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Empirical modelling
Empirical modelling
Empirical modelling
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Empirical modelling refers to any kind of (computer) modelling based on empirical observations rather than on mathematically describable relationships of the system modelled.

Empirical Modelling

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Empirical Modelling as a variety of empirical modelling

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Empirical modelling is a generic term for activities that create models by observation and experiment. Empirical Modelling (with the initial letters capitalised, and often abbreviated to EM) refers to a specific variety of empirical modelling in which models are constructed following particular principles. Though the extent to which these principles can be applied to model-building without computers is an interesting issue (to be revisited below), there are at least two good reasons to consider Empirical Modelling in the first instance as computer-based. Without doubt, computer technologies have had a transformative impact where the full exploitation of Empirical Modelling principles is concerned. What is more, the conception of Empirical Modelling has been closely associated with thinking about the role of the computer in model-building.

An empirical model operates on a simple semantic principle: the maker observes a close correspondence between the behaviour of the model and that of its referent. The crafting of this correspondence can be 'empirical' in a wide variety of senses: it may entail a trial-and-error process, may be based on computational approximation to analytic formulae, it may be derived as a black-box relation that affords no insight into 'why it works'.

Empirical Modelling is rooted on the key principle of William James's radical empiricism, which postulates that all knowing is rooted in connections that are given-in-experience. Empirical Modelling aspires to craft the correspondence between the model and its referent in such a way that its derivation can be traced to connections given-in-experience. Making connections in experience is an essentially individual human activity that requires skill and is highly context-dependent. Examples of such connections include: identifying familiar objects in the stream of thought, associating natural languages words with objects to which they refer, and subliminally interpreting the rows and columns of a spreadsheet as exam results of particular students in particular subjects.

Principles

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In Empirical Modelling, the process of construction is an incremental one in which the intermediate products are artefacts that evoke aspects of the intended (and sometimes emerging) referent through live interaction and observation. The connections evoked in this way have distinctive qualities: they are of their essence personal and experiential in character and are provisional in so far as they may be undermined, refined and reinforced as the model builder's experience and understanding of the referent develops. Following a precedent established by David Gooding in his account of the role that artefacts played in Michael Faraday's experimental investigation of electromagnetism, the intermediate products of the Empirical Modelling process are described as 'construals'. Gooding's account is a powerful illustration of how making construals can support the sense-making activities that lead to conceptual insights (cf. the contribution that Faraday's work made to electromagnetic theory) and to practical products (cf. Faraday's invention of the electric motor).

Figure 1 Making a construal

The activities associated with making a construal in the Empirical Modelling framework are depicted in Figure 1.

The eye icon at the centre the figure represents the maker's observation of the current state of development of the construal and its referent. The two arrows emanating from the eye represent the connection given-in-experience between the construal and its referent that is established in the mind of the maker. This connection is crafted through experimental interaction with the construal under construction and its emerging referent. As in genuine experiment, the scope of the interactions that can be entertained by the maker is inconceivably broad. At the maker's discretion, the interactions that characterise the construal are those that respect the connection given in the maker's experience. As the Empirical Modelling process unfolds, the construal, the referent, the maker's understanding and the context for the maker's engagement co-evolve in such a way that:

  • the interactive experience that the construal affords is enhanced;
  • the interactive experience that characterises the referent is refined;
  • the repertoire of characteristic interactions with the construal and its referent is enlarged;
  • the contextual constraints on characteristic interactions with the construal and its referent are identified.

Empirical Modelling concepts

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In Empirical Modelling. making and maintaining the connection given-in-experience between the construal and referent is based on three primary concepts: observables, dependencies and agency. Within both the construal and its referent, the maker identifies observables as entities that can take on a range of different values, and whose current values determine its current state. All state-changing interactions with the construal and referent are conceived as changes to the values of observables. A change to the value of one observable may be directly attributable to a change in the value of another observable, in which case these values are linked by a dependency. Changes to observable values are attributed to agents, amongst which the most important is the maker of the construal. When changes to observable values are observed to occur simultaneously, this can be construed as concurrent action on the part of different agents, or as concomitant changes to observables derived from a single agent action via dependencies. To craft the connection given-in-experience between the construal and referent, the maker constructs the construal in such a way that its observables, dependencies and agency correspond closely to those that are observed in the referent. To this end, the maker must conceive appropriate ways in which observables and agent actions in the referent can be given suitable experiential counterparts in the construal.

The semantic framework shown in Figure 1 resembles that adopted in working with spreadsheets, where the state that is currently displayed in the grid is meaningful only when experienced in conjunction with an external referent. In this setting, the cells serve as observables, their definitions specify the dependencies, and agency is enacted by changing the values or the definitions of cells. In making a construal, the maker explores the roles of each relevant agent by projecting agency upon it as if it were a human agent and identifying observables and dependencies from that perspective. By automating agency, construals can then be used to specify behaviours in much the same way that behaviours can be expressed using macros in conjunction with spreadsheets. In this way, animated construals can emulate program-like behaviours in which the intermediate states are meaningful and live to auditing by the maker.

Environments to support Empirical Modelling

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The development of computer environments for making construals has been an ongoing subject of research over the last thirty years. The many variants of such environments that have been implemented are based on common principles. The network of dependencies that currently connect observables is recorded as a family of definitions. Semantically such definitions resemble the definitions of spreadsheet cells, whereby changes to the values of observables on the right hand side propagate so as to change the value of the observable on the LHS in a conceptually indivisible manner. The dependencies in these networks are acyclic but are also reconfigurable: redefining an observable may introduce a new definition that alters the dependency structure. Observables built into the environment include scalars, geometric and screen display elements: these can be elaborated using multi-level list structures. A dependency is typically represented by a definition which uses a relatively simple functional expression to relate the value of an observable to the values of other observables. Such functions have typically been expressed in fragments of simple procedural code, but the most recent variants of environments of making construals also enable dependency relations to be expressed by suitably contextualised families of definitions. The maker can interact with a construal through redefining existing observables or introducing new observables in an open-ended unconstrained manner. Such interaction has a crucial role in the experimental activity that informs the incremental development of the construal. Triggered actions can be introduced to automate state-change: these perform redefinitions in response to specified changes in the values of observables.

Empirical Modelling as a broader view of computing

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In Figure 1, identifying 'the computer' as the medium in which the construal is created is potentially misleading. The term COMPUTER is not merely a reference to a powerful computational device. In making construals, the primary emphasis is on the rich potential scope for interaction and perceptualisation that the computer enables when used in conjunction with other technologies and devices. The primary motivation for developing Empirical Modelling is to give a satisfactory account of computing that integrates these two complementary roles of the computer. The principles by which James and Dewey sought to reconcile perspectives on agency informed by logic and experience play a crucial role in achieving this integration.

The dual role for the computer implicit in Figure 1 is widely relevant to contemporary computing applications. On this basis, Empirical Modelling can be viewed as providing a foundation for a broader view of computing. This perspective is reflected in numerous Empirical Modelling publications on topics such as educational technology, computer-aided design and software development. Making construals has also been proposed as a suitable technique to support constructionism, as conceived by Seymour Papert, and to meet the guarantees for 'construction' as identified by Bruno Latour.

Empirical Modelling as generic sense-making?

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The Turing machine provides the theoretical foundation for the role of the computer as a computational device: it can be regarded as modelling 'a mind following rules'. The practical applications of Empirical Modelling to date suggest that making construals is well-suited to supporting the supplementary role the computer can play in orchestrating rich experience. In particular, in keeping with the pragmatic philosophical stance of James and Dewey, making construals can fulfill an explanatory role by offering contingent explanations for human experience in contexts where computational rules cannot be invoked. In this respect, making construals may be regarded as modelling 'a mind making sense of a situation'.

In the same way that the Turing machine is a conceptual tool for understanding the nature of algorithms whose value is independent of the existence of the computer, Empirical Modelling principles and concepts may have generic relevance as a framework for thinking about sense-making without specific reference to the use of a computer. The contribution that William James's analysis of human experience makes to the concept of Empirical Modelling may be seen as evidence for this. By this token, Empirical Modelling principles may be an appropriate way to analyse varieties of empirical modelling that are not computer-based. For instance, it is plausible that the analysis in terms of observables, dependencies and agency that applies to interaction with electronic spreadsheets would also be appropriate for the manual spreadsheets that predated them.

Background

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Empirical Modelling has been pioneered since the early 1980s by Meurig Beynon and the Empirical Modelling Research Group in Computer Science at the University of Warwick.

The term 'Empirical Modelling' (EM) has been adopted for this work since about 1995 to reflect the experiential basis of the modelling process in observation and experiment. Special purpose software supporting the central concepts of observable, dependency and agency has been under continuous development (mainly led by research students) since the late 1980s.

The principles and tools of EM have been used and developed by many hundreds of students within coursework, project work, and research theses. The undergraduate and MSc module 'Introduction to Empirical Modelling' was taught for many years up to 2013-14 until the retirement of Meurig Beynon and Steve Russ (authors of this article). There is a large website [1] containing research and teaching material with an extensive collection of refereed publications and conference proceedings.

The term 'construal' has been used since the early 2000s for the artefacts, or models, made with EM tools. The term has been adapted from its use by David Gooding in the book 'Experiment and the Making of Meaning' (1990) to describe the emerging, provisional ideas that formed in Faraday's mind, and were recorded in his notebooks, as he investigated electromagnetism, and made the first electric motors, in the 1800s.

The main practical activity associated with EM - that of 'making construals' - was the subject of an Erasmus+ Project CONSTRUIT! (2014-2017)[2].

See also

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Notes, References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Empirical modelling

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from Grokipedia
Empirical Modelling (EM) is a human-centred, situated, computer-based modelling approach that emphasizes the construction of interactive artefacts to support personal understanding and sense-making through observation and experience, rather than relying on preconceived abstractions or mathematical theories. Developed at the University of Warwick since 1983, EM draws on empirical principles to create environments where meaning emerges from skilful human interaction with dynamic representations of real-world phenomena. At its core, EM revolves around three fundamental concepts: observables, which are perceivable elements representing the state of a domain; dependencies, which capture predictable relationships between observables as indivisible links; and agency, which denotes entities (human or computational) responsible for state changes. These concepts are operationalized through definitive scripts in tools like EDEN (Evaluator for Definitive Notations), enabling state-based, observation-oriented modelling that contrasts with traditional object-oriented or procedural paradigms by being open-ended and experiential. The Empirical Modelling Project originated from Meurig Beynon's 1983 study of the ARCA tool for interactive manipulation of Cayley diagrams, evolving as an alternative to classical computation theory to better address situated problem-solving in and beyond. Key milestones include the introduction of the EDEN interpreter in 1990 for definitive notations, the development of specialized scripting languages like (1986) for line drawings and SCOUT (1993) for screen layouts, and the formal adoption of the term "empirical modelling" in 1995 to highlight its distinction from conventional mathematical approaches. Led by Beynon and collaborators such as Alan Cartwright, Simon Yung, and Edward Yung, the approach has integrated with geometric tools like CADNO and advanced to support agent-oriented modelling in contemporary systems. EM's principles—observation-oriented analysis, emphasis on lived experience over theory, and support for amethodical creativity—have found applications across diverse fields, including , , concurrent engineering, , program comprehension, , decision support systems, and . By fostering interactive environments that bridge subjective experience and objective realities, EM promotes a more intuitive and collaborative form of computational modelling, influencing modern practices in human-computer interaction and experiential computing as of 2024.

Overview

Definition and Scope

Empirical modelling refers to any form of computer-based modelling that derives its structure and behavior from direct observations of real-world phenomena, rather than from predefined mathematical equations or theoretical abstractions. This approach prioritizes data-driven approximations and to represent systems, often employed in fields like and where exact theoretical formulations are impractical or unavailable. In contrast, Empirical Modelling (EM), with capitalization denoting a specific computational framework, is an experiential and human-centered methodology for constructing interactive models known as construals. These construals maintain a close, dynamic linkage to their real-world referents through iterative processes of trial-and-error experimentation and successive approximation, enabling users to explore and refine personal understandings of complex situations. Developed primarily at the , EM emphasizes situated, observation-based construction over , using computer tools to support fluid interaction and sense-making. The scope of EM centers on the creation of personal, evolving models that facilitate thinking and collaboration in domains such as , and , where subjective experience and direct manipulation are key. It focuses on exploratory artefacts that evolve through user agency and interaction, rather than or . The Empirical Modelling Research Group at the continues to develop interactive environments based on these principles as of 2024. At its foundation lies a triad of core building blocks—observables (perceived elements of the domain), dependencies (relationships linking these elements), and agency (mechanisms for state changes)—which together enable the construction of responsive, meaningful representations. EM draws inspiration from the philosophical tradition of , which posits that knowledge arises holistically from rather than isolated propositions.

Distinction from Traditional Modelling

Empirical Modelling (EM) differs fundamentally from traditional mathematical modelling by eschewing formal equations and abstract derivations in favor of observable dependencies that capture describable relationships through direct experience and black-box approximations. In mathematical modelling, systems are typically represented using predefined variables and analytical solutions to predict outcomes with precision, whereas EM prioritizes the construction of interactive construals based on empirical observations, allowing relationships to emerge incrementally without requiring an upfront commitment to a mathematical framework. This approach, termed "definitive scripting," enables modellers to define states and transitions via scripts that propagate changes akin to rule-based systems, rather than solving explicit formulas. In contrast to simulation modelling, which often relies on closed-form solutions or numerical methods to achieve high predictive accuracy—such as methods or agent-based simulations with fixed parameters—EM emphasizes interactive exploration and user-driven experimentation over deterministic forecasting. Traditional simulations typically model underlying mechanisms architecturally, enforcing a separation between model structure and behavior, while EM integrates observables and dependencies in a concurrent, state-as-experienced manner, fostering open-ended inquiry without the need for exhaustive parameter tuning or validation against theoretical ideals. This shift supports a more phenomenological view, where the model's fidelity lies in its alignment with the modeller's rather than in replicable predictions. A primary advantage of EM is its maintenance of experiential fidelity to the referents of the model, ensuring that construals remain grounded in observable phenomena even as complexity increases, unlike traditional methods that may abstract away ambiguities to achieve solvability. It also facilitates incremental development, permitting rapid prototyping and "what-if" adjustments without recompilation or global re-evaluation, which accommodates inherent uncertainties in complex, real-world systems more effectively than rigid mathematical paradigms. These features make EM particularly suited for domains where understanding evolves through interaction, promoting flexibility over optimization. For instance, simple spreadsheets exemplify EM construals, where cell dependencies automatically update states upon input changes, mirroring observable interactions without differential equations, in contrast to simulation models of physical systems like pendulums that solve ordinary differential equations for trajectory predictions. In a spreadsheet-based EM approach, users can explore financial scenarios by adjusting variables and observing propagated effects directly, preserving experiential closeness, whereas traditional simulations might require specifying initial conditions and integration algorithms to approximate the same dynamics. This distinction highlights EM's role in enabling intuitive, ambiguity-tolerant modelling for exploratory purposes.

Principles

Foundational Philosophical Roots

Empirical Modelling (EM) draws significant inspiration from William James's philosophy of , which posits that experience encompasses not only discrete particulars but also the conjunctive relations between them, such as transitions and identities, as integral aspects of reality. In EM, this manifests as a computational framework that prioritizes the connections among experiential elements over isolated facts, enabling models to emerge from the interplay of observables rather than predefined abstractions. James's emphasis on the first-person perspective in apprehending knowledge—where one experience directly knows another—aligns with EM's approach to constructing personal, situated interpretations of phenomena. The experimental practices of further underpin EM's foundations, as analyzed by David Gooding, who highlights how Faraday's investigations in relied on physical artefacts to externalize and manipulate observations, allowing models to arise inductively from direct interaction rather than deductive theory. For instance, Faraday's trials with involved constructing tangible setups that revealed patterns through , embodying an empirical process where understanding evolves from observational engagement. EM adopts this precedent by treating computational construals as analogous artefacts, facilitating exploratory modelling that mirrors the provisional, hands-on nature of Faraday's work. EM also resonates with Bruno Latour's concept of "construction guarantees," which outline criteria for robust constructivist practices in science and design, including acknowledging stable realities, admitting revisions, enabling progressive composition, uniting human and non-human agencies, and differentiating qualities of constructions. In EM, these guarantees are supported through flexible, interactive environments that allow modellers to incrementally build and audit experiential representations, ensuring constructions remain verifiable and adaptable to new observations. This alignment promotes EM as a tool for experiential validation in collaborative settings, akin to Latour's vision of negotiated, empirically grounded knowledge production. Unlike positivism, which seeks objective universality through propositional logic and closed-world assumptions, EM embraces subjective, personal interpretations rooted in lived experience, rejecting the notion of a singular, theory-driven truth in favor of pluralistic, provisional understandings. This distinction underscores EM's commitment to an open-ended empiricism that values interpretive agency over deterministic rationalism.

Key Operational Principles

Empirical Modelling (EM) operationalizes its philosophical foundations in radical empiricism by providing practical guidelines for constructing interactive computational artefacts that remain closely tied to human experience. These principles emphasize user-driven processes that foster ongoing exploration and refinement, distinguishing EM from formal, deductive approaches in traditional modelling. A core operational principle is incremental construction, where models are developed through successive approximations via trial-and-error and iterative user interactions. This approach allows modellers to build and evolve artefacts step-by-step, starting from simple observables and dependencies, and refining them as understanding deepens without requiring a complete upfront specification. For instance, in EM environments, users can add or modify definitions in scripts progressively, enabling continuous experimentation and adaptation to emerging insights. The principle of experiential connection underscores the need to maintain a direct, "lived" relation between the model and its , avoiding abstractions that disconnect from . In EM, meaning emerges through skilful interaction with the artefact, where observables and dependencies mirror those in personal , ensuring the model supports intuitive rather than detached . This connection is achieved by aligning the patterns of interaction in the computational environment with real-world dynamics, allowing users to apprehend relations as they occur in lived contexts. EM principles explicitly support by permitting incomplete or provisional models that accommodate and multiple interpretations, in contrast to rigid formal systems that demand full specification. Models in EM are inherently subjective and context-dependent, reflecting the modeller's evolving viewpoint and allowing for intermittent or partial representations of phenomena without enforcing closure. This flexibility enables diverse perspectives to coexist within the same artefact, fostering creative and exploratory engagement. Finally, EM integrates with constructionism as articulated by , positioning it as a computational tool for learner-driven knowledge creation through active artefact building. By emphasizing —concrete experimentation with tangible digital objects—EM aligns with Papert's view that learning is enhanced when individuals construct public, shareable models that embody personal understanding and invite reflection. This synergy supports situated problem-solving, where users develop insights incrementally in real-world contexts, much like Papert's environments but extended to broader experiential modelling.

Core Concepts

Observables and Their Role

In Empirical Modelling (EM), observables are defined as the fundamental entities representing perceivable features of a modelled domain, each characterized by an identifiable current value or status that corresponds to empirical observations. These entities encompass a range of attributes, such as scalar quantities like temperature or speed, and geometric elements like points, lines, or positions, which serve as variables holding data reflective of real-world or conceptual states rather than abstract mathematical constructs. Unlike traditional variables in formal models, observables are directly tied to the modeller's experiential understanding, enabling a representation that prioritizes observable phenomena over predefined theoretical relationships. Observables function as the primary building blocks in EM construals, forming the state of the model and facilitating interaction with the domain being explored. They act as referents that ground the model in empirical reality, allowing modellers to construct and manipulate representations incrementally based on direct or inputs. For instance, in a physics construal, the position of a might be defined as an observable, initially set by user input and subsequently updated through computational means to reflect motion, thereby embodying observable attributes like location and . This role underscores their capacity to mediate between the modeller's perspective and the model's behaviour, supporting exploratory activities without imposing rigid structures. Properties of observables in EM include their potential to be static—maintaining fixed values for stable features—or dynamic, permitting redefinition to accommodate changes in or interaction. Dynamic observables, such as the state of a (open or closed) in a model, enable real-time updates that enhance . Furthermore, observables support visualization through tools like EDEN and DoNaLD, where they can be rendered graphically—for example, as movable points or adjustable lines—allowing users to perceive and manipulate them intuitively. This visualization aspect reinforces their empirical grounding, as changes in observables propagate to visual outputs, fostering a tangible connection to the modelled situation. In EM, observables may link to others via dependencies to express interrelations, but their intrinsic role remains as isolated carriers of state.

Dependencies and Interactions

In Empirical Modelling, dependencies are defined as relationships between observables that capture how changes in one observable propagate to others, typically expressed through procedural scripts or rules to reflect observed patterns in experience. These dependencies form the of a model, enabling the of interactive artefacts where the status of linked s updates dynamically upon alteration. For stability, dependencies are structured as acyclic graphs, preventing infinite loops during propagation, akin to the directed acyclic graphs (DAGs) used in dependency visualization tools. Dependencies in Empirical Modelling are categorized into explicit and implicit types, with the former being user-defined relationships directly specified in model scripts, such as formulae linking s (e.g., "profit is minus "). Implicit dependencies, in contrast, emerge through interactions or procedural actions, such as those triggered by external events that indirectly affect states without explicit declaration. Both types support reconfigurability, allowing modellers to evolve the model by redefining or negotiating dependencies as understanding deepens, thereby adapting the artefact to new observational insights. The primary role of dependencies in interactions is to facilitate reactive updates that simulate real-world , where a change in one automatically triggers adjustments in connected ones without relying on mathematical proofs or . This propagation occurs through hierarchical evaluation in explicit cases, following a in the DAG, while implicit dependencies may involve action monitoring for less predictable but experientially grounded responses. Such mechanisms enable the model to exhibit emergent behaviors that align with direct , with activation often stemming from agency in the form of user or environmental interventions. A representative example of dependencies in action is found in spreadsheet-like construals within Empirical Modelling, where cell formulas serve as explicit dependencies linking numerical observables; for instance, altering the value in one cell (e.g., input ) immediately propagates to dependent cells (e.g., total profit calculation), mirroring the reactive nature of EM artefacts. In more complex scenarios, such as a model, the state of a drawer (an ) explicitly depends on its open/closed position via scripted rules, with changes propagating to visual representations like LED indicators.

Agency in Model Construction

In Empirical Modelling, agency refers to the attribution of responsibility for changes in the states of to specific agents, which can be participants or automated processes, often operationalized through definitive scripts that specify actions and protocols. These scripts or actions alter observable states either manually, via user interactions, or automatically, through event triggers and emulated behaviors. Agency plays a central role in facilitating exploration and experimentation, empowering users to actively intervene in the model and observe emergent patterns that arise from their actions. By enabling such interventions, agency transforms static representations into dynamic environments where participants can probe the model's responsiveness, fostering deeper experiential understanding of the underlying phenomena. Within the core triad, agency integrates seamlessly by initiating updates to , which in turn invoke dependencies to propagate changes across the model, thereby sustaining coherent and interactive construals. Construals, as the holistic outcomes of these triad elements, emerge through ongoing agency-driven interactions. A representative example involves a simulation where a user drags a slider to adjust an applied force—an —prompting dependencies to recalculate object trajectories and velocities in real time. In contrast, automated agency might employ scripts for event triggers, such as simulating ongoing collisions or without manual input, to reveal long-term behavioral dynamics.

History and Development

Origins in the 1980s

Empirical Modelling originated in the early at the , where Meurig Beynon initiated the project in 1983 through a study of the ARCA tool for interactive manipulation of Cayley diagrams, as a response to the limitations of formal programming paradigms in supporting experiential and experimental computing tasks. Beynon's early work sought to create interactive environments that emphasized human-centered exploration, moving beyond symbolic to foster observational and constructive activities in computing. This motivation stemmed from the need for more flexible computational tools that aligned with constructivist educational principles, enabling users to build knowledge through direct interaction rather than predefined specifications. The foundational influences drew briefly from philosophical ideas such as William James's , which informed an approach prioritizing subjective experience and pre-theoretical experimentation in model construction. By the mid-1980s, the project had evolved to address these goals through initial prototypes for interactive modelling, particularly in educational contexts, allowing users to experiment with dependencies and observables in real-time. A key milestone came in 1987 with the development of EDEN, an early software prototype created as an undergraduate project by Y.W. Yung, which supported definitive notations for constructing and exploring models informally. Around this time, Steve Russ joined the Department of at in 1987 and began collaborating with Beynon on the core principles of Empirical Modelling, contributing to its theoretical underpinnings through work on logic, , and human-computer integration. Between 1985 and 1990, the initiative gained momentum through student projects, internal publications, and conference presentations that demonstrated its potential for interdisciplinary applications, though it received limited mainstream recognition during this formative period. These efforts laid the groundwork for Empirical Modelling as an alternative paradigm, focusing on agency and situated understanding in .

Evolution and Key Milestones

Following the initial development in the , the term "Empirical Modelling" was formally adopted in 1995 to distinguish the approach from broader empirical methods in computing and to emphasize its roots in , experiment, and experiential engagement. This terminology shift, led by Meurig Beynon at the , marked a maturation of the , enabling clearer articulation of its principles in academic discourse and tool development throughout the . In the early 2000s, the concept of a "construal" was introduced to describe the interactive artifacts central to Empirical Modelling, drawing inspiration from David Gooding's analysis of Michael Faraday's experimental practices as provisional, situated interpretations of phenomena. This term, adapted from Gooding's work on scientific discovery, provided a framework for viewing Empirical Modelling outputs as dynamic cognitive tools that support sense-making through construction and interaction, influencing subsequent theoretical expansions. Key milestones in the 2010s included the sustained teaching of Empirical Modelling principles through the University of Warwick's "Introduction to Empirical Modelling" module (CS405), which ran until the 2013-14 , fostering hands-on among undergraduate and postgraduate students. This was followed by the CONSTRUIT! project (2014-2017), an Erasmus+ initiative led by Warwick with international partners, which developed and tools to promote construal-based learning in secondary and higher education across . As of 2025, active development of Empirical Modelling has been limited since 2017, following the retirement of key figures like Beynon in 2011, though the research group at the remains operational with occasional outreach and maintenance of legacy tools.

Tools and Environments

Early Software Prototypes

The development of early software prototypes for Empirical Modelling (EM) began in the late at the , driven by the need to operationalize core concepts such as observables and dependencies through interactive environments. The foundational prototype, EDEN (Engine for Definitive Notations), was created by Edward Yung as part of his MSc thesis in 1989. EDEN provided a general-purpose interpreter for definitive notations, enabling users to define observables—such as variables representing measurable quantities—and express dependencies between them in a declarative manner, without relying on traditional paradigms. This tool laid the groundwork for constructing situated, experiential models that emphasized human interpretation over algorithmic computation. Building on EDEN, subsequent prototypes in the early 1990s incorporated graphical and scripting capabilities to enhance interactivity. A key advancement was tkeden, developed around 1992 by Simon Yung, which integrated the Tcl/Tk toolkit (often abbreviated as ) to support the creation of dynamic, scriptable models. allowed for the rapid prototyping of user interfaces where observables could be visualized and manipulated in real-time, with dependencies automatically propagating changes across the model. For instance, tkeden supported notations like Eden for general definitions and Scout for exploratory scripting, facilitating the construction of interactive environments that mirrored empirical observation and experimentation. These features enabled early EM practitioners to build construals—coherent assemblies of observables and dependencies—that responded fluidly to user interventions. Representative examples of early construals developed with these prototypes included physics simulations, such as a simple model demonstrating oscillatory motion through interdependent observables for , , and gravitational , and geometric constructions like interactive diagrams for exploring Euclidean properties via linked points and lines. These models highlighted EM's emphasis on experiential engagement, where users could adjust parameters to observe emergent behaviors without predefined outcomes. However, these prototypes were primarily research-oriented tools confined to the EM group, lacking the robustness, documentation, and distribution channels necessary for broader adoption beyond academic settings. Their focus remained on proof-of-concept demonstrations rather than scalable, user-friendly software for general use.

Modern Support Systems

The CONSTRUIT! project, running from 2014 to 2017, represented a significant advancement in Empirical Modelling support systems as an initiative funded by the . Led by the University of Warwick's Empirical Modelling Research Group in collaboration with six partner institutions across , it aimed to develop web-based environments for creating interactive construals—dynamic models emphasizing observables, dependencies, and user agency—while promoting for STEM education. Key features of CONSTRUIT! included robust support for distributed , enabling multiple users to co-construct and refine construals in real-time through a shared online platform. The system facilitated visualization of dependencies via interactive dependency networks, allowing users to observe how changes in observables propagate through the model, akin to spreadsheet-like reactivity but extended to complex, experiential scenarios. Agency was empowered through JavaScript-based scripting in the Construal Runtime Environment (JSeden), where users could define behaviors and interactions without rigid programming paradigms, fostering incremental and provisional model-building. As of 2025, CONSTRUIT! resources remain accessible and hosted by the , with the core platform available at jseden.dcs.warwick.ac.uk/construit/ for ongoing use in educational and research contexts. The Empirical Modelling Research Group continues to maintain and develop these tools as of 2024. While extensions to (VR) or (AR) have been explored conceptually in Empirical Modelling literature as ways to enhance experiential sense-making, these remain underdeveloped in practice. A notable gap in modern systems like CONSTRUIT! is the absence of integration with tools for automated dependency generation, relying instead on manual construction to preserve the emphasis on human agency and observation. These tools have supported educational applications by enabling students to build interactive models of phenomena such as .

Applications

Educational Uses

Empirical Modelling (EM) aligns closely with Seymour Papert's constructionist , which emphasizes learners actively constructing through personal, interactive artifacts rather than passive reception of information. In EM, students build "construals"—dynamic models composed of observables and dependencies—that embody their evolving understanding, allowing for experimentation and reflection akin to Papert's vision of children as makers in computational environments. This approach fosters a unified perspective where learners act as both constructors and interpreters of their models, bridging the gap between conceptual exploration and practical implementation. A notable example of EM in higher education is the CS405 module "Introduction to Empirical Modelling" at the , taught from the early 2000s until the 2013-14 . The module utilized construals to teach core concepts, such as algorithms and software dependencies, through hands-on construction of interactive models that students could manipulate and debug in real-time. For instance, students explored design by modeling functional dependencies and decompositions, enabling them to observe emergent behaviors and refine their intuitions iteratively. Similarly, EM has supported explorations in physics and ; an for problems allows learners to construct models of Newtonian dynamics using observables like position and velocity, facilitating intuitive grasp of physical laws without initial reliance on formal equations. The benefits of EM in educational settings include promoting exploratory learning, where students engage in trial-and-error processes to uncover dependencies, thereby developing and skills essential for computational . By externalizing internal models as interactive construals, EM encourages collaborative refinement and personal ownership, enhancing and deeper conceptual understanding over rote . These practices support constructionist principles by making abstract ideas tangible and experiential, as evidenced in case studies where learners simulate errors to diagnose behaviors. Recent developments offer untapped potential for broader adoption, particularly through open resources from the CONSTRUIT! project (2014-2017), which provides tools and tutorials for creating construals in K-12 and higher education contexts. Although activity has waned since the project's EU-funded phase ended in 2017, the accessible online materials enable educators to develop custom resources for subjects like physics or , potentially revitalizing EM as a constructionist tool in diverse curricula.

Software and Design Applications

Empirical Modelling (EM) has been applied in to support the prototyping of interactive systems, where it enables developers to construct dynamic artefacts that emphasize user agency and experiential interaction. By focusing on observables, dependencies, and agents, EM facilitates exploratory modelling that aligns closely with the evolving needs of system design, particularly in (UI) development. For instance, EM tools like the EDEN interpreter allow for rapid iteration on interactive prototypes, such as simple games or device simulations, bridging personal interpretation and shared understanding without rigid preconceptions. In design applications, EM supports the construal of complex systems by integrating simulation and human intervention, making it suitable for domains requiring flexible representation of interactions. One notable example is its use in modelling digital interfaces, where EM principles help simulate user navigation and content delivery in interactive environments. Similarly, in timetabling, the Temposcope instrument exemplifies EM's role in creating open-ended tools for scheduling tasks, such as allocating project oral presentations across rooms and timeslots; it incorporates agency through user-driven adjustments to constraints like staff availability, enabling semi-automated simulations that adapt to real-world inconsistencies. A prominent case in safety-critical design is the 2005 reconstruction of the Clayton Tunnel rail accident using EM, which models the 1861 incident involving signal failures and human errors through interactive construals. This approach captures subjective factors like and via first-person simulations of train positions, telegraph states, and agent actions, allowing analysts to explore emergent dependencies and test protocol robustness in a provisional manner. EM's advantages in these contexts stem from its ability to handle ill-defined requirements more effectively than , which often impose abstract, predefined structures unsuitable for concurrent or experiential systems. EM's agent-oriented, visual, and flexible framework supports real-time exploration and adaptation, reducing the gap between informal human understanding and computational representation while accommodating evolving contexts in software and design processes.

Broader Implications

EM as an Alternative Computing Paradigm

Empirical Modelling (EM) challenges the dominance of declarative and imperative paradigms in mainstream computing by advocating for a more integrated approach that transcends rigid algorithmic specifications. Traditional paradigms often prioritize abstract, formal representations of computation, leading to a disconnect between computational models and human experiential understanding. In contrast, EM emphasizes "state interpretation," where computational artefacts—termed construals—are constructed through observable dependencies and interactive exploration rather than predefined algorithms or declarations. This shift allows modellers to engage directly with evolving states of a system, fostering a dynamic interplay between observation and adjustment that avoids the limitations of algorithm-centric views. At its core, EM redefines as a of sense-making through human interaction, positioning it as a medium for mediating personal understanding rather than merely processing or executing functions. Construals in EM serve as interactive environments that reflect the modeller's ongoing interpretation of observables, dependencies, and agency, enabling a form of grounded in . This broader perspective critiques the rationalistic tradition in for overlooking the exploratory, pre-formal stages of problem-solving, instead promoting artefacts that adapt to shifting perceptions and support creative experimentation. By focusing on the construction and refinement of these interactive models, EM offers a where facilitates intuitive engagement over exhaustive . Steve Russ has significantly contributed to conceptualizing EM as a foundation for new models of , emphasizing its alignment with creative and meaning-oriented mathematical practices. Drawing from influences like Emil Post's work on undecidability, Russ advocates for EM's role in enabling exploratory experiments that blend human intuition with computational support, as seen in collaborative developments such as the OXO laboratory models. His ideas highlight how EM can reformulate to prioritize agency and dependency in interactive settings, providing a complementary framework to formal logics. Looking ahead, EM holds potential as a basis for human-AI collaboration, where empirical models evolve through iterative interaction between users and , though this application remains underdeveloped as of 2025. By supporting concurrent human and computational activities in non-routine tasks like and learning, EM could enable AI to assist in sense-making without imposing rigid structures, allowing models to adapt empirically to user-driven insights. This paradigm's emphasis on experiential evolution positions it to bridge gaps in current AI paradigms, fostering more intuitive and collaborative computational environments.

Connections to Sense-Making and Constructionism

Empirical Modelling (EM) serves as a framework for generic sense-making, enabling individuals to interpret and navigate experiences in ambiguous or complex domains by constructing interactive representations that mirror human cognitive processes. In EM, sense-making emerges through the development of "construals"—artefacts that capture observables, dependencies, and agency from personal experience, allowing users to explore and refine their understanding iteratively. This approach aligns closely with human cognition by integrating deliberate reflection and automatic , such as in perceptual tasks, thereby facilitating the transition from raw experience to conceptual insight without relying on formal abstractions. EM's ties to constructionism extend beyond Seymour Papert's emphasis on learning through artefact creation, incorporating broader socio-technical perspectives like Bruno Latour's actor-network theory (ANT). In constructionist terms, EM promotes active knowledge construction via interactive model-building, where learners develop personal artefacts that embody their evolving interpretations, fostering endogenous exploration and discovery. Latour's ANT complements this by viewing EM construals as networks of human and non-human actors, where dependencies and interactions construct shared realities in technical and social contexts, emphasizing the "promises of constructivism" through verifiable, experiential guarantees rather than abstract guarantees. This integration highlights EM's role in democratizing model-building, making it accessible for collaborative sense-making in interdisciplinary settings. The implications of these connections lie in EM's support for collaborative model-building, which cultivates shared understanding by allowing participants to co-construct and negotiate construals, as seen in educational scenarios like exploring game strategies in or algorithmic dependencies in . Such processes enable scientific experimentation by resolving ambiguities through empirical interaction, promoting a and dependency that mirrors real-world socio-technical dynamics. For instance, in group activities, EM facilitates the alignment of diverse perspectives into coherent networks, enhancing mutual comprehension without predefined hierarchies. Despite its affinities with cognitive processes, as of 2025, EM's exploration in and AI sense-making remains limited, with few integrations into mainstream frameworks for human-like reasoning or . This gap persists despite EM's potential to inform AI through experiential construals, as evidenced by the scarcity of recent interdisciplinary studies bridging these fields.

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