Andy Cavatorta

Whale is an acoustic and kinetic sculpture. It sings a 225-year-long song that is a weaving of songs of whales, neural network algorithms, and the twelfth century music of Hildegard von Bingen — who attributed much of her work to mystical forces beyond herself.

It is a meditation on end times, algorithms, visions, lives larger than our own, and the possibility that everything is alive.

No human will ever hear this long song. It’s made to fit in the lifespan of a bowhead whale.

Around any current discussion of whales hovers the growing possibility of their extinction. They face their own very real end of days. But I want to talk for a moment about the enormity of their lives.

Bowheads born today may live into the 23rd century — living their own adventures together and improvising their songs in a lifespan beyond our imagining. They are social, like us, with long and complex relationships. They are musically creative. They are explorers.

Their lived adventure may last two and a half centuries. If collected, the songs sung and heard may exceed the length of a human life.

Whales are frequently associated with the mythical creature Leviathan (fig. 1) ― the enormous chaos monster that may lurk in the still of the deep of any sea. Whale and Leviathan are used interchangeably in myths from ancient times on up to Moby Dick. By extension, whales play a role in myths of the End Times.

“To the Leviathan God gave the seventh part of Earth filled with water, and He reserved it for the end of days when it shall be eaten by the righteous.”
― The Book of Enoch

“There is the music of Heaven in all things.”
― Hildegard von Bingen

The long song Whale sings grows from musical soil containing thousands of whale song recordings and the compositions of twelfth century polymath Hildegard von Bingen. Both are sources of nonhuman music with long perspectives on time.

Hildegard was born around 1098 and given to the Benedictine monastery at Disibodenberg as an oblate (spiritual servant). As a child, she was enclosed (permanently walled-in) with another girl, Jutta. It was common for enclosed persons to receive the Office of the Dead upon entering, signifying their death to the world. Both girls experienced ecstatic visions.

Hildegard eventually became a scholar and polymath. Her documentation of her visions of the End Times (fig. 2) were approved by Pope Eugenius III. These visions also inspired her many musical compositions and revealed to her that all matter is alive.

If there are no mystical dimensions in the Universe, if only the physical world exists, then this does not negate our mysteries but instead imbues matter with a numinous power. All of our mysteries, including consciousness, must then be emergent properties of matter.

The philosophical concept of panpsychism explores the idea that all matter is conscious to some degree. Can a machine have consciousness? The new questions are the old questions.

This 16th century automaton in the form of a monk (fig. 3) performs a complex perpetual ritual of devotion. It marches ever forward in a trapezoidal pattern, kissing a rosary, pounding its chest in penance, and roughly mouthing “mea culpa” as its moving eyes observe the moral world around it.

This machine was considered to be not just a novelty but the personification of Saint Diego and an extension of his spiritual mission beyond the boundary of his earthly death.

The collections of natural history museums are filled with the spoils of the colonial conquest of both human and animal kingdoms. The provenance of many pieces is intertwined with the ending of a culture, a people, or a species.

The skeletons of whales hanging in museums radiate a sense of the wondrous, the tragic, and the eternal. Especially the skeletons of cetaceans hunted to extinction by humans seeking to convert their bodies into money and exploitable energy — humanity’s preferred forms of negative entropy.

Whale’s form is not separable from any of this history. Even the language models and fungible processing power used to dream its long song are inseparable from the exploitable energy we are sacrificing to create our AIs.

Can we invent a way of being that causes no suffering? Blue whale skeleton in National History Museum in London

Whale’s 225 year-long song was composed by a recurrent neural network trained on the compositions of Hildegard von Bingen and recordings of the songs of Bowhead and Humpback whales.

Hildegard's ~77 musical works were originally written as neumes and lack notation for note length and musical key. Modern reconstructions are based on scholarly research and some likely guesses.

The whale songs come from audio data cataloged, and shared by NOAA.

This music from whales and Hildegard was digitized and encoded in the MIDI format — a lossy, reductive process in both cases. These scores were then musically transposed to use C as their root notes.

This corpus of scores was used to train a recurrent neural network built with the Python library TensorFlow.

The resulting musical score is Whale's long song (fig. 4).

When two or more waves overlap in the same space, the resulting amplitude at any time is the sum of the wave amplitudes at that time (fig. 5).

Overlapping waves can result in amplitudes higher than either wave. This is called constructive interference.

Overlapping waves can also result in lower amplitudes or even zero amplitude if the waves cancel each other out. This is called destructive interference.

Waves with similar frequencies traveling in opposite directions can combine to result in standing waves (fig. 6). A standing wave is a wave that oscillates in time but whose peak amplitude profile does not move in space. The points of small amplitude are called nodes. The points of high amplitude are antinodes.

The bottom row below shows a full cycle of standing waves rising and falling.

All tuned acoustic instruments create stable tones by creating standing waves in strings, membranes, columns of air, or other mediums.

Air flowing through the tubes creates turbulent vortices as it passes over the corrugations. These create disorganized sound waves with a wide range of frequencies. (fig. 7)

The higher pressure wavefronts in the tube partially reflect back when they reach the lower pressure at the ends of the tubes (fig. 8). At certain energies, these create stable standing waves that organize the turbulent vortices around a dominant frequency. This process is called entrainment.

All octaves are equidistant when viewed as musical pitch. The interval from A3 to A4 is the same size as the interval from A4 to A5.

But viewed as frequencies, each octave is double the frequency of the octave below it. Pitch and frequency have a logarithmic relationship (fig. 9).

The frequency difference between any two adjacent pitches is given by equation 1 below

fig. 10 above illustrates a blue sound wave originating in a tube (left) and propagating two more wavelengths to the right. The Greek letter lambda (λ) is the standard physics symbol for wavelength.

Wavelength measures the physical length of a wave. Frequency measures the temporal length of a wave. The faster a wave of a certain length propagates through its medium, the shorter its frequency (equation 2)

As air flows faster through the tube, the energy in the vortices increases. This can cause the standing waves to jump to a higher harmonic mode with more nodes (fig. 11). This pattern of increasing nodes and pitches is called the Harmonic Series.

The next mode is called the second harmonic or h2 mode. This corresponds to a wavelength equal to the length of the tube. It produces a pitch one octave above the fundamental.

The lowest harmonic mode is called the fundamental or h1 mode. In open-ended tubes, this corresponds to a wavelength twice as long as the tube.

The third harmonic (h3) corresponds to a wavelength that is one third as long as the fundamental, making it two thirds the length of the tube. It produces a pitch that is one octave plus one perfect fifth above the fundamental.

When we substitute f in equation 2 with its value from equation 1, we get a formula for calculating the length of a tube to produce a specific musical pitch. This is equation 3 below.

The table below (fig. 12) shows the lengths of all of Whale's tubes.

It also shows the pitches of the second and third harmonics for each tube length.