From Pythagoras to WMAP: The ‘Music of the Spheres’ Revisited
Dr. Kristine Larsen
Professor of Physics and Astronomy
Central Connecticut State University
Presented to the Society of Literature, Science, and the Arts, November 13, 2005
§ 1. Introduction
Shortly before Halloween, the December 2005 issue of Astronomy, a popular-level magazine for armchair and amateur astronomers, arrived in the mailbox. Blazoned on the glossy cover was the eye-catching title of a featured article: “The Music of the Spheres.” But rather than a review of a poetic yet archaic view of the heavens from centuries gone by, this article was firmly focused on current and cutting edge research in astronomy. The long-abandoned Pythagorean notion had apparently been resurrected as a powerful metaphor, as the article described how “planetary scientists, astronomers, and cosmologists tune in to the ‘sounds’ of space” in their search for an understanding of the cosmos. The authors noted that a “kind of cosmic symphony is playing all around us. What better term for it than the music of the spheres, even if it’s not what ancient Greek philosophers once imagined?” [Boyle and Grimes 2005, 41] Other popular-level astronomy articles appearing in recent years have included such terms as “Big Bang acoustics,” “solar symphony,” and “heavenly music.” This paper seeks to explore three related themes: what is behind the seeming resurrection of the terminology of Pythagoras and Kepler; is the use of this metaphor truly representative of the actual science, or merely an attempt to catch the eye of the general public; and what benefit can this be to science education?
§ 2. Pre-modern concepts of the Music of the Spheres
In his 1993 popular-level book The Music of the Spheres: Music, Science, and the Natural Order of the Universe, Jamie James laments
Science has drifted so far from its original aims that even to bother with the question of its relationship to music might appear to be an exercise in irrelevancy, like chronicling the connection between military history and confectionary. Yet every scholar of the history of science or of music can attest to the intimate connection between the two. In the classical view it was not really a connection but an identity. [10]
Aristotle wrote in his Metaphysics how the Pythagoreans ascribed numerical values to the musical scales, which could then be related to the universe at large, especially the motions of the planets. This “music of the spheres” could not be heard by any but the especially gifted (reportedly including Pythagoras himself). This was just as well, according to Philo of Alexandria, as “like the song of the Sirens, it would induce frenzied longings.” [Chadwick 1981, 79] Aristotle himself believed the idea to be “beautiful and poetical but absurd, since a principal feature of the heavenly bodies is their silence.” [Chadwick 1981, 79] Plato’s Republic (Book X) contained within the myth of Er the idea that the each of the planets and the fixed stars are accompanied in their circular motions by a siren, whose combined song creates “one harmony.” Ptolemy, as well, wrote in the third book of his Harmonica that the motions of the stars “correspond to musical intervals.” [Chadwick 1981, 82] Boethius, the Roman philosopher, wrote about three types of music: that of the universe, human music, and music created by instruments. He believed that the first
is especially to be studied in the combining of the elements and the variety of the seasons which are observed in the heavens. How indeed could the swift mechanism of the sky move silently in its course? And although this sound does not reach our ears…. the extremely rapid motion of such great bodies could not be altogether without sound, especially since the courses of the stars are joined together by such mutual adaptation that nothing more equally compacted or united could be imagined. [Strunk 1965, 84]
Johannes Kepler gave the idea serious consideration (one might say obsessively so), in his Harmonices Mundi. He discovered that the ratio of certain properties of planetary and lunar motions were approximately the same numerical value as that between the notes in chords. For example, he calculated the ratio of the extreme values of the “hourly motions in arc” (apparent angular distance traveled in the sky per hour) of the moon at its closest and farthest approach to earth to be nearly 3:4, or a musical fourth. [Field 1988, 148] On the basis of the observational “relationships” he found, he constructed musical scales composed of notes representing each of the planets. Interestingly, in order to do so, he had to ignore the octave of the notes (for exampling lowering the “sound” of Mercury at its aphelion by six octaves in order to fit it into the scale). [Field 1988, 150] Kepler’s contemporary, the blind poet John Milton, lamented that
our impotence to hear this harmony seems to be a consequence of the insolence of the robber, Prometheus, which brought so many evils upon men, and at the same time deprived us of that felicity which we shall never be permitted to enjoy as long as we wallow in sin and are brutalized by our animal desires. [Hughes 1957: 604]
Despite the fact the idea’s “poetic qualities” and “the reassurance it offered to humanity that the universe has principles of order,” the concept of the music of the spheres became little more than a historical footnote in the minds of scientists for nearly five centuries. [Chadwick 1981, 79]. It was only in literature and the arts that the idea remained, bubbling just beneath the surface. For example, Gustav Holst created his famous The Planets Suite (1914-16) based on his personal meditation “on the nature of the planets (‘my’ planets as he called them, in other words his [astrological] chart)” and through that process discovered “new worlds of sound.” [Head 1993, 17] In the same decade, fantasy author J.R.R. Tolkien crafted the Ainulindalë, the grand creation myth of his legendary Middle-earth, based on the concept that music was a cosmologically creative force. In his writing, he took the “well-constructed historical and religious theory and belief from ancient and medieval literature and transplant[ed] it wholesale into his world.” [Eden 2003, 192-3] Ironically, it was in the late twentieth century that astronomers realized that sound indeed played a vital role in the creation of structure in the real universe.
§ 3. Sound as Metaphor in Astronomy
Sound is created by the propagation of longitudinal pressure waves through a medium. As with any wave, it is described by its velocity of propagation (which depends on the medium), wavelength, intensity (“loudness”), and frequency (“pitch”). Since the word “sound” is usually thought of in connection with the sense of hearing, a more generic term is acoustic wave, which encompasses frequencies both too high and too low for the human ear to register.
Despite the well-defined nature of sound in the physical sciences, in popular-level works various authors have attempted to use the metaphor of sound (specifically the music of the spheres) to describe vastly different phenomena. For example, in their 1988 book Longing for Harmonies: Themes and Variations from Modern Physics, Frank Wilczek and Betsy Devine posit that the “marvelous dream” of the music of the spheres “is in fact closely realized in the physical world. The spheres, however, are not planets but electrons and atomic nuclei, and the music they emit is not in sound but in light.” [14] They refer to the collection of wavelengths of light emitted from an object of particular composition (its spectrum) as “its own, unique chord…. If our eyes were more perfect, we would see the atoms sing.” [14-15] In her popular-level work on gravity waves entitled Einstein’s Unfinished Symphony: Listening to the Sounds of Space-time, Marcia Bartusiak [2000: 197] described the possibility of detecting a black hole “by the melody of its gravity wave ‘song’.”
A modern convenience commonly misunderstood by the general public is the radio. Sound waves are converted into an electromagnetic signal (light waves in the low frequency, or radio, end of the spectrum), travel through the air as light to an antenna where they are received, and are converted back into sound waves via an electromagnetic circuit (which explains why you cannot directly hear a radio station’s broadcast with your ears alone). However, for several decades astronomers and science writers have capitalized on this common misconception in order to help the general public understand astronomical objects that emit light waves in radio frequencies. For example, rapidly rotating neutron stars emit characteristic beams of radio light at their poles, creating a phenomenon known as a pulsar. The exceedingly regular “ticks” of radio signals have been likened to “a bongo player in the sky” [Boyle and Grimes 2005, 40], and Joseph Taylor and Russell Hulse’s Nobel Prize-winning radio observations of the decay of the orbit of a binary pulsar was termed “patient listening.” [Flam 1993, 507] Pulsar radio signals have also been converted into audible signals of the same frequency as pedagogical aids [Bourke 2005].
Closer to home, a number of atmospheric phenomenon are created when charged particles such as electrons interact with the Earth’s magnetic field and generate radio waves, which scientists can “translate into sounds we can hear.” [Boyle and Grimes 2005, 37] These are sometimes termed “Natural Radio”, and include lightning, meteors, and aurora. In fact, these can be “heard” through their affect on AM or shortwave radio signals (as crackles, whistles, or a general hum) [Richards 2001, 63] Stephen P. McGreevy’s website hosts audio “recordings” of such phenomena. [2005] Meteor showers have also been directly heard via what are termed “electrophonic meteor sounds.” Very low frequency (VLF) radio signals are converted into sound by something on the ground acting as a “transducer.” [Hullander and Phillips 2002, 3] Radio emissions have been noted by spacecraft passing by the Jovian planets [Gurnett, Kurth and Scarf 1981; Scarf, Gurnett and Kurth 1979] and Flagg’s Listening to Jupiter is a guide for amateur radio astronomy enthusiasts wishing to turn their “ears” towards the giant planet.
One very important translation of astronomical radio waves into audible sound is in the arena of SETI – the Search for Extraterrestrial Intelligence. As depicted in the movie Contact, the search for signals of intelligent life hidden in radio waves is frequently referred to as “listening.” In the film, this was explicitly reflected in the character of Kent Clark, modeled after real-life blind SETI astronomer Kent Cullers. Blind since infancy, Cullers has described his work on signal detection as “one of the few fields where being blind is a help. It causes me to concentrate on what I hear.” [Stephans 58] Music itself has also been depicted as a kind of universal language which might be helpful in communication between alien species, such as in the film Close Encounters of the Third Kind and the inclusion of various musical pieces (including whale songs) on the gold record attached to the Voyager spacecraft.
§ 4. Solar Symphonies and Black Holes in B-flat
As the trailers for the film Alien correctly warned, “in space, no one can hear you scream.” In general, interstellar space is currently so close to a perfect vacuum that sound waves cannot propagate. However, in astronomical locations where the gas density is high enough, acoustic waves can and do occur. For example, sound waves can travel through the atmospheres of Venus, Mars, and Saturn’s moon Titan. During its January 2005 descent and landing on Titan, microphones on the Huygens probe made the first extraterrestrial recording of its kind [Boyle and Grimes 2005, 38].
Stars, as hot spheres of dense gas, are also laboratories for the detection of acoustic waves. In 1962 it was discovered that the visible surface of the sun – its photosphere – is bubbling with a period of about five minutes. This “five minute oscillation” was found to be a global rather than local phenomenon caused by sound waves (called p-modes) traveling through the sun. [Demarque and Guenther 1999, 5356] This “solar symphony” is commonly likened to a “quivering gong,” “large-spherical organ pipe” or “ringing bell”, as the sun is now known to have millions of different overtones. [Stokstad 1998, 987; ESO 2002] Helioseismologists have monitored these oscillations for a number of years through the Global Oscillation Network Group of ground-based telescope (GONG) as well as the Solar and Heliospheric Observatory (SOHO). Such studies allow astronomers to map the sun’s interior. As Richard Kerr described, “the idea of a heavenly harmonics is now making a comeback among astronomers. But instead of listening to the revolutions of the spheres, modern astronomers are tuning in to vibrations within stars.” [1991, 1207] Similar observations have been made of a number of stars, including Alpha Centauri and Beta Hydri. The giant star Xi Hydrae was described as a “sub-ultra-bass instrument” with oscillations of several hours. [ESO 2002] As Govert Schilling summarized this field of research,
It is said that a blind musician can recognize a Stradivarius from its sound and even sense the occasional crack in its plate. Similarly, astronomers hope that they will soon be able to detect the provenance and health of stars by listening to their sound. [2002, 1595]
The action of black holes has also been associated with sound. NASA’s Chandra x-ray satellite has detected evidence of acoustic waves in the gaseous regions surrounding two super-massive black holes. The first, at the center of the Perseus galaxy cluster, was touted as the deepest note in the universe – corresponding to B-flat fifty-seven octaves below middle-C. [Savage et al. 2003] The second was found in M 87, an elliptical galaxy in the Virgo Cluster. The suggested mechanism is an
infall of material toward a central supermassive black hole produce[ing] a magnetized jet of high-energy particles that blasts away from the vicinity of the black hole at near the speed of light. As a jet plows into the surrounding gas, a buoyant, magnetized bubble of high-energy particles is created, and an intense sound wave rushes ahead of the expanding bubble. [Roy and Watzke 2004]
§ 5. “The Big Bang Was Neither – Discuss”
The foundation of modern cosmology is the Big Bang theory, unfortunately saddled with a rather poorly chosen name. The term was coined as a pejorative in 1950 by British astronomer Fred Hoyle, one of the three main authors of the rival Steady State model. The “bang” refers to the analogy often used of an explosion, and was not meant to represent sound. However, George Gamow and colleagues did predict that there would be an “echo” of the small, hot, dense state of the early universe, not of sound but of electromagnetic radiation (light). As Mike Myers’ infamous character Linda Richman, hostess of the talk show parody “Coffee Talk” might say, “The Big Bang was neither – discuss.” Nevertheless, this “echo” was vitally important in the intellectual war between the rival cosmological models in the 1950s and 1960s, and its discovery eventually led to the Big Bang ascendance to the throne of cosmology. As Charles Seife described it,
The blind John Milton said that if we could hear the celestial music of the spheres, time would reverse itself, and we would glimpse the purity of Eden and the golden age of the universe, In a sense, Milton was right. [2003, 75]
The early universe was a hot sea of radiation which finally cooled enough to allow the formation of matter (leptons and quarks), which eventually led to hydrogen and helium nuclei, and free electrons, approximately three minutes after the Big Bang. For the next roughly 400,000 years, the universe was in its “Radiation Dominated” phase, where the temperature was too high to allow atoms to form. When the universe cooled to around 5000 K, the electrons were suddenly able to combine with the nuclei to form stable atoms, and the opaque fog caused by constantly scattered light cleared. With this “recombination”, light scattered for the last time, and formed a background radiation which has continued to cool over the past 14 billion or so years. Today the radiation is that of a blackbody at 2.7 K, and peaks in the microwave portion of the spectrum. Arno Penzias and Robert Wilson shared the 1978 Nobel Prize in Physics for their serendipitous discovery of theis cosmic microwave background (CMB).
Detailed measurements of the CMB were made by the Cosmic Background Explorer (COBE) in 1992, which verified the effective temperature of the radiation and discovered slight variations in temperature across the sky to about 1 part in 100,000. Angular variations or anisotropies smaller than about 7 degrees could not be seen because of the satellite’s limited resolution, and had to wait until the Wilkinson Microwave Anisotropy Probe (WMAP) in 2002 to be discovered. These smaller anisotropies were very important, as their existence had been predicted decades before.
It has become standard procedure to describe variations in the CMB in terms of mathematical functions called spherical harmonics. An analogy can be found (in a single dimension) in a guitar string. The fundamental tone of the string is such that the entire string moves back and forth except the two points where the strings are connected to the guitar. The first harmonic tone occurs when there is one stationary point on the string other than the ends, and so forth. In terms of spherical harmonics, these are described by the angular frequency l, where l=0 represents the fundamental tone, the first harmonic, l=1, etc. In terms of the CMB, cosmologists plot the size of temperature variations versus l, creating a graph called the angular power spectrum. Since l = 180/θ, the larger the value of l (or multipole), the smaller the angular size of the variations. Therefore, since COBE could not see angles less than 7 degrees, it could not pick up multipoles larger than about 25 or 26. The ability to see higher multipoles is vitally important, as theory predicts acoustic waves in the early universe led to several pronounced peaks at multipoles higher than l=50 (or angles smaller than 2 degrees). [Whittle “Newborn”]
But how could acoustic waves form in the vacuum of space? The key point is that although interstellar space is unbelievably cold (2.7 K) and relatively empty at this point in the universe’s evolution, during the first 400,000 years or so it was nothing of the sort. In the opaque interactive fog of radiation and matter, pressure waves formed, as gravity’s pull constantly battled with the inherent push of radiation. The sizes of these acoustic pressure waves varied, from the longest (“fundamental”) to smaller “harmonics,” and depend on the speed the waves travel and how much time had elapsed from the start of the universe. Since the speed of sound in this dense “soup” was approximately 60% the speed of light, in the 400,000 year span of this “acoustic era” the longest waves (and deepest “tones”) that could be generated were approximately 220,000 ly in length. [Whittle “Newborn”] This should appear in the CMB as a noticeable peak at around 1 degree (or l~ 220). Smaller peaks should also appear at multiples of this multipole (or fractions of a degree). At Recombination when electrons formed stable atoms and radiation ran free, the speed of sound slowed dramatically, and eventually stopped, and the waves “froze” into place as the pressure ceased. Thanks to WMAP and other CMB measurements, the existence of the first three acoustic peaks has been confirmed, and the precise values of l and other parameters strongly supports the so-called “concordance model” of the early universe. [Scott 2005]
Popular-level articles have capitalized on this acoustic connection to the early universe, with eye-catching titles such as “Detecting Harmonics in the Heavenly Music” [Starkman and Schwarz 2005a] and “Tuning in to the Early Universe.” [Silk 2002] However a full breaching of the “sound barrier” did not occur until a June 2004 meeting of the American Astronomical Society, thanks to the creative work of one galactic astronomer.
§ 6. Music of the Spheres Redux
Large Physics and Astronomy conferences will typically issue press releases about selected papers of special importance or interest to the media and general public. One of the papers so chosen for the June 2004 meeting of the American Astronomical Society (AAS) was “Sounds from the Infant Universe” submitted by Mark Whittle of the University of Virginia. His work, which he dubbed “rather obvious,” was “to reproduce the CMB power spectrum as an audible sound,” covering the first million years of the cosmos in ten seconds. [Whittle “Infant”]
In contrast to the popular misconception fostered by the term “Big Bang,” Whittle’s work dramatically demonstrated that the universe began in silence, because there were no initial acoustic waves (due to the fact that the expansion of the infant universe was symmetrical). However, inherent inhomogeneities in the density of matter and energy are predicted by inflationary models. These eventually gave rise to acoustic waves of increasing wavelength (or deeper tone) once enough time had elapsed for pressure waves to complete an oscillation. An overall drop in pitch was also caused by the expansion of the universe, which stretched the wavelengths. The largest pressure variations correspond to approximately 110 dB, which Whittle compared to “rock concert volume” [“Big Bang Acoustics”]
In order to make the acoustic waves “hearable” by the human ear, he had to shift them upward approximately fifty octaves. He chose to place the fundamental peak at 220 Hz, corresponding to A below concert A, in order to mirror the actual observed peak in the power spectrum at l=220. [“Primordial”] After Recombination, matter (no longer bound to radiation) settles into the “gravity wells” created by dark matter, and the acoustic oscillations cease. In the “concordance model” of the Big Bang, smaller “clumps” form more often than larger ones, leading to domination by what Whittle models as a high pitched hiss, even though true acoustic oscillations in time begin to drop off sharply. He described the evolving sound as “a descending scream, building into a deep rasping roar, and ending in a deafening hiss.” [“Primordial”].
Not unexpectedly, Whittle’s work was picked up by the popular science press, in articles such as “Is This What the Big Bang Sounded Like?” and “Listen to the Universe’s Primal Scream.” [Cocke 2005; David 2004] Whittle himself believed the importance of his work to be strictly pedagogical:
When communicating scientific topics, especially remote or abstract ones, it is always important to use diagrams or images or, in this case, sounds. All of them are representations, none of them are perfect, but each brings the listener closer to grasping the concepts and ideas, and can even help establish an emotional connection with the subject. I think these sounds add to that repertoire in a novel and potentially powerful way. [“Primordial”]
The connection between these important acoustic waves in the early universe and “sound” remained an important one in the publicity surrounding one of the most crucial cosmological discoveries of 2005. It had been predicted that the acoustic waves in the CMB would be reflected in a similar “ripple” in the distribution of galaxies in the universe, but gleaning such direct evidence from observations proved difficult. At the January 2005 meeting of the AAS, groups working with data from the Two-Degree Field Redshift Gravity Survey, and Sloan Digital Sky Survey presented evidence of the predicted clumpiness, on the scale of 500 million light years. [Cole et al. 2005; Eisenstein et al. 2005] The discovery was likened to “detecting the surviving notes of a cosmic symphony” and the difficulty in doing such observations as trying to pick up the “last ring” of a bell that “gets forever quieter and deeper in tone as the Universe expands.” [Cowen 2005; UA News 2005] In addition, lingering problems with the relative strengths of the non-acoustic peaks in the CMB (at low values of l) were discussed in a Scientific American article entitled “Is the Universe Out of Tune”? [Starkman and Schwarz 2005b] The musical metaphor appears to be here to stay.
§ 7. Conclusion
From ancient times, music and astronomy have had an undeniable connection in the minds of some of each field’s purveyors. In modern day, there has been a return to this relationship, sometimes metaphorical, other times literal. The result continues to be an increasing appreciation of the pedagogical value of couching astronomical abstractions in the more familiar framework of music. For example, Design Rhythmics Sonification Research Lab turns scientific data into music for educational and educational projects. Among its projects has been the “sonification” of the solar wind, the Northridge earthquake, and ice core climate change data [Quinn nd]
Whittle applauds the “wonderful pedagogical value” of recent advances in cosmology “in educating and inspiring both students and the wider public.” His acoustic modeling of the early universe can certainly “enhance both the intellectual and the emotional impact of the subject on its audience,” and most importantly can achieve this “without sacrificing scientific honesty.” [“Infant”] This resonates with blind astronomer Kent Cullers’ experience:
When I hear signals from distance regions, my mind goes out there. I try to ride those waves, extend my senses to a realm they’ve never been, hear songs from a cloud of gas. [Richards 2001]
It is with this philosophy in mind that the author plans to offer a Freshman-level seminar in the Fall 2006 semester entitled (not surprisingly) “The Music of the Spheres,” incorporating all of the material discussed in this paper. The main outcome of the course will be for students to appreciate the fact that “The tapestry of galaxies, the star filled sky, the mind that holds both these, all have their roots in primordial sound. It is only fitting that one of our primary senses is sound, and one of our primary arts is music. Both can help us bring closer an appreciation of the Universe, which for so long has yielded only to visual or abstract experience” As Mark Whittle further reminds us, “With a little coaxing, it is now possible to listen directly to Nature whisper some of her oldest and deepest secrets.” [“Primal”]
The curse of Prometheus is broken, and no longer is Pythagoras the only gifted soul to hear the music of the spheres.
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