THOUGHT EXPERIMENT. The figure below is a square defined by four dots. A square is a rectangle with four equal sides and four 90-degree angles. Your challenge is to move 2 dots and create a square twice as big as the one defined by the dots as they are presently arranged. Try to solve this before you read further.The reason many of us have difficulty with this problem is the definition of the word square. The word square biases our perception of the problem which closes off but one line of thought. Consequently, we try to solve it by keeping the sides of the larger square parallel with the smaller one. That won’t work.
Leonardo Da Vinci believed that to gain knowledge about the form of problems, you began by learning how to restructure it to see it in many different ways. He felt the first way he looked at a problem was too biased toward his usual way of seeing things. He would restructure his problem by looking at it from one perspective and move to another perspective and still another. With each move, his understanding would deepen and he would begin to understand the essence of the problem. Leonardo called this thinking strategy saper vedere or “knowing how to see.”
A different way to look at our problem is to tilt the diagram so that it is standing vertical on one dot. Now you realize that you can think of the illustration as a diamond with a point. Then by connecting one diagonal and then moving the two other dots to make the remainder of the points, you’ve got a square twice as large as the original one. Reframing the square as a diamond put it into a different framework for context than it was previously been perceived and the problem is more easily solved.
If you survey the history of the world, it is apparent that most individuals who have created radical innovations did not do so simply because they knew more than others. A great deal of our education may be regarded as the inculcation of mindsets. We were taught how to handle problems and new phenomena with fixed mental attitudes (based on what past thinkers thought) that pre-determine our response to problems or situations. Consequently, we tend to process information the same way over and over again instead of searching for alternative ways. Once we think we know what works or can be done, it becomes hard for us to consider alternative ideas. We tend to develop narrow ideas and stick with them until proven wrong.
Creative thinking requires the generation of alternative perspectives. One can always look at a system from different levels of abstraction to create different perspectives. A very fine-grained description of a beach would include every position of every grain of sand. Viewed from a higher vantage point, the details become smeared together, the grains become a smooth expanse of brown. At this level of description, different qualities emerge: the shape of the coastline, the height of the dunes, and so on.
In the 1950s, experts believed that the ocean-going freighter was dying. Costs were rising, and it took longer and longer to get merchandise delivered. The shipping industry experts built faster ships that required less fuel and downsized the crew. Costs still kept going up, but the industry kept focusing its efforts on reducing specific costs related to ships while at sea and doing work.
A ship is capital equipment and the biggest cost for the capital equipment is the cost of not working, because interest has to be paid without income being generated to pay for it. Finally, an outsider abstracted the challenge from how to build more efficient ships to how can the shipping industry reduce cost.
This allowed them to consider all aspects of shipping, including loading and stowing. The innovation that saved the industry was to separate loading from stowing, by doing the loading on land, before the ship is in port. It is much quicker to put on and take off preloaded freight. The answer was the roll-on, roll-off ship and the container ship. Port time has been reduced by three quarters, and with it, congestion and theft. Freighter traffic has increased fivefold since this innovation and costs are down by 60%.
Abstraction is one of the most basic principles in restructuring a problem. For instance, the standard procedure in physical science is to make observations or to collect systematic data and to derive principles and theories. Einstein despaired of creating new knowledge from already existing knowledge. How, he thought, can the conclusion go beyond the premises? So he reversed this procedure and worked at a higher level of abstraction. This bold stance enabled him to creatively examine first principles (e.g., the constancy of speed of light independent of relative motion). The abstractions that others were not willing to accept because they could not be demonstrated by experimentation, Einstein took as his starting premise and simply reasoned from them.
Even Galileo used thought experiments to abstract to a possible world in which a vacuum exists. In this way he could propose the astounding hypothesis that all objects fall through a vacuum with the same acceleration regardless of their weight. There were no laboratory vacuums large enough to demonstrate this spectacular idea until years after Galileo’s death. Today, this demonstration is standard fare in many science museums, where there are two evacuated columns in which a brick and feather released at the same moment fall side by side and hit the floor together.
Consider the incredible opportunity that the U.S. Postal Service and UPS both missed by failing to create an “overnight” delivery service. Their entire focus was on using established systems and theories to create the service. If, for instance, using the established system you want to connect one hundred markets with one another, and if you do it all with direct point-to-point deliveries, it will take one hundred times ninety-nine — or 9,900 — direct deliveries. They failed to look for alternative ideas and simply concluded that the cost was prohibitive. There was no way they could make it economically feasible.
It took an individual who looked at the problem in a different way to solve the problem. After a tour of duty with the Marines in Vietnam, Fred Smith returned home in 1971 to find that computers were becoming an indispensable part of doing business and delivery systems were not keeping up with the increased demand for speed and reliability when delivering computer parts.
Fred abstracted the problem from delivery services to one of “movement.” How do things move?
He thought about how information is moved, and how banks move money around the world. Both information systems and banks, he discovered, put all points in a network and connect them through a central hub. He decided to create a delivery system — Federal Express, now known as FedEx — that operates essentially the way information and bank clearinghouses do. He realized that a hub-and-spoke network could create an enormous number of connections more efficiently than a point-to-point delivery system. The delivery system he conceived used both airplanes and trucks, which was unheard of at the time. His system was 100 times more efficient than existing systems at the time and was subsequently employed in, of course, all air cargo delivery systems in the airline industry.
Robert Dilts, an expert in Neuro Linguistic Programming (NLP), wrote about an enlightening experiment which was done by gestalt psychologists with a group of dogs in Anchor Point Magazine. The dogs were trained to approach something when shown a “white” square and avoid it when shown a “gray” square. When the dogs learned this, the experimenters switched to using a gray square and a black square. The dogs immediately shifted to approaching the object in response to the gray square (which had previously triggered avoidance), and avoiding the object when shown the black square (which had not been conditioned to anything). Presumably, rather than perceive the gray as an absolute stimulus, the dogs were responding to the deeper essence of “lighter versus darker” as opposed to gray, white or black being properties.
You can train a human to approach something when shown a “white” square and avoid it when shown a “gray” square. When the squares are switched to gray and black, the human will still avoid the “gray” square. Once gray has been defined in our minds, we see the gray as independent and entirely self-contained. This means nothing can interact with it or exert an influence on it. It, in fact, becomes an absolute. We have lost the sensitivity to deeper relationships, functions, and patterns because we are educated to focus on the particulars of experience as opposed to the universals. We see them as independent parts of an objective reality.
All of the experts in the Postal Service and UPS were unable to conceive of alternatives to what existed because they focused on the particulars of existing delivery systems. Fred Smith’s abstraction of the problem from delivery systems to “movement” allowed him to make the relationship between moving money to moving air freight.
BLUEPRINT. When you are searching for ideas, try the technique of abstraction. Think about your subject and decide the universal principle or essence of the subject. Suppose, for example, you want to invent a new can opener:
- You might decide that the essence of a can opener is “opening things.”
- Then spend time thinking about how things open in different domains. In nature, for example, pea pods open by ripening. Ripening weakens the seams and the pea pod opens.
- This inspires the idea of “opening a can by pulling a weak seam (like a pea pod). Instead of an idea to improve the can opener, we produced an idea for a new can design.