On Creativity and Calculation: Attempts at and Rejections of Formal Definitions of Creativity

Article Information

  • Author(s): Thor Magnusson
  • Affiliation(s): University of Sussex
  • Publication Date: 16th November 2013
  • Issue: 3
  • Citation: Thor Magnusson. “On Creativity and Calculation: Attempts at and Rejections of Formal Definitions of Creativity.” Computational Culture 3 (16th November 2013). http://computationalculture.net/on-creativity-and-calculation-attempts-at-and-rejections-of-formal-definitions-of-creativity/.


Review of Computers and Creativity, Jon McCormack and Mark d’Inverno (editors), Berlin: Springer, 2012. 430 p. 96 illus., 51 illus. in color. ISBN 978-3-642-31727-9

A popular fable goes like this: on May 11th 1997, when a computer called Deep Blue beat the world champion Gary Kasparov in a six-game chess match, researchers in artificial intelligence had to replace their old milestone for another. The event had made it clear that, even if outperforming the world champion in chess, computers were nowhere near as intelligent as humans. With technological singularity still in the wild blue yonder, the researchers searched for what might be the quintessential human characteristic, and subsequently set up a new goal for AI: creativity.

This is, of course, a strong simplification, since computational creativity is nothing new, aptly demonstrated by the fact that one of the first pieces of computer music, the Illiac Suite, was composed using artificial intelligence techniques by Hiller and Isaacson in 1956, applying Markov chains and generative grammars. Furthermore, artists like Nake, Noll, and Nees made spectacularly beautiful computer generated visual art in the 1960s, and theoreticians such as Margaret A. Boden, wrote influential texts on computation and creativity in the 1980s and 90s.

Any history of computer art shows that computational creativity has coincided with – and indeed been at the forefront of – such art, as opposed to works manually created by humans using digital production tools. Should this distinction not be clear, we could generalise by defining the former as art where algorithms are written for the machine to execute, often to the artists’ great surprise, whereas the latter typically involves manual one-to-one mapping between the human gesture and output. As this book illustrates, it is the difference between creating a system that draws, as opposed to drawing in something like Photoshop. This distinction is important but, for various historical, technological, and economical reasons that will not be discussed here, the majority of computer art from the last three decades has been art made by production software, by the human hand, and not fully harnessing the algorithmic power of the computer.

This situation is rapidly changing. The first decade of the 21st century has seen a strong increase in the study and applications of computational creativity, with conferences, university courses, journal issues and book publications on the topic. Tools for writing audiovisual works have become easily available and user-friendly, and the term “creative coder” has almost become a profession with a specified job description. This strong increase is not simply because the frameworks for writing code have improved and become more user-friendly, but largely also because our primary media devices are portable pocket computers, capable of rendering generative and interactive audiovisual works through notation written in code. When the media environment has changed so favourably for works of algorithmic art, we can predict an explosion in the application and research of computational creativity in the diverse fields of art.

This book, Computers and Creativity, is a timely theoretical contribution to the fast developing and highly energetic field of computer arts. It results from a seminar on interdisciplinary creativity held in 2009 at Schloss Dagstuhl-Leibniz-Zentrum für Informatik in Germany. The seminar was organised by the book editors, Jon McCormack and Mark d’Inverno, together with Margaret Boden, who writes the foreword to the book. This is an impressive team, since the three of them are active researchers in the field: the editors being both practitioners and theoreticians, and Boden is often considered to be one of the most influential philosophers of computational creativity. The seminar was attended by researchers in creativity studies from relatively diverse, albeit connected, academic backgrounds. Such research setting is bound to inspire and engender important discussions, and although the origin of the book can be traced to this meeting of minds, the editors state that the individual chapters were written after the seminar, in response to the group discussions and through an extended editorial review process.

The book sets out to “examine how computers are changing our understanding of creativity in humans and machines” (p. vii). The aim is to engage with the question whether a thinking machine can be creative and, importantly, shift the focus from computers as a tools for artistic creativity to computers as creative agents on their own. The discussion therefore invariably enters the domain of cognitive science and the philosophy of mind, raising questions around whether human creative behaviour can be formalised, and if so, which algorithms (or AI techniques) can be used to replicate that behaviour. The discussion is also one of art and aesthetics, probing into the concepts of value, beauty, expression and the role of embodiment and society. The book engages with the questions of “why and how” computers can be creative, seeking to clarify and make explicit attempts at establishing the locus of creativity, whether in the human or the creative algorithm itself.

The book contains 16 chapters and is divided into four parts: Art, Music, Theory and an Epilogue, which gives a general overview of the authors’ approaches, although both the Art and Music parts typically contain chapters impregnated with theory and the Theory part contains descriptions of various practical projects. This strong relationship between theory and practice is one of the book’s strengths. All the authors in the book are practitioners and researchers in computational creativity, and base their theoretical insight and knowledge upon having actually engaged with the problems and thought about them in relation to work that requires functioning solutions.

In the first chapter, “The Painting Fool: Stories from Building an Automated Painter,” Simon Colton describes a system that produces art work using an array of AI techniques. The goal is to challenge the state of the art in AI, by applying the latest algorithms to create an art making system, but also to reciprocally contribute solutions back to the knowledge pool of AI. The project is inspired by Cohen’s AARON system, but slightly updated as the goal is to implement “critical ability” and “cultural awareness” – both features that are lacking in AARON. The chapter gives an extensive context to the automated painter “that we hope one day will be taken seriously as a creative artist in its own right” (p. 16). The authors promise to fully explain how the system is implemented, although this reviewer did not find information about the source code available anywhere, thus limiting a study of the system.

In the next chapter, “Creative Ecosystems,” one of the editors, Jon McCormack, discusses the problems inherent in the attempt of defining creativity. He argues for clarity in specifying goals, such that the system can apply strong criteria (or fitness functions) when guiding itself to a good creative output. Defining such goals means to know well the search space for the creative exploration, or rather, “take the structural design of the creative space very seriously” (p. 41). McCormack’s chapter is strong in both practical and theoretical considerations. He discusses the distinction between what is creative on the one hand and aesthetically pleasing on the other, noting that those are independent concepts, i.e., something might be aesthetically pleasing without being the result of a creative process and vice versa.

The veteran computer artist Frieder Nake contributes a chapter – “Construction and Intuition: Creativity in Early Computer Art” – tracing a history of early computer art (which he prefers to call “algorithmic art”). For Nake, computers are automata and he stresses that all creativity exhibited by the machines originate in the human creator. Creativity is not an object, a noun, but a behaviour, a subjective activity. Nake brings forth his own definition of art, “People generate objects and they generate processes. They do not generate art. Art, in my view, is a product of society – a judgement” (p. 74). Nake’s rejection of computers being creative is based on the view that computers are not embedded in culture, that they are disembodied and disinterested, and, according to Nake, “can never” gain those features. This is an interesting chapter with strong views, but considering Nake’s pioneering role within the field, the chapter’s historical survey, and its views of artificial creativity that are rejected by many later in the book, it could be asked why this is not the opening chapter of the book.

The next chapter is an edited conversation, “Discussion on Evaluation,” where the authors discuss questions such as: What are the main features of human creative and aesthetic evaluation? What aspects of evaluation can be made computational? Is it necessary for computational evaluation to mimic the evaluation methods of humans? Does it make sense to automate a task that is so especially human? (p. 96). The authors all agree upon the important role of evaluation in computational creativity. In essence it means that the creative system becomes a feedback system, where the results of the evaluation feed back into the creative algorithm itself. In the discussion, Harold Cohen doubts that evaluation can be successfully implemented as an algorithm within a creative system during the creative process, but he believes it can be done post-hoc. For Cohen, this has to be done from the same program (knowing the rules presumably). Cohen’s views diverge strongly from Colton’s system discussed in the first chapter, where a system of plug-ins is described as a solution to the well-known problem of creative systems always containing their author’s artistic signature 1

The discussion dwells at length on different aspects of whether we can formulate our artistic intentions, and if not, it follows that we cannot create a computational aesthetic agent (the views of Nake and Cohen). Others, such as Brown, McCormack and Galanter, are more optimistic, stating that we should at least try, but they acknowledge that such creativity or evaluation might not necessarily mimic human evaluation in full detail. Furthermore, why should we suppose that all humans perform such evaluation the same way? Later in the discussion Brown points out that if human creativity involves tasks that cannot be describable as computer operations, we may never be able to attain real creativity via computers. However, if we are indeed logical and finite beings, we can at least try to model this, no matter how difficult. This question of formalisation seems central in the discussions of creativity in AI systems, suffice to remind ourselves of Nake’s rejection of this possibility in his chapter, where he quotes Nees: “if you tell me explicitly how you paint, then I can write a program that does it” (p. 92).

In François Pachet’s chapter “Musical Virtuosity and Creativity,” we find a fine discussion about virtuosity in the field of improvisation, jazz in particular, where the author argues that modelling virtuosity can contribute substantially to our understanding of creativity in both humans and machines. Pachet states that there is a lack of good definition of what virtuosity involves, but he focusses on problem solving, the “capacity to navigate in large search space in real-time” (p. 119). Having explained his Virtuoso system in details, Pachet proclaims that it is proficient in fast improvisation, but not so successful in slower tempo situations. In fact, what it lacks, as most automatic systems do, is a musical common sense. What makes slow improvisation difficult, in Pachet’s view, is that it focusses more on timbre and expressivity, and those are much harder to model. Again, we are faced with the problem discussed in the preceding chapter of rationalisation and formalisation of fuzzy phenomena, or, as Nietzsche phrased it, it is a result of us consistently throwing our “pale, cold, grey conceptual networks” over “the motley whirl of the senses”. 2

Tim Blackwell, Oliver Bown and Michael Young’s chapter, “Live Algorithms: Towards Autonomous Computer Improvisers,” focus on a topic related to funded collaborative research on live algorithms by Goldsmiths College. The authors explore how an autonomous musical agent can contribute to a live improvisational context. The agent would have to base its actions on what it perceives. The chapter provides a typology of musical practice, using “wiring diagrams” for different types of computer music applications, based on three principles of “P (listening/analysis), Q (performing/synthesis), and f (patterning, reasoning, or even intuiting)” (p. 153), a common input-processing-output framework. The paper argues for a bottom-up approach, one of dynamic machine learning rather than a symbolic knowledge instruction that would require a practically impossible amount of data to be available to the system before it can run. The strength of the dynamic system is to adapt and learn in real-time. The authors discuss topics of embodiment and cultural embeddedness in the last section of the chapter, pointing out how social networks and online music repositories, such as Soundcloud or Last.fm present an ideal platform for the analysis of musical interaction, enabling computational music to be more amenable to currents taking place in the general music culture.

In a chapter called “The Extended Composer,” Daniel Jones, Andrew R. Brown, and Mark d’Inverno discuss compositional tools that include a degree of autonomy, to the extent that computers can be seen to extend human composers in their creative process. Such prosthesis is seen to be valuable as it can serve in reshaping “our creative behaviours in response to its own creative acts, encouraging unusual creative directions, or enabling actions which are otherwise unlikely” (p. 176). These technologies also help to reflect upon our own practices, “our own stylistic habits or tropes” (ibid). The chapter analyses themes in the Human-Computer partnership, namely those of: feedback, exploration, intimacy, interactivity, introspection, time, authorship, and value, which are all given their individual subchapters. The chapter contains a useful taxonomy of creative systems, but perhaps its main value is the discussion of how we can learn about our own creativity through the use of computational algorithms that extend, learn, and respond our own playing in diverse ways. The authors see creative systems as augmenting human capacity, not replacing it, encouraging us to replace the question “Can technology be creative?” with “Can we be more creative with technology?” (p. 197).

In his chapter “Between Material and Ideas: A Process-Based Spatial Model of Artistic Creativity,” Palle Dahlstedt proposes a model of the creative process from a first person perspective. Dahlstedt describes creativity in Boden’s terms of exploring a search space, but unlike many researchers in artificial intelligence, he emphasises the roles of tools and materiality. This is a welcome contribution to the field of computational creativity, as computer science can often underestimate the role of materials and serendipitous results coming from artist engagement with materials at hand. For Dahlstedt, “ideas emerge from this dialogue, from misunderstandings, ambiguities and mistakes” (p. 207). The original concept is but a seed, which sometimes doesn’t even exist, for example in improvisation. Dahlstedt introduces the concept of “material space,” i.e., the way the tools or materials we work with constrain our creative options in a bidirectional process of implementation and re-conceptualisation that directs our creative process.

Alex McLean and Geraint Wiggins explore programming as an act of perception, cognition and computation in their chapter called “Computer Programming in the Creative Arts.” They situate programming and algorithmic art strongly in the domain of the human and show how programmers use anthropomorphs and metaphors in their work. The chapter introduces a distinction between two modes of programming computers (although existing on a continuous rather than a binary scale), that of the bricoleur and the planner. The bricoleur does not plan ahead too much, but engages with the act of programming as an interactive and reflective play between materiality and ideas. Here perception and embodiment become important factors in creating the conceptual space of the programmer. The chapter ends with an interesting discussion of how time is represented in code, but also in the head of the programmer. Exploring Csikszentmihalyi’s concept of flow, the authors wonder if the “programmer is thinking in algorithmic time, attending to control flow as it replays over and over in their imagination, and not to the world around them” (p. 249).

In “Computational Aesthetic Evaluation: Past and Future,” Philip Galanter reviews a large array of topics related to the evaluation of computational creativity. The chapter is very extensive and provides a good general overview of many of the theoretical issues that pertain to the study of computational aesthetic evaluation. Galanter discusses diverse fitness functions in neurologically and biologically inspired systems. He traverses the territory of empirical studies of human aesthetics quickly, but concludes that we are far from having any understanding of computational aesthetic evaluation, for the simple reason that we don’t know enough about the mind yet.

Computational aesthetics and the evaluation of art are the central themes of a chapter called “Computing Aesthetics with Image Judgement Systems,” by Juan Romero, Penousal Machado, Adrian Carballal, and João Correia. They make a distinction between art and aesthetics, the former including various factors that should be external to aesthetic evaluation, such as cultural context and novelty. For Romero et al. computational aesthetics deal with properties such as symmetry, balance, rhythm, contrast, proportion, repetition, unity, etc. They note that they are not creating a general “art critic” that would have to understand the work’s context, but simply focussing on its form. The chapter discusses their Aesthetic Judgement System (AJS) in great detail, contextualising it with a broad theoretical scope.

In “A Formal Theory of Creativity to Model the Creation of Art,” Jürgen Schmidhuber discusses his “Formal Theory of Creativity”, which he differentiates from other systems of creativity as it contains an “intrinsic reward” system, and not an external one (feedback from humans or other outside fitness functions), as most of the other systems described in this book have. The chapter seeks to provide a formal definition of things that are highly subjective, such as a “formal definition of fun,” leaving this reviewer somewhat puzzled. The chapter is highly mathematical, and might suffer from the attempt to reduce human language into formal structures or equations, an endeavour that the philosophy of the latter half of the 20th century proved a problematic and arguably impossible project.

Alan Dorin and Kevin B. Korb seek to bypass the concepts of value and appropriateness in their definition of autonomous creativity in their chapter “Creativity Refined: Bypassing the Gatekeepers of Appropriateness and Value.” The authors seek to establish a “clear, formal conception of creativity,” a task that is bound to be irrevocably difficult, yet the authors are optimistic. Finding faults in Boden’s definition of creativity (“Creativity is the ability to come up with ideas or artefacts that are (a) new, (b) surprising and (c) valuable”) (p. 342) they present their own definition “independent of notions of usefulness and appropriateness”. They acknowledge that this definition is not “altogether plain”: “Creativity is the introduction and use of a framework that has a relatively high probability of producing representations of patterns that can arise only with a smaller probability in previously existing frameworks” (p. 344). Indeed not a very clear definition, perhaps bespoke to the authors’ work?

Oliver Bown points out in “Generative and Adaptive Creativity: A Unified Approach to Creativity in Nature, Humans and Machines” that creativity should not be limited to or modelled solely on human psychology or human activity. For him “computational creativity is the study of creativity by any computational means, not necessarily those modelled on human minds, or even human goals” (p. 361). Bown makes a distinction between generative creativity and adaptive creativity, with the latter having a feedback mechanism such that the output of the system will be beneficial to its functioning, in other words: learning. Bown brings this distinction into the discussion of natural, human and machine-based creative systems.

Peter Cariani’s chapter “Creating New Informational Primitives in Mind and Machines” discusses the possibility of creative systems actually evolving out of their own framework. The goal is to create open-ended systems that can “autonomously find new and unexpected solutions to combinatorically-complex and ill-defined problems” (p. 383). Cariani brings forth a distinction of two creative modes: combinatoric emergence and creative emergence. Computers are excellent at the former, as analysing patterns and producing new combinations of defined rule sets are tasks ideal for programmable machines. However, the possibility of the system evolving and extending itself, by building new primitives, is where the edge of this type of research is currently at. The chapter discusses this problem of emergence and autonomy in the context of sub-symbolic neural networks, cybernetics and autopoiesis, exploring the possibility of how novel primitives can be formed.

It is interesting that a central question of computational creativity, namely whether computers could demonstrate what Boden 3 calls “transformative creativity,” (a question that has been simmering underneath or popping up in most of the chapters in this volume), is dealt with quite explicitly in both the first and the last chapter of this book. The solutions are different: Colton and his collaborators have set up a “Computational Creative collective” where people can upload their creative plugins to the system (who often engage with online and social media material), thus allowing for artistic “influences” that extend beyond the authors to other developers, and into the infinitely inspirational world of the web. This type of solution is also discussed by Bown. Cariani, on the other hand, aims to build a unique system that can extend itself and evolve. It is likely that both methods can be complimentary on the path to achieve success in this area.

The volume closes with an epilogue, “Computers and Creativity: The Road Ahead,” written by the editors, where they discuss what the future might hold in research and practice of computational creativity. They raise questions as to whether computers can enhance human creativity, whether computer art can ever be properly valued, and what computing can tell us about creativity. The issues here are many and complex, with answers differing greatly depending upon which research field tries to deal with them. The authors also ask how creativity and computers matter to education.

Computational creativity is a field that has become interesting to researchers from diverse fields for numerous reasons. It represents a challenging area within artificial intelligence and it addresses an aspect of human behaviour that can be defined as one of its key characteristics. This book serves as a fine overview of the field, raising some of the key questions, but we should not forget that it is the outcome of a unique meeting of computer scientists and generative artists discussing topics related to computational art aesthetics. Another step in this interesting journey would be to add to the consortium some art historians, new media theoreticians, curators of contemporary art and psychologists researching creativity. Even if this would strongly increase the entropy factor of the already diverse definitions, it would create a healthy platform of self-reflection and sensitivity of term usage, as it is becoming clear that many of the difficult problems of this research field could benefit from a further philosophical engagement. Terminology, criteria, goals, and definitions need to be clarified, simplified and expounded, or rather, in the words of the philosopher: the fly has to be shown the way out of the fly-bottle. A clear understanding of the term “creativity” is needed, its etymology studied (it is a young word indeed, derived from creationist theology), perhaps in the way Heidegger traces the Greek concept of techne as the activities of craftsmen and artists, intrinsically linked to the word poiesis.

Most of the chapters of this book define the concept of creativity and what is meant by the evaluation of creativity. They emphasise the necessity that systems have clear goals and assessment criteria, which are, of course, set by the creators of the systems. Some chapters discuss aesthetics as a separate concept from art, since in some strands of aesthetics, certain key parameters can be measured objectively, such as symmetry, balance, rhythm, harmony, and so on. Thus defined, the terms creativity and aesthetics can be studied from psychological and cognitive science perspectives, where the results can feed into our artificial intelligence systems. This book provides much source material for thinking further about human and machine creativity – the similarities and the differences – and the necessarily related concept of computational evaluation of creativity.

The Achilles heel of computational creativity, as presented in this book, seems to be the relationship the field tends to try to establish with the world of art. Much like the concept of creativity, art is a concept with long and shapeshifting history, but today it typically connotes a highly specialist discourse derived from 20th century Western Modernism. The difference, causing the field some headache, is that the concept needs to be understood from the perspective of culture rather than that of psychology. The rules of this discourse vary greatly within different historical periods in different cultures. Therefore, a computer scientist forcing their way into the complex world of 21st century art, through some formal analysis or conceptualisation of the art world, is unlikely to be very successful, but an artist already working within it, who decides to use computational creativity as a technique in their work or use an artificial agent to create it, might be. The concepts of cultural context, sensitivity, or intuition are bound to be hard to implement in our systems at this stage, and makes the task much harder than applying computational creativity to output that can be evaluated with stronger criteria, such as bridge design, traffic control, etc. We may never agree upon the evaluation of art, but we could concur whether a system is creative provided the goals and the criteria for assessment are clear.

This does not mean that we should cease to make art or music with computationally creative systems, quite the opposite, since they are great tools of ingenious invention that can support us, or even replace us when we want, in the creative process as artists. What is suggested here is that we should be careful when using terms such as “computer artist” or “artwork” in a narrative where we claim to have replaced the human with a machine. It not only frightens people, but it also paints a slightly skewed picture, since the creator of the system might always prove to be the ultimate locus we have to fall back to when searching for the true source of creative expression. Indeed, what strikes me as being of more relevance to the current art discourse, is the act itself of creating generative systems, rather than these system’s artistic outputs. Equally, in software studies terms, we should advance the discussion of such software as inherently cultural.

The book might seem to have had a relatively light hand in the editing, as it feels like some of the texts could benefit from a stronger editorial process. Some chapters could do with a trimming, especially if details become too specific or the content steers away from the book’s theme. There are small nuances here and there that could have been ironed out, such as when Nake, in his fine chapter, not only asks readers to shed their fear of formulas (considering the readership of this book, such fear would be unlikely) but also encourages them to “enter postmodern times!” (p. 64). Even if the book might feel fragmented on occasions, the seemingly diverse opinions, definitions, and term usage in the book is mainly a positive thing since the field is young and the subject matter complex. We would not be doing ourselves any favours by deciding upon rigid definitions at this stage; better is the multiplicity of definitions derived from and contextualised within the different technical or philosophical approaches.

This volume serves as a great example of the diversity of ideas, technologies, and projections that characterise the study of computers and creativity in the early 21st century. The book is a welcome source for any researcher or student of computational creativity and is likely to become a central reference within the field. It should be highly recommended for any student of creativity, computing, computational aesthetics, and artificial intelligence; and it is bound to interest people from a wide range of disciplines, including aesthetics, media arts, computer science, cognitive science, artificial intelligence and the philosophy of mind.


Boden, Margaret A. The Creative Mind: Myths and Mechanisms. (London: Wiedenfield and Nicholson, 1990).

Brown, Paul; Bigge, Bill; Bird, Jon; Husbands, Phil; Perris, Martin; Stokes, Dustin. “The Drawbots”, in Proceedings of MutaMorphosis: Challenging Arts and Sciences, (Prague, 2007)

Nietzsche, Friedrich. Beyond Good and Evil. Rockwille, (Maryland: Serenity Publishers, 2008)

Thor Magnusson is a musician and software developer who lectures in music and sound arts at University of Sussex’s Department of Music. His research involves work on the conceptual foundation of digital music tools and expression from the perspective of philosophy of technology. Magnusson develops musical software with the ixi-audio (www.ixi-audio.net) collective, which he co-founded in 2000. Magnusson is an avid live coder and has developed two live coding systems for musical expression. Further information: http://www.ixi-audio.net/thor/


  1. Brown, Paul; Bigge, Bill; Bird, Jon; Husbands, Phil; Perris, Martin; Stokes, Dustin. “The Drawbots”, in Proceedings of MutaMorphosis: Challenging Arts and Sciences, (Prague, 2007)
  2. Nietzsche, Friedrich. Beyond Good and Evil. Rockwille, (Maryland: Serenity Publishers, 2008)
  3. Boden, Margaret A. The Creative Mind: Myths and Mechanisms. (London: Wiedenfield and Nicholson, 1990).