his word, Picasso began his well-known The Bull series with a realistic image of a bull. Then he became interested in the planes defining the bull’s form. But as he experimented with these planes, he realized that what defined them were their edges, which he then reduced to simple outlines. Finally, he eliminated most of these lines, leaving a pure outline that still conveys the essence of “bullness.” Note that the head, which is massive ion the original print, has become insignificant in the final print, yet we still have no difficulty recognizing the image as a representation of a bull. For Picasso, bullness was not the size or shape of the head but in other very simple features such as the horns. None of this was obvious at the outset.

The Bull by Pablo Picasso, 1946

The lesson we may draw is that many abstractions are possible for any given object, each of which illuminates some hidden truth. One might even say that reality is the sum of all possible abstractions and that in coming to know these possibilities, we understand reality better.

This is a lesson scientist, too, have learned. Biologists have often found it useful to “cut” — sometimes literally — the objects of their study into various forms to study their fundamental structures.

Thus, nineteenth-century botantists such as Asa Gray frequently characterized flowers by means of a series of abstract sections, none of which, singly, looks like the flower as we view it. To understand the development of the structure of a fruit, such as a pineapple, botanists have cut through the outer surface and flattened it out. In this abstraction a previously hidden pattern suddenly emerges from the apparent randomness of the fruit’s surface.

Indeed, a mathematician can take this pattern a step further by writing an equation for it, as Leonardo Fibonacci did in the twelfth-century. He developed a sequence of numbers (1, 2, 3, 5, 8, 13, 55 …each number is the sum of the previous two). This sequence gives us some of nature’s common patterns.

Plants do not know about this sequence — they just grow in the most efficient ways. Many plants show the Fibonacci numbers in the arrangement of the leaves around the stem. Some pine cones and fir cones also show the numbers, as do daisies and sunflowers. Sunflowers can contain the number 89, or even 144. Many other plants, such as succulents, also show the numbers. Some coniferous trees show these numbers in the bumps on their trunks. And palm trees show the numbers in the rings on their trunks.

Why do these arrangements occur? In the case of leaf arrangement, or phyllotaxis, some of the cases may be related to maximizing the space for each leaf, or the average amount of light falling on each one. Even a tiny advantage would come to dominate, over many generations. In the case of close-packed leaves in cabbages and succulents the correct arrangement may be crucial for availability of space.

So nature isn't trying to use the Fibonacci numbers: they are appearing as a by-product of a deeper physical process. That is why nature’s spirals are imperfect.

The plant is responding to physical constraints, not to a mathematical rule. The basic idea is that the position of each new growth is about 222.5 degrees away from the previous one, because it provides, on average, the maximum space for all the shoots. This angle is called the golden angle.

Probably most of us have never taken the time to examine very carefully the number or arrangement of petals on a flower. If we were to do so, we would find that the number of petals on a flower that still has all of its petals intact and has not lost any, for many flowers is a Fibonacci number.

Continue to article page 3 »

© 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.

04/24/08