This article has been reviewed according to Science X's editorial process and policies. Editors have highlighted the following attributes while ensuring the content's credibility: When is a billiard ball not a billiard ball? When mathematicians get involved and view a popular game as a model computer.
When you send a ball across a table and it hits the sides, it follows simple physical rules. However, mathematicians see a particle (the ball) whose motion can represent information, while each bounce can help guide it through a calculation. For years, mathematicians have wondered whether billiards are capable of universal computation—in other words, whether a simple two-dimensional billiard system can run any computer program imaginable.
It turns out that the answer is yes. Eva Miranda at the Polytechnic University of Catalonia in Spain and Isaac Ramos at ETH Zurich in Switzerland have shown that a two-dimensional billiard table can act as a universal Turing machine, a theoretical blueprint for all computers devised by British mathematician Alan Turing in 1936. They write about their work and what it means in a paper published in the Proceedings of the National Academy of Sciences.
What Miranda and Ramos did was map the graph of a computer program directly onto a billiard table. In their design, the position of the ball at particular sections of the table represents the computer's memory and current state. Narrow corridors connect different sections of the table, while straight, curved and endlessly wiggling walls bounce the ball in precise ways to read data, alter it and move to the next step.
If the calculation reaches a conclusion, the ball hits a designated wall section, signaling that the program has finished. Because a universal Turing machine can process any algorithm, this theoretical construct shows that a single ball bouncing off fixed walls can simulate any computation that can be carried out by one. "We show that two-dimensional billiard systems can simulate universal Turing machines," Miranda and Ramos wrote in their paper.
Beyond proving that simple billiard trajectories can mirror the logic of computation, this research reveals a hard limit on predicting the future. Because the ball's path acts like a computer program, some questions about its long-term journey can be equivalent to asking whether a piece of code will eventually stop or run forever. Computer science has already proved that no algorithm can determine whether any given program will finish.
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