At The Laborastory National Science Week Edition the Gaussian Ensemble are singing a song they wrote called Gaussian Rhapsody. They have kindly provided an explanation to the maths behind their lyrics. We’ll put the lyrics up here after the show.
Gauss was a mathematician and physicist, who described mathematics as “The Queen of the Sciences” and, being the greatest mathematician of all time, he is known to us as “The Prince of Mathematicians”.
Normality & Gaussianity refer to the familiar bell-curve in statistics, which we call the ‘normal’ or ‘Gaussian’ or ‘Laplacian’ distribution. It appears in science all the time, and indeed in the day-to-day world, because of its unique property that if you add up a lot of unrelated variables then the total is approximately Gaussian (this is called the ‘Central Limit Theorem’). Gauss and Laplace made fundamental discoveries in the statistics of the normal distribution.
Woooooah this stuff really blows our minds.
Polygons are 2-dimensional closed shapes with straight edges, like squares, trapezoids and hexagons. A ‘regular polygon’ is one where all the angles are the same and all the edges have the same length.
Fermat polygons refers to ‘constructible polygons’, which are regular polygonals with the number of sides given by a product of Fermat primes and a power of 2. The Gauss-Wantzel theorem says that these polygons can all be constructed with a compass and a straight piece of something (as long as it’s straight).
A heptadecagon is one of these constructible polygons, and Gauss was the first to make one. People had been trying for 2000 years before he finally got it.
Ceres, Piazzi’s rock is a dwarf planet in the asteroid belt, and it was the first asteroid to be discovered (probably because it’s the biggest) in 1801 by Piazzi. Gauss managed to predict where it would appear after Piazzi lost track of it when it passed behind the sun—to do this he used Kepler’s elliptical orbits, which was in contradiction to Galileo, who believed that the planetry orbits were circular and not elliptical.
A geodesic is the shortest path between two points on a curved surface.
A Danish geodesic refers to the land survey of Denmark, which Gauss extended to his native Hanover. He undertook the entire enterprise, and spent several years riding around the countryside. It led him to fundamental mathematical insights into geometry and curvature.
Wilhelm, my friend, let’s build a telegraph, refers to Gauss and Wilhelm Weber building one of the world’s first telegraph systems at their university in Goettingen. It extended from the institute of physics to the astronomical observatory, a distance of about 3km.
Gauss’s Law! is one of Carl’s greatest contributions. It tells you that the electric or magnetic flux through any three-dimensional space can be easily calculated by knowing how much charge is inside the space.
Monopoles are the fundamental units of electric or magnetic charge. For example, an electron has a -1 charge, and it is an electric monopole, while a proton has a +1 electric charge and is also a monopole. A magnetic monopole has just a north or south end, not both. Gauss law for magnets says there are no magnetic monopoles—and so far, nobody has found any.
Mr. Maxwell, Mr. Maxwell refers to James Clerk Maxwell who listed the four fundamental laws of electromagnetism that we still use today—and Gauss’s Law accounts for two of them. So devote half your thanks to Gauss whenever you switch on the toaster.