Sum is greater than the parts

Experts in design, computer science and many other fields have long debated the definition of complexity. Seth Lloyd of MIT`s mechanical engineering department famously gave a lecture during which he presented 32 different definitions of complexity. Although the debate rages on, at least one definition of complexity measures the degree to which a system is more than the sum of its parts.

Mosaics are nothing but colored tiles arranged into patterns. Separately, the tiles mean little. When assembled, they can be great works of art. The pointillists and impressionists created moving scenes with nothing but small dots of paint. Great works of literature are composed entirely of words. Fine cuisine is made from relatively simple ingredients which treat the senses and stir the soul when combined.

Great architecture is made from stone blocks, glass plates, and metal beams. Robots are made of nuts and bolts, switches and wires, metal and plastic. All of these things are far more than the sum of their parts. They are all complex systems in their own ways.

As the complexity of a system increases, the desirability or usefulness of the system often increases. In the process, the difficulty in designing and analyzing the system also increases. Although the sum of the parts is complex, often the individual pieces are not. Interestingly, you can at least partially reverse the effects of complexity by disassembling the whole.

I previously advocated making assumptions which would permit you to solve a simpler problem. But according to Einstein, "Everything should be made as simple as possible, but not simpler." There comes a time when your simplifications change the original problem so much that the resulting answer is meaningless. In this case, the best course of action is to break the problem down into as many pieces as possible, solve each individual piece separately and combine the answers back together at the end to provide the final solution.

In engineering, both the finite element method and the finite difference method are based on this approach. It is assumed that the physics of the problem is relatively well-understood. The complexity is in the geometry of the system and in the number and nature of the boundary conditions.

If we want to determine the net heat flux on a cow in a pasture, we could assume that the cow is a sphere. But if that assumption gives us funny answers, we can try another approach.

We don`t know the closed form heat transfer equation for a cow. We could probably derive such an equation but it would be unpleasant to solve. However, we do know the closed form heat transfer equation for a cube. So we break the cow up into little cubes and analyze each cube separately. In effect, we turn the cow into a (very large) series of simultaneous equations that we know how to solve instead of a single unpleasant equation that we don`t know how to solve.

If your cow is composed of a large number of cubes, you might need a computer to do the math. For the finite element method, you get the exact answer for an approximate cow. Using the finite difference method, you get an approximate answer for the exact cow. In either case, you get an answer that`s reasonably close to reality.

Writing books is much the same way. No one sits down to write a book in a single session. Books are written sentence by sentence, paragraph by paragraph, chapter by chapter. Each idea is formed separately and put into sequence.

A single word is a simple thing. Stringing words together to form a coherent thought takes practice to do elegantly but most people master the basic process in their first few years of life. You already have all of the tools needed to write a book. If you have the ideas to fill a book and can break those ideas down into discrete thoughts, then all you really need is the courage to try.

Sun Tzu said: "[T]he art of using troops is this: When 10 to the enemy`s one, surround him; When five times his strength, attack him; If double his strength, divide him." When faced with difficulty in your daily life, consider using a similar strategy to conquer complexity.

Lao Tzu said that a journey of a thousand miles must begin with a single step. Although the road is long, the path may be steep, and the weather may be disagreeable, the distance is still traveled a step at a time. A single step is easy to take. The next is also easy to take. One foot after the other, the miles go by. The whole journey may be a complex experience and intimidating to begin, but broken down into millions, perhaps billions, of steps it becomes possible.



Mary Kathryn Thompson, Ph.D., is an assistant professor in the Department of Civil and Environmental Engineering, the Korea Advanced Institute of Science and Technology. She can be reached at mkthompson@an.kaist.ac.kr. - Ed.