computational creativity theory: inspirations behind the face...

Computational Creativity Theory:Inspirations behind the FACE and the IDEA models

Alison Pease1 and Simon Colton2

1 School of Informatics, University of Edinburgh, UK.2Computational Creativity Group, Department of Computing,

Imperial College, London, UK. ccg.doc.ic.ac.uk

Abstract

We introduce two descriptive models for evaluating cre-ative software; the FACE model, which describes cre-ative acts performed by software in terms of tuples ofgenerative acts, and the IDEA model, which describeshow such creative acts can have an impact upon an au-dience. We show how these models have been inspiredboth by ideas in the psychology of creativity and by ananalysis of acts of human creativity.

IntroductionThe Computational Creativity (CC) community needs con-crete measures of evaluation to enable us to make objective,falsifiable claims about progress made from one version of aprogram to another, or for comparing and contrasting differ-ent software systems for the same creative task. There aretwo notions of evaluation in CC: (i) judgements which deter-mine whether an idea or artefact is valuable, and (ii ) judge-ments to determine whether a system is acting creatively.Our thesis is that ideas from the psychology of creativitycan help us to develop such measures, and we demonstratethis via our two models, which form a framework to aid us inthe development and evaluation of creative software. Notethat while we draw on psychology and examples of humancreativity for inspiration, our goal lies squarely within CC –to provide a means of formalising some aspects of compu-tational creativity– we by no means claim that our modelswould be appropriate for evaluating human creativity. Themain test and value of such models lies in their applicabilityto CC systems: we defer such application to a sister paper[4].

The FACE modelThe FACE model assumes eight kinds of generative acts, inwhich both processes (p) and artefacts (g) are produced:

Fp: a method for generating framing informationFg: an item of framing information for A/C/Ep/g

Ap: a method for generating aesthetic measuresAg: an aesthetic measure for process or productCp: a method for generating conceptsCg: a conceptEp: a method for generating expressions of a conceptEg: an expression of a concept

Any particular creative episode can be expressed in termsof at least one of these components (it may well be the casethat not all of the components will be present). In orderto cover as many creative acts as possible, we assume onlythat there must be something new created for the question ofcreativity to arise. This could be very small, a brush strokeof an artist, an inference step by a mathematician, a singlenote in a piece of music. Thus, we avoid the thorny issueof where an act of creation starts and important questionsabout where on the scale from basic to sophisticated an actmust be, to be judged creative, can be postponed. This posi-tion is in line with the argument by Cardosoet al., that “Toachieve human levels of computational creativity, we do notnecessarily need to start big, at the level of whole poems,songs, stories or paintings; we are more likely to succeedif we are allowed to start small, at the level of simple butcreative phrases, fragments and images” [3, p. 17].

The IDEA modelIn order to assess the impact of the creative acts performedby software, we assume an (I)terative (D)evelopment-(E)xecution-(A)ppreciation cycle within which software isengineered and its behaviour is exposed to an audience. TheIDEA descriptive model recognises that in some creativetasks, the invention of measures of value forms a part of thecreative act. Hence usual models of value are abandoned infavour of describing the impact that creative acts can have.The model introduces some simplifying assumptions aboutthe nature of (i) the software development process (ii) thebackground information known in general, known by theprogrammer, and given to the software, and (iii) the natureof the audience who assess the impact of the creative actsperformed by the software. Using these simplifications, themodel comprises two branches. The first of these is a de-scriptive model for the stage of development that software isin, in terms of how close its creative acts are to those per-formed by the programmer in engineering the software, andhow close they are to those that have been performed bycommunity members in the wider context in which the soft-ware works. The second branch uses the notion of an idealaudience who can perfectly assess both their personal hedo-nistic value of a creative act, and the time they are preparedto spend interpreting the act and its results. These measuresare used to capture certain notions that are usually associated

Proceedings of the Second International Conference on Computational Creativity 72

with impact. In particular, notions such as shock (when au-dience members tend to take an instant dislike to a creativeact), acquired taste (when audience members tend to spenda long time in eventually positively assessing a creative act)and opinion splitting (when a creative act is particularly di-visive) are formally developed.

The creation of prime numbersThe many aspects which contributed to the creation and ap-preciation of the concept of prime number have inspired ourdevelopment of the FACE model. These include inventingthe concept itself and inventing ways of developing newconcepts in number theory. Along with the concept defini-tion we find examples, or expressions, of the concept, in theform of numbers which are either known to be prime (eg.2, 3, 5, 7), known not to be prime (eg. 4, 6, 8, 9),1 or havean unknown status (eg. 213466917 + 1) and algorithms fordetermining whether a given number is prime have been de-veloped, such as the Sieve of Eratosthenes, as well as waysof generating further primes. The concept of primes wasembedded into number theory by developing specialisations(eg. Cuban, happy, illegal and lucky primes) and theoremsand conjectures (eg.the fundamental theorem of arithmetic);and into the wider field of mathematics as uses for primeshave been found in group and ring theory, cryptography, andso on, as well as its application to other areas of human expe-rience (eg. Messiaen used prime numbers to create ametri-cal music). In addition to actually developing such concepts,theorems and applications, we can create techniques for de-veloping them,eg. the use of analogical reasoning to createanalogous concepts in other areas of mathematics. We alsoevaluate the concept (primes are considered to be the “basicbuilding blocks” of the natural numbers) and suggest newways in which to make such a judgement. We break thiscomplex story down into the FACE components below:

FACE Prime numbers

Fp: Ways in which theorems involving primes can be foundFg: Theorems involving primes, which embed the concept

within the field of number theoryAp: Ways in which which we judge the value of concepts in

number theory (for instance, their applicability and use inmultiple mathematical domains)

Ag: Judgements on the value of the concept of prime numberCp: Ways of finding new concepts in number theoryCg: The concept of a prime numberEp: Algorithms for determining whether a given number is

prime or not (for instance the Sieve of Eratosthenes)Eg: Numbers with an evaluation as to whether they are prime

The creation of upsidedownsIn [3], Cardosoet al. describeThe Upsidedowns of Gus-tav Verbeek. These are panels which tell a story up to ahalf way point, the continuation of which then appears al-most magically when one turns the panels upside down. Weshow another example of this type in Figure 1. In terms ofour model, starting with the artefact level, we could describe

1Whether 1 should be considered prime is still debated today.

the final piece of art as an expression of the concept Eg;the concept Cg as the constraint that the picture must makesense when upside down (and fit into the story); the aes-thetic Ag as the idea of art having multiple meanings whenviewed from multiple perspectives; and the framing Fg be-ing the contextual history of this genre of art, the motivation,justification, etc. At the process level, Ep is the generationof methods for producing expressions of art which have adifferent meaning when viewed upside down (for example,birds flying in the sky can double as waves in the sea, or a haton one’s head can double as a mouth on one’s face); Cp rep-resents methods for generating new perspectives from whichthe art might make sense (other examples include rotating90◦ rather than180◦); methods for generating the aestheticof art having multiple meanings when viewed from multi-ple perspectives would be Ap (another example would bethe aesthetic of art having multiple meanings when viewedfrom a single perspective); and Fp would be methods forgenerating new motivations, justifications, and so on.

Figure 1: A man coming out of the water – turn upside downto see the same man drowning.

Not all of these aspects may be present in a single act ofcreativity, and they may be performed by different parties.We can express the upsidedowns as follows:

FACE Upsidedowns

Fp: Methods for generating the contextual history of this genreof art

Fg: The contextual history of this genre of art, motivation, jus-tification, etc.

Ap: Methods for generating the idea of art having multiplemeanings when viewing from multiple perspectives

Ag: The idea of art having multiple meanings when viewingfrom multiple perspectives

Cp: Methods for generating new perspectives from which theart might make sense

Cg: The constraint that a picture must make sense when upsidedown

Ep: Methods for generating expressions of art which have a dif-ferent meaning when viewed upsidedown

Eg: Expressions of art which have a different meaning whenviewed upsidedown (see figure 1)

Lessons from psychologyThere is much work on creativity and little cross-fertilizationbetween fields. In particular, the relationship between CCand the psychology of creativity (in Europe at least) hasbeen oddly disjointed: this is a waste, and our models con-stitute one attempt to embed various aspects of creativity


research from psychology into a CC context. Simonton[22] identifies four perspectives in basic research in psychol-ogy on the nature of creativity: cognitive psychologists areconcerned with mental operations which underlie the cre-ative process; developmental psychologists investigate cir-cumstances which contribute to creative growth; differen-tial psychologists focus on individual differences; and socialpsychologists investigate sociocultural environments whichshape or favour creative activity. Of most relevance to CCare Simonton’s first and final categories. The first is the mostobvious and much work in CC is motivated by giving a com-putational representation of mechanisms which can underliecreative behaviour: these may be cognitive or otherwise, de-pending on the motivation of the CC researcher. The finalcategory is far less common in CC, although work such asthat by Saunders [21] has demonstrated its relevance to theCC community. Our models are thus inspired by ideas inthese two areas.

Types of creativityDespite being notoriously difficult to define, researchershave distinguished different types of creativity. These of-ten include some sort of conceptual space, which is an areaof work defined culturally by a set of rules and approachesinto which individuals are socialised as they master the skillsof their field. Some individuals will produce work whichviolates the rules but is considered by the community tobe highly creative, and new work produced according toa new set of rules then becomes the standard for that do-main. Csikszentmihalyi [5] distinguishes between little-ccreativity which might be within a cultural paradigm andincludes everyday, mundane creativity which is not domain-changing, and big-C creativity, which is a rare, eminent cre-ativity in which a problem is solved or an object createdthat has a major impact on other people and changes thefield. Boden [2] draws a similar distinction in her view ofcreativity as search within a conceptual space, where ex-ploratory creativity searches within the space, and transfor-mational creativity involves expanding the space by break-ing one or more of the defining characteristics. Boden alsodistinguishes between psychological (P-creativity) and his-torical creativity (H-creativity), concerning ideas which arenovel with respect to a particular mind, or the whole of hu-man history. In our FACE and IDEA models we have triedto be sufficiently general so as to capture each of these threetypes of creativity.

There are some controversies in creativity research re-garding how general creativity is. For instance, there isdisagreement over whether everyday creativity involves thesame processes as eminent creativity [11; 27]. Anothercommon debate (also heard at CC conferences) concernswhether creativity is domain specific [1], and in particularwhether it is the same phenomenon in the arts as in science.While most investigators assume that there are a small num-ber of cognitive operations which underlie creativity in di-verse domains, Simonton [22] notes that it is also possiblethat no processes are unique to creativity, or that there are noprocesses which are present in every instance of creativity.There is also debate on where creativity starts, and which,

of the different types, ismorecreative. We occupy a com-fortable vantage point on the fence, attempting to create aframework which is general enough to capture all aspects.Specific claims can then be expressed and tested in terms ofour models.

The distinction between process and productThe distinction between a product or idea and the processesused to create it is a common one in psychology. Torranceargues that creativity is a combination of person, process andproduct, seeing a fine line between studying processes andproduct (reported in [25]). Maheret al. point out that “Acreative process is one in which the process that generatesthe design is novel, and a creative product is when we eval-uate the result of the design process as being novel” [15].Much work in creative cognition research seeks to under-stand the mental representations and processes underlyingcreative thought. Examples of processes include Finkeetal.’s Geneplore model [7], in which mental processes suchas retrieval, association, transformation, analogical transfer,categorical reduction, and so on, might enter phases of cre-ative invention. Conceptual combination, in which conceptsare combined to yield emergent features, is another processthought to be important for creative behaviour, and this pro-cess is frequently mentioned in historical accounts of cre-ative accomplishments (see [13; 2]). Analogical reasoning,in which structured knowledge from a familiar domain is ap-plied to a novel or less familiar one, is also thought to be aprocess with a special link to creativity [10].

There is also justification from historical case studies ofcreativity for considering a process to be the creative outputof interest. For example, consider young Euler’s discoveryof Arithmetic Series, in which he and his classmates weretold to add up all the numbers between1 and100. Otherpupils arrived at the answer5050, but everyone except Eulerlaboriously added each of the numbers individually. Eulerrealised that if they were written in ascending order and thenunderneath in descending order, the sum of each of the pairswas101, and there were100 pairs. Therefore twice the re-quired sum was10100, and the answer was5050. As in theexample of the Basel problem described below, there are (atleast) two interesting creative outputs: the expression5050

and the process by which the expression is generated,Sn =

sum ton terms=n∗(first+last)

2 . This example shows theimportance of a generative process for evaluations of cre-ativity – much more so than the Basel problem, since the ex-pressionπ2

6 was itself H-creative, whereas Euler’s solution5050 was only P-creative. We can break it down as follows:

FACE Euler Problem

Fp: –Fg: Embed into mathematics,eg.AP’s and GP’sAp: –Ag: Proof that the solution is correctCp: Ways of finding new problemsCg: Sum the numbers between1 and100

Ep: Sum ton terms= n∗(first+last)2

Eg: The solution5050


In the CC literature, the focus is often on the product,and virtually all systems in CC discuss the creation of arte-facts, rather than processes. One strong motivation behindour development of the FACE model is to emphasize the im-portance of the process by which an artefact is created in ajudgement of creativity. We have done this via our distinc-tion between process and product in each of the four aspectsof FACE.

Evaluation in creativityIn the introduction we noted two senses of evaluation whichare relevant to creativity: evaluating whether an idea orproduct is valuable, and evaluating whether a person hasbeen creative. The former, which is judged both internallyby a creator and externally by a community, is an essen-tial component of creativity. This notion of evaluation ofproducts as being a key part of the creative process was in-troduced early on by thinkers such as Wallas [26], who pre-sented one of the first models of the creative process, out-lining a four-stage model of creativity: (i) preparation, (ii )incubation, (iii ) illumination and (iv) verification. The fi-nal stage, where an idea is consciously verified, elaborated,and applied may be carried out by either the creator or bythe community. Similarly, Parnes [18] introduced evalua-tion into the creative process in his theory that creativity is afunction of knowledge, imagination and evaluation, arguingthat the highly creative person must be able to make eval-uative judgements about his or her products. This kind ofevaluation is also linked to Williams’ divergent-productivethinking (described in [16]) in which multiple solutions to aproblem are generated and then evaluated to select the best.Mcgraw and Hofstadter account for evaluation in their two-stage model of guesswork and evaluation [17], and refer tothe “necessarily iterative process of guesswork and evalua-tion as the ‘central feedback loop of creativity”’ [9, p. 451].Additionally, Maher, Merrick and Macindoe point out thatthere are numerous characteristics associated with creativedesign in addition to simply producing novel material, in-cluding aesthetic appeal, quality, unexpectedness, uncom-monness, peer-recognition, influence, intelligence, learning,and popularity [15]. Thus, the twin processes of generationand evaluation are firmly embedded into notions of creativ-ity. We maintain this distinction in our two complementarymodels; FACE, which describes generative acts of creativ-ity and IDEA, which describes ways of evaluating the acts.We further reflect notions of internal and external evaluationof a product via ourAestheticandFraming aspects of theFACE model. The IDEA model complements these aspectsand provides a fine grained approach to evaluation.

Kreitler and Kreitler [14] distinguish between creatorsand spectators of the creative products and argue that thereare two types of creative people, those who create art andthose who view it. They have developed a theory of experi-encing art consisting of two phases. In the first (perceptual-cognitive) phase, the spectator responds to the work of art,and in the second (motivational) phase, the experience ismotivated by psychological tensions which exist in the spec-tator independently of the current experience. These ten-sions trigger new tensions in response to the work of art and

allow the spectator to give meaning to the art: such meaningdevelops with the gradual unfolding of different aspects ofthe artwork. This work has formed the inspiration behindour IDEA model and our thoughts on the cognitive effortrequired to understand a creative artwork.

Theories of creativity

In view of the difficulties of defining this nebulous concept,some psychologists have moved on from considering ‘whatis creativity?’ to considering ‘where is creativity?’ Csik-szentmihalyi [5] answers this with his systems view of cre-ativity. He sees creativity as an interactive process betweenthree elements: an individual innovator, his or her knowl-edge about a domain, and a field or community of expertswho decide which individuals and products are valued. Ofparticular interest to us is Csikszentmihalyi’s emphasis onthe role of the community in which creators operate and howit affects creative outcomes. Uzzi and Spiro [24] also em-phasise the role of a community in amplifying (or stifling)creativity. They discuss work which traces the history ofkey innovations and show that in nearly all cases the creatoris embedded in a network of artists or scientists who shareideas and act as each other’s critics, creating an atmosphereof cross-fertilisation of ideas. These theories have inspiredthe social aspects of our model, in particular the framing as-pect, in which a creator embeds his or her creation withina field. Attempts at framing may well inspire further inno-vations in the field. Similarly, our IDEA model is based ontheories of how creative work is received. Noting the diffi-culties experienced by psychologists when trying to definecreativity, the fine level of granularity of our models enablesus to pinpointwherecreativity in a particular act has oc-curred, without having to answer the question of what cre-ativity is.

Gardner [8] holds that an individual must be consistentlycreative, in order to be considered to be creative. He arguesthat “the creative individual is a person who regularly solvesproblems, fashions products or defines new questions in adomain in a way that is initially considered novel but thatultimately becomes accepted in a particular cultural setting.”[8, p. 35]. In order to accommodate this criterion, we havedesigned our FACE model to be used in a cumulative way.

Creative acts and the FACE/IDEA models

We break down two further examples of creativity in order todemonstrate the various aspects of our models. In an attemptto avoid charges of cherry-picking examples which fit ourmodel, we analyse two very different examples in differentdomains. The first is an example of big-C, transformational,H-creativity in mathematics and the second concerns little-c,P-creativity in general problem solving. It is difficult at thisstage to show generality: we invite the reader to similarlydecompose other creative acts in order to develop the FACEand IDEA models. Recall that our models are intended tohelp us to develop and evaluate creative software and areinspired by, rather thanmodels of, human creativity.


The Basel problemEuler’s solution of the Basel problem in mathematics is aseminal historical episode of human creativity. This is theproblem of finding the sum of the reciprocals of the squaresof the natural numbers,i.e. finding the exact value of theinfinite series1 +

14 +

19 +

116 +

125 +

136 + . . . In Euler’s

time this was a difficult and well known problem. It hadbeen around at least since Pietro Mengoli posed it in 1650,and had eluded efforts by Wallis, Leibniz and the Bernoullibrothers: Sandifer refers to it as “the best known problemof the time” [20, p. 58]. In 1734 Euler found the solutionπ2

6 , solving the problem in three different ways.2 In his thirdsolution, Euler drew an analogy between finite and infiniteseries, and applied a rule about finite series to infinite seriesto get what is referred to by Polya as an “extremely daringconjecture” [19, p. 18]. Euler continued to evaluate this con-jecture, and his analogous rule. For instance, he used empir-ical tests, calculating the value for more and more terms inthe series. He also applied the rule to other infinite series,to form predictions which could then be tested: both serieswith unknown solutions (eg.1+

116 +

181 +

1256 + . . . =

π4

90 )and series where the solution was known (eg.Leibniz’s infi-nite series1− 1

3 +15 −

17 +

19 −

111 + . . . =

π4 ). In all tests

the conjecture and analogous rule held strong.This creative episode involves several different aspects.

Firstly, finding the solution to the Basel problem was a majorresult. This has inspired our Eg, the expression of a concept.Of even greater value was Euler’s discovery of the analo-gous rule, and in general, ways of converting rules aboutfinite series to rules about infinite series, which – once con-firmed – could be applied generally. This has inspired Ep.Euler’s proofs that his solution is consistent and sound haveinspired Ag. While the modern mathematical concept of in-finity was not developed in Euler’s time, the concept of in-finite series was well established;3 therefore, his work withinfinite series had to fit with the structure already developed.Euler’s extended work on the applications and limitations ofhis analogy and his independent proofs of the solution in-spire our framing aspect, Fg. We summarise these creativeacts in terms of our FACE model below.

FACE Basel Problem

Fp: –Fg: Euler’s extended work on the applications and limitations

of his analogy; his independent proofs of the solution; gen-eral ways in which analogies can be used in mathematics

Ap: –Ag: Euler’s proofs that his solution was soundCp: Ways to find problems such as the Basel problemCg: The Basel problem (Pietro Mengoli)Ep: Ways which Euler discovered of converting rules about fi-

nite series to rules about infinite seriesEg: The solutionπ2

6

We see that, in describing how Euler solved the Baselproblem, authors such as Polya and Sandifer refer to other

2For excellent commentary on this work, see [20, pp. 157-165]3Infinite series have been around at least since Zeno.

creative acts in relevant mathematics communities. Theyalso describe the amount of time Euler took, and the effort hewent to in order to justify his result and his methods. Theyuse emotive terms such as “daring” to describe the results.In effect, this is all an attempt to quantify and qualify the im-pact this creative act had on mathematical society. This mo-tivates our emphasis on impact rather than just value judge-ment in the IDEA model. In particular, by highlighting thetime taken, Polya and Sandifer indicate the level of devel-opment Euler’s methods went through as he tried and failedrepeatedly to find a solution. They also highlight how diffi-cult people had previously found the Basel problem, hencehow different Euler’s creative act(s) were to the sum of thosecoming before him. These aspects of the description of im-pact give us motivation for the branch of the IDEA modelthat deals with the stage of development software is in, andthe utility of understanding exactly the background knowl-edge available before, during and after the development andexecution of the software. In addition, the emotive descrip-tions highlight that creative acts are intended to affect peo-ple’s well being. Finally, the description of Euler going togreat lengths to justify his methods can be seen as motiva-tion for why we measure the level of cognitive effort thataudience members expend in understanding creative acts inthe IDEA model. Clearly, Euler was trying to convince peo-ple to understand his approach and spend time appreciatingthe implications it had for mathematics.

Duncker’s candle task

Duncker’s candle task [6] is a cognitive performance testinvented by the Gestalt psychologist Duncker, intended tomeasure the influence of functional fixedness4 on a partic-ipant’s problem solving capabilities, and has been used ina variety of experiments concerning creative thinking. Thechallenge in the candle task is to fix a lit candle on a wall(a cork board) in such a way that the candle wax won’t driponto the table below. One may only use a book of matches,a box of thumbtacks and the candle. The solution, to tackthe empty box of tacks onto the wall and sit the candle in thebox, is difficult since people typically see the box as a con-tainer for the tacks rather than a piece of equipment for thetask. Some people find partial solutions, such as tacking thecandle to the wall or melting some of the candles wax andusing it to stick the candle to the wall. The task is interestingfor us since its solution is an example of everyday, little-c,exploratory, P-creativity (other components surrounding thetask could be argued to be a different type of creativity, suchas Duncker’s invention of the problem, which could be seenas H-creative and possibly big-C creativity). We show ourdecomposition of various creative acts connected to this taskin terms of our FACE model below. Since we are interestedin the everyday, creative problem-solving aspects in this ex-ample we do not consider the IDEA model: there is usuallyno audience in such contexts.

4Functional fixedness is a cognitive bias which limits a personto using an object only in the way it is traditionally intended, forinstance a person with a hammer who needs a paper weight, but isunable to see how the hammer could be used for such a purpose.


FACE Duncker’s candle task

Fp: –Fg: An explanation as to how the task was completedAp: –Ag: Evaluation of the solutionCp: Ways of finding problems like Duncker’s candle taskCg: Duncker’s candle taskEp: Techniques to overcome functional fixedness,eg. analogi-

cal transfer, in which the problem is framed as an analogy,or reorganization of mental categories

Eg: Tack the box onto the wall and sit the candle in it

Further work and conclusionsWhile our FACE and IDEA models are not broad enough tocover all potentially creative software systems, we believethat they cover enough to guide and describe the first waveof creative systems. These models constitute a start, ratherthan endpoint, to our thinking about how to evaluate cre-ativity in machines. This project is ongoing, and we expectto evaluate our two models principally by their utility in de-scribing creative systems: we begin this task in a companionpaper [4]. Philosophers of science can also help us to evalu-ate and compare such measures: recent work has suggestedcriteria which a good theory should satisfy.5

In their analysis of one hundred recent doctoral disserta-tions on creativity, Wehneret al. found a “parochial iso-lation” and no cross-disciplinary ideas (reported in [23]).They compared the situation to the parable of the blind menwho attempt to understand an elephant by touching a dif-ferent part, thus each building a very different picture of it.We hope that, by drawing inspiration from work in the psy-chology of creativity, we will help to contribute to a fruitfulmultidisciplinary approach.

AcknowledgementsWe are very grateful to John Charnley for his thoughts onthe FACE and IDEA descriptive models. We would alsolike to thank our three anonymous reviewers for their help-ful comments. This work is supported by EPSRC grantsEP/F035594/1 and EP/F036647/1.

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