15 Root 63-68 © 2001 ISAST LEONARDO, Vol. 34, No. 1, pp. 63–68, 2001 63 A N D I N T E R S E N S E S S Y N E S T H E S 8 I A Mathematics and music! The most glaring possible opposites of human thought! and yet connected, mutually sustained! It is as if they would demonstrate the hidden consensus of all the actions of our mind, which in the revelations of genius makes us forefeel unconscious utterances of a mysteriously active intelligence. —Hermann von Helmholtz, “On The Physiological Causes of Harmony in Music,” 1857 [1] Imagine that you are attending an orchestral concert. You listen with great appreciation to compositions by William Herschel (1738–1822), Hector Berlioz (1803–1869), Aleksandr Borodin (1833–1887), Sir Edward Elgar (1857– 1934) and Ernest Ansermet (1883–1969); and new pieces by Iannis Xenakis (b. 1922) and Richard Bing (b. 1909). At the end of the concert, the conductor, Tom Eisner (b. 1930), mo- tions for silence and makes the following announcement: This has been a very special concert in ways in which most of you are probably unaware. Everything about this concert is per- meated with science. I, myself, am an expert in insects. The en- tire orchestra is made up of scientists and physicians. Indeed, you may well know that “doctor’s symphonies” exist in most major cities in the United States. But most importantly, all of the composers whose music we have played tonight also have ties to science. Herschel was perhaps the most famous astrono- mer of the early nineteenth century and some of his composi- tions have recently been recorded on the Newport Classics la- bel [2]. Berlioz was a practicing physician; Borodin was a Professor of Chemistry who pursued two professional careers si- multaneously throughout his life; Ansermet trained as a math- ematician and taught mathematics at the University of Lausanne before turning his attention solely to music [3]. Iannis Xenakis is also a mathematician, who adds to his accom- plishments those of a practicing architect, and he has written extensively on the interconnections between the arts and sci- ences [4]. Elgar not only had a private chemistry laboratory, but actually filed a patent for a process for producing hydrogen sulfide [5]. Bing is a cardiologist and medical researcher of in- ternational repute who has been awarded such international prizes as the Claude Bernard Medal for his scientific work [6]. What you have heard, then, is not just music, but music cre- ated by people with an unusual facility to cross the boundaries of disciplinary knowledge. In our super-specialized world, it is worth considering what they, and their musical accomplish- ments, tell us about creativity. Thank you, and good night. The concert just described never happened and Tom Eisner never said the words I have put into his mouth. But Eisner, Schurman Professor of Biology at Cornell University, really is an entomologist who plays piano and conducts concerts. He was trained by the conductor Fritz Busch [7]. The list of scien- tist-composers and of composers who have dabbled in science is actually much longer than the one I have had Eisner use (see Table 1) and could be extended significantly if scientists who have set their science to mu- sic were included [8]. For ex- ample, biochemist Harold Baum’s The Biochemists’ Songbook [9] is a complete guide to biochemical pathways—available on cassette— that is scientifically accurate and amusing. (Imagine the tricarboxy- lic acid pathway sung to the tune of “Waltzing Matilda.” That gives you the idea . . .) Or think of Harvard-trained mathematician and professional entertainer Tom Lehrer and his song “The Ele- ments” [10]. As I have Eisner say, there really are doctors’ symphonies and other orchestras, such as the New Orchestra of Boston, composed largely of medical and scientific professionals and, once again, the par- ticipants include an unusually large proportion of well-known scientists, including many Nobel laureates [11]. Less formal concerts take place regularly at institutions such as the Woods Hole Oceanographic Institute and meetings of the Geological Society [12]. In fact, in 1987, Walter Thirring (b. 1927), an in- ternationally known physicist and composer at the Institut fur Theoretische Physik of the University of Vienna, actually car- ried out a concert like the imaginary one described above. Thirring tells me he studied with Anton von Webern during World War II, with Josef Marx and with two pupils of Arnold Schönberg—Edwin Ratz and Josef Polnauer—after the War. For the concert, he gathered his scientific colleagues together to perform music, including some of his own, all of which was composed by scientists. Enough scientists have actually designed or built musical instruments that one could even play such a concert with those instruments alone. Hermann von Helmholtz, for ex- ample, was an accomplished poet and a fine pianist who had a piano built with an unusual tonal development upon which he experimented both privately and for his physics and psy- chology students [13]. Walther Nernst, the Nobel laureate who coined the third law of thermodynamics, is also credited with inventing the first electronically amplified musical in- struments [14] (although that honor may arguably belong to inventor Elisha Gray, whose attempts to invent the telephone Music, Creativity and Scientific Thinking Robert S. Root-Bernstein A B S T R A C T Are music and sci- ence different types of intel- ligence (as posited in the context of Howard Gardner’s multiple intelligences), or are they two manifestations of common ways of think- ing? By focusing on scien- tists who have been musi- cians and on the ways they have used their musical knowledge to inform their scientific work, the author argues in this article that music and science are two ways of using a common set of “tools for thinking” that unify all disciplines. He explores the notion that cre- ative individuals are usually polymaths who think in trans-disciplinary ways. Robert S. Root-Bernstein (physiologist), Department of Physiology, Michigan State Uni- versity, East Lansing, MI 48824, U.S.A.. E-mail: . This article is modified from the keynote address for Music and the Brain: A Sympo- sium, organized by the Foundation for Human Potential, Chicago, Illinois, at The Art Institute of Chicago, 18–20 November 1992. 64 Root-Bernstein, Musical Creativity and Scientific Thinking A N D I N T E R S E N S E S S Y N E S T H E S 8 I A utilized electrified keyboards and violins [15]). James Dewar, the ultra-low tem- perature physicist who invented flasks designed to hold frozen gases, made his own violins [16]. Virginia Apgar, the ob- stetrician whose name attends the birth of every child when they are given an Apgar score, made her own stringed in- struments. Colleagues recently played a quartet using her instruments [17]. Okay: so what? What difference does it make that so many scientists indulge in musical avocations? Well, on the one hand, we have cognitive theories, such as Howard Gardner’s multiple intelli- gences [18], which argue for domain- specific ideation linked to disciplinary specialization. In other words, skills learned in one domain do not inform work in another. I, on the other hand, believe that creative thinking is trans-dis- ciplinar y and transferable from one field to another. More specifically, I be- lieve that musical and scientific abilities are what I call “correlative talents” [19]. By correlative talents, I mean skills or abilities in several different areas that can be integrated to yield surprising and effective results. Skills associated with music—pattern-forming and pattern recognition, kinesthetic ability, imaging, aesthetic sensibility, analogizing and analysis—and indeed an understanding of music itself—have often been impor- tant components of the correlative tal- ents of many famous scientists. One way to summarize my basic thesis would be to say that correlative talents represent harmonious ensembles of skills that en- able musical scientists to “duet” better. How does music help the scientist per- form better (yes, the puns are purpose- ful!)? Musical scientists often make sci- entific use of their musical training and interests. A musical geophysicist at the California Institute of Technology, who wished to remain anonymous, justified his dual interests to me as follows: sup- pose, he said, “someone is getting inter- ested in musical problems. He may then apply what he finds there back to his sci- entific research. That is something that may affect very much the result. I think it is good. I think for a scientist who is working very hard, anything is good that brings from time to time another angle about general ideas into the picture” [20]. Numerous historical examples bear him out [21]. Rene Leannec, an early nineteenth- century physician, painted, played the flute and invented the stethoscope [22]. Is it really conceivable that chance dic- tated that his invention, and even its spe- cific form (a long, thin wooden tube), is so similar to the instrument he played? Could he have made the instrument without the kinesthetic skills of an artist? Could he have used it effectively without the trained ear of a musician that can hear the whisper of a valve not closing properly as easily as the difference be- tween the styles of James Galway and Jean-Pierre Rampal? The answer I get from my cardiologist colleagues is that you certainly do not want a tone-deaf doctor performing stethoscopy! Karl Rudolph Koenig was a violinist and one of Helmholtz’s physics stu- dents, who also melded music and sci- ence. As a young man, he became so in- terested in musical instruments that he apprenticed himself to the violin maker Vuillaume. Melding vocation and avoca- tion, he began to invent new types of acoustical and optical equipment, some of which was incorporated into Edison’s inventions and the apparatus used by Michelson and Morley to measure the speed of light [23]. Many inventors of scientific instruments, including physi- cists Dewar and Charles Wheatstone and physical chemists Wilhelm Ostwald and Martin Kamen, have similarly musi- cal backgrounds [24]. Helmholtz himself not only invented a new tonal development for the piano but was also one of the major developers of the siren, which he used, notably, not to make obnoxious noise as we do today, but more in keeping with the original meaning of its name, to make beautifully pure tones that would woo the listener. Helmholtz used his sirens to investigate the psychological and physiological bases of harmony. He also invented a va- riety of new harmonic oscillators, includ- ing the “resonator,” and worked out the basic physical laws governing their func- tion [25]. He used these resonators to demonstrate that complex sounds can be generated by adding simple, pure tones—the logical and historical basis for modern-day synthesizers. Helmholtz’s resonators became mod- els both mechanistically and mathemati- cally for the development of black body theory—the historical basis of quantum theory—at the hands of two other musi- cally talented scientists, Ludwig Boltzmann and Max Planck, at the be- ginning of this century. Planck’s notion of the quantum—meaning simply a dis- crete state—is based purely on the math- ematics of resonating strings, or har- monic frequencies. Electrons, as the Prince Louis de Broglie, another of our musically active physicists, discovered, can vibrate like strings around the nucleus of the atom. It followed from this discovery that electrons, like strings, should have harmonic frequencies, a musical analogy that de Broglie pub- lished with predictions of what these harmonic frequencies would be; these harmonics were experimentally verified. Table 1. Scientist-Composers [76]* Ernest Ansermet (1883–1969) Mathematician George Antheil (1900–1959) Endocrinologist and Inventor Joseph Auenbrugger (1722–1809) Physician M.A. Balakirev (1837–1910) Mathematician Hector Berlioz (1803–1869) Physician Theodor Billroth (1829–1894) Surgeon Richard Bing (b. 1909) Cardiologist Aleksandr Borodin (1833–1887) Chemist Diana S. Dabby (contemporary) Mathematician Edward Elgar (1857–1934) Chemist John Conrad Hemmeter (1863–1931) Physiologist William Herschel (1738–1822) Astronomer Elie Gagnebin (1891–1949) Geologist Hilary Koprowski (b. 1916) Microbiologist B.G.E. Lacepede (1756–1825) Zoologist Alexis Meinong (1853–1920) Experimental Psychologist Albert Michelson (1852–1931) Physicist Arthur Roberts (nd — 20th century) Chemist Ronald Ross (1857–1932) Epidemiologist Camille St. Saens (1835–1921) Astronomy Bela Schick (1877–1967) Microbiologist Joseph Schillinger (1895–1943) Mathematician Walter Thirring (b. 1927) Physicist Georges Urbain (1872–1938) Inorganic Chemist Emile Votocek (1872–1950) Chemist Iannis Xenakis (b. 1922) Mathematician and Engineer * Based on material from references [2], [4], [5], [8], [65] and [76]. Root-Bernstein, Musical Creativity and Scientific Thinking 65 A N D I N T E R S E N S E S S Y N E S T H E S 8 I A These harmonics, like those of a vibrat- ing string, are “quantized,” or divided, into discrete standing waves. Planck’s discover y of quantum states also re- sulted directly from treating these elec- tron waves as if they were vibrating strings making music. The mathematical formalisms of these cases are identical [26]. Thus, the histories of music and quantum physics are inextricably linked, as Einstein recognized when he pro- claimed Planck’s version of Bohr’s atomic model “the highest form of musi- cality in the sphere of thought”—a double tribute to its “miraculous” har- mony with experimental results and its literally musical structure [27]. Einstein went on to say that his own relativity theory “. . . occurred to me by intuition. And music is the driving force behind this intuition. My parents had me study the violin from the time I was six. My new discovery is the result of musical perception [28].” Contemporary scientists continue this integrative tradition. Almost everyone has heard of Johann Kepler’s music of the spheres; analogously, Heinrich Kai- ser has written out De Broglie’s tonal harmonies and harmonics of the atoms [29]. The use of musical techniques to analyze scientific data is also coming into its own: biochemists at Michigan State University, for example, have invented musical urinalysis [30]. This transforma- tion makes data accessible to visually im- paired individuals and to physicians whose eyes and hands may be busy else- where (e.g. operating on the patient). Also, people are much more sensitive to tonal discrepancies than they are to vi- sual alterations in peak height or nu- merical differences, so that they can ana- lyze musical data more quickly and accurately than visual forms. For these reasons, geneticist Susumo Ohno has converted DNA sequences into musical equivalents that sound like Chopin noc- turnes in order to listen for the patterns that lie hidden within our genes [31]. Meanwhile, John Dunn and Mary Anne Clark [32] and Phil Ortiz [33] have transformed protein sequences into mu- sical equivalents that convey not only lin- ear but conformational data simulta- neously. And physiologist Hugh S. Lusted and electrical engineer R. Ben- jamin Knapp have collaborated to con- vert electrical signals and muscle move- ments into music by means of a simple electronic instrument known as the Biomuse. They note that their research reveals that “the body is literally a sym- phony (or society) of electrical voices, sounding at different frequencies and intensities” [34]. Physician Lloyd Morey notes (another pun!) that the sympho- nies that emerge through Biomuse or similar technologies may someday “help us understand various psychiatric prob- lems, mood swings and probably brain- dysfunction disorders as well” [35]. After all, we are not merely a set of param- eters, such as blood pH, hematocrit, blood glucose and melatonin levels, but a complex interweaving of all of these and many more—multi-stranded inter- weavings that only music can allow us to eavesdrop upon in real time. These selected examples illustrate a phenomenon I call synosia. Synosia is a term I invented as an analogy to the neu- rological concept of synaesthesia [36]. In neurology, synaesthesia refers to a phe- nomenon in which a person experiences a sensation in one of the five senses when another of the senses is stimulated. For example, a person eating a banana may experience the sound of bells, or a per- son seeing the color red may smell a cake baking. While only a small percentage of people experience such unusual synaes- thetic experiences, we all know things (“know” being from the root word gnosis) in several ways simultaneously. An equa- tion can have mathematical, verbal, aural and visual meanings, and some people experience all simultaneously. We may know a gene sequence as music, chemis- try and a set of alphabet letters all at once. Synosia, then, is derived from the words synaesthesis and gnosis—to know and feel simultaneously in a multi-modal, synthetic way. Music plays a special role in my con- cept of synosia because it can simulta- neously be kinesthetic (we must move to make music), emotional, analytical and sensory. “Music is unique in combining quality and quantity precisely and sponta- neously so that sense impression can be measured and proportion can be experi- enced,” writes Siegmund Levarie [37]. “The human sense of hearing has re- markable powers of pattern recognition,” adds chemist Robert Morrison, “but hear- ing has largely been ignored as a means of searching for patterns in numerical data” [38]. “We have really great comput- ers between our ears,” agrees Joseph Mezrich, formerly of AT&T Bell Labs [39]. In consequence, these and other re- searchers at Lucent Technologies, Exxon, Xerox, and various universities are ex- ploring methods for transforming com- plex data such as taxonomic and eco- nomic data into music. Very simply, it is possible for the ear to hear the patterns in dozens of variables changing simulta- neously, just as it can hear and analyze an entire symphony orchestra with dozens of separate musical parts, whereas it is im- possible for the eye (or even for most computers) to handle that many chang- ing variables and derive sense from them [40]. Thus, the mathematician, poet and musician Joseph Sylvester asked himself a century ago: “May not Music be described as the Mathematic of sense, Mathematic as Music of the reason? The soul of each the same! Thus the musician feels Mathematic, and the mathematician thinks Music—Music the dream, Mathematic the working life” [41]. I believe Sylvester is right, and I would add that mathematics (like most ways of knowing) is convertible into many other forms, including visual and kinesthetic ones, as well as into music. Certainly, most scientists and mathematicians of any stature in their field report a semi- conscious stream of thought composed of kinesthetic feelings, images, verbal or acoustical patterns, and/or musical themes accompanying their problem- solving. Einstein said that he never thought in equations; he felt or visual- ized the answers, then converted his in- sights into mathematics at a later stage for communicating his insights to others [42]. Richard Feynman, arguably the most creative physicist since Einstein, also described this translation process following an initial period of imagistic and kinesthetic insight consisting of a literally synaesthetic sense of equations that appeared to his imagination as spe- cifically colored symbols. Equations also manifested themselves to him as particu- lar sounds that he would express to col- leagues and students as whoops, glissandos or patterns of drumbeats. He even described thinking in “acoustical images” [43]. Rolf Nevanlinna, a Scandi- navian mathematician who was also a concert-caliber violinist and president of the Sibelius Society, remarked that mu- sic was in some mysterious way a con- stant accompaniment to his mathemati- cal researches [44]. Similarly, Philip Davis and Reuben Hersh, the authors of The Mathematical Experience, report hav- ing worked on a mathematical problem for many months to the accompaniment of various mathematical images and re- petitive musical themes. Other commit- ments caused them to lay aside their work for several years, but when they took it up again, the images and musical themes also recurred [45]. The synosial phenomenon is common enough that many scientists report work- 66 Root-Bernstein, Musical Creativity and Scientific Thinking A N D I N T E R S E N S E S S Y N E S T H E S 8 I A ing best to the sound of music. Metallur- gist Charles Martin Hall, who discovered how to extract aluminum from its ore in economical quantities, was reported to go to his piano whenever an intractable problem presented itself, thinking more clearly as a result of the music [46]. Einstein’s son also said of his father that, “Whenever he had come to the end of the road or into a difficult situation in his work, he would take refuge in music, and that would usually resolve all his dif- ficulties” [47]. Einstein himself said, “both [music and research] are born of the same source and complement each other through the satisfaction they be- stow” [48]. Richard Bing, our cardiolo- gist-composer, has also stated, “Writing music enriches me to look at science in a different way. It helps me emotionally to feel more about science. You see, I am a romanticist. I perceive science as an emotional exercise of searching the un- known” [49]. For Charles Darwin, music was too effective in stimulating the mind. He found that he had to avoid concerts as he became older because they “set my mind to too rapid perambulations” [50]. Is synosia all-pervasive? Does everyone do their best problem-solving while doing something else? Does the musical theme link and carry diverse thoughts, bridging the silences or gaps between them? Do its patterns provide structured guidance, or themes, along which ideas can travel and merge like the carrier waves of radio fre- quencies? Or, do these musical patterns simply remove the intellectual constraints that have blocked the paths of creative solutions by focusing the conscious mind elsewhere, so that intuition can do its work? Recent work by Rauscher and other investigators on the so-called “Mozart effect,” in which students listen- ing to Mozart regularly or learning how to play musical instruments scored higher on visual problem-solving tests, suggests that something like this phenomenon may be going on [51]. A physical basis for this may exist, since structural brain asym- metries have been observed in musicians that are not present in non-musicians [52] and it appears that the unusual ne- cessity of using the left hand (especially in string players) actually restructures the right, visual side of the brain [53]. Indeed, I have found that musical scientists use visual forms of thinking to a greater degree than even scientists with visual arts avocations [54], but this is a topic on which much more needs to be known. The critical point here is that ideas manifest themselves to creative scientists as sensory images, musical themes or ki- nesthetic feelings and must, as Faraday and Maxwell pointed out long ago [55], then be translated laboriously into for- mal languages such as words or math- ematics in order to be communicated. The creative individual must therefore be synosic in order to link the preverbal, intuitive forms in which ideas occur to their descriptive, communicable forms. Thus, no one with monomaniacal inter- ests or limited to a single talent or skill can, to my mind, be creative, since noth- ing novel or worthy can emerge without making surprising and effective links be- tween things—like the puns with which I have purposefully peppered this article in order to reveal commonalities be- tween musical and scientific language. To create is to combine, to connect, to analogize, to link and to transform. Thus, everyone of eminence, to quote novelist Henry Miller (himself an artist), “has his or her violin d’Ingres” [56]. Ingres, of course, was one of many artists (Henri Matisse and Ansel Adams also come to mind) well known for musical performance. Miller’s point is that all creative individuals have avocations that they practice at very high levels along with their vocations. This is not to equate having multiple interests or skills with creativity; it is not simply that the people I have described are multi-talented, or polymathic. Their talents are correlated in such a way that they interact fruitfully. I stress the fruitfulness. Creativity comes from finding the unexpected connec- tions, from making use of skills, ideas, insights and analogies from disparate fields. Thus, my concept of correlative talents and its own correlate, synosia, help explain for me why true creative ability is so rare. Of the set of multi-tal- ented people, who are in turn a subset of all the people who are singly talented, only some will develop the necessary in- tegration of thinking modes necessary to make their talents interactive. It is my belief, after many years of study, that those who do develop interactive or cor- relative talents often do so because they have a predisposition—learned or innate or a combination of the two, I cannot tell—to view their intellectual world glo- bally and holistically. Thus, the view I have just given of music as a manifesta- tion of thinking, rather than as an inde- pendent type of thinking, is colored by my interest in these polymaths and by my particular theory of creativity as being an integrative, transformational process. Needless to say, I am stretching the available data, but there are hints that my interpretation may be correct. Many very successful scientists have themselves associated their success with their polymathic aptitudes. Flautist-poet J.H. van’t Hoff, the first Nobel laureate in chemistry [57], physicist-artist Pierre Duhem [58], biologist-artist David Nachmansohn [59], physicist-historian- philosopher Gerald Holton [60] and physicist-inventor-novelist Mitchell Wil- son [61] all claim that the entire com- plex of skills and experiences that we call personality are reflected in the specific form that individual scientists’ discover- ies take. Two other Nobel laureates, art- ist-neuroanatomist Santiago Ramon y Cajal [62] and novelist-immunologist Charles Richet [63], both argued that the great advances in science are not due to monomaniacal specialists, but to people who have excelled broadly in their vocations and avocations [64]. Pioneers of psychology such as Francis Galton [65], Henri Fehr [66], P.J. Moebius [67], R.K. White [68] and Jacques Hadamard [69] have verified this idea with anecdotal evidence, show- ing that scientific and mathematical “ge- niuses” have always been unusually “ver- satile” in their range of skills and hobbies. Historian Paul Cranefield found the same thing when he did re- search on the founders of biophysics, such as Helmholtz, Du Bois Reymond and their students. The more hobbies and cultural pursuits each scientist had, the more discoveries he made [70]. More recently, Roberta Milgram has been studying the professional success of thousands of Israeli students who have performed extremely well in the sciences and mathematics. She has found that a much better predictor of career success than IQ, grades or discipline-specific test scores, or any combination of these, was presence or absence of challenging lei- sure-time activities that require substan- tial cognitive input and practice. Playing an instrument or composing music, painting, writing poetry, carpentry, build- ing electronic devices and computer pro- gramming are examples [71]. I and my collaborators have compiled similar data. We have shown in a group of 40 male sci- entists that success (whether measured by impact of publications or other re- lated measures) was statistically corre- lated with their active participation in music, arts and literature as adults. We also found that the scientists’ styles of thinking (visual, verbal, auditory, kines- thetic, etc.) were correlated with their hobbies in that visually oriented scien- tists have more images in their imagina- Root-Bernstein, Musical Creativity and Scientific Thinking 67 A N D I N T E R S E N S E S S Y N E S T H E S 8 I A tion, while verbally oriented ones are more likely to become science commen- tators and theorists [72]. So, if we are to succeed in under- standing creativity, we must understand polymathic people and their multiple talents. We must understand how to deal with integrative intersections in the field of creativity, where music and science meld too completely to be differen- tiable. Inventions are a result of a con- tinuum of experiences that necessitate the rethinking and re-categorization of all that went before [73]. We will there- fore be able to recognize the greatest breakthroughs in the use of the human imagination precisely by their inability to be subsumed into the existing catego- ries of sciences or arts. Each such ad- vance will create new possibilities that we could not even have imagined be- fore, which is just why biologist John Rader Platt believes that the melding of sciences and arts will remain so exciting: “Our verbal and musical symbols scarcely represent the whole field of pos- sible sounds; painting, sculpture and ar- chitecture scarcely scratch the surface of the organization of visual space; and I am not sure that mathematical symbols represent all the forms of biological logic. What new kinds of symbols are we preparing to manipulate, color organs, Labanotation for the ballet, or a dozen others, calling for new talents and devel- oping new types of youthful genius? . . . What symphonies they will compose! What laws they will discover!” [74] And what insights can polymaths such as Apgar, Bing, Borodin, Dewar, Einstein, Thirring and Xenakis provide for our understanding of creativity! Music the dream, Mathematic the working life—each to receive its con- summation from the other when the human intelligence, elevated to its per- fect type, shall shine forth glorified in some future Mozart-Dirichlet or Beethoven-Gauss—a union already not indistinctly foreshadowed in the genius and labors of a Helmholtz! —Joseph Sylvester, 1864 [75] References and Notes 1. R.M. Warren and R.P. Warren, Helmholtz on Percep- tion: Its Physiology and Development (New York, NY: John Wiley and Sons, 1968). 2. The Mozart Orchestra, Sir William Herschel. Music by the Father of Modern Astronomy (Newport Classics CD, 1995). 3. B.J. Novak and G.R. Barnett, “Scientists and Mu- sicians,” Science Teacher 23 (1956) pp. 229–232. 4. See Iannis Xenakis, Arts-Science, Alloys: The Thesis Defense of Iannis Xenakis, et al., (New York: Pendragon Press, 1985) and I. Xenakis, Formalized Music: Thought and Mathematics in Composition (Harmonologia Series: No. 6) (New York: Pendragon Press, 1992). 5. G.B. Kauffman and K. Bumpass, “An Apparent Conflict between Art and Science: The Case of Aleksandr Por firevich Borodin (1833–1887),” Leonardo 21, No. 4, 429–436 (1988). 6. See R.S. Root-Bernstein, “Harmony and Beauty in Medical Research,” Molecular and Cellular Cardiol- ogy 19, 1043–1051 (1987); R.J. Bing, “My Search for the Romantic Unknown,” on Distar: The Voice of the Physician (record) (Muenchen-Graefeling, Ger- many: Werk-Verlag Dr. Edmund Bansschewski GmbH LP, 1981). 7. J. Pettifer and R. Brown, Nature Watch (London: Michael Joseph, 1981) pp. 87–103. 8. See W.J.M. Rankine, Songs and Fables (London: Macmillan, 1874); L. Campbell and W. Garnett, The Life of James Clerk Maxwell (London: Macmillan, 1882); Lord Rayleigh, The Life of Sir J.J. Thomson, O.M. (Cambridge, U.K.: Cambridge Univ. Press, 1943) p. 147; and G. Beadle and M. Beadle, The Language of Life (New York: Doubleday, 1966) p. 162. 9. H. Baum, The Biochemists’ Songbook (Elmsford, NY: Pergamon Press; Hants, U.K.: Taylor & Francis, 1982 [reprint]; Pergamon Press cassette tape, 1983). 10. T. Lehrer, An Evening Wasted with Tom Lehrer (Re- prise Records CD, 1959). 11. See W. Marmelszadt, Musical Sons of Aesculapius (New York, NY: Froben Press, 1946); B. Holland, “Scientists Who Make Music as Readily as They Do Research,” New York Times (25 March 1984) Part H, p. 23; and R.S. Root-Bernstein, Discovering (Cam- bridge, MA: Harvard Univ. Press, 1989) pp. 322–324. 12. See G. Weissmann, Woods Hole Cantata: Essays on Science and Society (New York: Raven Press, 1985); I learned about the meetings of the Geological Soci- ety from Holly Stein of the U.S. Geological Survey, personal communication, 1998. 13. C.C. Gillispie, ed., Dictionary of Scientific Biogra- phy (New York: Charles Scribner’s Sons, 1973– 1981). 14. E. Heibert, “Walther Nernst and the Applica- tion of Physics to Chemistry,” in Springs of Scientific Creativity, R. Aris, H.T. Davis, R.H. Stuewer, eds. (Minneapolis, MN: Univ. of Minnesota Press, 1983) pp. 203–231. 15. D.A. Hounshell, “Two Paths to the Telephone,” in Scientific American 244 (1981) pp. 156–163. 16. J.G. Crowther, Scientific Types (London: Barrie and Rockliff, 1968). 17. A.A. Skolnick, “Apgar Quartet Plays Peri- natologist’s Instruments,” in Journal of the American Medical Association 276, No. 24, 1939–1940 (1996). 18. See H. Gardner, Frames of Mind: The Theor y of Multiple Intelligences (New York: Basic Books, 1983); and H. Gardner, Creating Minds (New York: Basic Books, 1993). 19. See R.S. Root-Bernstein [6,11]. Also, see R.S. Root-Bernstein, “Creative Process As a Unifying Theme of Human Cultures,” Daedalus 113 (1984) pp. 197–218; R.S. Root-Bernstein, “Visual Thinking: The Art of Imagining Reality,” Transactions of the American Philosophical Society 75 (1985) pp. 50–67; R.S. Root-Bernstein, “Tools of Thought: Designing an Integrated Curriculum for Lifelong Learners,” Roeper Review 10 (1987) pp. 17–21; R.S. Root- Bernstein, M. Bernstein and H. Garnier, “Correla- tions between Avocations and Professional Success of 40 Scientists of the Eiduson Study,” Journal of Cre- ativity Research 8 (1995) pp. 115–137; R.S. Root- Bernstein, “The Sciences and Arts Share a Com- mon Creative Aesthetic,” in The Elusive Synthesis: Aesthetics and Science, A.I. Tauber, ed. (New York: Kluwer, 1996) pp. 49–82; R.S. Root-Bernstein and M.M. Root-Bernstein, Sparks of Genius (Boston, MA: Houghton Mifflin, 1999); and R.S. Root-Bernstein, “Sensual Education,” The Sciences (Sept.–Oct. 1990) pp. 12–14. 20. Root-Bernstein, Bernstein and Garnier [19] p. 126. 21. See J.C. Kassler, “Music As a Model in Early Sci- ence,” History of Science 20 (1982) pp. 103–139; and J.C. Kassler, “Man—A Musical Instrument: Models of the Brain and Mental Functioning Before the Computer,” History of Science 22 (1984) pp. 59–92. 22. Marmelszadt [11]. 23. Gillispie [13] Vols. 7–8, pp. 444–446. 24. Root-Bernstein [11] pp. 312–340; Martin Kamen, Radiant Science, Dark Politics (Berkeley: Uni- versity of California Press, 1985). 25. Warren and Warren [1]. 26. See G. Gamow, Thirty Years That Shook Physics: The Stor y of Quantum Theor y (Garden City, NY: Doubleday, 1966); and T.S. Kuhn, Black Body Theory and the Quantum Discontinuity, 1894–1912 (Oxford, U.K.: Clarendon, 1978). 27. P.A. Schilpp, ed., Albert Einstein: Philosopher-Scien- tist (New York: Harpers, 1959) Vol. 2, p. 45. 28. S. Suzuki, Nurtured by Love: A New Approach to Education, Waltraud Suzuki, trans. (New York: Ex- position Press, 1969). 29. J. Brandmueller and R. Claus, “Symmetry: Its Significance in Science and Art,” Interdisciplinar y Science Reviews 7, 296–308 (1982). 30. C.C. Sweeley, J.F. Holland, D.S. Towson, B.A. Chamberlin, “Interactive and Multi-Sensory Analy- sis of Complex Mixtures by an Automated Gas Chromatography System,” Journal of Chromatography 399 (1987) pp. 173–181. 31. See S. Ohno and M. Ohno, “The All Pervasive Principle of Repetitious Recurrence Governs Not Only Coding Sequence Construction but Also Hu- man Endeavor in Musical Composition,” Immunoge- netics 24 (1986) pp. 71–78; and S. Ohno, “A Song in Praise of Peptide Palindromes,” Leukemia 7 Supp. 2 (1993) S157–S159. 32. J. Dunn and M.A. Clark, “Life Music: The Sonification of Proteins,” Leonardo 32, No. 1, 25–32 (1999). 33. P. Ortiz, “Sounds of Science” . 34. I. Amato, “Muscle Melodies and Brain Refrains: Turning Bioelectric Signals into Music,” Science News 135 (1989) pp. 202–203. 35. L.W. Morey, “Musings on Biomuse,” Science News 135 (1989) p. 307. 36. See Root-Bernstein [11]; R.S. Root-Bernstein, “The Sciences and Arts Share a Common Creative Aesthetic,” in A.I. Tauber, ed., The Elusive Synthesis: Aesthetics and Science (Amsterdam: Kluwer, 1996) pp. 49–82; and R.S. Root-Bernstein and M.M. Root- Bernstein, Sparks of Genius [19]. 37. S. Levarie, “Music As a Structural Model,” Social and Biological Structures 3 (1980) pp. 237–245. 38. I. Peterson, “The Sound of Data,” Science News 127 (1985) pp. 348–350. 39. I. Peterson [38] p. 349. 40. I. Peterson [38] p. 349. 41. J. Sylvester, “Algebraical Researches Containing a Disquisition on Newton’s Rule for the Discovery of Imaginary Roots,” Philosophical Transactions of the Royal Society of London 154, 613n (1864). 42. J. Hadamard, The Psychology of Invention in the Mathematical Field (Princeton, NJ: Princeton Univ. Press, 1945). 68 Root-Bernstein, Musical Creativity and Scientific Thinking A N D I N T E R S E N S E S S Y N E S T H E S 8 I A 43. J. Gleick, Genius: The Life and Science of Richard Feynman (New York: Pantheon, 1992). 44. O. Lehto, “Rolf Nevanlinna,” Suomalainen TiedeakatemiaVuosikirja (Finnish Academy of Sci- ences Yearbook, 1980) pp. 108–112. 45. P.J. Davis and R. Hersh, The Mathematical Experi- ence (Boston, MA: Houghton Mifflin, 1981). 46. A.B. Garrett, The Flash of Genius (Princeton, NJ: Van Nostrand, 1963). 47. R. Clark, Einstein: The Life and Times (New York: World Publishing, 1971) p. 106. 48. Clark [47] p. 106. 49. Pettifer and Brown [7]. 50. C. Darwin, The Autobiography of Charles Darwin, 1809–1882 (New York: Harcourt, Brace, World, 1958). 51. See F.H. Rauscher, G.L. Shaw and K.N. Ky, “Lis- tening to Mozart Enhances Spatial-Temporal Rea- soning: Towards a Neurophysiological Basis,” Neuro- sciences Letters 185 (1995) pp. 44–47; Rauscher, Shaw and Ky, “Music Training Causes Long-Term En- hancement of Preschool Children’s Spatial-Tempo- ral Reasoning,” Neurological Research 19, No. 1, 2–8 (1997); and A.B. Graziano, M. Peterson and G.L. Shaw, “Enhanced Learning of Proportional Math through Music Training and Spatial-Temporal Train- ing,” Neurological Research 21, No. 2, 139–152 (1999). 52. G. Schlaug, L. Jancke, Y. Huang and H. Steinmetz, “In Vivo Evidence of Structural Brain Asymmetry in Musicians,” Science 267 (1995) pp. 699–701. 53. T. Elbert, C. Pantev, C. Wienbruch, B. Rockstroh and E. Taub, “Increased Cortical Repre- sentation of the Fingers of the Left Hand in String Players,” Science 270 (1995) pp. 305–307. 54. See Root-Bernstein, Bernstein and Garnier [19]. 55. C.W.F. Everitt, “Maxwell’s Scientific Creativity,” in Springs of Scientific Creativity, R. Aris, H.T. Davis and R.H. Steuwer, eds. (Minneapolis, MN: Univ. of Minnesota Press, 1983) pp. 44–70. 56. See K. Hjerter, Doubly Gifted: The Author as Visual Artist (New York: Abrams, 1986); J.H. van’t Hoff, “Imagination in Science,” G.F. Springer, trans., Mo- lecular Biology, Biochemistry, and Biophysics 1 (1967) pp. 1–18. 57. Van’t Hoff [56]. 58. A. Lowinger, The Methodology of Pierre Duhem (New York: Columbia Univ. Press, 1940). 59. D. Nachmansohn, “Biochemistry As Part of My Life,” Annual Review of Biochemistry 41 (1972) pp. 1– 21. 60. G. Holton, Thematic Origins of Scientific Thought: Kepler to Einstein (Cambridge, MA: Harvard Univ. Press, 1973). 61. M. Wilson, A Passion to Know (Garden City, NY: Doubleday, 1972). 62. S. Ramon y Cajal, Recollections of My Life, E.H. Craigie and J. Cano, trans. (Cambridge, MA: MIT Press, 1937). 63. C. Richet, The Natural History of a Savant, Oliver Lodge, trans. (London: J.M. Dent, 1927). 64. See also Root-Bernstein, Bernstein and Garnier [19] and O. Lehto [44]. 65. F. Galton, English Men of Science: Their Nature and Nurture (London: Macmillan, 1874). 66. H. Fehr, Enquete de L’Enseignement Mathematique sur la Methode de Travail des Mathematiciens (Paris: Gauthier-Villars, 1912). 67. P.J. Moebius, Die Anlage zur Mathematik (Leipzig: J.U. Barth, 1900). 68. R.K. White, “The Versatility of Genius,” Journal of Social Psychology 2 (1931) pp. 460–489. 69. See Hadamard [42]. 70. P. Cranefield, “The Philosophical and Cultural Interests of the Biophysics Movement of 1847,” Journal of the History of Medicine 21 (1966) pp. 1–7. 71. See R.M. Milgram, R. Dunn and G.E. Price, eds., Teaching and Counseling Gifted and Talented Ado- lescents: An International Learning Style Perspective (New York: Praeger, 1993); E. Hong, R.M. Milgram and S.C. Whiston, “Leisure Activities in Adoles- cence As a Predictor of Occupational Choice in Young Adults: A Longitudinal Study,” Journal of Ca- reer Development 19 (1993) pp. 221–229; and E. Hong, S.C. Whiston and R.M. Milgram, “Leisure Activities in Career Guidance for Gifted and Tal- ented Adolescents: A Validation Study of the Tel- Aviv Activities Inventory,” Gifted Child Quarterly 37 (1993) pp. 65–68. 72. See Root-Bernstein, Bernstein and Garnier [19] pp. 136–137. 73. Root-Bernstein [11]. 74. J.R. Platt, The Excitement of Science (Boston, MA: Houghton Mifflin, 1962). 75. Sylvester [41] p. 613n. 76. For further information, see G. Antheil, Bad Boy of Music (Garden City, NY: Double Day Doran, 1945), J.C. Hemmeter, “Theodor Billroth, Musical and Surgical Philosopher: A Biography and a Review of His Work on Psychophysiological Aphorisms on Music,” Johns Hopkins Hospital Bulletin 11 (1900) pp. 297–317; Hilary Koprowski, Fleeting Thoughts. Songs and Chamber Music by Hilar y Koprowski (Woburn, MA: MMC Recordings CD, 1999); R.L. Megroz, Ronald Ross, Discoverer and Creator (London: George Allen & Unwin, 1931); I. Peterson, “Bach to Chaos: Chaotic Variations on a Classical Theme,” Science News 146 (1994) pp. 428–429; J. Schillinger, Math- ematical Basis of the Arts (New York: Philosophical Library, 1948); and F.W. Sunderman, “Theodor Billroth as Musician,” Bulletin of the Medical Library Association 25 (1937) pp. 209–220. Robert Root-Bernstein, biologist, historian and artist, believes in synthesis through complementarity. His unusual mixture of ac- tivities was made possible by a MacArthur fellowship. Manuscript received 1 September 1999.