The solution is so enormous that it exceeds the total number of particles in the universe.
Here’s the problem: Imagine that you have 128 tennis balls and can arrange them any way you want. It is now your job to determine how many arrangements of these tennis balls are possible.
Believe it or not, if you took the time to work out all of the possible arrangements, it would take you several lifetimes to solve. It must be a really big number!
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And it is, according to researchers at the University of Cambridge who developed a computer program to answer the mind-numbing question, which had actually been deemed hopeless for any system involving more than 20 particles. The number of possible solutions is so big that it is incomprehensible to most of us, however the process used to find it has several applications.
Granular Physics
Granular physics focuses on the behavior of substances such as snow, sand and soil, and how these substance behave under different conditions. This study now provides researchers with a working example of configurational entropy — which measures how disordered the particles within a system or structure are.
For example, since this computer program can calculate configurational entropy, we could potentially predict the movement of avalanches or how shifting sand dunes might change desert topography. Luckily, other fields including string theory, cosmology, artificial intelligence, and branches of mathematics also need to calculate this entropy, and this is what the Cambridge team finds so exciting.
“The problem is completely general. Granular materials themselves are the second most processed kind of material in the world after water and even the shape of the surface of the Earth is defined by how they behave,” Stefano Martiniani, a Benefactor Scholar at St John's College, University of Cambridge, who lead the study with colleagues in the Department of Chemistry said in a press release.
Entropy
Even though humans are a long way from predicting avalanches, the generality of predicting the movement of particles, known as entropy, is extremely useful. Entropy describes how disordered the particles in a system are.
For example, when an ice cube is heated until it becomes water, its molecules become more disordered, meaning the water has a higher entropy than the tighter ice cube structure.
Although it is fairly easy to predict how particles move at the molecular level, it is not so easy in granular physics — which deals with materials large enough to be seen by the naked eye — since outside factors such as temperature and wind can also affect the movement. To do so would involve measuring the changes in the disorder of all the particles in the system, or the many different ways a system can be structured — its configurational entropy.
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Luckily, this is what the team did after developing a computer model. They used a small sample of tennis balls, determined all the possible configurations, and then worked out the probability of them occurring. Martiniani said, “By answering the problem we are opening up uncharted territory. This methodology could be used anywhere that people are trying to work out how many possible solutions to a problem you can find.”
The answer to the 128 tennis ball problem by the way is 10^250, which is 1 followed by 250 zeros. The number is referred to as ten unquadragintilliard — so enormous that it exceeds the total number of particles in the universe.
Mind blown!
