Creativity and Computation: Rethinking the Divide
How can the notions of creativity and computation meet? In everyday speech these two terms are often treated as if they stand in opposition. Creativity tends to be linked with the arts and is associated with human fantasy, inspiration, or imagination. In this framing, creativity surfaces when new objects or concepts with aesthetic weight are invented. Computation, by contrast, is tied to mathematical procedures that provide repeatable answers to practical problems in a positivist fashion. Against this assumed opposition, this article argues that creativity and computation can sometimes be deeply interconnected and interdependent.
Carnovalini and Rodà note that our expectation of deterministic behaviour from computers "seems to be the exact opposite of our understanding of the concept of creativity." Whether human behaviour — and human creativity specifically — is itself deterministic remains an open question, but that question is not tackled here. What matters for now is that the unknown degree of determinism in human creativity means determinism alone does not rule out creativity in computational systems.
Consider a common misunderstanding. Many primary-school children do not view mathematics as creative when they are asked to memorise multiplication tables. Teaching methods may shape this perception, of course. In any case, not every application of a computational operation produces a creative result; playing a single note on an instrument is not necessarily creative either. Yet an original sequence of notes may strike a listener as creative. Similarly, the assembly of basic mathematical operations into larger complexes, along with the interpretation of those complexes and their real-world applications, can be seen as creative. Most mathematicians would probably agree that their discipline demands creativity even though computation is central to it. For them, creativity and computation are intertwined. Composers who use integral serialism apply mathematical relations as tools for composition, again navigating a zone where computation and creativity interlock and depend on one another.
The discussion here takes a wide view, spanning performative musical creativity and computer systems. Instances where creativity and computation depend on each other can arise when groups of musicians and computer-based improviser systems perform together. Not all such performances are deemed creative by attentive listeners, but this analysis starts from the premise that human improvisation is at least potentially creative. Consequently the scope is limited to improvised performances that interested listeners consider creative, leaving aside cases that audiences or performers themselves might regard as pedestrian.
This linking of creativity and computation opens the door to human-computer co-creative partnerships. In such collaborations, distributed creativity — involving both musicians and computational systems — may emerge. The computational agent can take part in group improvisation, where, as Linson and Clarke put it, "improvisation can be productively understood as 'listening-while-performing' – a clear-cut example of the pervasive ecological principle of perception-action coupling in which playing informs listening, and listening informs playing."
Need the idea of listening be off-limits when we talk about machines? The term usually implies conscious interpretation of sound, so it may seem inapplicable to computational systems. In practice, though, computational listening is often reduced to the calculation of features — feature extraction — from microphone input, and those features represent the music the system then interprets. Machine listening differs from human listening, but computational systems can interpret sound without consciousness. The term emergence is also disputed. Here it refers to an effect produced by the self-organising members of a performing group, both human or computational. The system in this sense includes the performing group, the venue, the audience, and the larger intertextual network that may influence what happens musically.
Categories of human and computational creativity
Human improvisation is probably tightly bound to cognition. Dror and Harnad contend that machines "can sometimes contribute to human cognition, but that does not make them cognizers" because machines lack mental states. They equate cognition with mental states, so in their view machines may extend human cognition without being cognitive systems themselves. This leads to an understanding of distributed cognition and therefore distributed creativity as an environmental extension of human cognition and creativity.
Computational creativity may require human cognitive involvement. Yet even without mental states, computational systems can qualify as a category of creativity because they contribute to distributed creative outcomes. Human creativity, too, may depend on functional involvement as a contributor to distributed creativity. Boden's category of Historical Creativity, for instance, implies that what she calls transformational creativity only arises in a social and ecological context; the individual person's creativity is possible only as part of a larger network unfolding across human history. Boden's Personal Creativity, meanwhile, looks closer to learning — perhaps experiential learning — since what is new in a personally creative act is a discovery for the individual alone.
The claim here is that computational creativity can belong to the same general class of contributors to ecological or distributed creativity as human creativity. Yet human creativity and computational creativity remain categorically different. A computational contributor to group creativity is functionally and operationally distinct from a human one. It does not have to model human creativity even when it engages in an activity such as music making, which is often considered uniquely human. The following sections examine this position within the context of group improvisation, where the performance can act as a setting for human-computer co-creativity.
Computation and the human mind
If computation and creativity are distinct yet not in conflict, how do their referents interact in a performance setting? First, what does it mean for something to be computational? A computer is taken here as an entity that executes an encoding of a computation. This distinction carries weight: the computer exists along a time axis, but the computation itself is an abstract fact — or formally, a theorem — of a consistent formal system and may not be time-dependent.
In a mathematical sense, computation can be a static truth. The result of a particular calculation does not depend on when or by whom it is performed historically; it is generally offered as a logical constant within a given formal system. The validity of a formal proof is considered ahistorical even if it takes mathematicians years or generations to find it. Consequently, computations that are sound and coherent are accepted as perpetually valid, retroactively as well, regardless of when they were formulated. This holds even when the computational result cannot be predicted without actually running the process.
These terms can be treated as designating families of concepts in Wittgenstein's sense. The term computer then covers a family of system types that implement (or realise) an encoding of a computation type. While the mathematical truth of a particular computation may be universally valid independent of time, the computer that realises it in encoded form exists and functions within a specific timeframe.
With this understanding, humans can be considered computers in the older, pre-digital sense of the word: they can execute an encoded computation. That encoding may alternately reside in a machine, such as a digital computer, but it must be programmed into that machine. Even if a new mathematical proof comes out of a computer, the encoding needed to arrive at that proof — effectively a kind of meta-proof — must be supplied by a human. The instructions in a Universal Turing Machine have to come from some meta-machine, which for present purposes is one or more humans.
Is that meta-machine necessarily human? Code that generates other code already exists, yet where the earlier code counts as an originating meta-machine is an open question. Pinpointing an originating meta-machine resembles a chicken-or-egg puzzle. Evolutionary theory tells us Homo sapiens evolved from earlier species; if machines evolved, would their lineage include some originating meta-machine acting as a link between biology and machine? A Turing Machine is not a biological species, but finding an originating computational meta-machine remains an open problem. Such a meta-machine, by definition, would be a computational creativity because its creative output would be the criterion for identifying it.
Bringsjord, Bello, and Ferrucci proposed a "Lovelace Test" that a computational creativity could pass only if it could originate things. The test requires the computational system to produce output that cannot be explained by analysing its formal system. In effect, the system must show a kind of emergent output it cannot generate within its own formal definition. The authors saw this as a paradoxical demand and concluded that a Universal Turing Machine is unlikely, if not impossible, to be an originating machine.
Still, computation as such may be a characteristic intrinsic to human cognitive interaction. Seen this way, computation is a method for structuring some cognitive activities — a characteristic way of perceiving and interacting with the world, though not shared by non-human entities or the rest of nature. If computation and human cognition are interdependent, perhaps something qualifies as computational only when we apply the computational method in our cognitive involvement with a delimited system. In other words, human interpretation is necessary for computation to exist.
Computation in a musical context
If human interpretation is essential for computation, then computation happens in music only when there is an associated activity involving human cognition. When we interpret computational output, we align our thinking with non-living computers, using them to run processes that we read as problem‑solving. This claim does not deny that physical processes could be considered computational; what it suggests is that these processes yield computational results only when humans interpret those results as such. In a group improvisation where computational agents contribute to co-creative results alongside human players, interpretation occurs as performers and audiences listen to the computationally generated music. Responses to that computational output show up in the performers' musical gestures as well as in the emotional or analytical reactions of audiences.
A clarification: the phrase problem‑solving processes is used here in a limited sense. Music itself is not a problem to be solved, nor is music making necessarily a problem‑solving exercise. But a formal system such as a Universal Turing Machine runs a process over time and produces computed results that solve the formal problems — or kinds of problems — that the system was built to address. In a music generating system, the computer (a formal system) is expected to transform input and produce output over time according to its formal structure, thereby solving its formal problems. While such solutions may produce sound, a listener's perception of musical qualities in that sound is not itself a formal problem‑solving task.
Two broad categories can be distinguished:
- humanly motivated computation — intrinsically motivated action
- non‑humanly motivated computation
Two prototype categories relate computational systems involving human-driven imperatives. A “computation” is a bounded system encoding processes that generate outputs representing possible solutions to a defined problem. These categories align with two broad concepts of sound: 1) sounds organized by human intentions; and 2) sounds organized or occurring without human intentions.
In organizing sound, a computational system may take the form of an algorithm on paper. During 1950s “integral serialism,” composers computed music on paper using this method. Brindle employs “integral serialism” as composer Luigi Nono did when referencing “so-called ‘totally organized’ methods of composition.” “Totally organized” implies computability. Integral serialism arguably aimed to create codified generative music systems that were potentially interactive with and appealing to human musical sensibilities.
Composers’ ability to apply computational solutions to compositional problems did not define them as purely computational beings. Rather, computing seemed a necessary but insufficient part of being a human music creator. Composers’ engagement with computational systems made integral serialism possible. Where digital computers aid these processes, understanding computers as problem-solvers depends on human involvement — computation occurs only when humans use and attend to computer outputs.
To illustrate how interpretation may be crucial for computation, consider the Sun as Earth’s essential energy source. We could interpret the Sun as an enormous computer programmed to solve problems of nuclear fission and fusion over billions of years. These two interpretations express different cognitive involvements. The first does not categorize the Sun as computational; the second does. The computational interpretation sees the Sun as an instance of computation in time within a physical system part of Physics. A physical process becomes “computational” through human engagement. This interpretation expresses a post-positivist view not obviously controversial. Understanding the Sun as a computational system clearly depends on our cognitive involvement.
5. Group music improvisation
Taking music improvisation as a non-verbal mode of interaction, group improvisation with humans and computers can be understood as human-machine interaction. Human-computer group improvisation is human interaction with procedures realized by a Universal Turing Machine. A human-computer duo’s improvisation becomes interaction between a human and a concrete instantiation of a formal system.
Thus humans improvising with machines constitute human-algorithm interactions — essentially interactions between humans and mathematics, or non-verbal “dialogues” with an abstract, ideal world expressed within Universal Turing Machine limits.
In human-computer group performance, the improvisation “dialogue” involves humans and procedures outputting computable numbers. These numbers must be computable, as a subset of all numbers. Does this dialogue involve semantic exchange of meaning, or is it purely syntactic?
The potential for semantic qualities in human-computer interactions seems necessary for co-creativity. Without potential semantic qualities, a system’s “creativity” would be solely human activity, making creativity one-sided. The computer then becomes a tool-like entity that, though interactive, does not contribute to co-creative results. As a tool, it extends human cognition and creativity environmentally.
Semantic contents of a procedure may arise from input-to-output transformations, while human semantic content may derive from transformations of reference—enmeshed with memory and the intertextual network of human culture. In music, semantic contents include sonic phenomena and concepts of structure or form. Despite human and computational semantic processes belonging to different categories, their output manifestations can interrelate. Such inter-category interactions serve simultaneously as inputs or influences for both categories. Humans respond to computer-generated music; some computers extract performance features and use them for generation. The human experience of sound as music remains a human experience, even when computational semantics contribute.
6. Human creativity and formal systems
With our formal understanding of Universal Turing Machines, human creativity likely cannot be represented as such. Gödel’s Theorem shows consistent number systems include unprovable statements, meaning computational systems are incomplete and cannot examine themselves. Possibly humans are not consistent systems computationally—a source of human creativity. Human creativity therefore seems distinct from creativity based on formal systems, especially assuming humans are not reducible to consistent number systems. Thus the mind is not a Universal Turing Machine; human creativity cannot be completely computationally modeled, nor do humans necessarily function computationally. Computational creativity must differ from human creativity if defined functionally.
If creativity is a product, functional differences may not profoundly matter. A creative product could arise from experiential learning processes.
Experiential learning likely features in human life; computational systems may encode similar functionality using dynamic concept spaces. These spaces can support combinational, exploratory, or transformational creativity in Boden’s sense. Current machine learning treats “experiential” learning as accumulation of memory in neural network weights—probably differing from human experiential learning, which includes embodied knowledge and musical imagination. These features, if computable at all, remain inadequately modeled.
Creative “musicking” may depend on knowing how to be musically creative—an active, experientially learned practice distinct from theoretical models. Gilbert Ryle argued “knowing how” is not reducible to “knowing that.” Both machine and human improvisation may contribute musically without theoretical self-examination. Knowing how to contribute to distributed creativity constitutes a kind of creativity.
7. Knowing how to contribute
“Knowing how” to contribute to improvised music implies a skill or capacity for creative products; computational systems may embody such skills. Gifford et al. proposed taxonomy for computational music improvisation systems like Cypher, Voyager, Shimon, Omax, finding ad-hoc design, often tied to specific improvisers and performance styles, with the field lacking cohesive framework.
Evaluation points to dichotomy: formal systems ‘knowing how’ may rely on an explanatory theory or be ad hoc. The authors imply a framework approach was superior for achieving human-like agency. This implication seems doubtful. Agency and theory may interrelate, but neither prerequisite applies for human activity; “knowing how” remains irreducible. Therefore agency and theory need not be co-dependent in computational systems. A coherent framework is unnecessary for programming a computer improviser; the result may “know how” to contribute without theoretic rationale.
Does a computer system truly “know”? Ryle applied “knowing how” to human activity, not computation. Human “knowing how” implies subjective capacity. Whether subjective experience emerges from a sufficiently complex Universal Turing Machine is open. More accurately, computational “knowing how” means a trained computational system: software and hardware programmed and trained via neural network techniques. This computationally embodied knowing how requires no internal subjective experience to produce human-heard music.
8. Conclusion
Computational creativity for improvised music can contribute alongside human activity to distributed group creativity—the music product. The system’s contribution depends on human cognitive involvement. Computational improvisation does not model human activity but constitutes a categorically different process. Human and computational semantic capacities differ yet interact. A computationally embodied “knowing how” to improvise may exist in a Universal Turing Machine without explaining “knowing why.” Such embodied knowing how represents computational creativity contributing to improvised music performance.
A human or computer agent may contribute to distributed group improvisation. This distributed creativity likely emerges as a property of group activity, experienced as the music product. Group members interact, enabling emergent distributed creativity evident in the creative product. Purposefulness of human musicking likely differs greatly from programmed or “trained” computer agency. Yet in group improvisation, both forms of purposefulness can contribute to music, resulting in co-creative performance.