Monday, July 19, 2021


You like music?  Can you think of a song, symphony or soundtrack that moves you or makes you evoke a moment? 

 In everyone it occurs to us in every corner of the world.  The melodies have been with us for at least 40 years, as their basis is very simple: for example, a simple stretch of tight string that, when pulsed, varies between tens and a few thousand times per second, emits a musical note.  But music is a very complex art and it can have a big influence on us.

 Scientists such as Nobel Prize winner Richard Feynman consider the moment when Pythagoras (6th-5th centuries BC) generalized an experimental result to the workings of the cosmos as key to the origin of physics: two steps of a tense string played at a time create two musical notes that they are harmonic, that is, they look pleasant, when the relationship between their lengths is a quotient of small integers.

 When the length of one is twice that of the other, quotient 2:1, the two notes sound so nice together that in Western music they have the same name: they are separated by an octave (for example, one C and the next plus acute).  The second oscillates exactly twice as much as the first.  Other harmonies are obtained for ratios of 3:2, 4:3, etc.

 Pythagoras and the harmony of the spheres 🎡

 Pythagoras and his followers even thought that there would also be ′′ numerical relationships between the orbits of the planets or among other things in nature ′′ and that the stars would move with the so-called ′′ harmony of the spheres', an idea that inspired astronomers. They also mathematized and gave rise to Western music theory, which was taught alongside astronomy and mathematics, making it a bridge between art and science.

 Those pioneers of physics observed the firmament with the tools at their disposal and attributed to the orbits of the stars their mystical ideas about harmony and numbers.  But the cosmos turned out to be more complex.  To see this complexity, more accurate observations and, above all, new experiences analyzed mathematically are needed.  It took ages to arrive.

 Kepler: a new kind of harmony.  🎡

 At the beginning of the 17th century Johannes Kepler would tirelessly search for the Pythagorean harmony of the stars.  He didn't find her.  It would remain for posterity only as a metaphor.  But thanks to his pursuit of that idealized goal, his mathematical genius, and Tycho Brahe's precise astronomical observations, he was able to enunciate Kepler's laws of planetary motion.  These were keys for Newton to demonstrate the validity of the law of universal gravitation.

 As a story, among other research methods, Kepler sonicated the data from planetary orbits, that is, translated them into musical notes.  It has been a few decades that the scientific use of this technique has been resumed, which, without being its own music, uses some of its properties.

 Galileo, rhythm and acceleration.  🎡

 In addition, many consider that who marked the beginning of physics as such was Galileo Galilei, Kepler's peer and a very competent musician.  Among many other contributions, he carried out an experiment of great relevance to physics, with which he was able to mathematically describe the displacement as a function of time of a ball that falls on an inclined plane.  And it is said that he used his musical training, concrete rhythm, to determine identical time intervals.  The result of the experiment is well known: the distance covered is proportional to the square of the elapsed time.

 Galileo.  🎡

 With him, he introduced the concept of acceleration, essential to Newton's mechanics and his universal gravitation.  Furthermore, it reaffirmed itself in mathematics and experiments as a means of knowing natural laws.  However, in this case music would not have played such a crucial role, as it also used other methods to determine time intervals.

 Understand physics through music.  🎡

 From that moment on, it doesn't seem that music has been relevant to the advancement of physics.  And at times it can even be a siren call, motivating but also throwing off the scent.  Perhaps this was the case with John AR Newlands' periodic table of elements, who was the first to organize them according to their atomic mass, but did so by proposing the wrong "law of octaves", suggesting the musical analogy. five years later (1869) Dmitri Mendeleev took the cat to the water proposing the precursor to the periodic table used today.

 However, certain musical analogies can be effective for teaching and disseminating some aspects of physics, given the extensive use of some harmonic-based mathematical tools.  This is the case of Fourier analysis and spherical harmonics, widely used, for example, in the quantum-mechanical model of atoms or to analyze variations in the cosmic microwave background.

 In short, some of the early physicists, inspired by music, pointed to one of the most powerful ways of understanding the universe.  As Carl Sagan said, thanks to them we know that ′′ there is a resonance, a harmony between our way of thinking and the way the world works. We will always be left with metaphors. 🎡 

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