How Chaos Theory Works

The Birth of Determinism

The 1600s enjoyed a slow and steady illumination as a collection of visionary thinkers brought reason, form and structure to the great mysteries of the world. First came Johannes Kepler, the German astronomer who, in 1609 and 1618, described how planets moved in elliptical orbits with the sun as one focus of the ellipse. Next came Galileo Galilei, who made fundamental contributions to the scientific studies of motion, astronomy and optics throughout the early 1600s. These empirical concepts and ideas joined the inventive thinking of philosophers such as René Descartes. In 1641, Descartes published his Third Meditation, in which he discussed the principle of causality -- "nothing comes from nothing," or "every effect has a cause."

All of these ideas set the stage for Isaac Newton, whose laws of motion and gravitation shaped science for centuries to come. Newton's laws were so powerful that, if you were so inclined, you could use them to make predictions about an object far into the future, as long as you knew information about its initial conditions. For example, you could calculate precisely where the planets would be hundreds of years from the current date, making it possible to presage transits, eclipses and other astronomical phenomena. His equations were so powerful that scientists came to expect that nothing lay beyond their grasp. Everything in the universe could be determined -- calculated -- simply by plugging known values into the well-oiled mathematical machinery.

In the late 18th and early 19th centuries, a French physicist named Pierre-Simon Laplace pushed the concept of determinism into overdrive. He summarized his philosophy like this:

We ought then to regard the present state of the universe as the effect of its anterior state and as the cause of the one which is to follow. Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it -- an intelligence sufficiently vast to submit these data to analysis -- it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes.

Using this notion, Laplace's colleague Urbain Jean Joseph Le Verrier correctly predicted the planet Neptune in 1846, relying not on direct observation but on mathematical inference. Englishman John Couch Adams had made the same prediction just a few months earlier [source: StarChild Team]. Other similar scientific achievements followed and fueled numerous technological advances, from steel and electricity to the telephone and telegraph, to steam engines and internal combustion.

But the structured, ordered world of Newton and Laplace was about to be challenged, albeit slowly, fitfully. The first seeds of chaos were planted by another Frenchman and with an analysis of a system that should have been a no-brainer -- the motion of planets.

This gets to a second key concept: uncertainty or scientific error. Even greenhorn Galileos accept the presence of uncertainty when making measurements, but they also assume they can reduce the uncertainty by measuring initial conditions with increasing accuracy. Much of 19th- and early-20th-century science occupied itself with improving the quality of measuring equipment, all in the pursuit of determinism.

The Myth of Measurement

Two important concepts underpin the philosophy of determinism. First, for any given system, the same initial conditions always produce the same outcome. Think of a game of billiards. Describe the initial conditions of the table, quantify the speed and trajectory of the cue ball, and you can calculate, using math alone, what the table will look like after a shot. Set up the table exactly the same way and strike the cue ball in the same spot, with the same force, and the outcome will be the same -- without exception. Of course, this is easier said than done. Duplicating a set of initial conditions is tricky because there's always going to be slight variation in how you set up the table.