### SCIENTIFIC COMPLEXITY

If you thought that science was certain - well, that is just an error on your part

Dr. R. Feynman – Theoretical Physicist

Scientific Precision: it is one thing to discover the continents are drifting; it is quite another to predict the plates' positions in the distant future

The art shown here was "painted" by a computer. To create the patterns the programmer used a simulation of the physical laws of magnetism, a pendulum with an iron tip, and an estimated (damping) factor to simulate the friction and resistance on the pendulum. The release point of the pendulum tip defined the location to paint, and the color was based upon which magnet the steel tip came to rest above (see explanation sketch at bottom of this page). The greater the number of pendulum swings, to and fro, the darker the image. The glowing white circles indicate the locations of the three magnets.

The pattern is quite complex; but near the four corners the complexity becomes extreme. In real life this means it would be virtually impossible to predict which magnet would eventually attract the pendulum tip.

Imagine what the picture would look like if the pendulum swung in a cross-flow of air or even with the air flow rotating around the pendulum. Although much more complicated, by using a different computational technique, those situations could also be modeled and a new even more complex theoretical picture could be "painted".

The image above was designed by using an inexact engineering theory with no serious attempt to model the real world, and no ability to model moving air. Now assume a scientist wanted to upgrade the program to model air movement and then build a laboratory model to compare with the upgraded picture.

The program would need to have the following features: use a different analytical method - finite difference or finite elements; require the time intervals and element sizes to be carefully determined; and the pivot point "boundary condition" to be modeled. It would need precise details about the pendulum – its cross-sectional shape, its material, and its surface texture, in order to calculate its air resistance dynamics and vibrations in simulation of its passage through the air. The scientist would also need to control the conditions in the laboratory itself: the air temperature and lighting, the mechanism that locates the pendulum release position, and the power and orientation of the magnets?

The test results from the first laboratory experiment, displayed graphically, when compared to the computer "painting", would be unrecognizable. The middle part of the picture may be vaguely identifiable but certainly not the edges. The problem is caused by two variables: time and precision. The longer the pendulum swings in the air the less the computer picture would conform to the laboratory results and the more intricate and convoluted the pictures would become.

With a sufficient number of trials, followed by the adjustment of various input factors, the computer and the laboratory models could, for engineering purposes, be made to be relatively similar. But so far this analogy has not really approached the problem of scientific complexity. We have gone from the computer world to the laboratory world; now we need to move into the real world. Reality introduces details that vary and are beyond our control - the fine points we don’t or can't fully understand or precisely model. And they have the potential to significantly change the picture and increase the degree of complexity even more.

By being able to fine-tune laboratory work to computer models, engineering has the luxury of mathematically determining probabilities. Complex Science typically has to live with Complexity and Chaos as fine-tuning to reality is rarely feasible. This accounts for the long list of complex topics that are currently unresolved. It also confirms that the attitudes of skepticism and lack of bias are as crucial to science today as they were in the past.