You believe in a God who plays dice, and I in complete law and order.
– Albert Einstein, Letter to Max Born
By the 18th century, many scientists were convinced that they were well on the way to identifying the essential, immutable laws of nature. There was a strongly held belief that the world could be systematically recorded, studied and analyzed. Thus chaos and uncertainty would soon be banished from the world system, replaced by a mechanistic, disciplined, clockwork world — at least in theory.
The French mathematician and physicist, Pierre-Simon de Laplace (1749-1827) made the astonishing claim that the universe was so regular and orderly that a superior intellect, if given access to the fixed positions and velocities of all particles, could predict with mathematical certainty what every particle would be doing forever after:
An intellect which at any given moment knows all the forces that animate Nature and the mutual positions of the beings that comprise it, if this intellect were vast enough to submit its data to analysis, could condense into a single formula the movement of the greatest bodies of the universe and that of the lightest atom: for such an intellect nothing could be uncertain; and the future just like the past would be present before its eyes.
Laplace’s bold assertion marked a highwater mark of the idea that the universe is a strictly predictable machine governed by the eternal laws of celestial mechanics as systematized by the theories of Sir Isaac Newton. The cosmos was a giant clock.
But this explanation began to change over time. With the advent of quantum mechanics — a theory that Albert Einstein felt cast God in the role of a cosmic dice-player — the clockwork world began to seem more like a “cosmic lottery.” It is now widely held that such fundamental events as the decay of radioactive atoms are determined more by randomness than universal law. The principles behind the universe appear now more a matter of probability than predictability.
In both science and mathematics, chaos is becoming a technical term. It is the branch of science dealing with erratic activity, “noises in the system.” First developed in 1975 by mathematician James Yorke, chaos theory attempts to deal with the apparently unpredictable behavior within a system once seen as governed by mathematical rules. To its proponents, chaos theory suggests the limitations of predictability more than wild, confused behavior. One of the controlling ideas is that the behavior of a system tends to change drastically in response to slight changes in initial conditions.
But how does this work?
Ed Lorenz, a meteorologist from Massachusetts Institute of Technology, developed some of the early theoretical underpinnings while experimenting with computational models of the atmosphere. He discovered what has come to be called the Butterfly Effect. This is the notion that in meteorological models such as Lorenz’s, a butterfly fluttering its wings today in Australia can so disturb the atmosphere so as to cause a rainstorm in Great Britain tomorrow. To put it technically: The deterministic laws governing weather formation are unstable in the worst possible way. Tiny differences in input can quickly become overwhelming differences in output. Infinitely small changes at one location percolate through the system to bring about major effects elsewhere.
Chaos theory for weather-forecasting is one thing. Some think most forecasts are only as dependable as a coin toss. But there are other natural phenomena, long considered the epitome of predictability, that are now revealing themselves to be equally fickle. Jacques Laskar of the French Bureau des Longitudes in Paris, has reported that the orbits of the inner planets show signs of irregularity. “The amount of chaos is quite high: the positions of the inner planets become effectively unpredictable in just a few tens of millions of years.” (Unravelling The Mind of God, Robert Matthews).
What we now know is that the ‘safe’ world of deterministic, classical mechanics is much more mysterious than either Newton or Einstein imagined. The very distinction Einstein was trying to emphasize between randomness and law is being called into question. Does God play dice with the universe after all?
British mathematician Ian Stewart responds to this question:
The cycle has come full turn — but at a higher level. For we are beginning to discover that systems obeying immutable and precise laws do not always act in predictable and regular ways. Simple laws may not produce simple behaviour. Deterministic laws can produce behaviour that appears random. Order can breed its own kind of chaos. The question is not so much whether God plays dice, but how God plays dice. (Does God Play Dice?, page xx).
Joseph Ford of the Georgia Institute of Technology amplifies the point: “God plays dice with the universe. But they’re loaded dice. And the main objective of physics now is to find out by what rules were they loaded and how we can use them for our own ends.”
Chaos theory may be only in its infancy, but it is already leading some cosmologists to ponder anew the breathtaking complexity of our universe.