At the beginning of the twenty-first century, numerous models attempting to explain the origin and development of the universe enjoy some currency. Cyclical cosmological theory, which still has its proponents, suggests that physical changes in the world are similar to the phases of the moon, and that once a given sequence of events has reached completion, conditions are such as to give rise to yet another cycle. If this view is correct, a trillion-year phase of accelerating expansion has recently begun which will ultimately be followed by contraction, "bounce," and re-expansion. String theory (see below) even raises the possibility that we inhabit a three-brane or three-dimensional space in a cosmos that may ultimately consist of branes with even more dimensions. If our three-brane should collide repeatedly with another nearby brane, "time as we know it would span only one of the universe's many cycles, with one bang followed by another, and then another."²⁷

This model demonstrates on the macro scale the cyclical recurrence that we have already noted in connection with natural phenomena, which, in turn, is imitated in music through the principle of repetition.

Recent emphasis has been placed on the inflationary cosmological model, which posits that in the early universe space underwent a relatively brief but immensely powerful burst of expansion following the Big Bang. Absent a sufficient quantity of dark matter, the universe will continue to age and expand indefinitely.

Conventional wisdom has it that time flies irreversibly in just one direction, from the past through the present into the future, and this view is consistent, given certain caveats, with the inflationary model. The most likely explanation for the "arrow of time," if there is one, depends on a particular interpretation of the Second Law of Thermodynamics, which predicts that the entropy of an isolated system never decreases. This is not good news, however, either for the universe or for the arts.

Even if it could be demonstrated that the "arrow of time" required by the inflationary model were real, it points towards a future of continuing disintegration and ultimate heat death. However remote its direst consequences may be from present-day humanity, this cosmological theory seems unlikely to furnish anything more inspirational for music and the arts than a slender pretext for further decadence and complexity.

On the other hand, since the Second Law is not exempted from time-reversal symmetry, entropy—the measure of the disorder and complexity of a physical system—is just as likely to increase towards what we call the past as it is towards what we call the future.

Although everyday experience suggests that entropy increases towards what we think of as the future—glasses that fall to the floor shatter but don't unshatter, and human beings grow older, not younger—we cannot arbitrarily bend the time-symmetric Second Law to our will and impose a one-way direction on time. In order for the inflationary model to work, in order for there to be an "arrow of time," we cannot simply insist that certain conditions about which we are ignorant prevailed in the early universe. We do not know what the Big Bang was, since the equations of general relativity "break down at time-zero." We do not even know whether conditions required for an inflationary burst actually occurred.²⁹

Thus far, the inflationary model does not fit seamlessly within string theory (see below) or within any contemporary theoretical framework intended to reconcile quantum mechanics and general relativity. If entropy had been steadily increasing throughout what we think of as the past, we would expect the universe to have become extremely disorderly: "the more ordered the universe is today . . . the greater the statistical aberration required to bring it into existence."³⁰ Instead, after fourteen billion years of inflationary expansion, planets, stars, and galaxies have formed; our memories and records, including the laws of science, have not become a jumbled mess and remain reasonably reliable; and the conditions necessary to support and sustain life have been maintained.

The inflationary model attempts to explain the harmonious order of the cosmos as we know it today by assuming the prior existence of a past with exceedingly low gravitational entropy. As we have seen, however, this explanation remains highly problematic.

There are dissenting voices in the scientific community who reject the concept of a timeless universe such as that envisioned by Einstein. The late Nobel Laureate Ilya Prigogine (1917–2003), whose work centered on elucidating the role of time in biology and the physical sciences, compared Einstein to Bruno Giordano, the sixteenth-century Italian philosopher burned alive for his heretical views, implying that Einstein opposed time-irreversibility because of personal unhappiness.³¹ Prigogine balked at the idea that past, present, and future were indistinguishable, and insisted with French poet Paul Valéry that, "time is construction" in a universe where the "arrow of time" is objectively real and increasingly so as one ascends from lower to higher levels of biological organization.³² Pointing to a schizophrenic dichotomy between "time felt and time understood" and a "clash" between the temporal symmetry of dynamics and directional time of thermodynamics, it was Prigogine's goal to insert that one-way arrow into mainstream physics without entirely disavowing the presence of "a past with which we coexist."³³ He argued that scientists in various disciplines, having moved beyond the "imperfect knowledge" and "insufficient control" of the past, were finally receptive to his revolutionary new ideas:

People in the creative fields have been especially attracted to Prigogine's heterodox conclusions, which imply that entropy is fundamental to the creative process, enabling the artist to extract order from chaos:

Physicist Jean Bricmont, on the other hand, maintains that although Prigogine's upbeat presentation of nonequilibrium thermodynamics may make poets happy by painting a picture of a nondeterministic universe in which free will is not disallowed, it is misleading to apply the findings of microscopic research to macroscopic human behavior in psychology and the social sciences. He also argues that by implying there is a crisis in science, Prigogine may be setting the stage for unscientific, pseudoscientific, or even antiscientific reactions.³⁶

There is no evidence that a paradigm shift from classical physics to Prigoginian physics is imminent, but as in physics so in the arts, the question of being versus becoming remains an issue of critical importance.

In classical physics, which includes the laws of Newton and Maxwell and the general and special relativity theories of Einstein, by determining the positions and velocities of all macroscopic objects at any given moment, it is possible to determine their positions and velocities at other moments, past or future.

Quantum mechanics, on the other hand, applied to the ultramicroscopic realm of atoms and subatomic particles, offers no such certainty. The closer one comes to determining the velocity of a particle, the further one gets from determining its position. The closer one gets to determining the position of a particle, the further one gets from determining its velocity. The very act of observing defines reality, and as a consequence of Heisenberg's Uncertainty Principle, the observer inevitably changes that reality. This means that even the most careful measurements are at best predictions based on the laws of probability. Since time-reversal symmetry still applies, and none of the familiar macroscopic signs that time is "passing" are present in the ultramicroscopic quantum realm, it is impossible to say that particles are moving in any particular chronological direction.

Thus, space and time may be mere approximations of an even more fundamental reality at a scale where macroscopic space and time morph into their ultramicroscopic counterparts and such familiar concepts as length and duration become meaningless.

Loop quantum gravity, another theory that aims to reconcile general relativity and quantum mechanics, does not require any background spacetime. If successfully adapted to string theory (see below), an essentially spaceless and timeless view of reality could be inevitable.³⁹

The view that consciousness and mental activity are closely related to the structures and functions of the human brain is widely accepted. It may be tempting to dismiss quantum phenomena as irrelevant to the creative process because these phenomena occur at a scale infinitesimally smaller than that of everyday waking experience. Since, however, "quantum theory is the most fundamental theory of matter that is currently available, it is a legitimate question to ask whether quantum theory can help us to understand consciousness."⁴⁰ Indeed, the role of the conscious observer is one of the most important factors that distinguishes quantum physics from classical physics.

Various quantum theories of consciousness have been advanced in the course of the past several decades, resulting in a literature that is both voluminous and in many cases highly technical. Some of these theories promise to elucidate how the fundamental nature and perception of time might shape the products of human creativity.

Hartmann Römer has proposed on the basis of Weak Quantum Theory that the perception of time arises after an "epistemic splitting" of the underlying timeless unity of mind and matter (Jung's unus mundus) gives rise to a conscious observer.

Römer emphasizes that attempts to derive the arrow of time from time-symmetric physical laws have met with little success, and typically fall back on the "psychological arrow of internal time." But as he points out, this psychological arrow begins to lose all sense of direction in the dream state and is utterly meaningless at the deepest levels of consciousness.

This is highly significant from an aesthetic perspective, since there is substantial evidence linking the unconscious mind and musical creativity. In The Interpretation of Dreams, Freud cites the research of P. Haffner (1887), who noted that "the first mark of a dream is its independence of space and time."⁴² Gardner relates the seminal importance of this time-and-space-independent dream state to Stravinsky's The Rite of Spring, which is set in the prehistoric past of Russia:

Freud was struck by the visionary origin of Tartini's famous "Trillo del diavolo" sonata, conceived by the composer in a vivid dream and written down upon waking. His words still ring true after more than a hundred years:

If this is true, and dreams and the unconscious mind are unfettered by the temporal constraints of the waking state, then an essentially timeless quantum theory of creativity begins to emerge which could not be more different than the time-conscious and time-bound position of modernism. By rejecting the past and attempting to confine themselves to an illusory present, the most dogmatic of the modernists may have succeeded only in impeding access to that vast reservoir of ideas, images, memories, and experiences lying at the deepest levels of consciousness. The inevitable result would have been a music that, for all its self-conscious intellectualism, seemed strangely superficial and vacuous. By contrast, the music of Stravinsky, who remained relatively immune to the temporal myopia of many of his contemporaries, has enjoyed far greater success with musicians and music-lovers alike.

We know, too, that Mozart was unaffected by any such compulsive attachment to modernity and seems to have felt little of the anxiety of influence that affected succeeding generations of composers: "He made liberal use of musical ideas of others, the urge for originality being as alien to him as to any composer of his time."⁴⁵ Indeed, Mozart prided himself on his ability to write fluently in the manner of other composers. In a letter of 7 February 1778, he confidently reminded his father, "As you know, I can more or less adopt or imitate any kind and any style of composition." Thanks to his intimate association with Baron van Swieten and other musically inclined antiquarians, Mozart assimilated the styles of Bach, Handel, and other masters of the past whose works greatly influenced his own creative output. Enthusiastically embracing the presence of the past, which mysteriously came to him in the form of musical thoughts, Mozart seems to have been able to transcend the conventional notions of time and place imposed by ordinary waking consciousness and to access creative resources lying deep within the unconscious mind. Not only did entire works assemble themselves in his imagination as if my magic, but once those works were completed in his head, Mozart could hear them non-successively, as if they were compressed into a single timeless moment:

Max Frisch describes time as a prism-like tool operating at the conscious level that imposes a successive spectral order on the essentially timeless, holistic content of the unconscious mind:

Cosmic Strings

One of the most remarkable developments in modern physics began with an astonishing blast from the past. In 1968 Italian physicist Gabriele Veneziano, conducting research at CERN in Geneva, Switzerland, was stunned to realize that an eighteenth-century mathematical formula invented by Leonhard Euler (1707–1783) seemed mysteriously ready-made to describe many features of the strong nuclear force. In 1970, scientists working at the University of Chicago, Stanford, and the Niels Bohr Institute found that by modeling elementary particles as extremely tiny, one-dimensional vibrating strings, nuclear interactions could be precisely described by Euler's beta function:

Although the earliest formulation of string theory contradicted experimental observations, it failed mainly because its significance had been underestimated. As it turned out, string theory was both a theory of the strong force and a quantum theory that incorporated gravity. Indeed, it is the first successful theoretical approach to uniting gravity and quantum mechanics, and holds the promise of providing a unified description of all matter and all forces in the universe. Little excitement, however, was generated until 1984, when John Schwarz and Michael Green demonstrated that earlier conflicts had been resolved and string theory was actually the first quantum mechanical theory of the gravitational force. This discovery would rock the scientific world, as researchers around the globe felt that they might at last have discovered the key to unlocking the deepest secrets of the cosmos.⁴⁸

String theory, or superstring theory as it is now called, owes even more to Euler and his historical antecedents than is commonly supposed. Euler was not only an ingenious mathematician but also an important music theorist who developed string theories of his own. Along with d’Alembert and Bernoulli, Euler sought a solution to the problematic mathematical model of a vibrating string, and engaged with them in a ten-year debate about the meaning of "function." In 1726, Euler published a thesis in which he compared the sounds produced by vibrating strings to those generated by wind instruments. In the second chapter of his Tentamen novae theoriae musicae ex certissimis harmoniae principiis dilucide expositae (1739), Euler introduced an aesthetic theory in which the pleasures of music are attributed to the indirect perception of perfect order, in distinction to the more direct perception of order represented by a clock. According to Euler's text, order is of two kinds, corresponding to pitch and duration. In his view, the former is superior because it is determined by vibratory frequencies: musical pleasure is ultimately dependent on the arithmetic proportions associated with pitch. ⁴⁹

The theory of proportions can be traced directly back to Classical antiquity and had been variously revived and reinterpreted. Pythagoras (c. 550–c. 500 BC) and his followers saw an intimate relationship between music, mathematics, and the cosmos, and believed the laws of nature could be expressed in terms of pure number. They are credited with the invention of the monochord and for discovering the fact that by allowing specific fractions of the total length of its single string to vibrate, it is possible to derive all of the tones used in music. Thus, when the string of the monochord was divided precisely in two and only half of it was plucked, the resulting tone sounded exactly an octave higher than the open (undivided) string. By allowing only two-thirds of the string to vibrate, the tone a perfect fifth above the open string could be sounded. By allowing only three-fourths of the string to vibrate, the tone a perfect fourth above the open string was produced, and so on, for all the notes contained in a musical scale.

In his De Institutione Musica, Boethius (c. 400–c. 526) described the derivation of musical tones by divisions of the monochord, using Latin letters for musical notation. Subsequent theorists in music, architecture, and other disciplines would recur to Pythagorean tradition, more often than not attributing the mathematical proportions underlying music and the arts to supernatural design. The magic of numbers they discerned in vibrating strings was readily taken as evidence of an harmonious order that informed the whole of creation, from the human body to the stars and planets.

Deeply immersed in this same tradition, Robert Fludd (1573–1637) published an extravagant graphical interpretation of the mathematical harmony of the universe in The History of the Macrocosm (1619) less than a century before Euler's birth. The central image in Fludd's illustration is a gigantic monochord, intended as a metaphor for the cosmos, that is being tuned by the hand of God. The harmonic proportions corresponding to the tones of a musical scale (the modern Mixolydian) are clearly marked, as well as the four elements believed then to constitute the material universe—earth, water, air, and fire.