257 years ago, Joseph Fourier was born on this day. In 1822, Fourier showed that any wave can be broken down into an infinite sum of sine waves, using a technique now called the Fourier transform. The Fourier transform is like a recipe generator. You input a complicated wave and you get back its ingredients, the amplitude and frequency of each component sine wave. Fourier analysis is an essential part of modern technology. Its applications range from JPEG compression and image recognition to quantum physics and MRI's. Fourier theory has two components: basic building blocks and labels. Imagine a child's toy castle. This castle can be disassembled into individual building blocks. And these building blocks can then be sorted by color into bins and labeled. Similarly, the Fourier transform disassembles a complex wave into individual sine waves. These are like the building blocks. Each sine wave can be labeled with its frequency, or how quickly it oscillates per second. The labels on the bins are more than just a way to organize things. They can be used to rebuild the original complex wave and as an efficient shorthand for communicating information. For example, when you send a voice message, your phone doesn't transmit an entire complex sound wave. Instead, it breaks it down and sends just the labels or frequencies of the component sine waves. The receiver's phone then reverses this process, converting the labels back into the contents of the bins to reconstruct the message’s original sound wave.