The Ordered Mathematics of Chaos

There is a very involved study of chaotic geometry, the patterns traced out by objects under complex force systems. Using attractor theory, modern scientists seek to describe the path followed by these objects and find particle position as a function of the attractors. The mathematical solution to this problem shows that the term "chaos" is actually a misnomer. The intricate bands and striped patterns observed by physicists are really a product of cause and effect, as the given object subscribes to the given force system, and accurate streamlines of flow can be calculated. The problem remains, of course, because the complexity of the motion is often beyond contemporary equation solving, and the employment of numeric computing systems is necessary. Numeric integration uses a very basic technique of approximation which provides a solution after many iterations of the algorithm. This solution converges to the required curve in the limit of hypothetically infinite iterations, providing greater and greater precision, or more decimal places in the coefficients of the function.

However, it is well-known that the ancient Greeks had calculated universal constants in their studies of math and geometry. They were able to use beads of similar lengths to approximate a curve. They then reduced the length of the beads to get a more and more accurate answer. It is widely believed that this was the method used to make the first calculations of the number pi, by dividing the number of beads in a circle's circumference by the number in its diameter. This shows that the most basic trial-and-error methods can give rise to general solutions for the most complex mathematical problems. The struggle is to engage oneself into a tedious and potentially endless procedure, but people have done this with great success. In general, the solutions to life's unanswered questions are often found in the most obvious place.

This is convenient...