By Steven Gimbel, Ph.D., Gettysburg College
In the 20th century, chaos theory developed out of mathematical structures that scientists thought provided a picture of an elegant universe. But these mathematical structures actually revealed a much more complex and chaotic universe.
Dice and the Theory of Probability
Dice play a significant role in our understanding of probability and its relation to the universe. In 1654, a French nobleman, the Chevalier de Méré, noticed something while gambling. He was playing a game in which a pair of dice would be rolled 24 times and players bet on whether double sixes would be thrown or not. The Chevalier realized that he seemed to win more often when he bet against, but only slightly more often, than when he bet on.
This is a transcript from the video series Redefining Reality: The Intellectual Implications of Modern Science. Watch it now, Wondrium.
He wanted to know if he was correct and contacted the famous French philosopher and mathematician Blaise Pascal. Pascal, in turn, got in touch with his friend and colleague, the great mathematician, Pierre de Fermat, and asked him. Fermat answered by creating the mathematical theory of probability, which helped prove that the Chevalier was, in fact, correct.
Learn more about a numerical way to make decisions.
Laplace and Probability in Science
A century and a half later, Pierre-Simon Laplace, one of the greatest geniuses of the 19th century, became interested in extending Fermat’s notion of probability beyond games of chance to show how it functions in science. So, amidst all of his other great advances in physics, he wrote a pair of books on the subject.
Laplace’s first book was An Analytic Theory of Probability. Two years later, Laplace wrote another book called A Philosophical Essay on Probabilities. In it, Laplace argued that the use of probabilities in science is the result of our own lack of knowledge, not the result of a random world. In the second book, Laplace imagines an ‘intellect’, for whom ‘nothing would be uncertain, and the future, just like the past, would be present before its eyes’. This intellect had special powers.
Laplace’s Demon and the True Aim of Science
This intellect has been called ‘Laplace’s demon’. This demon was imagined to be capable of remembering an infinite amount of facts and would be able to compute with infinite quickness. Now give this super-brained demon two things: First, the true laws of nature, and second, complete information about all of the masses and energy in the universe at any one moment.
The demon could then predict with absolute certainty the state of the universe at any time in the future, or in the past. The universe, Laplace claimed, would be completely transparent to this mega-intellect. Laplace’s demon is the ultimate statement of the Enlightenment project embodied in Science.
The true aim of Science, according to this thought taken up by Laplace—and later, by Einstein and many others—is to develop a unified account that’s capable of predicting and explaining every event, every occurrence, everywhere. But, this makes four basic assumptions about science and the universe it’s trying to describe.
The Four Basic Assumptions about the Universe
The first assumption is that the universe is deterministic. This means that the state of the universe at any given time is completely determined by the state of the universe immediately before. If the universe is in state A, then it will always transition to state B. The second related assumption is that the rules have steady-state solutions. That means that the development of states over time is well-behaved and follows a simple pattern.
The third assumption is the stability of those steady-state solutions: that a small difference in initial the state makes only a small difference to the next state.
The fourth is predictability. The idea is that if we know the rules and the data, we can predict what is to come.
This would mean that the future is not only determined by the past, but determined in ways that are simple, elegant, and clean. Scientists use equations to describe the behavior of physical systems because mathematical language, the language of patterns, is presumed to apply to the behavior of the world.
However, as quantum theory developed in modern times, inherent randomness in the universe became apparent.
Learn more about randomness and its quantification through probability.
Playing Dice with the Universe
This unpredictability is apparent in many quantum solutions. For instance, Schrödinger’s equation for a physical system is a wave function; a mathematical combination of every possible state the system can occupy.
But the interesting thing is that we can never see all the states together. The moment an observer looks at it, only one of the many possible states is observed. This means that we are powerless to predict which state will be seen or observed, no matter how much we know about its past state.
It was this inability to determine the future from the past based on a complete scientific theory that upset Einstein. This led him to make his famous statement: ‘God does not play dice with the universe’. Einstein could not accept a random universe; he wanted it to be deterministic and predictable.
Common Questions about Probability and Quantum Theory
In 1654, the Chevalier de Méré noticed that he seemed to win more often in one type of game when he bet against the odds. He contacted Blaise Pascal, the mathematician. Pascal asked the great mathematician Pierre de Fermat. Fermat, in answering the Chevalier, created the mathematical theory of probability.
Laplace’s Demon is the name given to an intellect imagined by Laplace. This is an intellect capable of remembering an infinite amount of facts and would be able to compute with infinite quickness. Given enough knowledge, this intellect could correctly predict the state of the universe at any time in the future, or in the past.
Schrödinger’s equation for a physical system is a wave function, which is a combination of all possible states. The interesting thing is that the moment an observer views the system, only one of all the possible states are observed. In addition, it can’t be predicted what state will be observed.
By stating that ‘God does not play dice with the universe‘ Einstein meant to say that he believed that the universe was deterministic and predictable.