Photo: Wikimedia Commons
The world can be explained with maths.New Scientist’s Ian Stewart has compiled the seven equations that you – or anything else for that matter — could not exist without.
Stewart selected the equations that can be used to describe most things in our modern lives. They explain everything from how our appliances are powered to how data is stored on our computers.
As Stewart gracefully puts it, “We are afloat on a hidden ocean of equations.”
The first equation, the Wave Equation, describes the movement of all energy waves — light, sound or heat. (All equation images are from New Scientist).
It says that for a given function with a given constant over a given period of time, the function’s solution will take the form of a wave.
Every sensation you feel, hear or see is simply your brain interpreting wave functions. To run with Stewart’s initial analogy, we are not so much floating on this equation as swimming in it.
The next equation is technically a set of four equations known as Maxwell’s equations (after the Scottish scientist who figured them out):
The two equations on the left explain conservation of electrical and magnetic energy. They say that the net electromagnetic flux created in an electromagnetic field is zero.
The two on the right explain how that electromagnetic field can be controlled and measured. They say the vector of an electric field equals the magnitude of a magnetic field, and vice-versa.
Together, these are the equations that dictate how every device you’ve every owned is powered, and how we can measure the aforementioned waves they emit.
The most profound equation on the list is Schrödinger’s equation, which describes the behaviour of electrons.
It shows how much energy would be contained in the given parameters of an electron’s quantum (or static) wave function.
This equation allowed for the creation of semiconductors, the metal films found in the memory transistors powering the screen you’re reading this on.
The final equation in some ways is the product of the previous six. It is called Fourier’s transform, and it explains how we can take energy wave measurements and apply them to all sorts of applications.
For a given series of sine curves, we can use this equation to calculate their amplitudes and frequencies. Clever engineers have come up with a digital version of Fourier’s transform to make image processing and storage in your computer possible.
Stewart notes that scientists continue to search for a way to boil down these and all other equations into the famous “unified theorem.”
For now, we’ll have to be content with grabbing our swimming trunks and splashing around with these.