Équation qui régit le monde (document en anglais)

Equations that rule the world

We humans will be nothing without our tools, stones axis made hunting easier and food more abundant, telescopes showed us a broader universe and nowadays we’re pretty helpless without our cell phone. But what is the most important to us? Our physical subjects at all but instead exist only our imagination. Without these imaginary tools, modern technology would be impossible and understanding about ourselves and universe would be greatly diminished. They are the equations that rule the world. It would be impossible to list all the ways that mathematics affects our daily lives. But a few equations in particular make it possible to do things we modern humans takes for granted: a talk on a cell phone, watch videos on the internet at work.

The first is the wave equation. We are constantly bombarded by waves but it wasn’t until the seventeen hundred (1700) that we began to figure out how they work. Swiss mathematician, John Bernoulli use new laws of motion to work out the simplest shape for a vibrating string is a sine curve. Then French physicist Jean D’Alembert built on us, discovering that the acceleration of a small bit of vibrating string is proportional to the tension on the string. He captures this in an elegant formula describing one- dimensional waves. This new understanding of waves would lead to one of the great technological discoveries of the last few hundred years: radio. But first we need another mathematical tool.

Electricity and magnetism have long been carried curiosities. But in early 1800, English man; Michael Faraday began to capture their behavior mathematically. Later that century, James Clerk Maxwell built on Faraday’s work showing that electricity and magnetism are inextricably linked and assembling the equations to prove it. Maxwell first two equations show how to calculate electric and magnetic fields. The second two say that a changing electric field creates a magnetic field and vice versa. Maxwell uses these equations to show that electromagnetic waves travel at the speed of light. But more than that he showed that these waves come in many more varieties than just with the human eyes can perceive. Maxwell’s equations allow us to use all kinds of electromagnetic radiation from radio waves to x-rays to visible light. But to take full advantage of these waves, we need one more equation.

The Fourier transform

Before Maxwell and Faraday conquered electromagnetism, French military officer Joseph Fourier was hot on the trail the surprising property of waves. By studying the way heat propagates across the wire, Fourier found that any waves no matter how complicated can be broken up into a combination of simple sine waves. His equation now underlies much of modern digital technology. It use to designed internet for wireless devices, compressed digital photos even creating electronic music. These equations are just a few of the mathematical ideas that make our modern world go. They are of course many others, from the fluid equation that keep airplanes in the sky to the statistical methods that keep food supply safe. So our equations are purely inventions of human imagination they may will be our most powerful tools.

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