Foundations of Sound 'Visualization'

There are two very old instances to humans attempting to visualize or manifest sound in ways other than acoustics, and it would be difficult if not unlikely to assert which is the older. Ancient Meso-American Shamen, and those who follow in their practice today, utilize Icaros (song-forms) in conjunction with the psychoactive brew Ayahuasca to rendering their vocalizations into collectively experienced color forms as a part of their medicinal practice. Dr. Luis Eduardo Luna is considered to be one of the most renowned authorities on this practice.

The Nada-Bindu is a Indian text on the manifestation of sound in the world. Nada means sound, or vibration; Bindu, a more complex translation, most generally relates to the concept of a dot, point, or seed. The concept of a dot it the surface meaning, while the more spiritual meaning relates to the concept of Prayer, or communion, while also including the more mundane definition, which could also be translated as "fiber."


Nada-Bindu Upanishad

Translated by K. Narayanasvami Aiyar 

A translation of the Nada-Bindu (sound-prayer/fiber/seed) Upanishad

Om ! May my speech be based on (i.e. accord with) the mind; May my mind be based on speech. O Self-effulgent One, reveal Thyself to me. May you both (speech and mind) be the carriers of the Veda to me. May not all that I have heard depart from me. I shall join together (i.e. obliterate the difference of) day And night through this study. I shall utter what is verbally true; I shall utter what is mentally true. May that (Brahman) protect me; May That protect the speaker (i.e. the teacher), may That protect me; May that protect the speaker – may That protect the speaker.

Om ! Let there be Peace in me ! Let there be Peace in my environment ! Let there be Peace in the forces that act on me !

Om ! May my speech be based on (i.e. accord with) the mind; May my mind be based on speech. O Self-effulgent One, reveal Thyself to me. May you both (speech and mind) be the carriers of the Veda to me. May not all that I have heard depart from me. I shall join together (i.e. obliterate the difference of) day And night through this study. I shall utter what is verbally true; I shall utter what is mentally true. May that (Brahman) protect me; May That protect the speaker (i.e. the teacher), may That protect me; May that protect the speaker – may That protect the speaker.

Om ! Let there be Peace in me ! Let there be Peace in my environment ! Let there be Peace in the forces that act on me !

Here ends the Nadabindu Upanishad, as contained in the Rig-Veda.

Historical Visualization

There is loose suggestion that ancient Tibetans would place water inside of their bronze singing bowls during prayer and other ritual. Whether the practice had any explicit purpose for acoustic visualization is uncertain, though doubtlessly the 'visualization' was a part of the experience.

The study of acoustic visualization was arguably part of the foundations of Science (presuming we locate the origins of Science around Greece), and inspired large advancements in Mathematics. The Middle eastern and Meso-American cultures were utilizing weaving and looming methods to explore rhythm visualization, and is perhaps outside of the scope of 'acoustic visualization. The history of this discipline shows how the investigation of questions which, at a first glance, appear quite abstract and academic, can yield methods of enormous practical value, often after decades or centuries of research.

The Pythagoreans (6th - 5th century BC) studied the vibrations of a taut string, finding that harmonically consonant sounds are produced when the string is divided in simple numerical ratios. This observation corroborated their tenet that everything in the world is governed by relations of numbers. The Pythagorean Hippasos of Metapontum, credited, among other things, with the invention of the regular dodecahedron and the irrational numbers, is said to have investigated the vibrations of metal plates as well. At the medieval universities, music - essentially the ancient theory of harmony - was taught in the quadrivium (fourfold way) along with arithmetic, geometry and astronomy; together with the trivium of grammar, logic and rhetoric, these constituted the seven liberal arts.

Johannes Kepler (1571-1630) tried to explain the radii of the planetary orbits in terms of geometrical ratios, the so-called harmony of the spheres. As a by-product of his speculations on this question (which is still unsolved today) he found Kepler's laws, the basis of the modern picture of the solar system. John Wallis (1616-1703) described the relation between the harmonics of a vibrating string and the number of its nodes of vibration. In 1717, Brook Taylor (1685-1731) published the first mathematical paper on the vibrating string, but he did not yet know the differential equation of wave propagation.

In 1746, Jean le Rond d'Alembert (1717-1783) wrote down the one-dimensional wave equation and found a method of its solution for `arbitrary' initial data; the solution is a superposition of two waves, traveling to the right and left, respectively. The question how `arbitrary' the initial data can really be, i.e. which functions are admissible as solutions of the wave equation, was taken up by d'Alembert, Daniel Bernoulli (1700-1782) and Leonhard Euler (1707-1783). This was the beginning of the struggle for an exact definition of the concept of a function, which became one of the principal achievements of 19th century mathematics.

D. Bernoulli saw a general method of solving the wave equation in the superposition of (infinitely many) simple vibratory modes, an idea previously used by Euler in specific situations. This technique, along with separation of variables, became prominent in Joseph Fourier's (1768-1830) treatment of the heat equation (1822). However, the actual scope of the method remained obscure at first because of the limit process involved. The idea of separation of variables, which reduces problems in two or more dimensions to a family of one-dimensional problems, is also the basis of tomography, a widely used tool of contemporary medicine.

The fundamental question of Fourier's method, visualizations. which functions can be expanded in their Fourier series, turned out to be very complicated and very fertile for the further development of mathematics. For piecewise continuous and piecewise monotonic functions and the trigonometric Fourier series, it was answered in 1829 by Peter Gustav Lejeune-Dirichlet (1805-1859); in its general form, it is the core of the mathematical field of harmonic analysis. Fourier analysis is of great importance in many areas of science and technology; e.g. it is used in astronomy to enhance the optical resolution of telescopes.

References

Books on Nada Bindu