Academic - index

Computer Creativity

(30 April 2003)


Essentially, there are two issues here. Firstly, we need to define what creativity actually is. Secondly, we need to address whether this process can be done by a computer, or whether it is an inherently human ability. I have sidestepped this second issue, by redefining the question slightly - can a computer do things that would be considered creative if a human did them?


Boden [2] divides creativity into two categories: P-creativity (psychological) and H-creativity (historical). Essentially, P-creativity is when an individual comes up with an idea that they have never thought of before. H-creativity is when nobody else has ever come up with this idea before. Boden notes that it is difficult to conclusively prove H-creativity, due to events such as the destruction of the great library at Alexandria.

Haase [3] suggests that there are other categories between these two extremes: "as the size of the community grows, novelty becomes rarer". For instance, when Gauss came up with a quick solution to the problem of summing a series of numbers [6], this was certainly unique in his class (who had presumably received the same mathematical education as him up until this point), which reflects well on him, even if someone had previously discovered the same solution in a different school, or even a different country.

Another important condition for creativity is that the idea must have some value. This means that it is essential to have some way of evaluating concepts. In the case of algorithms (such as Gauss’ method for summing a series), an objective assessment that can be made; we first prove that it is correct, then consider the time complexity. In other cases, particularly when it comes to art, this is a subjective process, and as such is difficult to define. The controversy over the Turner Prize in recent years is a good example of this [1]. Schank and Foster [7] have also commented on this: "there is an inescapable subjective element in the assessment of the degree of creativity, based on the evaluator’s experience, knowledge, and values. [...] There just is no simple test of whether something is creative."

In fact, Boden goes further, differentiating between novelty and creativity. A novel idea is one that did not occur before, but has been reached by an existing set of generative rules. By contrast, a creative idea is one that could not occur before. For example, if a child (or a computer program) is told that every sentence must take the form "determiner-adjective-noun", then sentences such as "the big dog" or "a red house" may be novel, but they aren’t creative. However, a sentence such as "the big bad" would be creative, since it can't be generated by that rule. Again, value is essential here - it has long been claimed that a million monkeys, using a million typewriters, would eventually produce the complete works of Shakespeare. But we must bear in mind that they would also produce a large amount of gibberish, which would not be allowed under the standard generative rules.

This apparently leaves us with a paradox. A creative idea is one that could not have occurred, and yet has occurred. How is this possible for a human or a computer? The answer to this will be dealt with in the following section.

Conceptual spaces

In AI, we have search spaces. For instance, in a game of chess, a state would be a board position. The state space would consist of the initial board position, and all the positions that can be reached from that, by making legal moves. A conceptual space is not the same as a search space, but they are similar.

Keeping our chess example, in a search space we have heuristics to select states. By changing the heuristics involved, we create a new strategy, which will favour some states over others. For instance, we might consider pawns to be more valuable than queens.

In the corresponding conceptual space, each concept is, again, a board position. However, there are positions we can visualise, which are impossible to achieve under the rules of chess, such as one that is identical to the starting position, except that the white pawns have exchanged places with the black pawns.

Chess board

By contrast to a search space, changing the rules of a conceptual space allows us to reach different states, rather than just making it more or less likely that we will reach a particular state. We can remove constraints to add possibilities, e.g. allowing two pieces to occupy the same square on the board. Adding constraints won’t add new concepts to the space, but may help to generate concepts of value. For instance, Boden comments that while Schoenberg abandoned the constraints of tonality, he introduced new constraints, such as using every note of the chromatic scale.

So, like Alexander cutting the Gordian knot, the key concept here is to change the rules in order to generate new concepts. Of course, the process of changing the rules will itself need to be established – Boden suggests approaches such as negating a constraint. This then resolves the paradox of how to think the unthinkable. However, Ram et al [5] dispute this: "it is not obvious why the search space generated by application of conceptual change operators is not considered part of the thinkable".

Wiggins [8] makes a distinction between exploratory and transformational creativity. In his view, exploratory creativity is when you select a concept using the existing generative rules, whereas transformational creativity is the result of changing the rules. It should be noted that this conflicts with Boden's terminology, since she wouldn’t consider "exploratory creativity" to be creativity at all. Rather, she would refer to that as novelty. Wiggins has said that "transformational creativity may (at least) be characterised as exploratory creativity at the (appropriate) meta-level".

Both Boden and Wiggins have drawn a parallel between transformational creativity and the 17th century modernist movement in music. Particularly in an artistic context, there may not be any one “accepted” style; this will vary with the audience. For instance, Boden states, "it is a standard rule of fugue (occasionally broken) that the first note is either the tonic or the dominant". So, if someone composes a fugue that violates this rule, then she would consider this to be an example of transformational creativity. However, if one disagrees that this is a standard rule, then a fugue that violates it would just be seen as an example of explorational novelty. Lustig [4] is particularly sceptical of this notion: "Can Bach's creativity consist of, or reside in, his ignoring of rules stated by Longuet-Higgins? This can only make sense if we can establish that Bach knew of such rules - and he clearly did not." In Boden's opinion, transformational creativity is what defines the great artists, although others (such as Wiggins) have disagreed with this.


Wiggins has formalised some of the concepts that Boden introduced. He initially defines this terminology:

C – a conceptual space.

U – a multidimensional space, which contains every possible conceptual space.

R – a set of rules that constrains a conceptual space.

T – a set of rules that are used to traverse a conceptual space.

ε – a set of rules that are used to evaluate concepts in a conceptual space.

L – a language in which to express T, R, and ε.

┴ – the empty concept.

⟦.⟧ – an interpretation function that takes a set of rules, and returns a function to select concepts.

«.» – an enumeration function which takes a set of rules, and returns a function to map one list of concepts to another list of concepts.

Boden referred to null concepts, and hinted at partial concepts; Wiggins extended this by referring to partial concepts explicitly (he refers to the empty concept as "the most partial concept of all"). However, it should be noted that the border between partial concepts and complete concepts is a grey area.

So, let us first consider exploratory creativity (using Wiggins' terminology). He proposes that an exploratory creative system can be characterised with the following septuple:

<U, L, ⟦.⟧, «.», R, T, ε>

The idea here is that we should start with an initial concept, and then explore all the related concepts, using the generative rules. To do this, we compute:

«R ∪ T»({┴})

We then need to evaluate the resulting concepts:

⟦ε⟧(«R ∪ T»⋄({┴}))

Now we need to consider transformational creativity. The issue here is that rather than trying to find every concept in a given conceptual space C (as we do with exploratory creativity), we are instead transforming C into C1. We do this by transforming R into R1, or by transforming T into T1, or both. The transformation of T is significant, because of an extra subtlety that Wiggins introduces. He suggests that there may be some concepts in a given conceptual space that are inaccessible, i.e. that we can distinguish "what is in principle possible in a creative domain from what is actually possible according to the properties of a given creator." So, by transforming T, even though C remains the same, more of it may become accessible. If we only consider the subset of C that is accessible, then transforming T can in fact transform this subset.

Wiggins then proposes that a transformational creative system can be characterised with the following septuple:

<L, LL, ⟦.⟧, «.», RL, TL, εL>

using this terminology:

Ψ – a search algorithm used to construct elements of L.

LL – a new rule language which allows us to construct sequences in L.

RL – a rule set which picks those members of L which are syntactically well-formed with respect to Ψ.

TL – a rule set which is used to traverse an agenda of potential sequences in L.

εL – the rule set which selects pairs of RL and TL such that new concepts are added to the conceptual space under consideration, and that those new concepts are valued by ε.

This model doesn't (yet) cover interaction between creative agents, which may be the most interesting aspect of this research.


Clearly, it must be possible to come up with concepts that are generally accepted as creative, since humans have been doing so for thousands of years. Different authors may use different terminology for this, e.g. novelty as opposed to creativity, but the idea of changing the rules (or "thinking outside the box") in order to generate new concepts seems valid. If we can understand how humans are creative, then we may be able to apply these techniques to computers. So, Boden's theories, and Wiggins' formalism of them, provide a good starting point for further research in this area.


[1] BBC News. (2001) Critics split over Turner winner
Available: [accessed 30 April 2003]

[2] Margaret A. Boden. (1991) The Creative Mind: Myths & Mechanisms

[3] Kenneth B. Haase. (1995) Too many ideas, just one word: a review of Margaret Boden's The Creative Mind: Myths and Mechanisms
Artificial Intelligence Journal 79:69-82

[4] Roger Lustig. (1995) Margaret Boden, The Creative Mind: Myths and Mechanisms
Artificial Intelligence Journal 79:83-96

[5] Ashwin Ram, Linda Wills, Eric Domeshek, Nancy Nersessian, Janet Kolodner. (1995) Understanding the Creative Mind: a review of Margaret Boden's Creative Mind
Artificial Intelligence Journal 79:111-128

[6] Roper. (No date given) Math 106 Handouts: Karl Freidrich Gauss
Available: [accessed 30 April 2003]

[7] Roger C. Shank, David A. Foster. (1995) The engineering of creativity: a review of Boden's The Creative Mind
Artificial Intelligence Journal 79:129-143

[8] Geraint A. Wiggins. (2001) Towards a more precise characterisation of creativity in AI
Available: [accessed 30 April 2003]
(Also delivered as a seminar at Kings College London on 19 March 2003)

This page was last updated on 2004-09-05 by John C. Kirk

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