Laplace's Equation: Mathematical Key to Everything

PHYSICS HAS ITS own Rosetta Stones. They’re ciphers, used to translate seemingly disparate regimes of the universe. They tie pure math to any branch of physics your heart might desire.It’s in electricity. It’s in magnetism. It’s in fluid mechanics. It’s in gravity. It’s in heat. It’s in soap films. It’s called Laplace’s equation. It’s everywhere.Laplace’s equation is named for Pierre-Simon Laplace, a French mathematician prolific enough to get a Wikipedia page with several eponymous entries. In 1799, he proved that the the solar system was stable over astronomical timescales—contrary to what Newton had thought a century earlier. In the course of proving Newton wrong, Laplace investigated the equation that bears his name.It has just five symbols. There’s an upside-down triangle called a nabla that’s being squared, the squiggly Greek letter phi (other people use psi or V or even an A with an arrow above it), an equals sign, and a zero. And with just those five symbols, Laplace read the universe.

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