Armand Hatchuel

Benoit Pascal Le Masson

Benoit Weil

Weil Minesparistech

MODELLING CREATIVE THINKING AND ITS IMPACT ON RESEARCH

Keywords: Creativity, Design Theory, C-K theory, Design Science

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Introduction: creative thinking as both ideation and knowledge generation

In this paper, we present a new approach to creativity research coming from recent advances in Design science [Le Masson, Subrahmanian and Dorst 2010] namely from the development and advancement of C-K theory [Hatchuel andWeil 2003, 2009]. This theory offers a unified and formal model for creative thinking, be it creative ideation or creative design. It also opens new paths and methodologies for research.

Traditionally, creativity has been studied as a psychological phenomenon and without any connections to Design. The literature on creativity has mainly explored two different series of research issues : i) the identification of the psychological, cultural and educational processes that favor creativity as an individual or collective mindset; ii) the study of specific traits of "creative thinking" [START_REF] Boden | The creative mind George Weidenfeld and Nicolson Ltd, Great Britain Boden MA[END_REF]] : classically, creative thinking has been related to "divergent" and flexible forms of thinking; to the capacity to think "out of the box" and to welcome ideas which strongly differ from ordinary ones. But if one asks how creative thinking does work? What makes it possible? The literature only brings partial and fragmented answers. For sure, metaphors, analogies, surprising associations of ideas, illuminations, as well as serendipity have long been recognized as usual "traits" of creative thinking. Yet, if we compare the development of creativity research, to other psychological fields like decision making, behavior under risk or learning, the science of creative processes obviously lacked a sufficient level of formalization and axiomatization at least equivalent to decision theory and probability theory and this limits the analytical understanding and modelling of the creative process, or even the implementation of conclusive experiments.

Revisiting standard assumptions of creativity research

We argue that the elaboration of a formal theory of creative thinking has been hindered by two unquestioned assumptions that we have abandoned in our research programs.

a) The first assumption is the naturalistic perspective that dominates the psychology of creativity. The phenomenon under study is defined as the observed production of creative ideas or creative ideation, and research aims to capture its natural variability among individuals. It was not systematically intended to identify the type of reasoning or the models of thought through which one can generate creative ideas or explain the possibility and ontological structure of creative thought. Finally, creativity was described as a hidden psychological capacity that could only be recognized by its outputs and may be stimulated or inhibited. Contrasting with such academic trend, our research program was built on the hypothesis that creative thinking was a generic and specific reasoning process that could be made explicit and the subject of analytical study.

b) The second assumption is less visible and appears when creativity is compared to design. It is widely recognized that design can be a creative process. Yet, design is much more than pure ideation. Design is an active process that requires efforts, inquiries, tests, discussions. Thus a whole set of cognitive activities (learning, comparing, arguing …) contributes to creative design. Therefore, we should have learned from design activity that creative thinking encompasses two different processes: i) creative ideation; ii) a process of knowledge generation, in relation with some context and environment. In common words, creativity research has approached creative ideas as pure inventions of the mind, while Design research had to account both for such inventions and for cognitive discoveries that may be provoked or emerge during the design process. These preliminary remarks have major scientific implications: a) the ideation process should necessarily be associated to a knowledge process; b) yet, what are the interactions between ideation and knowledge generation? What is generated by such dual processes? These issues played a key role in the development of the research program that led to the elaboration of C-K theory (Hatchuel andWeil 2001, 2003) and this paper aims to be an introduction to this theory and to its main findings. Before, let us indicate some of the immediate consequences of the previous remarks.

The missing background: Revealing the role of knowledge in the creative process

If creative thinking is interpreted as the design of an idea, even if it is purely mental and partly unconscious, it becomes necessary to associate to creative ideation, a cognitive process where knowledge activation, organization, and evaluation also take place in the mind. Actually, it is easy to admit that the memory and past knowledge (of all types) of a subject acts as a complex and evolving cognitive resource that will impact ideation. It is however less intuitive to consider that ideation can also impact memory and knowledge. But a new and more rigorous perspective appears: where ideation is distinguished, yet not separated, from its cognitive resources, and both should be seen as potentials for mutual activation and development.

This new approach leads, at first, to critically revisit classic propositions from creativity research.

Revisiting convergent thinking and divergent thinking. The distinction between divergent thinking (DT) and convergent thinking (CT) is at the root of the psychological description of creative ideation [START_REF] Guilford | Traits of Creativity[END_REF][START_REF] Torrance | The Nature of Creativity as Manifest in its Testing[END_REF]. DT was traditionally seen as enabling novelty i.e. the definition of some new entity; whereas CT was needed for value achievement and control, i.e. giving reality and relevance to this new entity [START_REF] Cropley | In Praise of Convergent Thinking[END_REF][START_REF] Eris | Effective Inquiry for Innovative Engineering design[END_REF]]. Yet, if we do not take into account the knowledge process coupled to the ideation process, the impact of DT and CT becomes undetermined. DT followed by CT can lead to poor creativity if the most original ideas generated by DT are rejected because of a lack of knowledge to elaborate them. Conversely, CT can also contribute to novelty by warranting feasibility to the most creative ideas of the process. Therefore the divergence/convergence model is not sufficient to explain novelty and value. What is missing is the specific knowledge content which activates CT or DT and their combinations. Without a clarification of the interplay between knowledge processes and standard notions like CT and DT, it was also not surprising that the impact of "expertise" on the creative processes remained controversial.

The role of expertise: prison or escape tool? The potential tension between existing expertise (skilled knowledge) and creativity is well described. Weisberg [START_REF] Weisberg | creativity and Knowledge: A Challenge to Theories[END_REF]] suggested that existing competences limit novelty but are needed for value achievement. According to Boden, a creative idea cannot be produced by "the same set of generative rules as are other, familiar ideas" (p.40) [START_REF] Boden | The creative mind George Weidenfeld and Nicolson Ltd, Great Britain Boden MA[END_REF]]. It was also observed that value would require specific expertise whereas novelty comes mainly from general and abstract models [START_REF] Ward | Creative Cognition[END_REF]. It is also common place that expertise matters: ideas appearing as novel to some people may present no such novelty for an expert. Finally, if we take into account the interaction between ideation and knowledge processes, the impact of expertise on creative processes cannot be predicted in advance. It can be both a resource and an obstacle for the creative process.

The conditions of creative generation: unknown objects and the changing of object definitions. Any creative process aims to generate new artefacts and new ideas. This implies a necessary condition that is often overlooked, yet is key to the understanding of the underlying creative mechanisms. One have to assume the progressive description of objects that were necessarily partly unknown when the creative activity begins. Moreover, as already stated before, "unknown" is always relative to some state of knowledge associated to the creative process. Thus, a crucial and necessary operation of the creative process is the activation of old and new knowledge in order to temptatively define and make exist some unknown objects. The operation that transforms unknown objects into new known ones plays a major role in the formalization of the creative process. Boden underlined the notion of "transformational creativity" and stressed the need to change "the generative rules of familiar ideas". But this formulation may have been misleading for creativity research. Transforming ideas is not enough to obtain a creative process. What is necessary is to transform previous knowledge and previous definitions of objects. "Objects" or "things" are organizers of knowledge that have to be transformed by generative rules [START_REF] Abadi | A Theory of Objects Springer[END_REF]. Actually, the basic generative rules of any language or knowledge background are those that stabilize or change the definition, be it syntactic or semantic, of "objects" (i.e. "names", sorts, or relations between names). Thus, any creative process is the transformation of existing knowledge by introducing new objects and maintaining the definition of older ones.

Finally, it is more rigorous and general to define creative thinking as the temptative elaboration of new objects, rather than new ideas. Moreover, the interplay between the redefinition of objects and the generation of new knowledge, ignored by standard creativity research, appears as a central mechanism of creative thinking. So far, these first conclusions indicate that any rigorous and consistent formalization of creative thinking have to capture and integrate these interplaying elements within a same formalized model. These were the objectives of C-K theory that we introduce in the next section.

Elements of C-K theory: the dual expansion of concepts and knowledge

C-K theory (an acronym of Concept Knowledge theory) has been introduced by Hatchuel and Weil [Hatchuel and[START_REF] Hatchuel | A new approach of innovative design: an introduction to C-K theory[END_REF][START_REF] Hatchuel | C-K theory : an advanced formulation[END_REF] as a model of creative design. It has now important scholarly developments and a wide range of applications in research and practice [Agogué and Kazakci 2014]. The name "C-K theory" mirrors the assumption that creative Design can be modelled as the interplay between two interdependent spaces having different structures and logics: the space of concepts (C) and the space of knowledge (K). The structures and expansions of these two spaces determine the core propositions of C-K theory. In this paper, we only insist on the implications of C-K theory for our understanding and research about creative thinking,

The two spaces C and K: basic assumptions.

Space K is expandable and contains all established (true) propositions (the available knowledge). It makes explicit the missing background of any creative process that was already mentioned. It plays several roles: it is a reference space, a resource space and an output space that is transformed during the creative process. Knowledge is the collection of established true propositions 1 , from the point of view of a "creative" person or group of persons.

Space C is also expandable and is the space where "creative ideation" is explicitly organized. Yet, we have to give to this expression a more precise definition: we call "creative ideation", the temptative and progressive definition (or description) of a partially unknown, yet desirable, object. Such definition is always relative to a certain state of space K. Thus space C, is the space where new definitions of objects are progressively elaborated. Whereas, Space K is the space that contains all available knowledge that is used by the definitional process in space C. In standard approaches of creativity, only space C is observed and space K is ignored.

More technically, in C-K theory, the attempting definitions of new objects in space C are called concepts, and the formalism of C-K theory has allowed to establish that: Concepts are propositions about some partially unknown objects X and are all of the form: "There exists some object X, for which a group of properties P1, P2, Pk hold in K". Moreover, it can be proved that if concepts are about unknown objects then concepts are undecidable propositions in K (neither true nor false in K). Concepts define unusual sets of objects: they are sets of partly unknown objects, which implies that their elements have an existence that is not warranted in K. The sets of Space C are special sets which can be defined by classic axioms of Set theory (ZF), excepting those that assume the existence of elements (like the axiom of Choice which has to be rejected). Yet important results in Set theory have established that this rejection could be done without impact on the other axioms [START_REF] Cohen | The independence of the Continuum Hypothesis[END_REF] 2 . . Having defined Space C and Space K, the creative process can be formalized as the process by which undecidable concepts -that are usually called ideas or "briefs" in design activities are generated and transformed into one or several new objects, i.e. true propositions of K. New ideas or design solutions 1 Regardless of how "truth" is assessed. For instance emotions can be seen as "truths" that can impact the creative process as any other type of truths, for instance, "scientific"propositions. This flexibility in the construction of space K, gives to C-K theory a very high level of generality and allows to capture and understand creative processes and different types of human activity.

2 Moreover, it has been established that C-K theory was in deep correspondence with the Forcing method in Set theory [START_REF] Cohen | The independence of the Continuum Hypothesis[END_REF]] Forcing is a major result of Modern Set theory; it has been developed in 1963 by Paul Cohen for the design of new collections of sets (called extension models). Thus Forcing can be interpreted as a method for creative design in the pure world of sets. And to put it shortly, if space K is limited to Set theory and number theory, C-K theory becomes the Forcing method. Thus C-K theory can be seen as a generalization of forcing to knowledge spaces where objects are not only numbers or classic sets [Hatchuel and[START_REF] Masson | Creativity and Design Reasoning: How C-K Theory can enhance creative design[END_REF]Weil 2010]. are selected among these new propositions. During the design process C and K are jointly expanded through the action of four different C-K operators that reveal the hidden and ignored complexity of creative thinking.

The design process and the four C-K operators.

According to C-K theory, design proceeds in space C, by a step by step partitioning of C sets using propositions coming from K. Beginning with a first concept C0, the partitioning operation is repeated whenever there is a partitioning proposition in K and until some partitioned "Ci" becomes a new object "Ki" i.e. an object which existence is warranted by propositions in K. Under such construction, the following propositions hold [Hatchuel andWeil 2003, 2009]:

Space C takes necessarily a tree expanding structure which describes the expansion of C0 (see fig 1). Therefore this proves why the opposition between divergent and convergent thinking was misleading. Any attempt to define new objects (things, methods, solutions) gives birth to divergence and refinement. Creativity only appears if the interplay between such divergence and the knowledge generation gives birth to established new objects Space K is necessarily expanded by the operations of evaluation and activation that are triggered by C expansions. In classic terms, creative ideation not only transform ideas but also provokes the generation of new knowledge, which is the necessary conditions for transforming concepts into objects. Again, C-K theory reveals central mechanisms of creative thinking that were ignored by standard approaches that were guided by a biased notion of "ideation".

C-K theory predicts the necessity of four types of operators: CàC, CàK, KàK, and KàC. Implicitly, standard approaches of creativity were focused on KàC operations: generating novel ideas finding. This left in the dark, three other operators. I) CàC operators which organize the progressive refinement and structuring of ideation and is precisely where creative reflexivity, i.e. judgements on originality, novelty, value can be developed. II) CàK operators which transform ideation into new knowledge, and not only capture all validation practices (sketches, tests, prototypes, mock ups…), but also new independent sources of knowledge; and finally KàK operators which not only contain classic reasoning, but also re ordering operations that allow a new object to be integrated to other old objects without creating loss of meaning and nonsense.

The identification of these four operators reveals a completely new understanding of creative thinking. Not only they invite to a complete new phenomenology of creation, but they also provide a unique and rigorous formalism, i.e. a scientific model, that captures creative design and was lacking since the early days of the field

The generic mechanism of creative power: expanding partitions and knowledge expansions.

One key prediction of C-K theory deserves a more detailed description: the distinction between two types of C partitions, i.e. between two types of refinements in the C space.

-If the partition expands the definition of an object with a new property that is not known in K as a possible property of this object, it is called an expanding partition. -Conversely, if the partition relies on an existing definition or property of the object in K, it is called a restricting partition.

For instance, "a house with a red roof" is a restricting partition if "houses with red roofs" are already known in K; "A house without roof" is an expanding partition if there is no such types of houses in K. Moreover, C-K theory tells us that this notion cannot be defined per se, it is always relative to a certain space K that should be made explicit to recognize the expanding type of the partition.

It is easy to see that the notion of "expanding partition" rigorously describes a generic operation that unifies a large collection of operations that were usually seen as the "spark" of the creative process: metaphors, analogies, idea associations, illuminations and so on.... By generic we mean that the expanding partition opens the path to the generation of new objects, and it can occur on all types of description of an object (structural, physical, sensorial…) and at all levels of definition of this object. Now, a key finding of C-K theory is that expanding partitions are a necessary but not sufficient, instrument of creative thinking. New objects will appear, only and only if, K expansions (new K) allow to continue the refinement and definition of expanding partitions until a concept becomes "reality", i.e. a decidable (and decided) truth in K. Figure 1 synthesizes the four C-K operators and their interplay.

Figure 1. C-K design process and its operators.

A scientific model of creative thinking: a synthesis in five propositions.

C-K theory offers a model that rigorously capture and understands the creative process. This claim can be synthesized through five propositions that step by step reinterpret classical notions and offers an operational, predictive and consistent theory of creative design that can be easily tested by empirical observations or applications.

P1. Design and creativity are C-K processes.

Design needs usually some initial requirements while creativity may have no clear starting point. C-K theory can model both processes. In design some C0 may be stated at the beginning of the process by some external person that is not the designer. But C-K theory can be equally seen as a continuous and recursive process: propositions in C are generated continuously and expanded through a C-K process. This fits quite well with the description of creativity as a self-triggering mode of thinking.

P2. Novelty and value are K dependent and generated by joint C-K expansions.

Even if novelty is defined as some new object appearing for "the first time in history", this is still a K dependent definition. History is simply the name we give to our knowledge about the past. The same argument stands for value. Any value criteria is a piece of established knowledge in the social system where creativity and designed are situated (be it the opinion or emotion of a user or a client). Thus novelty and value are not external to the design process and are embedded in K. If a client rejects a design, this only means that sufficient knowledge about its needs was lacking or wrong in K.

Novelty is necessarily triggered by one or several expanding partitions. Yet, the knowledge used to form these partitions could have been present at the beginning of the process (existing one) or generated during the process (new one). Moreover, designed solutions will not use all the partitions developed in C, and will be composed by a list of attributes mixing restrictive and expansive partitions. A creative solution is a design that may combine knowledge generated by all different paths in C. Thus, the whole expansion in C and the whole expansion K could have contributed to form novelty. Similar arguments hold about value. A corollary proposition is that novelty and value are not contradictory. C-K theory shows no such thing. Space C and Space K are not in opposition they are co generated.

P3. Expanding partitions generate new propositions in C and in K. This is one of the deepest results provided by C-K theory. It can be imaged as such: the "crazy" ideas allowed in C have two modes of action: 1) they can open a new path in C ; 2) they can activate new knowledge in K that may, in return, form a new more valuable concept expansion elsewhere in C. These two different mechanisms explain the seemingly irrational process of creativity when rationality is only defined as the result of standard KàK operator's i.e. Classic logic. In Space C, thanks to the undecidability of concepts, any strange associations of concepts (ideas) can be formulated without provoking contradiction or nonsense in K. They would have no impact unless the generated Knowledge transforms these strange ideas into a creative and decidable design in K. Thus, C-K operators provide a rational process that transforms irrational propositions into new valid knowledge and creative designs! P4. C-K theory captures all forms of creativity. The interplay of C-K captures a wide range of possible expansions in C and K as well as well-known types of creativity like the following:

-Pseudo creativity is easily modelled by a wide expansion in C which never generates any expansion in K. A lot of surprising partitions are produced yet none of them can be transformed into decidable propositions. -Bounded creativity can be related to two different types of C-K expansions. I) a wide expansion in C is generated but a small subset of K blocks almost all alternatives. II) Few alternatives are generated through the activation of a small subset of K. in both cases we can find the existence of a dominant subset of K (fixated knowledge) which either kills any new concepts or even impedes their formation. In practice, these two types of creativity are quite different.

P5. Creative thinking and design conveys a redefinition of objects and a re-ordering in K.

The path from and undecidable concepts to decidable solutions is warranted by expansions in C and K spaces. These expansions can be of little impact on the general structure in K. Yet, in some other cases, it is the definition of a common class of objects (an ontology) that have to be changed or created. For instance, when electricity was used to transport sounds or voices, a new complete class of objects appeared (the telephones) and the definition of other ways to transmit sound had to be revised. Such necessary reorganization of K is necessary to preserve meaning and consistency, it is also a condition to regenerate independences that will allow for new C expansions: creative thinking nurtures the creative potential.

An intuitive interpretation of C-K theory: chimeras, discoveries, re ordering of objects and knowledge

C-K theory does not contradict standard knowledge about creativity but it reveals unique and hidden features of creativity thinking that were neglected or mistakenly treated. In addition, these features allows to perceive creative thinking as a rational, rigorous and consistent logic that was not yet described and explicitly unveiled.

Creative thinking needs "ideas" but not all ideas can trigger creativity. Likewise not all metaphors, analogies, unusual association can be at the root of a creative process. Something additional is required: that the new idea expresses a "chimera", a description of a new entity that is defines by attributes that are connecting "independent" pieces of existing knowledge; and this independence is not universal, it is relative and contextual to a specific structure of knowledge. Yet, this relativity was not analyzed and not seen as a resource for creativity. If we visualize a chimera as a "hole" in existing knowledge (Hatchuel et al…), we understand that creative thinking would disappear if there was no such holes in our knowledge.

Traditionally, chimeras are imaginary monsters, half man and half animal. They com bine properties that came from knowledge about humans and knowledge about animals, properties that are not connected in K. Yet, in modern science, a man can live with animal implants. These are no more chimeras. Chimerization is the intuitive image that fits well with the abstract notion of expanding partitions.

Yet, chimerization is only one operator of creative thinking. Discoveries are also needed, creative thinking needs the provocation of surprising learnings. Creative thinking has to be an active and inquiring process. But not all surprises will transform a chimera into a real thing! Creative thinking generates knowledge in excess, knowledge that finds itself useless.

Chimeras become reality thanks to cognitive conquests. But chimeras are also themselves good triggers for the activation and exploration of new independent sources of Knowledge! Monsters stimulate reflexivity and invite to search for new means (new K) to make them exist or to temper their strangeness.

Now when monsters come to existence, by design, they force to rethink old things and established relations. Creative thinking needs re organizing, re-structuring, re shaping of things. This is not a process that is outside creative ideation, it is an essential part of it. Creative thinking is not only about one new thing, it also addresses the re ordering of the available knowledge that is required to "host" the new thing in a consistent and meaningful way.

Finally, the intuitive perception was that creativity was irrational and irrationality was the condition of creativity. As it is often the case, this intuitive perception was not wrong but it was biased and incomplete due to unquestioned assumptions that distorted observations and research. C-K theory suggests that creative thinking is completely rational when its dual logic and context is clarified. It is a general form of design that is independent of what is designed. It can be also interpreted as the rationality of any generation process.

Conclusion: implications and applications of C-K theory for research

The elaboration of a formalized model of creative thinking has important impact on research issues and methods. A wide range of new programs become possible thanks to the variety of analytical properties and predictions that may be derived from the model. In the following section, we will mention some programs and their published findings that have been allowed using C-K theory.

1. Capturing forms of creative thinking in different fields (art, science, and engineering).

C-K theory generates many testable predictions. One of them, mentioned previously, is that to allow for the generation of a new object in C, the structure of the K space has to present "independences" that will be transformed. More operationally, this means that the K space has neither a deterministic structure (all thinking is reduced to deductions, no independence), nor a modular one (all thinking is reduced to free combination of existing and compatible bricks: no independence) ((Le Masson P., [START_REF] Masson | Design theory at Bauhaus: teaching "splitting" knowledge[END_REF]. Thus one could predict that the task of Art based schools would be to restructure student's knowledge in order to ban determinism and modularity. The validity of this prediction was confirmed (Le Masson P., [START_REF] Masson | Design theory at Bauhaus: teaching "splitting" knowledge[END_REF]) by recent research that studied the teachings of famous Bauhaus professors such as Paul Klee and Johannes Itten. This finding also contributed to explain the prominent role of Bauhaus in the creation of new styles in a wide range of industrial designs. It has also contributed to a new understanding of sketching, not as a process of idea expression as usually seen, but also as media for the re ordering of knowledge [START_REF] Brun | Analyzing the generative effects of sketches with design theory: sketching to foster knowledge reordering[END_REF].

Relying on contemporary C-K theory it was also possible to identify a different creative logic in engineering design and science (Le Masson P., [START_REF] Masson | The Interplay between Creativity issues and Design Theories: a new perspective for Design Management Studies?[END_REF][START_REF] Kazakçi | On the imaginative constructivist nature of design: a theoretical ap proach[END_REF]. To preserve robustness and easy design, engineers tend to favor determinism and modularity in the structuring of their actionable knowledge. However, engineering science frees the engineer from fixated relationships between functions and organs. Performance, functions, use cases and, specifications trigger new concepts as unknown combinations and hence promote creativity. Moreover, Science is regularly re ordered to integrate discoveries and new objects or to allow constant regeneration with limited re ordering. Thus C-K theory invites to avoid any dogmatic views about how to teach creative thinking. The same theoretical model can guide towards different forms of teaching that are adapted to the special expansions of C and K that fit with one specific domain, depending on its ontology (objects and knowledge) and epistemology (theory of truth).

Building new theory driven experimental protocols

Thanks to its rigor and predictions, C-K theory enables the design of theory driven experimental protocols in design and creativity research. Without clear theoretical frameworks, experimental research may lead to weak findings and even to general inconclusiveness. This was the case in the various experiments that have been conducted in order to know whether examples tend to fix or de fix ideation processes [START_REF] Agogué | Theory driven experiments : modeling and testing fixation and stimulation effects on creativity[END_REF]). C-K theory predicts that examples will play a different role if they belong to the fixation zone in Space and K, or if they do not belong to this zone (ie. Belong to the "expanding" zone). The problem is that the fixation zone is K dependent and have to be identified before the experimentation. This prediction allowed to design a new set of experiments where the impact of the examples became highly predictable, proving that without the control offered by C-K theory, hidden variables existed in previous experiments (Agogué M. et al. 2014).

More generally, C-K theory could have predicted and explained a large variety of observations that appeared in design experiments: namely "generative design questions" [START_REF] Eris | Asking generative questions: a fundamental cognitive mechanism in design thinking[END_REF][START_REF] Eris | Effective Inquiry for Innovative Engineering design[END_REF]; the emergence of new nouns by recording noun phrase in design exercises (Mabogunje and Leifer 1997). C-K theory also helps to formulate hypotheses and follow experiments based on specific types of design media like sketching [START_REF] Brun | Analyzing the generative effects of sketches with design theory: sketching to foster knowledge reordering[END_REF]. It contributed to confirm the differences resulting from specific forms of design reasoning between design professions (Savanovic P. and Zeiler W. 2007;[START_REF] Agogué | Resisting classical so lutions: The creative mind of industrial designers and engineers[END_REF]. In brainstorming experiments, design theory predicts the low generative power of brainstorming: theory predicts that the quantity of ideas is not related to originality and quality as originality is also K dependent; it also predicts that focusing on de fixing concepts generates more new knowledge and hence more original ideas and design value comes from the consistent use of this new knowledge [START_REF] Kazakçi | Brainstorming vs. Creative Design Rea soning: A Theory Driven Experimental Investigation of Novelty, Feasibility and Value of Ideas[END_REF].

3 Supporting a transdisciplinary paradigmatic shift: design science as a science of creative thinking and processes C-K theory leads to new connections with contemporary mathematics and logic. It has stimulated the new notion of imaginative constructivism (Kazakçi A.O;[START_REF] Kazakçi | On the imaginative constructivist nature of design: a theoretical ap proach[END_REF] that generates new bridges between creation and brouwerian constructivism. C-K theory also helps modelling new approaches of system engineering and technology management [START_REF] Kokshagina | Risk Management in Double Unknown: Theory, Model and Organ ization for the Design of Generic Technologies[END_REF]. C-K theory provides a solid ground for the merging of design theory and creative thinking theory. This helps to clarify the ontology of design and can nurture a wide range of human and social studies of design (sociological, anthropological, organizational, epistemological and linguistic studies). An example of such impact is the notion of "common unknown" that allows to understand the governance of collective design situations (in firms or in non profit-organisations) where creative thinking is needed not only about means of action but also about the ends to be generated and reached (Le [START_REF] Masson | Design theories as languages for the unknown: insights from the German roots of systematic design (1840 1960)[END_REF] .

Hence, C-K theory appears today as a solid scientific ground for a transdisciplinary shift. Creative processes are better understood and modelled within Design theory and science. Then, such new science can contribute to research on human activities that were already seen as creative; it can also help studying creative forms in domains where they are less visible or hidden. Finally, creative thinking is no more reduced to a psychological and natural phenomena, it reveals a forgotten class of scientific thinking, the generic design of unknown objects and its co expansion with the transformation of knowledge. Through the formalization of C-K theory such paradigmatic shift has already opened new ways of research and provided unexpected findings. Yet, all this could be only the early steps of a much wider scientific impact.


Joel Kalvesmaki
email: joelkalvesmakikalvesmaki@gmail.com

Dumbarton Oaks

Intertextual Pointers in the Text Alignment Network

Keywords: XML, TAN, TEI, pointers, alignment, intertextuality, canonical references

The Text Alignment Network (TAN) is a suite of XML encoding formats intended to serve anyone who wishes to encode, exchange, and study multiple versions of texts (e.g., translations, paraphrases), and annotations on those texts (e.g., quotations, word-for-word correspondences). This article focuses on TAN's innovative intertextual pointers, which, I argue, provide an unprecedented level of readability, interoperability, and semantic context. Because TAN is a new, experimental format, this article provides a brief introduction to the format and concludes with comments on progress and future prospects.

Interoperability of multiple versions within a single project is relatively easy. Many TEI projects have done just that. But TEI offers no mechanism to try to check or enforce cross-project alignment. Four different projects that each encode a version of Aristotle's Categories are likely to come up with as many ways of structuring the transcriptions in TEI. Anyone who wishes to synthesize those four versions, say into an HTML page that aligns the versions in parallel, must spend considerable effort reconciling differences. And every time a new TEI version of the Categories is found, the exercise must be repeated.

Or consider the humble cross-reference. TEI allows many ways to represent a claim that work A passage x is a quotation of work B passage y. But any representation in TEI is almost guaranteed to be meaningless outside a given TEI file or project (Kalvesmaki 2015). TEI code requires both syntactic and semantic interpretation, and is not predictably applicable to other versions of the same work.

I've singled out TEI, but the problem is true for other markup schemes. HTML, TMX, and XLIFF allow users to align multiple versions of the same work, but no effort has been made to try to make data interoperable across projects using the same markup method.1 II A New Approach to Intertexts: The Text Alignment Network I have often wondered what would have happened if the designers of TEI had taken a different approach. Could TEI be constrained to maximize the likelihood that the texts I produce, and the things I want to say about them, will be interoperable with other versions and annotations you produce? Can I write intertextual pointers that have value not just for my TEI transcription, but to the ones other people have made for the same work?

Over the last several years I have worked to answer "yes" to both questions by means of the Text Alignment Network (TAN), a suite of XML encoding formats intended to serve anyone who wishes to encode, exchange, and study translations, paraphrases, adaptations, quotations, and other varieties of text reuse. The TAN syntax is meant to be maximally readable and editable by both humans and machines. The RELAX-NG and Schematron schemas that drive the validation routines not only check the syntactic and semantic interoperability of a text, but provide feedback and help (via Schematron Quick Fixes) in the context of an XML editor such as oXygen. 2 TAN is a format, not a tool. It does not make intertextual pointers for you. It does not try to identify quotations or to reconcile differences in alignment. But it lays a foundation for such efforts. The extensive library of XSLT functions upon which TAN validation is built definitively interpret the format and provide a starting point for further use (some examples are discussed at the end of this article).

TAN is not intended to replace other formats such as TEI. In fact, TAN is built partly on a customization of TEI All. Rather, TAN is meant to complement other formats, because it has been designed around a set of distinctive principles:

 Annotations should always be separated from what is annotated (stand-off markup):

Anything that is not a transcription but comments on one-e.g., remarks on quotations, the analysis of the morphological parts of a given word-should stand apart from the transcription itself. Such stand-off annotation brings many benefits not available with inline annotation. Multiple scholars can edit and remark on the same transcription independently and collaboratively. Any two annotations may point to overlapping ranges-one of the Great Impermissibles in a single XML file-without compromising XML rules. 3 Further, stand-off files can be combined and transformed into any number of derivative inline files. The reverse is not always true. A heavily marked up TEI file is like a baked cake. Each type of tag set is like a set of ingredients or form of preparation. You might get a TEI file shaped baked into the shape of a star, sprinkled with walnuts (I'm allergic to them). But to make it the cake you want, you have to unbake it, remove the ingredients you don't like, add the ones you do, then bake it again. In adopting stand-off annotation I argue that we should not be baking cakes. Rather we should be providing simple ingredients, so others can bake cakes without having to first unbake them.

 One file per task : As a corollary to the previous principle, a given file should be focused upon a single task, and kept simple. Each version of a work should be in its own transcription file, and restricted more or less to the plain text. An index of quotations should be in a separate file, and simply point to the transcription files rather than trying to mark them up. Most important is the requirement that every TAN/TEI transcription file must be restricted to a single version of a single conceptual work found on a single text-bearing object, segmented and labeled according to a single reference system (canonical or not  Content and assertions should be deeply validated : It is fine, of course, that our files' structure is checked for validity, but the content should be checked as well, when possible. If a word is marked as having particular grammatical features, the code we use should comport with the rules we have adopted for the language (e.g., that there should be no such thing as a first-person nominative conjunction). Text should be checked to make sure it is normalized (according to Unicode NFC). In a given element with both @from and @to, the date in the latter should not precede the one in the former.

In TAN, more than one hundred such rules are checked, at different depths. Users are permitted to specify how deeply these checks should be made, to save time during editing. The underlying XSLT functions have been designed to provide contextual help to editors through Schematron Quick Fixes (SQFs). If an SQF-aware XML application (e.g., oXygen) flags text as not normalized, the software will give the user the option to automatically replace the text with a normalized version, saving perhaps hours of hunting and retyping.  We should be able not just to collaborate but to communicate across projects : As textual scholars, we should be able to work not just independently but collaboratively. Good collaboration should include some form of communication. Suppose you have published on your website a TAN transcription that I find important and I want to refer to it in my own TAN file. To do so, I must specify when I last consulted your file (via @accessed-when). Now, suppose you find errors in your file. You make the correction, and explain and date this change in your file. The next time I validate my dependent TAN file, I will be informed or warned that your source file has since changed. Suppose your alteration is serious. You can specify how serious it is, and describe the correction. My validation process will not only mark my file at the level of error you've specified but convey your message. I can ignore that message if I want, or I can take into account the changes you have made. If I update @accessed-when, I can squelch those older messages.

Much more could be said about the design principles, but such an effort would wind up repeating the comprehensive documentation already available at the project's website, http://textalign.net. All material is released under a Creative Commons Attribution 4.0 license, in the hopes that the project will outlive and outgrow me.

III Pointers 1 Current Pointing Systems

I wish here to focus on TAN pointers, since they are at the heart of intertextuality, the theme of this issue of the journal. TAN pointers are most similar to those defined by Canonical Text Services. But, or so I argue, they provide a new level of readability and refinement. TAN pointers are provide an unprecedented level of integration with the semantics of the source and the target. And they show that the syntax we already use in the notes of our articles and books to quote primary sources is adequate for digital texts. We don't need long, cumbersome URNs ; we can use shorthand forms that are already familiar.

For comparison it is worthwhile mentioning some other pointing mechanisms that are well known and have been around for a long time:

 HTML : click here  XPointer : <xi:include href="http://example.com/index.htm " xpointer="chapter1"/>  XSLT: <xsl:copy-of select="//tei:div[@type = 'chapter' and @n='1']/tei:p" />  TEI (one method): <link target="#chapter1 #chapter2"/>  TEI (another method) : <app corresp="http://example.com/example.xml##range(left(//lb[@n='3']),left(//lb[@n='4']) )"/> (Cayless 2013, ¶18) A few observations are in order, treating readability, interoperability, and semantics.

First, each of these pointers have limited readability to any human who needs either to write or to read them. Different people respond differently to these kinds of pointers, based on familiarity. The URLs (HTML and XPointer) and IDRefs (HTML, XPointer, TEI) might be recognizable, even if long. The pointers dependent upon XPath (TEI) will probably not be clear to those who do not work in XSLT or XQuery. All of them, though, are pretty long and cumbersome. Few of us type them out ; we normally rely upon cutting and pasting.

Second, each pointer has coinage in only one file. The HTML, XPointer, and TEI examples point to a single node within a single document. Even if they could be tried on other files (like the XSLT example, which is meant to be applied to an unspecified number of files), the intention built into the pointer will be respected only if those other files have been encoded using the same syntactical markup. But the syntax is necessarily arbitrary, and people working independently will come up with their own naming systems. So any success will be a happy but rare coincidence.

Third, the underlying semantics are ignored. Even if we humans intuit their meaning, the terms « chapter1 » and « chapter » are not computationally defined. The syntax may be computable, but the computer has no means to fetch the meaning (semantics) behind that syntax. That is, a computer does not « understand » (we seem forced to anthropomorphize the algorithms we write) that « chapter » refers to a such-and-such a type of textual division.

The examples above illustrate simple, one way pointers. Now, consider the humble cross-reference, which requires at minimum a double pointer, set in the context of a sentence. Suppose we want to encode the idea « Matthew 4:15-16 is a quotation of Isaiah 8:23-9:1. » (Example A.) And suppose we want to use one of the traditional pointers above. The first issue, readability, still holds, although its greatest sin is its nuisance. The second issue, interoperability, presents more serious obstacles, since the sentence we want to requires us to use a syntax that transcends any individual version of the work. But all the pointing techniques above are restricted to individual files. And the third issue still holds : none of the pointing mechanisms are able to preserve the semantics behind the references, e.g., that the grammatical subject refers to a book of the New Testament.

Suppose we wanted to be more specific in our assertion. After all, there are parts of Isaiah 8 :23 that are not part of the quotation, which doesn't begin until around the 15th word, according to the Rahlfs edition of the Septuagint. Furthermore, a number of words or phrases differ between the quoting and quoted source. Revising Example A to be more specific could get pretty complicated. For the sake of illustration, we'll stay simple : « All of Matthew 4 :15-16 is a quotation of Isaiah 8 :23 word 15 through the end of Isaiah 9 :1. » (Example B.)

Strangely, the traditional pointing methods above are better suited to Example B than they are to Example A. That is because the latter was meant to be true independent of any version of the texts. We were flying about in a sort of zero gravity. But now that we are seeking to point to individual words, we must enter the gravitational field of a specific version, at least for the second text (and perhaps the first). We cannot expect a statement true of the Rahlfs edition of the Septuagint to be true for the Brenton one (where the quotation doesn't begin until the sixth word of Isaiah 9 :1 !). Which means that our second concern above, about interoperability, is not as relevant, since we must restrict our assertion to specific versions, which is what the pointing languages above were designed for. (But all the other concerns still hold, and even the issue of interoperability of multiple files handling the same version.)

I have framed the problem in this way because it seems to me that all textual pointers fall into one of two categories. A pointer either transcends any particular version or it does not.

Pointers from the first category rely upon a reference system that must necessarily be version-agnostic, even if that reference system originates from features endemic to a specific version. For example, the page numbers, column letters, and line numbers of Bekker's edition have been used as a standard reference scheme for Aristotle's works, applied to later print editions. But the typesetting in those later editions results in lineation that differs considerably from Bekker's. Typesetters have not tried to match exactly Bekker's line beginnings and ends, so a Bekker number is oftentimes only a good approximation. The Bekker reference system has transcended Bekker's edition.

In the second category are pointers that delve into a particlar version. The pointer may begin with a version-agnostic component (e.g., Isaiah 8 :23…) but they must terminate in something that does not (…word fifteen). Or it the pointer may dispense with the versionagnostic reference altogether, and rely completely upon a reference system that is native to only a single version (e.g., quire 43, fol. 4r, col. 4, line 43, character 11, which is where Isaiah 8 :23 begins in Codex Sinaiticus).

Version-agnostic pointers

Let us start with version-agnostic pointers such as those in Example A. Elsewhere in this special issue we have read about Canonical Text Services URNs, 5 which has been to my knowledge the first attempt to provide a digital language for pointers that transcend any specific version, and so strive to admit syntactic interoperability. So for Example A, we would begin with CTS URNs such as this (adopting the somewhat problematic catalog numbering of the Thesaurus Linguae Graecae [TLG]): 6  urn:cts:greekLit:tlg0031.tlg001:4.15-4.16  urn:cts:greekLit:tlg0527.tlg048:8.23-9.1 These URNs reliably point to Matthew 4:15-16 and Isaiah 8:23-9:1 independent of any mechanism, tool, or server. 7 They point to whatever version you can find of the cited works. But they are still just as cumbersome, opaque, and unreadable as the traditional pointers discussed above. And although they are syntactically interoperable, they are not semantically so (Kalvesmaki 2015). Nevertheless, it is admirable that we can pack so much into a single URN. A CTS URN is a good start to expressing Example A. To finish the job, we might adopt the data model of the Resource Description Framework (RDF), which defines three-part statements, made of subject, predicate, and object. Here is one way of using CTS URNs to create an RDF statement for Example A (using the Turtle syntax, and adopting a URL that has been minted to define the concept « quotation ») : urn:cts:greekLit:tlg0031.tlg001:4.15-4.16 http://purl.org/spar/fabio/Quotation urn:cts:greekLit:tlg0527.tlg048:8.23-9.1 .

The TAN approach also uses URNs (IRIs), but in the interest of readability, those IRIs have been moved into the background. They are retrieved either by looking up the value of an id value, or by calculating the value of a node from its context. Splitting the work this way allows editors to spend most of their time working with a syntax that close to ordinary conventions. Here is how Example A could be rendered in a TAN annotation file: <claim verb="quotes"> <subject work="nt-grc" ref="Mt 4:15-16"/> <object work="lxx" ref="Isa 8:23-9:1"/> </claim> <claim> indicates that a claim or assertion is being made. 8 <subject>, @verb, and <object> correspond to RDF's subject, predicate, and object. The arbitrary value of @verb is defined in the  by one or more IRIs. Each @work's value is defined by the corresponding source file, and can also be converted to IRI values. The value of @ref points to a specific part of one 5 [Link to other article.] 6 The TLG is problematic for identifying works, because some TLG numbers legitimately identify multiple works (e.g., any TLG number assigned to fragments), and some works are split across TLG numbers. For more concerns see Kalvesmaki 2014. 7 Because this example uses the TLG's numbering system, the version of Isaiah being pointed to is the Greek Septuagint, and it may not lead to other versions of the Old Testament without explicit instructions to equate this with other versions of Isaiah. 8 All claims must be attributed to a claimant, specified elsewhere in the TAN file. This departs from the RDF model, out of a concern that statements, assertions, and claims be attached to the person or entity making the claim.

or more source files that are part of the same work (as defined by the work IRI). The meaning and implications of @ref are calculated via the context of the relevant portions of the source TAN files.

Any TAN/TEI file or fragment may be algorithmically converted to a CTS URN. Unfortunately, the converse is not true. 9 Because the underlying TAN/TEI transcriptions are devoted to a single version of a single work in a single, standard reference scheme, the values in @ref are unique and are therefore just as reliable as any other method of pointing. Further, because every division in a TAN/TEI transcription must be defined as a particular kind of division, a computer can draw semantic inferences, e.g., that Mt and Isa both identify books, and that the numbers correspond to chapters and verses.

To refer to spans of text, the TAN syntax is more than are CTS URNs. For example, @ref may point to a discontinuous ranges of text, and it may also adopt numeration systems other than Arabic numerals : 10 <claim verb="quotes"> <subject work="src1" ref="4 b 5, 5c"/> <object work="src2" ref="12 b-d, f, 15 c"/> </claim> Ranges may be abbreviated economically, which results in a clean syntax that avoids repetition. That is, Mt 4:15-16 is sufficient. You don't need to write Mt 4:15-Mt 4:16. It is assumed that the first part of a range bestows upon any abbreviated second part the contextual hierarchy by which it can be resolved. 11 There are many other features that could be added to this example (e.g., certainty, or adverbial modifiers), but explaining them would transfer us from the topic of pointers to that of RDF. We save that much-needed discussion for another day.

Version-specific Pointers

In dealing with Example B, pointers in the CTS syntax must be supplied with subreferences, and would be marked like this, with additions emphasized:12  urn:cts:greekLit:tlg0031.tlg001:4.15-4.16  urn:cts:greekLit:tlg0527.tlg048-rahlfs:8.23@χώρα-9.1@ὑμᾶς The first insertion specifies through an arbitrary value some specific version. Nothing prevents one project from using -rahlfs, another, -lxx, and another, -1935, raising questions about the interoperability of a subreferenced URN. The last two insertions specify beginning 9 Any CTS URN is a compound of items, each of which in the TAN format requires its own IRI, or resolution into one. For example, "4.15" point to two different types of divisions, but the CTS URN gives no indication of what kind of thing "4" and "15" are. TAN requires that all reference numbers be tethered to textual divisions that are defined with an IRI. For other comments on CTS URNs, see Kalvesmaki 2014. 10 TAN permits the use of Arabic numerals, Roman numerals, alphabetic numerals, and combinations of Arabic and alphabetic numerals (e.g., 4a, D1). During validation all numerals are converted to an Arabic equivalent, and are evaluated on that basis (a combinatory numeral is converted to two Arabic numerals; the two preceding examples would become 4 and 1). Because of problems of ambiguity, Roman numerals may not be mixed with alphabetic numerals within the same file. 11 One may legitimately object that in the phrase "1.3-4" it is unclear whether one means 1.3 and 1.4 or 1.3 through the entirety of 4. The TAN validation rules mimic how I believe we already read such references. We assume 1.4, unless that reference cannot be located in at least one version of the work. In that case we treat it as 4. If that also cannot be found then the references is treated as invalid.

and ending points for the range of text. CTS allows character-specific references, so the second URN could be rendered:

 urn:cts:greekLit:tlg0527.tlg048-rahlfs:8.23@[85]-9.1@ [110] This character-based reference assumes space normalization, and precomposed Unicode characters. A CTS-based RDF rendering of Example B would look something like this: urn:cts:greekLit:tlg0031.tlg001:4. 15-4.16 http://purl.org/spar/fabio/Quotation urn:cts:greekLit:tlg0527.tlg048-rahlfs:8.23@χώρα-9.1@ὑμᾶς .

The TAN approach to Example B builds upon that of Example A. We assume that we want to point to a portion of a text node that is within a leaf element (any element that contains text and no other elements). I have adopted the principle that TAN syntax should whenever possible mimic real-life practice. I have observed that in ordinary conversation when we want to point to a specific part of text, we prefer to talk about the nth (e.g., first, seventh, last) paragraph, sentence, line, word, or character. When we get down to the word level, we might identify the word by position (e.g., "the fifth to last word") or by name (e.g., "the last 'from'").

TAN adopts space normalization as a default, which means that text can be indented as freely as one wishes. So a text node's new lines are no guide to identifying what we normally mean by "line" or "paragraph." Therefore, those terms cannot be reliably used to identify a portion of a TAN text node. The meaning of "sentence" is contested, and difficult to define computationally: the most common sentence separator (at least in modern Western languages), the period, is used for too many other purposes.

So we are left with words and characters. TAN integrates both into its pointer syntax. But each of those concepts are ambiguous, and need some discussion before we look at real examples.

The term "word" is notoriously difficult to define. In different contexts, "New York" and "didn't," for example, can each be justifiably defined as one or two words. Furthermore, some scholars consider punctuation to be words in their own right (e.g., linguists' study of modern English), whereas others ignore them as being anachronistic or arbitrary (e.g., classicists' study of ancient Greek and Latin). TAN adopts the adjunct term "token": a string of characters that are defined by a regular expression meant to approximate what we usually mean by "word." And when I ask you to look at the fifth word, you normally ignore any intervening punctuation. Therefore, TAN's default definition of a token is [\w]+one or more consecutive word characters, the soft hyphen, the zero-width space, or the zero-width joiner. Although that is the default, it is not The Law. In any TAN file, an editor is welcome to write their own regular expression that defines what a token is.

"Character" also has some issues, even if we agree, as I think we should, that it should refer to a notional Unicode codepoint, whether expressed in UTF-8, UTF-16, UTF-32, or an HTML or XML entity (e.g.,
). The main problem is that Unicode is complicated, and has had to differentiate three levels of support for regular expressions. 13 Only level-one conformance is guaranteed in any XML system. And combining characters fall in level two. Suppose we have a string of three characters: b (i.e., a, a combining underdot, and a b). If I ask you via a regular expression to fetch me the second character, will you return the dot or the b? That decision, at present, depends upon the implementation you are using, and the results are not predictable. Therefore, TAN defines a character as any non-modifying character along with any ensuing modifying characters (regular expression: \P{M}\p{M}*).

With that background, we can now look at how Example B could be rendered in TAN:

<claim verb="quotes"> <subject work="nt-grc" ref="Mt 4:15-16"/> <object src="lxx"> <tok ref="Isa 8:23" pos="15-last"/>
 </object> </claim>

The principal change is that we are pointing to a range in Isaiah 8:23 that extends from the fifteenth word to the last. (During validation TAN functions silently convert the term "last" to a digit.) Note that @work has become @src, since we are now making a version-specific reference.

Suppose we have another situation where we wish to refer to a specific word or specific set of characters. Some arbitrary examples: <tok ref="Isa 8:23" val="χώρα"/> (the first instance of the word) <tok ref="Isa 8:23" val="καὶ" pos="2"/> (the second instance of the word) <tok ref="Isa 8:23" pos="last" chars="1-2, last-2"/> (returns three characters from the last word, i.e., Ιοί from Ιουδαίας) Note that "last-2" means the second-to-last character-it is oftentimes so much easier to count from the end than from the beginning.

Because the values are resolved by means of regular expressions, @val may take a regular expression: <tok ref="Gen 4:15" val="θε[όὸ]ς" pos="2"/> This example points to the second instance of θεός regardless of whether the accent is grave or acute. 14 Of course, if the value of the attributes point to something that does not exist, the TAN validation routines will mark the element as invalid, and via Schematron Quick Fixes offer contextual suggestions on how to fix the error. In fact, it is possible to ask for help by placing three question marks in an attribute then running a validation check. Either the error report itself or an SQF will provide editing help. So a version-specific pointer in TAN is not only readable, it is a kind of heuristic, at least when used during validation.

Pointing Problems

Such ambitious pointing has problems. But the problems I have found most difficult pertain to the concept of textual pointing in general. We might fuss about them in our digital projects, but they were there ever before there was a computer.

One of the the general problems is that a reference system might not match across different versions of the same work. The Psalms, for example, have a significantly different numeration system in the Greek and Hebrew versions (Kalvesmaki 2014), which means that any reference you find to a Psalm, whether you read that reference on the screen or in print, could confuse you. A computer fares no better. What this means is that even within the same notional, version-agnostic reference system you not guaranteed the interoperability we strove for when we invented those systems. In practice many of them fall short, to one degree or another. That is why I have used terms above like « try », « maximize », and « maximally likely », because I recognize that nothing can guarantee that texts produced by different people (or even the same person) will be in sync. TAN, however, creates a framework that makes such interoperability more likely, and provides diagnostics to help make our texts more interoperable.

TAN validation can be set to any of three phases-terse, normal, and verbose-to allow for variations in speed and depth. 15 In the verbose phase of a TAN alignment file, you will be told where there are references that are defective (references found in some but not all versions of the same work). Sometimes you can and should do something about defective references ; other times you shouldn't because a source is fragmentary or an editor has sequestered some passages. Verbose validation will give you the opportunity to review the differences. In that same TAN alignment file you can write statements that synchronize versions. For example, one source may have used « Matt » and another « Mt » for the same book. Or, in the case of Isaiah 8 :29, the versification of the Brenton and Rahlfs versions are out of sync. You can reconcile such differences through specially designated elements.

Another pointing problem is the case where a work has multiple, overlapping reference systems. For example, citations from the works of Aristotle rely upon both bookchapter references and Bekker page-column-line numbers. Citations from the Church Fathers oftentimes need both book-chapter references and volume-column-subcolumn references from Migne's Patrology.

TEI handles this problem by allowing users to supplement a transcription's primary hierarchy with <milestone>s, which usually mark page or column breaks. The <milestone> is very useful, but it lacks the requisite semantics for representing a textual hierarchy, as required under TAN rules. 16 I have approached the problem differently. First, only one reference system may be applied to a TAN file. For each reference system desired, users should create a separate file with an identical transcription that is structured according to that reference system. These files should point to each other, which then makes reconciliation relatively straightforward. The verbose level of TAN validation allows one to check to make sure that the transcriptions are identical. If they are not, the specific differences are marked, and SQFs can be used to semiautomate the correction of the text.

Under this approach, a text can take as many flavors of hierarchies as you wish. And a cluster of differently segmented transcriptions can help TAN-based applications migrate texts from one reference system to another. In fact, I have been able to write an application that takes as input a transcription pair (a single version of a work in two files, each with its own reference system) and a third file that contains another version of the same work, perhaps in a completely different language, but styled according to one of the reference systems. The output is the third file restructured in the alternative reference system, with a best guess as to where the divisions should fall. 17 There are of course other problems about pointers that could be discussed. Some of them are treated in the official TAN guidelines and examples. Others not covered by the guidelines will be incorporated as they are encountered.

IV. Progress and Prospects

At present, TAN is an experimental format, under development. It has been used successfully in service to three different projects : the Guide to Evagrius Ponticus (GEP), the Chrysostomus Latinus in Iohannem Online project (CLIO), and a private collaborative effort to translate a fourth-century Greek work and its ancient Syriac translations (PRV). 18 The GEP relies upon TAN files to generate and publish HTML transcriptions of select primary sources. It also takes a TAN file that contains RDF-like claims, along with a bibliography database (in Zotero RDF), and automatically generates an extensively documented master checklist of writings from the fourth century monk, creating links between the TAN files and the relevant bibliographic entries.

CLIO, which is focused on the three Latin translations of eighty-eight homilies by John Chrysostom on the Gospel of John, has developed a small library of master TAN-TEI files that are used to populate a website correlates the translations (and textual variants) with manuscript images. The TAN files include both straightforward transcriptions and indications of textual variants. It is hoped that in the future other projects treating the same work but in other languages (e.g., Greek, Armenian, Syriac, Arabic) will be able to create comparable TAN files that synchronize with the CLIO files, to demonstrate genuine cross-project interoperability.

For its work, PRV has depended upon a library of TAN files to prepare a book that is under contract with Oxford University Press. To reach that goal, PRV has developed a number of TAN-based XSLT tools that create various forms of output that have been useful not only for the published project but for conducting initial work. That output includes :

(1) Master HTML pages that collate every version (Greek, Syriac, the working English translations, etc.) not just with each other but with juxtaposed commentary and quotations from Aristotle and the Bible (in different versions). The number and sequence of the versions are easily configured, without touching the underlying TAN files.

(2) Master indexes of textual quotations from the Bible and Aristotle, sortable in the order of the quoted or quoting work, with contextual snippets. (3) Master subject indexes. (4) Comparative statistical profiles of each version of each work (e.g., word counts, hapax legomena, most frequent words). (5) Reports that suggest how words in one particular language-version correspond to words in the others. (6) Word-by-word interlinear editions.

(7) Quotation detection. 19 Every one of these applications would merit its own article-length discussion. As time and opportunity permits I will do so, but in the meantime, do explore the examples that have already been posted. 20 Such progress is promising, but tentative. At the present, TAN needs people from other established projects in the digital humanities to use it and to actively contribute to the development of the schemas, examples, and documentation. By expanding the network, to see what rules work, what rules don't, and what can't be reduced to a rule, the TAN format will become more servicable, and provide insight into what kinds of rules can and cannot be reduced to an algorithm.

Trying it out incurs little risk, since TAN is not an exclusive format. A TAN file may sit happily side by side with TEI, HTML, plain text, or other formats. But it is primed to do things those other formats cannot do, namely, participate in a cross-project network, an ecosystem of peer-to-peer sharing of our sources and our annotations on those sources. Developing TAN has made me dream about someone to come along and create a Napster for digital texts. 21 TAN would be perfectly suited to a Text Napster. But whether or not such dream software materializes, I aim to continue developing TAN over the coming years, since I believe that even on its own it heralds a new Internet of primary sources.

All data must be human-and computer-readable : Everything in a TAN file must be

  ). If we are working with a book that features multiple versions of a work, each version of interest needs to be broken out into its own file. The purpose of a TAN/TEI file is to focus on the work, not on the physical exemplar, which means that a TAN transcription file is likely to cover only a portion of what appears in a book.

	metadata in a TAN file should fulfill scholarly expectations. It must de minimiis answer a core
	set of questions scholars need to know to be able to use the data responsibly: what is the name
	and version of this file, what are the sources of the data, under what license is the data
	released, who created the data and when, and what assumptions and definitions were adopted
	in editing the data. Neither empty fields nor obviously fake responses should be permitted.
	 both
	human-and computer-readable. The computer-readable component is oftentimes an
	Internationalized Resource Identifier (IRI, roughly synonymous with URI, Uniform Resource
	Identifier, i.e., a URN or URL), 4 so that TAN files can contribute to the Semantic Web.

 Metadata should be focused on the task at hand : But because a given file is devoted to one task, the metadata should as well. Yes, we want to know who was responsible for editing or proofreading a text. But we don't need to know the proofreaders' age, nationality, or background. A unique identifier for those people can point us to other places more authoritative where we can learn about them. So too with a book that is the basis for a transcription. We don't need a full catalogue entry. Our data is not about the book, it's about the work. Just point to one or more records where we can learn more, if we so choose. Metadata should be restricted to the data in the .

 The bare scholarly minimum should be expected and enforced in metadata : The

For TMX and XLIFF see https://en.wikipedia.org/wiki/Translation_Memory_eXchange and https://en.wikipedia.org/wiki/XLIFF.

https://www.oxygenxml.com/ (accessed 2017-10-17).

Other alternatives to the Great Impermissible have been proposed, e.g., the Layered Markup and Annotation Language (LMNL). http://lmnl-markup.org/. Such efforts dispense with XML altogether, and so cannot

Journal of Data Mining and Digital Humanities http://jdmdh.episciences.org

immediately take advantage of related XML technologies (e.g., XPath) without first being converted to derivative XML documents.4 The TAN guidelines prefers the term IRI, because IRIs accommodate most of Unicode. But this distinction is subtle and minor. All URLs and URIs are IRIs, and all IRIs can be expressed as a URI.

On CTS subreferences, see http://www.homermultitext.org/hmt-doc/cite/cts-subreferences.html (accessed 2017-10-18).

http://www.unicode.org/reports/tr18/ (accessed 2017-10-17).

http://jdmdh.episciences.org

TAN also permits an extension to regular expressions that makes it easier to identify classes of characters. In our example, one could write θε\k{.omicron}ς. I hope to publish more on this regular expression extension in the future.

As of this writing (2017-10-19), the three-phase validation described here is still under development, but is planned to be released in the near future.

The reasons are rather technical, but can be pointed to with a simple example of what a <milestone> should look like if it were to have the necessary semantics: <milestone unit="bk chap v" n="Mt 6 9"/>. This example is officially invalid because TEI disallows spaces in @unit. The TEI rules could, of course, be customized, but that would require us to move on to other technical problems. For example, <milestone>'s @n is a concatenation of several individual
 @n's. But
's @n allows spaces. So in the example <milestone unit="ch poem" n="Prelude One Treasure"/>, how would the hierarchy be restored? Are we talking about a chapter called Prelude One, or a poem called One Treasure?

This application has yet to be published.

GEP, director Joel Kalvesmaki, Dumbarton Oaks, http://evagriusponticus.net; CLIO, director Chris Nighman, Wilfrid Laurier University, https://www.chrisnighman.com/; PVT, director Robin Darling Young, Catholic University of America.