We wish to report on an attempt to create a visual and conceptual space that might be of some use for scholars in the STS community and for those of us engaged in teaching scientists and engineers. The aim of this note is to stimulate reflexion, to get criticisms and to exchange software and data in what can only be a collective project (see Jim Scott’s article in this issue).

In order to map the development of a scientific controversy or of a technical innovation the STS field has learned to doubt the dichotomy between nature on the one hand and society on the other. It is not clear however what other narrative resources could replace the convenient alternation of "not only... but also" ("not only social factors but also objective ones"; "not only technical constraints but also political factors.") Alternative narratives have been developed under the heading of actor-network theory that stress the heterogeneity and variability of associations of human and non-humans. Unfortunately, they are themselves made difficult to grasp because of the alternation between a social interpretation that seems to reduce the content of science to a purely strategic show of force where might makes right and a naturalistic interpretation that appears to grant back to non-humans the unproblematic presence of nature. It appeared to us that it would be of some advantage to replace the distinction between nature and society by another set of distinctions that would cut across the first and thus would render difficult or even impossible to fall back on the previous debates. Hence the idea of sociotechnical graphs (STG) that we are developing for pedagogical as well as for analytical purposes.

The principle of STG is a generalization and an operationalization of the study of scientific controversies.

The first task is to make more precise the definition of the two dimensions which will be used as the latitude and longitude for the mapping process. Linguistics offers two useful definitions. It is traditional in the exploration of a linguistic structure to distinguish the syntagmatic dimension from the paradigmatic one. A syntagm is a set of different units that may be added in a sentence while still being meaningful. A paradigm (no relation with Kuhn’s meaning) is the set of different units that may replace a unit in a syntagm without rendering the sentence meaningless. For instance the following set of sentences explores the syntagmatic dimension:

while this set explores the paradigmatic dimension:

The first (syntagmatic) dimension defines how many different elements may be held together in a meaningful assemblage while the second (paradigmatic) dimension defines the meaningful substitutions that may be done at each point along the syntagm. The first dimension defines association and the second substitution, or, still more synthetically, AND and OR.

An exploration of a locutor struggling for a sentence through the syntagmatic and the paradigmatic dimensions of language may be mapped onto a diagram that resembles that of figure 1:

Unfortunately the narrative of a scientific controversy or of a technical innovation is different from the exploration of a linguistic structure in one crucial aspect. For each language there exists a more or less fixed structure that endows each locutor with the basic competence to judge what is a meaningless association or substitution. The sentence :"the hotel manager beats his clients to bring their keys back" will be considered pragmatically meaningless while the sentence "the hotel manager eats its clients to bring us key back" will be deemed grammatically incorrect. No such grammar is available to decide whether a transformation of a scientific statement is possible or impossible since research and innovation aims at circumventing the preexisting limits of any given pragmatics.

Not only does there exist no deep stable a priori structure to evaluate the meaningfulness of a given association or substitution in the narratives of an innovation, but the very definition of units are in debate and so are the various points of view of the many locutors. This is the very reason why we all study controversies and innovation, that is, science in action. While we may retain the two dimensions AND and OR that extend earlier works on controversies, we have to devise an additional set of specific mapping principles in order to cope with the peculiar difficulties of our field.

Let us chose a very simple example of a narrative to show how it could work.

This narrative told from one point of view –Bernhard’s– outlines a (micro)controversy between two groups (the Berliner Homeowner Association and the Tenants) that goes through a series of successive transformations (verbal injunctions, printed signs, new mechanism) to a point where the Homeowners’ initial goal appears to be reached by enrolling the undisciplined tenants.

The question for STG is not to evaluate the credibility or realism of such a story, but only to see how it could be coded into a graph that would retain some of its relevant features for following an innovation.

The chosen point of view –not necessarily the same as that of the narrator– is denoted X1, X2 etc. (see Figure 3).

A first syntagm is defined by an association of units. Each of those units is considered as an actant and a specific file is opened for each of those actants when they enter a syntagm (see below).

A syntagm is defined only by associations of actants with no attempt at qualifying the relations between units. That they are associated together or not is the only piece of information retained.

Each syntagm is reconstructed into two branches: the program of actions that associate the allies; and the antiprograms that gather the opponents. The definition of what counts as an antiprogram depends on the choice of a point of view. If the story above is told from the tenants’ side, the program of action will be "to remain free to let friends go in and out at night without bothering to relock the front door". The boundary line between programs and antiprograms defines the front line the evolution of which we want to be able to trace.

The first syntagm is then modified in only two ways so as to obtain the next version –coded (2), (3) etc.: either a new element is added to the syntagm, or one of the old elements is replaced by another one. As long as there is no information to tell us that an actant has left a syntagm, it is repeated from one version to the next.

When a series of actants stay together through successive versions without defecting, they may be aggregated in a black-box and given either a new name or the name of one of the actants. It is important however to be able to reopen the black-box and to redistribute its components if necessary. At the beginning of a narrative each actant is a black-box that we will learn to reopen or not only later when comparing accounts.

Once this recoding is done, the story is limited to its bare outline and encapsulated in one diagram. The evolving drama of the story is retained however: every time the Homeowner Association adds a new element they extract more compliance from the tenants. With the invention of the new Berliner key they make the tenants shift from the antiprograms to their programs.

Simple tests may be done visually to see which actant is stable, which one is reliable, which one induces deep modifications when added, and which one is insignificant (see below). Although relations can no longer be qualified –since grammar is reduced to semantics– it is still possible to obtain very primitive association rules such as: for observer X1, at version (3), when the actant "New lock and key" is introduced then "Tenants" go from program to anti-program provided the other actants of version (2) remain present. This tells us something about the compatibility and incompatibility of tenants, keys, homeowners, janitors and printed warning. We lose most of the information given in the narrative, but we preserve the feature that interests us most: when an ally defects or is made reliable.

However since there exists no structure of science and technology that could tell us a priori which are the accounts that are meaningul and which ones meaningless, it is essential for us to be able to compare contradictory accounts. It is also the only way to repair the danger of giving a functionalist account of programs and anti-programs. What is dangerous in a functionalist argument is not the function per se, but the essentialism that goes with it and the avoidance of controversies about what counts as a function. In other words, relativism should redeem the sins of functionalism. This is why it is so essential to be able easily to shift points of view.

This is a rather different story. Only the Locksmith and the New key are the same as in the former one, but since they are not associated within the same syntagm by the two observers X1 and X2 they are not exactly the same. The Janitor appears in the two stories but is modified in the second since it now has the addtional property of being asleep! To the New key is added a crucial ingredient that reverses the previous state of associations: the file. As for the disciplined tenants of the first story, they have become one clever tenant, Manfred, who beats the System. The Home Owner Association is not mentioned in the second story but another actant appears that might be a synonym: the Fat Cats.

Tests may now be passed in order to decide the degree of dispersion of the two accounts. If we superimpose version (3) of account X1 and version (4) of version X2 (the sign // designating the front line between allies and opponents) we may obtain results such as this:

X1 (3) Homeowner’s Janitor Verbal notices Printed signs New lock & key All tenants comply//

X2 (4) Manfred Filed off key Friends in Fat Cats safe System beaten //Janitor New lock & key

If the two accounts were aligned it would mean that whenever an actant is cited in one narrative it is inserted in the same syntagm in the other. If two accounts were totally divergent it would mean that no two actants are the same or that they are engaged in completely different syntagms. Because of the principle of symmetry, it is crucial for our goal to have the same visualising devices for convergent and divergent accounts. The analyst should never have to decide a priori if there is a unity in the story he or she is telling (apart from being studied by the same analyst and to have the same code name, for instance here to be part of the "Berliner key" project) .

The same relativism should be maintained for the very definition of the actants. According to the specification above, we do not know what an actant is apart from the fact that it is mobilised in one version of one narrative viewed from the point of view of one observer. At the beginning an actant is nothing but a word in a text, a label. If for each actant named in a story we open a card, this card will then be incremented by the various entries alluding to this actant in all the various accounts. Who for instance is the "Janitor"? We know strictly nothing about this actant, except that the card that bears its name will read:

An actant is defined by all the syntagms in which it is successively engaged, exactly as a syntagm is defined by all the actants it associates. But in the same way that it is possible to compare the degree of convergence or dispersion of two accounts, it is possible to compare the relative coherence or incoherence of an actant. If, in all the successive versions, or in all the accounts, the same actant’s name is associated with the same syntagm, then we can consider it as a predictable entity or as a black-box. If on the contrary, no two accounts offer the same syntagm for the same name, then we will have to consider it as an unreliable actor. Between those two extremes, variations are more interesting. An actant may gain predictability from one version to the next, or from one account to the next, or it can lose predictability. It is essential to record this variable geometry of the actant since it is one of the main discoveries of science studies. The Tenants for instance vary from one version to the next in the first account, and vary again when we go from "All the tenants comply according to X1" to "Manfred defects and beats the System according to X2". If our visualisation does not allow us to follow the moving shape of actants, which are endowed with variable scale, motives, interests, definitions, and which can become stable or unstable, it will not be usable to trace the trajectories of innovations or of controversies.

One point deserves to be underlined again: it should be clear from the definition of an actant that exactly the same principles apply for the word "file" in the second story, although a file is considered a thing. We learn something on what is a file when we see that its association in version (4) completely modifies the situation –according to Manfred:

X2 (3) Manfred//Friends out screaming Locksmith New key

X2 (4) Manfred Filed off key Friends in Fat Cats safe System beaten //Janitor New lock & key

The essence of a file is modified by this narrative; that is, the card "File" is implemented with a new syntagm that make it able to modify the state of the relations between Fat Cats and tenants in Berlin. Since an actant is only what it does, there is no other way to modify the essence than modifying the action inside the card. This modification introduced by X2 may be small compared to all the other accounts in which "a file" is used unproblematically. But we know from our work in science studies that such is not always the case. The interpretative flexibility of a thing may be as great as that of an individual or of a social group like that of the Tenants above. It is essential to apply the same test of coherence or incoherence to the cards that designate non-humans, than to those who designate collective beings or indivual humans. The isotopy as semioticians say, –the stability in space and time of an actant in a narrative– should not be taken for granted but obtained by what the various stories make of it. In principle a non-human like a "file" is no more and no less flexible as a collective person like "Homeowner Association" or as an individual like "Manfred". More exactly, the many differences between them should not be defined a priori but should emerge from the chains of associations making up their definition.

Does this mean that might makes right? An anonymous referee made what appears to becogent criticism against the "simple minded counting of actants," by citing the following example:

It is precisely because we do not know the force of any given actor that we have to be completely agnostic in allocating their definition. In this story, a well defined patent is stronger than capital and techniques because it allows the weak Bell to tie himself to the whole legal system of the United States. As the words we have underlined indicate well enough, there is always a metrology at work in the accounts of those who critique the slogan "might makes right"; a metrology which is always, in the last instance, some sort of "simple minded counting of actants" (‘prevailed’, ‘forced’, ‘unassailable’, ‘key non humans’). The goal of STG is to push the analysts to be explicit about this metrology that allows them to say, as in the case of Bell’s patents, that right makes might, that right is thus stronger than might. It is this very variation of scale that we want to be able to document whereby a tiny actor becomes stronger than the strong but without believing in some a priori definition of who or what is strong and who or what is weak.

Such a diagram makes it possible to calculate a number of indicators, which should help in evaluating the unique signatures of a trajectory and in comparing projects and accounts.

Which are the most interesting Evolution Indicators for following one given innovation? The first one is obviously the indicator S for Size, which gives the number of associated elements in each successive version. The second indicator of interest to us is the one that compares the number of elements maintained from one version to the next: we will call it A for Allies. We shall call the new actors recruited in moving from one version to another N for New actors. For each version, identified by a subscript n, we thus obtain:

S(n) = A(n) + N(n)

(Note that, for the moment, the "seniority" of an actor is relative only to the transformations that occur from one version to the next. Thus a "lost" actor that gets recruited a second time counts as a new actor -see Appendix)

Thanks to these first few indicators we can define an Index of Negotiation IN:

The smaller the value of this index, the less the innovator has to negotiate to maintain his or her project in existence. Conversely, a high value of this index means that the project has to be highly renegotiated. For our imaginary example, we obtain the following numbers:

If we now draw the graph of our first three indicators, we obtain a series of curves which are specific for the innovation under examination and which should help in determining what part of the narrative one may wish to examine in more detail.

By using IN, the index of negotiation, and S, the index of size or of association, we can now recapitulate the path of an innovation and build with the same "buttons" as above the "Home card" of a project. We will call this map the Socio-Technical Graph of a project.

Similar indicators may be devised to evaluate the dispersion of accounts and the coherence of actants. If several accounts converge and if the actants they mobilise have a high degree of coherence, then the degree of predictability of the project increases. At the limit it might even be possible to predict the next move. If on the contrary there is a high degree of dispersion among accounts and if the actants they enroll have no stable definition, the interpetative flexibility will be so great that no prediction will be possible. In either cases the STG is built along the same principles and simply record the shifting shapes of the alliances. Indicators of Evolution, Observer and Isotopy, simply help in guiding the reader through the data-bank and in highlighting important phases.

More work is obviously needed to implement the specifications above, to be able to treat for analytical purposes large and complex case-studies. Still more work is needed to turn the shell of the STG into an interactive simulator adjusted to the teaching of science students. We welcome discussion of this note and collaboration on finding other ways to set up socio-technical graphs.

It is possible to produce a synthetic characterization of the paths of innovations by defining a few more Evolution Indicators (see also Jim Scott’s paper, this issue for other indicators). Until now, we have only compared different versions one by one. It is clear, however, that new actors can be re-mobilized by a version (n) which had been already mobilized by previous versions. Thus the cumulation of new actors form version to version over a given period can be different from the total number of actors associated with the project during this same period. We will therefore distinguish between Cumulated New Actors, CNA and the exploration E of the project. CNA indicates the variation of the degree of attachment of the actors, while E represents the size of the population of actors mobilized by the project. In the examples above, we obtain E by considering the rank of letters in alphabetical order. E is a synthetic indicator which allows us to distinguish innovations that explore a large number of new actors from those that recombine a small number of potential allies in different configurations. So for the example above:

Some projects are strongly attractive. This means that all the new actors which one day participated in the project in a version (n) find themselves associated again in the next version (n+1). These actors constitute the aggregate of new actors: they are those who move from the index N(n) to the index A(n+1). Conversely, some of these new actors have disappeared in the (n-1) version; these are the lost new actors. In order to measure our innovation, we calculate its Yield Index, Y. This index is calculated by dividing ((the cumulative number of the aggregate of new actors) - (the cumulated number of lost new actors)) by the exploration E. The indicator thus obtained measures either the capacity of a project to attach itself to the majority of the actors it mobilizes, or on the contrary its tendency to visit a large number of new actors without fixing itself anywhere.

This index takes values between "1" and "-1."

A final synthetic index can be obtained by dividing the number of associated elements A which remain stable in a version (n) by the size S of the previous version (n - 1). This index defines the "reality" R of the project - that is, the "resistance" it needs to be able to move from one version to the next without putting what it already acquired into question:

All these indicators allow us to compare trajectories whose size and content are completely dissimilar and who come from vastly distant empirical sources.

For the three indicators of negotiation (IN), reality (R), and yield (Y) we obtain the following profiles for the above example: