On a chilly night in 2004, I was with two of my college friends. One of us had a computer in our dorm room and we tried a little experiment. We started looking at the frequency spectra of a number of popular songs. Today, you can do the same by simply enabling the ‘fire’ visualization on your Windows Media Player. The most remarkable shape we saw was a pure dancing peak that came when we played the opera from Bruce Willis’ 1997 film, The Fifth Element (you can listen to it here). That was my first direct experience of the relation between beautiful music and elegant mathematics.
Almost all of us have studied the Pythagoras theorem about a right angled triangle in school. Pythagoras is also credited with discovering the relation between the length of a string and the note it produces. This led him to the discovery that the difference in the length of strings that produced ‘harmonious’ frequencies could be expressed as simple mathematical ratios.
These insights led him to speculate on the Music of the Spheres. This inaudible harmony was considered to pervade the whole cosmos and was a manifestation of its underlying order and system. The idea of beauty at the heart of the universe took shape.
Music of the spheres (Harmonices Mundi)
From ancient times, right up to the late middle-ages, the Ptolemaic geocentric model of the solar system held sway. In it, the Earth was at the centre of the universe, surrounded by transparent spheres on which were fixed, the sun, the moon, the planets and the stars. The movement of these spheres led to the visible movement of these objects in the night sky.
The problem was that the position of all these bodies as observed at night did not follow what they would have been if they were on a simple rotating sphere around the Earth. So refinements were added. Not only did heavenly bodies circle the Earth, they also moved in tiny circles while they were orbiting and then circles within circles till finally, a very messy and complicated path was devised that each of these bodies would have to follow to match their observed motion.
All this changed when Copernicus put forward his heliocentric model putting the Sun at the center and all the planets including the Earth around it. It is important to note that at the time, the predictions of this model were much worse than those of the complicated Ptolemaic model, but still natural philosophers greeted it because it was elegant and did away with the messiness of the Ptolemaic model.
It was the beauty of the system and not its close fit to the observed data that swayed opinion. Later when Kepler perfected the system, he did it by replacing one elegant shape, the circle with another, the ellipse with the Sun at one of its focii.
Simplicity has remained a powerful aesthetic in science. It is encapsulated in the maxim of Occam’s Razor. Given multiple explanations of a phenomenon, choose the simplest.
Copernicus wasn’t the only case where elegance was considered as important as observation. The Nobel prize winning physicist Murray Gell-Mann remarked
“Three or four of us in 1957 put forward a partially complete theory of the weak [nuclear] force, in disagreement with the results of seven experiments. It was beautiful and so we dared to publish it, believing that all those experiments must be wrong. In fact, they were all wrong.”
James Watson remarked in his autobiography that in 1953, when he and Francis Crick deduced the double helix structure of DNA, he knew it was right because it was so beautiful it had to be true.
Watson and Crick with their model of DNA
Einstein’s life long quest for a Grand Unified Theory was based on his faith in the underlying aesthetics of the universe. He said,
“I have deep faith that the principle of the universe will be beautiful and simple.”