The laws of physics appear to follow a mysterious mathematical pattern

Strange patterns running through physical equations may reveal something fundamental about the universe, or indicate that the human brain tends to ignore more complex explanations of reality, or both. There is.

This insight comes from physicists’ Zipf’s Law, a linguist’s observation that the most common words in a language occur twice as often as the second most common words, three times as often as the third, and so on. It’s coming. For example, in English, the word “the” tends to occupy about 7 percent of long texts, and the next most frequently used word, “of,” occurs about 3.5 percent of the time. Furthermore, it turns out that Zipf’s law seems to apply to other situations, such as income distribution and urban population.

now, Andrei Konstantin Researchers at the University of Oxford found that similar laws apply to the symbols used to construct the laws of physics. They looked at three sources for the equation. Feynman’s physics lecture;List of equations named after people found on Wikipedia. and a proposed set of equations to explain inflation in the early universe. You can analyze equations in a manner similar to Zipf’s law by treating each symbol and mathematical operator in the equation as a word and ranking its frequency.

“This may be expected, but [distribution] The three different sets of equations come from different places, so there should be quite a large difference between them,” team members say. degran bartlett I studied at the Sorbonne University in France, and to my surprise, that was not the case. Rather, all three sets seemed to fit the same pattern. This is not the case when applying the same analysis to randomly generated formulas.

What exactly it means for real-world equations to follow this pattern is unclear. One possible explanation is that it says something about how reality actually works. eddie kemin chen at the University of California, San Diego. Each equation by itself predicts real facts about the universe so accurately, Chen says, that the overall pattern they follow probably also contains information about the nature of reality. “We have invented languages, mathematics, and symbols for various purposes, but it turns out that physics, and therefore nature, uses only some of the simplest of them.”

Constantine believes the consistency of the patterns he discovers, even for symbols that rarely occur, is evidence for this. “The less frequently encountered operators, such as exponential, logarithmic, hyperbolic, and trigonometric functions, all follow the same rules, which is surprising,” he says.

But Professor Bartlett said the results could be a statistical byproduct of physicists simply trying to express their ideas more succinctly than revealing anything fundamental about the universe. I think there is. This explanation has also been proposed for Zipf’s law. “You want to convey as much information as possible in as few symbols as possible, or in as little time as possible, and the same is true for equations in physics,” he says. “We’re creating operators that we know are useful.”

Chen said both of these scenarios could apply at the same time. It could also reflect the way our brains work, such as our preference for simple explanations that help us predict the world, he said. “The tendency is to ignore more complex explanations,” he says.

Regardless of interpretation, Bartlett and Constantine hope that their discovery will help guide future machine learning models to discover new laws of physics. “It should be more efficient because we no longer have to search for equations that we know are unlikely to be physically realistic,” Bartlett says.