Introduction

A major problem in research on innovations is the understanding of creativity, that is, the origin of innovations. A common claim in the literature is that innovations are recombinations of current capabilities, as Schumpeter claimed, and that search is local (see e.g., March, 1991). This perspective treats creativity then as discovered in close proximity to current practice. A contrary perspective is to consider creativity as sudden blind insight. In our opinion, the local recombination and search perspective fails to treat the many cases of significant creativity that we observe, while the latter perspective yields little theoretical and conception gain.

The key point seems to us that those approaches lack an appropriate ontology. In particular, the recombination-centred perspective emphasises the role of artefacts, leaving the agents (whether humans or human organisations) a secondary role of pure recombinators. It becomes, therefore, possible to ignore the role of agents and to follow the pure technological trajectories of the artefacts. However, human agents – which are endowed with sophisticated cognitive and communication capabilities – can create and use artefacts in ways, which are not just obvious at all. Indeed, they are embedded in a web of relationships among themselves, with their organisations and with their environment, which affect their ways of thinking and of using artefacts. Therefore, in our view, in order to understand innovation it is much more appropriate to take explicitly into account the presence of both artefacts and agents, rather than trying to 'project out' of the description one of these two terms.

The fact that agents (be they human beings or groups or organisations) have an internal structure also affect their behaviours. Broadly speaking, interactions between particular (groups of) agents often take the form of recurring patterns that persist over time. Making (new) artefacts, for example, or generating (new) forms of organisation in a society, is a multi-faceted process that is based on recurrent sets of actions, in which a number of agents with different roles are involved. In this process, new concepts and objects are discovered and invented by simultaneously surveying the opportunities offered by the social and material environment, and adapting the existing categorisations of the agents. When looking for inventions (new strategies, new products, or organisational innovations) the different agents participating in this process can explore a variety of opportunities from one's own perspective. But for an innovation to emerge, there must also be a degree of convergence among their perspectives so that the group as a whole aligns itself around the creation and use of the invention.

In order to innovate, agents should share (or come to share) a common system of beliefs, which enables them to interact and otherwise express themselves in ways that they mutually recognise (e.g., do things in compatible ways, identify and use similar resources, share technology, have similar norms, similar institutions). Key features of this system are the categories, the tools the individuals use to process such a kind of information (Selby and El Guindi, 1976); in addition, a large body of literature in social psychology has emphasised the central role of categorical thinking in social relationships (Macrae and Bodenhausen, 2000; Markman and Gentner, 2001).

In this paper, we propose a model by which radical innovations are created by a process of 'exaptation' (Gould and Verba, 1982; Ceruti, 1995; Gould, 2002), which according to our hypotheses represents a key aspect of innovation processes. In particular, our model is focussed on the interplay between artefact innovation and the functionalities, which agents attribute to artefacts through their categories. Our claim is that the explicit representation of artefacts and categories eases the understanding of the exaptation phenomenon, seen in this context as a shift in terms of 'leading attributions', and allows the identification of the elements favouring the emergence of exaptation.

Artefacts are key components of human organisations and activities. Artefacts are entities forged by constituent entities of an organisation that enhance that organisation's functionality. One of their main properties of interest to us is their capability to convey information, although they may not be explicitly designed for this purpose. In addition, there are artefacts specifically designed to store and carry information: books, radios, televisions, human languages, including the very special kind of artefact represented by computers, objects able to process information at a very high abstraction level.

Since artefacts convey information, their explicit representation eases the understanding of the exaptation phenomenon, seen in this context as a shift in terms of 'leading attributions'. Actually, their introduction is important in order to characterise the ontology necessary to identify exaptation events. In the model presented here, we focus on phenomena occurring at the micro-level (how individuals collect information about the external world, categorise it, and combine existing categories in order to create new ones) and meso-level (the exchange of information among individuals). However, we do not explicitly include the details concerning the macro-level events (the shared system of beliefs and the common physical and technological resources), that are left for further research.

In the first two sections, we will provide a detailed introduction on the notion of exaptation. The third and fourth sections describe the model that we developed in order to explore some aspects of exaptation and its dynamics. Finally, we discuss the results of our first simulations.

Exaptation

Recently, the concept of exaptation has been introduced to explain the changes resulting from innovation processes and the rise of new technologies. Exaptation originates from the domain of biology, where it appears for the first time in Gould and Verba (1982) who referred to species evolution as the mechanism complementary to Darwinian adaptation. The following definition provided by Ceruti (1995) gives insight on the main idea of exaptation: '...the processes whereby an organ, a part, a characteristic (behavioural, morphologic, biochemical) of an organism, which was originally developed for a certain task, is employed for carrying out tasks that are completely different from the original one'. The typical example provided by Gould (2002) is represented by a line of feathered dinosaurs, arboreal or runners who developed the capability to take advantage of feathers for flying, when originally they were intended for thermoregulation purposes.

Furthermore, exaptation can provide a key to interpret the serendipity that characterises the generation of new products. Exaptation emphasises that the functionalities for which a technology has been selected are only a subset of the consequences generated by its introduction. In many cases, the number of consequences generated by a new technology, a product, or a process can be incredibly large and thus, its exaptive potential practically unbounded. Hence, exaptation is to be interpreted as a central idea connecting technological progress and emergence of recurrent patterns of interaction.

Mokyr (1998) defines the phenomenon of exaptation saying that 'it refers to cases in which an entity was selected for one trait, but eventually ended up carrying out a related but different function'. Such a definition captures the idea that exaptations are those characteristics of a certain technology that are co-opted by another origin or utility because of their current role. Different from adaptations, which present functions for which they are selected, the exaptations generate effects that are not subject to pressures from the current selections, but potentially relevant later on.

A classical example of technical innovation illustrating both adaptation and exaptation is the Compact Disk (CD). The CD was originally developed in 1960 in the Pacific Northwest National Laboratory in Richland, WA and it was designed for a specific task: solve the problem of the sound quality deterioration of the classical vinyl records. Its inventor, J.T. Russell, developed a system based on the idea of using light to carry information, avoiding the usual contact with mechanical parts of the recording device. The CD-ROM was patented in 1970 as a digital-optic system for recording and reproducing sound. Later, researchers used the technology of the CD-ROM for a different purpose: storage media for computer data. Although the latter represented a function not originally intended for the CD-ROM, it became very clear that it was indeed effective. As a result, during the 1970s, the Laboratory refined the CD-ROM technology commercialising a product that could be usefully employed for different purposes and improving some of its characteristics (increment of memory capacity, recording speed, recording and reproduction sound quality).

Another important aspect of such a phenomenon is represented by what Gould defines as 'exaptive pool'. The exaptive pool represents the potential allowed for future selection episodes (at all levels). There are two categories of potential: (i) intrinsic potential and (ii) real entities.

In order to understand intrinsic potential, the reader should recall the smallest and lightest among the US coins, the dime, which despite its very little purchasing value, is still in use. An unforeseen consequence of its technical characteristics is that the dime can be employed as an occasional screwdriver. Hence, the dime is an adaptation if considered as money and exaptation if considered as a screwdriver. Note that, the potential for the additional functionality as a screwdriver is an intrinsic characteristic of the dimensions and the shape of the coin and, thus, cannot be considered as disjoint or separated from it.

The second category of the exaptive pool includes real entities, matter or material things that became part of the item under exam, due to various reasons. They are not currently associated with a particular use and at the same time do not generate substantial damages, thus avoiding elimination by selection, a phenomenon called 'neutral mutation' in biology (Kimura, 1983). The members of this category can be generated in various ways as structures that previously were considered useful or as neutral characteristics introduced 'in incognito' with respect to the selection process. A now classical example, quoted in Gould and Lewontin (1979) can be found in architecture, where spandrels (initially empty spaces between the vaults and archs in churches) have been later used as a support for paintings and mosaics: while their initial role was that of structural elements, spandrels thus became a key aesthetic feature.

The origin and peculiar features of exaptation

In order to complete a picture of the exaptation phenomenon, we consider two questions. (i) What are the factors that lead to the birth of such a process? (ii) What are the traits that distinguish exaptation from other processes?

In order to answer the first question, we can remember that in our description exaptation originates from the interplay between the artefacts and the functionalities, which agents attribute to them through their categories: therefore, we have to describe what an artefact is, what a category is and which kind of relations can they have.

In a very general way, we can describe an artefact as a hierarchical structure composed by subparts that are approximately independent in the short term, but connected by a global behaviour in the long term (i.e., the notion of decomposability, introduced by Simon (1996). As a consequence, the subparts are selected and proliferate in time as a consequence of being only one among many aspects of the whole artefact. While some such subparts can have an important role with respect to the goal of the whole artefact, others remain latent waiting future activation.

Agents evaluate artefacts using their categories, a category being a tool the agents use in order to:

• focus the attention on a subset of the artefact characteristics;
• interpret the highlighted features;
• give an evaluation of the artefact functionality, based upon the highlighted features ('I like', 'I hate', 'very good', and so on).

Based on the above observations, we can divide the possible origins of an exaptation into three groups:

1. the case where a subpart is already providing a positive contribution to the functionality for which the technology was selected; only in a later moment and after changing the context, the subpart becomes the main component;
2. the case where the subpart has no role in the overall performance of the system;
3. the case where the subpart provides a negative contribution to the overall performance of the system.

An example of case (1) is represented by the phonograph invented by Edison in 1877. The innovative technology for amplifying and reproducing sound suggested the commercialisation of the invention as an office dictaphone. Only such a dramatic change of the context led to the exaptation of the phonograph, later re-named as gramophone, and nowadays considered one of the most popular inventions made during the 19th century. Case (2) is well identifiable in the process of vitrification, originally developed to reduce environmental pollution (safe waste disposition and limited radio-active waste), is now mainly exaptated for biological dangerous processes such as elimination of biochemical weapons. Finally, case (3) can be exemplified by the innovation in plastic production during the Second World War, based on sub-products deriving from oil refinement (Dew et al., 2004).

Next, we begin to address the second question of what traits distinguish exaptation from other processes. First, exaptation is not a simple side effect, that is, an unintended (and often undesirable) consequence of a particular treatment. Although the apparent affinity between the two notions, an exaptation is usually identifiable with respect to change of context, whereas we cannot say the same for a side effect. Second, exaptations are not an alternative description of the Schumpeter's process (Schumpeter, 1934), usually understood as a creative combination of existing ideas belonging to different entrepreneurs. Although it is true that in economics, exaptation is mainly due to entrepreneurs, it usually refers to the variation of context that generates a change in the utility of the technology, not to a simple mixture of existing elements.

One could think that an exaptation is simply an unintended consequence of technology. However, this statement ignores the fact that the act of exaptating requires the intentional activation of a technology that otherwise would remain latent; and it is actually the entrepreneur that makes possible such an activation.

Finally, the basic research often generates inventions that are initially designed without an immediate and defined target, and thus at least in the first phase are not properly adaptive. The process of exaptation points out that the principle of such research is non-adaptive in its nature.

The model

There are in literature models that describe the feedbacks between artefact innovation and attributions of functionality (e.g., see Ferrari et al., in press); nevertheless, these models do not take into account explicitly the presence of artefacts.

The aim of the EMIS system (Exaptation Model in Innovation Studies) is to highlight the factors that contribute to the occurrences of exaptation, by means of the explicit description of both artefacts and agents. EMIS is an agent-based model characterised by the presence of two kinds of social agents (A), producers and users. The agents have only partial knowledge of the world, and each producer owns: (i) a set of categories (C), utilised to interpret a certain set of artefacts and (ii) a set of weights representing the importance that a certain agent assigns to each cognitive characteristics of an artefact (represented by means of the correspondent categories). The model postulates a continuous interaction between producers and users: the artefacts are transferred from the producers to the users and subsequent feedback messages are sent from the users to the producers. The aim of the model is to analyse the effects of the ambiguities present in artefacts and categories on the exaptation phenomena. Obviously, this implementation is only a first step toward a more complete model of exaptation; in particular, we defer to further works the problem of the origins of the categories, as well as the representation of the interdependencies and complementarities among the features composing the agents' categories.

Agents

The agents A_i (i{1, ..., g}, gN⁰) are the model main active units. They have limited system knowledge and are distinguishable by means of their identifier ID. Their total number g is not changing in time, and are grouped in two different classes:

• producers (represented by means of the symbol A_p, where p{1, ..., l})
• users (represented by means of the symbol A_u, where u{1, ..., h})

Thus, the total number of agents is g=l+h.

Each agent owns a given number of categories, which can be different for agents belonging to the two different classes. We denote the categories belonging to producers and users by C_p and C_u, respectively.¹ The number of categories belonging to a given agent is constant at any time period. Moreover, each agent is characterised by a weight vector (different for agents belonging to different classes, respectively W_p and W_u).

Note that in our representation, only the producers are able to build and modify the artefacts (one artefact for each category owned by the producer). Conversely, only the users can evaluate the artefacts.

Categories

In this work, we use the term 'functional attribution', or simply 'attribution', referring to: 'the functionality carried out by the corresponding feature of the artefact I'm evaluating is useful/indifferent/damaging' (or 'I wish/don't_care/don't_wish to give to the artefact I'm building this particular functionality' if we are considering producers). Thus, we say that the set of categories owned by and agent corresponds to his/her collection of attributions. We define the knowledge space as the collection of all the possible functionality attributions.

In this context, each category is a D-dimensional vector, whose elements C_x^(j) (indicated by the words 'characteristic', or 'feature') are discrete random variables taking values {1, 0, -1} with the following probability distribution: if C_x^(j)=1, (1--) if C_x^(j)=0, and if C_x^(j)=-1, where and [0, 1]. Further, we assume that the number of relevant characteristics (i.e., the characteristics corresponding to symbols '1' and '-1') is only a fraction of the total number of features. A category composed only by relevant characteristics implies not realistic agents attributing relevance to each single cognitive detail.

The agents are also able to modify their categories: in case of categories trespassing such a threshold, not all the relevant features can be memorised (in the rest of the paper indicated by the symbol |1|). In order to simulate such a memory loss, the number of relevant features n_C|1| is computed after each modification. If K=n_C|1|->0, a removal process eliminates each relevant feature with probability

recovering in such a way a more realistic situation.

Weights

Each agent owns a D-dimensional vector of weights, whose elements, W_p⁽ⁱ⁾ and W_u^(j) take values in the interval [0, 1]. Each element represents the importance that the agent assigns to the corresponding cognitive feature of its categories. For example, we could appreciate a car because of several reasons: power, style, size, price, colour, maintenance costs, practicality, and so on; nevertheless, not all these characteristics have the same influence on our feeling. Namely, W_x⁽ⁱ⁾ ({u, p}) represents the weight that the agent assigns to the ith cognitive feature of the D-dimensional cognitive space (colour is more important than maintenance costs, or class more than price, etc.). In the present version of the model, these vectors are built during the initialisation phase at t=0 and are constant with respect to time.

Artefacts

The artefacts are 'goods', built by producers and utilised by users. Each artefact art_p^s is identified by an identification variable, IDs and corresponds to only one category (each category belonging to a particular producer Idp). The artefacts art_p^s are characterised by an extremely simple representation: they are D-dimensional vectors, whose elements (again indicated by the words 'characteristic' or 'feature') take values {0, 1}, where 1 indicates the presence of a given characteristic (feature) and 0 its absence. In such a representation, the producers can build new artefacts by modifying their categories.

Despite this simple representation, the artefacts are suitably defined for conveying information, and can be successfully 'interpreted' by users; this fact allows the system to produce interesting behaviours.

Artefact production

In this section, we introduce one of the more delicate aspects of the model: the production artefacts. In this model, a producer tries to build an artefact as much as possible similar to the prototype memorised in one of its categories, but despite his efforts it has to deal with errors and physical/technical constraints. Typically, a producer processes already existing artefacts, and tries to add some desirable characteristics to it. Namely, the producer selects one of its categories, and attaches the tag 1 to the artefact in correspondence to a 1 memorised for the chosen category. Similarly, the producer places a 0 tag in correspondence to a -1 tag, a 0 tag in the category meaning that the producer is not interested in changes in these positions and therefore, the already present values will not be altered (see Table 1 for a simple example).

Table 1 - Artefact production/innovation.

Full table

In particular, we wish to highlight that the artefact feature can take only two values (0 and 1), whereas the corresponding feature on the categories can take three values (1='wish', 0='indifference', -1='not desired'). Therefore, the feature correspondence represented in Table 1 can be characterised as follows:

• if the values are identical, there is no change in art_p^s
• if C_p^(j)=1, then art_p^s=1
• if C_p^(j)=0, then art_p^s is unchanged
• if C_p^(j)=-1, then art_p^s=0

If some additional restrictions were not imposed, this process would lead to the 'perfect' artefact, where all the desired characteristics are present at the maximum level (e.g., think of a unrealistic car, able to fly, navigate, interact with human beings, produce and translate documents and make excellent coffees). In order to take into account these constraints, we decided simply to bind the number of characteristics present simultaneously in the same artefact. If, after the producer processing, an artefact has number 1's exceeding the given threshold , a stochastic removal process eliminates a subset of the current characteristics.

Such a removal process is slightly more complex than the corresponding process acting on categories. For instance, characteristics that are judged to be irrelevant to the agent purposes should have a deletion probability higher than characteristics that are regarded as having higher importance. Therefore, we can have three main situations:

• N₁: the number of 1's in artefact art_p^s, corresponding to a feature 1 in C_p^(j)
• N₂: the number of 1's in artefact art_p^s, corresponding to a feature 0 in C_p^(j)
• N₃: the number of 1's in artefact art_p^s, corresponding to a feature -1 in C_p^(j)

In correspondence to these numbers, we have the following the removal probabilities:

• P₁: probability that a 1 in artefact art_p^s is eliminated, when the feature C_p^(j) is 1
• P₂: probability that a 1 in artefact art_p^s is eliminated, when the feature C_p^(j) is 0
• P₃: probability that a 1 in artefact art_p^s is eliminated, when the feature C_p^(j) is -1

The following relation holds for the above quantities:

Note that in order to set the probabilities P₁, P₂ and P₃, we have to fix

:

quotient between P₁ and P₃

:

quotient between P₁ and P₃

In particular, we wish to obtain P₁<P₂<P₃, that is,

Therefore, we have

and obtain the elimination probabilities

As a consequence, it is enough to act only on two parameters ( and ).

Finally, we remark that since the final goal is to simulate exaptation phenomena, we can disregard an overly detailed description of production processes and costs.

Functionality

In EMIS, we define the 'functionality of an artefact with respect to a particular category', as an index measuring the level of user's satisfaction with the artefact. The index appraises the satisfaction received from the artefact, when the user evaluates the corresponding category. Its maximum value, denoted by F_max, indicates that the artefact fits perfectly in the requirements contained in the associated category.

In order to evaluate an artefact, the agent must 'interpret' it by means of one of its categories. Practically, the agent performs a filtering operation on the artefact using the involved category, according to the scheme reported in Table 2.

Table 2 - Computation of the comparison vector art-C.

Full table

The hypotheses of Table 2 are very simple:

• if A_pⁱ=1 and C_u⁽ⁱ⁾=1 (user's desires and producer's realisation coincide), then the comparison produces a desirable outcome (denoted by 1);
• if A_pⁱ=1 and C_u⁽ⁱ⁾=-1, (user's desires and producer's realisation do not coincide), then the comparison results in an undesirable outcome (denoted by -1);
• all the other cases correspond to a situation of indifference.

Clearly, the dynamics generated by such a model should tend to produce the 'correct' positioning of 1's in the artefact vector. In order to achieve this goal, we can define the artefact functionality (with respect to a given category) simply as the scalar product between the comparison vector art-C and the agent's weight vector W_u. Note that the largest functionality value F_max of an artefact with respect to a given category is given by the scalar product between the weight vector and the category itself, where all the '-1's are set to be '0'.

Dynamics

The most critical interactions for the outcome of the model take places between producers and users. Two distinct parts compose the interaction process: (i) when the user receives and evaluates an artefact built by a producer; (ii) when the user provides feedback evaluation to the producer about the satisfaction level reached by the artefact (the artefact functionality).

First, we focus our attention to the delivery and subsequent evaluation of an artefact. In order to evaluate the artefact the user computes its functionality (already described in the previous paragraphs); filters the artefact with respect to all her/his categories and finally communicates the best result to the producer. Moreover, the user can deliver to the producer some additional information, which can result useful for the future artefact innovations. Specifically, the user can transmit to the producer particular subsets of the two categories that give the highest functionality values. These subset are composed of

• I_jq(q=1), Actual Information (AI). Features of the selected category that correspond to the art-C characteristics that highly contribute to the determination of the functionality value (it does not matter if in positive or negative direction).
• I_jq(q=2), Desired Information (DI). Features of the selected category that potentially have the highest contribution power (the I_jq features that highly contribute to the scalar product between the selected category C_u as is and the weight vector).

These two different kinds of information allow the user to explicit her/his requests. In particular:

• AI represents the features of the current artefact that give positive or negative contribution to the functionality.
• DI expresses what the agent likes or dislikes about the artefact (when it is filtered by means of the selected category).

Sometimes, it is possible that the two subsets have a non-empty intersection: for example, it is possible that an artefact feature be important for a category, and at the same time it gives a negative contribution to the functionality of another category. In other words, in the example we are supposing that for AI we observe C_u⁽ⁱ⁾=1, whereas for DI we have C_u⁽ⁱ⁾=-1, as a result of some other category. In such a case, we impose that either AI or DI is randomly left out of the transmission.

The producer uses the transmitted features in order to modify the features C_p⁽ⁱ⁾ of the category employed to build the artefact. The new value of each characteristic is computed by means of the following formula:

where a is the value of the feature C_p⁽ⁱ⁾ of the A_p, b is the value of the feature C_u⁽ⁱ⁾ of the A_u, is the influence of A_p on next feature value and is the influence of A_u on next feature value.

The feature will be

where is the lower bound for the upper interval and is upper bound for the lower interval (Figure 1).

Figure 1.

Modification schema of the A_p features.

Full figure and legend (5K)

The goal of the above calculation is to transform the features communicated to the producers by the user. All the remaining features are left unchanged, except the admittance of some random 'noise' obtained as: a 1 or a -1 starting from a 0 tag, a 0 or a -1 starting from a 1 tag, and a 1 or a 0 starting from a '-1' tag. Finally, in order to limit the number of relevant features, the new vector is filtered by the removal process described in the previous section, according to the given threshold . The final vector represents the new category that the producer employs to build the subsequent generations of the artefact.

EMIS and the study of exaptation

In the initial paragraph, we have defined exaptation as a sudden emergent phenomenon in evolution dynamics. Where does exaptation appear in our model? Recall that EMIS simulates exchanges of products (artefacts) between producers and users, the users evaluating the artefacts by means of their categories. In this context, an exaptation is a category change in interpreting the artefact. For example, after hundreds of steps the category that was systematically returning the best functionality is no longer the best one: the last innovation(s) has (have) increased the functionality of another category that in such a way becomes the new referring category for the selected artefact.

Recall that the producer supplies the user only with the best functionality value among all the values computed using all the categories it owns. The category that furnishes such a best value during one interaction is likely to have a large value also in the next interaction, and so forth. In a sense, such best category is, for the user, the 'leading' category for this particular artefact. Sometimes, but quite unlikely, another category reaches a functionality value larger than that of the leading category. In a sense, this can be interpreted as a variation of the utilisation context of the artefact under exam; in this case, we are observing an exaptation event.

Model dynamics

Initialisation

In order to test the model, we perform some preliminary simulations by avoiding unnecessary complications. Therefore, we reduce the number of the actors, maintaining only one producer and one user:

The knowledge space of the categories involved is D=1000 features. The user utilises five categories, which guarantee sufficient diversity, while the producer owns only one category, corresponding to the artefact that it is building.

The other parameters we have to fix in order to create the initial categories are:

1. the threshold , limiting the number of |1|'s in C_i^(j), is set to be 100;
2. the initial fraction of 1s in C_i^(j), is set to be 0.05;
3. the initial fraction of value -1s in C_i^(j), is set to be 0.05.

The value of is relatively low with respect to the D value and indicates that the space of all the possible characteristics of a category is very large with respect to the really imagined ones. Each feature of the initial artefact (at time t=0) takes the value 1 with probability

where is the threshold defining the maximum number of 1's that can be present on an artefact, and D being the total number of features composing the knowledge space. Thus, initially we have a 'raw' artefact that is able contains a large set of details. In order to correctly link each artefact to its referring category, this raw artefact is filtered following the schema proposed in Table 1, and in sequence trimmed by eliminating the accidental '1' exceeding the threshold , as during the usual production processes.

The parameters and , which tune the presence of 1s within the artefact during the final elimination process, are fixed to 0.01 and 0.05, respectively, while the upper bound is set to 200. Please note that >, that is, we are assuming that

• the producer can build artefacts with not explicitly desirable characteristics;
• the artefacts can carry out more characteristics than the planned ones;
• the typical user focuses its attention only within a subset of the whole potentiality of the artefacts.

Therefore, it is actually possible that an artefact carries out a number of functions larger than the number of functionalities for which it has been selected (exaptive pool of possibilities). In the last part of this paper, we will see that in order to study the exaptation phenomenon it is enough to trace the path for a single artefact.

In the second phase of the interaction process, the producer creates new categories (new knowledge). In order to do so it enriches its knowledge using the feedback messages sent by the user. Particularly, we choose to give the same relevance to both the agents, by setting the balancing weights ==0.5, and =1/3, =-1/3, in order to obtain three intervals of approximately equal length. Hence, we have that the producer averages the feature values of its category with the corresponding values provided by the user.

A typical run

Figure 2 shows some of the main variables simulated by EMIS. Figure 2a shows the best functionality value of the artefact at a given time step, and its F_max value. Note that at step 207 the user changes the leading category (exaptation) and F_max. In this case, it is observed that the upper limit for the achievable satisfaction decreases, despite an increase in the actual functionality

Figure 2.

Interactions between user and producer. At each step the user returns to the producer the best evaluation of the artefact on the basis of its own categories. (a) (left) Shows this variable and its maximum value (F_max in the text), obtainable only in the case of null distance among artefact and category. At step 207 exaptation occurs, as the user changes the referring category (thus leading to a change of F_max) value changes. In this case, the maximum reachable satisfaction decreases, although the actual functionality value increases. (b) (right) Shows the distance among the user categories and the artefact actually built by the producer.

Full figure and legend (64K)

Figure 2b shows the distance among user's categories and the artefact actually built by the producer. In this context, the distance describes the semantic discrepancy between the artefact and the category referred to that particular artefact. Table 3 is based on the two following principles:

• a distance between artefact and category occurs when the agent 'desires' a feature that is not currently present;
• a distance between artefact and category occurs when the agent 'does not desire' the present feature.

At each step the user analyses producer's artefacts, which are interpreted using her/his own categories and furnishes to the producer, the corresponding more elevated value of functionality. At step 207 the functionality value of category 2 outperforms the functionality value of category 4. In the rest of the simulations, category 2 maintains its superiority and we do not observe new other exaptation events (Figure 3).

Figure 3.

Artefacts' evaluation. The figure shows the evaluation the artefact received from the agent's categories during the same simulation of Figure 2. Please note that at step 207 the second category suddenly increases its value and becomes the referring category.

Full figure and legend (76K)

Table 3 - Example of semantic distance calculation between artefact and category.

Full table

Experimental results

We individuate three main factors that are able to favour the emergence of exaptation phenomena:

1. communication among different agents;
2. communication and production noise;
3. evolution of the users' categories.

In all the situations the user can utilise two different modalities of communication:

1. Symmetrical: both communicated categories provide the same amount of information 'actual' and 'desired'.
2. Asymmetrical: the category that better interprets the artefact provides 'actual' information, while the second one provides 'desired' information.

This specification has been introduced to verify whether the presence of communication symmetry/asymmetry can favour the occurrence of exaptation phenomena. Recall that the 'actual' information represents the objective user's evaluation, whereas the 'desired' information expresses what the user wants. Therefore, symmetric communication means that the user treats the categories without any bias, whereas asymmetric communication means that the user transmits an objective report about the first category, and then communicates some desires corresponding to a second one.

Communication

Typically, the user transmits to the producer a (small) subset of the features extracted from the two categories that are returning the best functionality values. In this paragraph, we analyse the behaviour of our model by varying the number of transmitted features, or bandwidth (B). In particular, in this set of experiments the total number of transmitted characteristics is set to be B={20, 40, 60, 80,100, 200}.

First, we observe that the number of exaptations found by using the asymmetric modality is consistently larger than the number of exaptations found by using the symmetric modality. Moreover, larger values for the bandwidth correspond to a larger number of exaptation events, in both short and long run (50 and 1000 time steps, respectively) (see Figure 4). In particular, we noticed that a larger bandwidth with asymmetric modality could favour the presence of exaptations during the long run. Conversely, if the number of transferred features is small, the exaptation events are rare.

Figure 4.

Effects of the communication modalities. The user can communicate to the producer the artefacts' features that mostly influenced the artefacts' evaluation, and/or the artefacts' features that potentially can influence the artefacts' evaluation. By using symmetric communication, for the first two categories the user transmits both the features that influenced the artefacts' evaluation and the features that potentially can influence the artefacts' evaluation. By using asymmetric communication, the user transmits for the best category the features that influenced the artefacts' evaluation, and for the second category the features that potentially can influence the artefacts' evaluation. Part (a) shows the percentage of simulations (over 10 runs) with at least one exaptation for different quantities of features transmitted to the producer. The time interval of reference (from 50 to 1000 steps) is also shown. Part (b) shows the average number of exaptations for each simulation over 10 runs.

Full figure and legend (77K)

These facts suggest that an unbiased communication modality is not able to favour a context change, whereas a qualitatively asymmetric communication modality could effectively support the success of categories that are not favoured initially. In this case, in order to favour exaptations phenomena, it is helpful to transmit a large amount of information, creating the potential for the discovery of new and previously disregarded solutions.

The exaptations occur mostly during the short period, whereas they are rarely observed during the long period. Actually, during the first interactions the producer can easily modify her/his artefacts and contemporarily increase the functionality values with respect to several different categories. However, when the artefact is highly specialised, the simultaneous satisfaction of several requirements is challenging. Conversely, symmetric information and large bandwidth values can support best performances of the model in terms of attainment of F_max, allowing producer to satisfy user's requests.

Noise

A second study concerns the analysis of two types of noise that can be possibly specified in the model:

• Communication noise. The value of the features communicated by the user agents is changed with probability (1 or -1 from a 0 tag, 0 or -1 from a 1 tag, and 1 or 0 from a -1 tag).
• Production noise. The value of the characteristics of the artefact built by the producer is changed with probability (0 from 1, and 1 from 0).

The communication noise does not affect the main behaviour of the model, although its presence makes it more difficult to reach larger functionality values. The production noise worsens such a tendency, but at the same time increases the frequency of exaptation occurrences, both in the long period and in presence of low bandwidth communications. Some innovations, obtained because of this type of error, are able to foster a change of context for the whole artefact.

Learning

In the study presented in this section, we allow the user to modify her/his own categories (so far considered as fixed), through two different modalities:

1. The user can randomly create a new category, and substitute one of the already existing ones (excluding the category, giving the highest functionality). This represents the knowledge the user can acquire by interacting in new environments not explicitly modelled,
2. The user can modify a randomly selected category (all five categories being involved) by introducing some information coming from the artefact. This modality allows the user to learn and to actively participate in defining its own satisfaction, measured by means of the already presented variable F_max.

Both modalities are characterised by the updating rate f, expressing the probability that at each time step the category of the user is selected for a substitution (updating). In addition, we remark that the second modality needs the change probability P_ch for each feature (in all our trials P_ch=0.02), once a feature is chosen for merging with the corresponding artefact characteristics. The merging algorithm is described in Table 4.

Table 4 - Learning from the environment.

Full table

The random modality shows a small increase in the number of exaptation events, for both symmetric and asymmetric communications. Such a phenomenon appears to be relevant and it is evident also during the longer simulation runs. An higher updating rate f does not enhance this phenomenon. The second modality shows more interesting features. We find a bigger exaptation frequency that increases almost linearly with the growth of the adjournment rate f (see also Figure 5a); also the F_max level of satisfaction increases with the adjournment rate (Figure 5b). A real example of 'learned' exaptation could be that of the SMSs (the Short Message Service), initially introduced to send brief official messages from the telephone company and subsequently became a new mean for the communication of mass. In this case, the users succeeded in understanding the communicative potentiality of this system overcoming limits of space by means of creation of a particular language, more 'assembled' and intuitive. As a result, the phone companies initiated a market strategy based upon this new functionality.

Figure 5.

Learning from the environment. Agents can modify their categories by learning from the environment: at each time step there is the probability f of selecting a category for modification; in this case, a fraction P_ch of the category's features change their value. The user can communicate to the producer the artefacts' features that mostly influenced the artefacts' evaluation, and/or the artefacts' features that potentially can heavily influence the artefacts' evaluation. By using symmetric communication, for the first two categories the user transmits both the features that influenced the artefacts' evaluation and the features that potentially can influence the artefacts' evaluation. By using asymmetric communication, the user transmits for the best category the features that influenced the artefacts' evaluation, and for the second category the features that potentially can influence the artefacts' evaluation. Part (a) shows learning modality: the percentage of simulations (over 10 runs) with atleast one exaptation, by varying the adjournment rate f. Part (b) shows the average for the same runs: the fraction of the satisfaction index F_max reached by the artefact functionality, by varying the adjournment rate f, for both random and learning modality. The learning increases the exaptation event probability.

Full figure and legend (79K)

Conclusion

Common claims in literature about innovation are that novelties are recombinations of current capabilities and that their search is local, or that creativity is constituted by sudden blind insight. Both views are not satisfactory, because the first hypothesis is not able to describe radical innovation, whereas the second one provides little conceptual gain.

In this paper, we propose that radical innovations are created by a process of 'exaptation'. We introduce an agent-based model designed to investigate the dynamics of some aspects of exaptation in a world populated by agents, whose activity is organised around production and utilisation of artefacts. The model, EMIS not only explicitly includes agents and artefacts, but also encompasses agents' subjective representation of the artefacts by means of cognitive categories. In our model, the agents build (as producers) and interpret (as users) the artefacts using cognitive categories.

One of the main features of EMIS is the description of the information exchange dynamics among agents. Two main processes characterise such a dynamics: (i) interpretation and storage of information by each agent and (ii) circulation of information through the exchange of artefacts. The first process takes place in the cognitive domain of each agent. In particular, at any given time, each agent owns a cognitive representation of a number of real objects (artefacts) in terms of a set of cognitive features (categories). The second process involves the communication among agents of a fraction of the information stored in categories. Eventually, the producers employ their sets of cognitive categories to make artefacts that are in turn submitted to the users. The users evaluate the functionality of such artefacts by means of their cognitive categories and next send signals to producers about their 'satisfaction' with such artefacts.

The agents in the model are able to attribute 'functionalities' to the artefacts in terms of categories; a given attribution can generate a certain reward associated with the artefact of reference. Thus, the type of representation proposed is suitable to take into account exaptation events, which are understood as shifts in terms of the 'leading attributions' (attributions corresponding to highest reward) that the agents assign to the artefacts.

The model has been implemented in a computer environment. The main goal of the computer simulations is to determine some of the factors playing a central role in the information-exchange processes, with particular attention to the study of exaptation. From our first simulations, we can conclude that some of the most important elements favouring the emergence of exaptation events are:

1. an asymmetrical communication, where evaluations and desires are differently expressed for different categories;
2. a high number of cognitive features (characteristics) communicated among the agents
3. a high level of production noise;
4. the plasticity of the users' categories.

In conclusion, we can assert that the explicit representation of artefacts and categories eases the understanding of the exaptation phenomenon, seen in this context as a shift in terms of 'leading attributions', and allows the identification of the elements favouring the emergence of exaptation.

Notes

¹ A more correct notation would be C_k, p and C_k, u, with k[1, ..., s], s being different for producers and users. Nevertheless, for reason of clarity, in the following we omit such an index: simply, the reader should remember that both users and producers possess more than one category (the producers owning one category for each artefact).

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