Multiple Levels of Heuristic Reasoning Processes in Scientific Model Construction

Abstract

Science historians have recognized the importance of heuristic reasoning strategies for constructing theories, but their extent and degree of organization are still poorly understood. This paper first consolidates a set of important heuristic strategies for constructing scientific models from three books, including studies in the history of genetics and electromagnetism, and an expert think-aloud study in the field of mechanics. The books focus on qualitative reasoning strategies (processes) involved in creative model construction, scientific breakthroughs, and conceptual change. Twenty four processes are examined, most of which are field-general, but all are heuristic in not being guaranteed to work. An organizing framework is then proposed as a four-level hierarchy of nested reasoning processes and subprocesses at different size and time scales, including: Level (L4) Several longer-time-scale Major Modeling Modes, such as Model Evolution and Model Competition; the former mode utilizes: (L3) Modeling Cycle Phases of Model Generation, Evaluation, and Modification under Constraints; which can utilize: (L2) Thirteen Tactical Heuristic Processes, e.g., Analogy, Infer new model feature (e.g., by running the model), etc.; many of which selectively utilize: (L1) Grounded Imagistic Processes, namely Mental Simulations and Structural Transformations. Incomplete serial ordering in the framework gives it an intermediate degree of organization that is neither anarchistic nor fully algorithmic. Its organizational structure is hypothesized to promote a difficult balance between divergent and convergent processes as it alternates between them in modeling cycles with increasingly constrained modifications. Videotaped think-aloud protocols that include depictive gestures and other imagery indicators indicate that the processes in L1 above can be imagistic. From neurological evidence that imagery uses many of the same brain regions as actual perception and action, it is argued that these expert reasoning processes are grounded in the sense of utilizing the perceptual and motor systems, and interconnections to and possible benefits for reasoning processes at higher levels are examined. The discussion examines whether this grounding and the various forms of organization in the framework may begin to explain how processes that are only sometimes useful and not guaranteed to work can combine successfully to achieve innovative scientific model construction.

Keywords: creativity; grounded cognition; heuristics; imagery; mental model; mental simulation; reasoning; science.

FIGURE 1

Model construction cycle of Model Generation, Evaluation, and Modification (GEM cycle). (1) A hypothesized model is generated. (2) The model is evaluated with respect to whether it plausibly explains target observations and whether there are any problems with the model in meeting certain scientific criteria, or conflicting with observations, constraints, or other theories. If it passes, other criteria may be found for further evaluation. If it doesn’t pass and the failure is fatal, the model is rejected, and one returns anew to the Generation process. Otherwise, a new constraint on the model can be noted and attempts can be made to modify the model within existing constraints. More than one modification may be made. (3) The modified model is evaluated, and the cycle of modifications and evaluations can continue until either the investigator gives up, or the model withstands evaluation sufficiently enough to satisfy the modeler for their purposes. (Reproduced with permission from Clement, 2008, p. 84).

FIGURE 2

Spring problem. A weight is hung on a spring. The original spring is replaced with a spring made of the same kind of wire, with the same number of coils, but with coils that are twice as wide in diameter. Will the spring stretch from its natural length more, less, or the same amount under the same weight? (Assume the mass of the spring is negligible). Why do you think so? (Reprinted with permission from Clement, 2008, p. 26).

FIGURE 3

Sequence of models considered by subject S2 that led to a conceptual breakthrough in Clement (2008). Bold capitalized type below signifies major Modeling Cycle Phases; bold lower case signifies tactical heuristic reasoning processes. (A) S2 generated an analogy to long and short bending rods, and his mental simulation of the longer rod bending more implied that perhaps the wider spring would stretch more. (Panels A,C–E are redrawn from diagrams made by the subject.) (B) But using this analogy to Generate a Model of elements of the spring wire bending as it stretches leads him to Evaluate the model via a conflict with relevant observations: the slope of a bending rod increases along its length, and he infers this means the coils at the bottom would be farther apart, in panel (B); whereas he knows that real springs stretch uniformly with a constant slope in their coils and equal distance between coils, which become heeded constraints. (C) After a long period of struggling with this conflict, he simplifies to a single coil and thinks of Modifying the model by altering the rod into a hexagonal coil model. He then has a sudden AHA in inferring a new feature by mental simulation: that the forces in it will introduce a twisting effect in the wire, not just bending. He also applies a schema to the model (here the scientific concept of torsion). (D) Evaluating the hexagon as not simple enough, he Modifies the model by simplifying it into a square coil model. (He appears to imagine the situation in panel (D) as if side ‘a’ were a wrench acting at ‘x’ to twist the end of side ‘b’ through an angle, while side ‘c’ keeps the other end of ‘b’ from turning in the same direction, resulting in a twisting deformation of the metal in side ‘b’). Via mental simulation he then sees that bending and twisting ‘start over’ at each corner and do not accumulate in a square spring. This allows Evaluation of the model by explaining the relevant observation of the equal space between coils constraint, resolving the earlier anomaly for this case. He then Modifies the model further by inferring a new feature by mental simulation– that a wider square spring will stretch more, explained by its longer sides experiencing both more bending and more twisting, confirmed by an extreme case. (E) Later he negatively Evaluates the bending part of the model with a Gedanken (thought) experiment via mentally simulating a spring made of a band of metal that “can’t bend…but can easily twist” as it stretches, indicating bending is not necessary for stretching. Here, conducting a Gedanken experiment means attempting to mentally predict the behavior of an unfamiliar, concrete system (the “experiment”) designed to help evaluate a scientific model (Clement, 2009b). (This Gedanken is from a second interview simulating empirical input where S2 was told that measurements show that the primary deformation in the spring segments is a twisting or torsion effect as opposed to bending, and asked to provide a further explanation or argument for that.) See also Table 2 for condensed transcript of this entire sequence.

FIGURE 4

Time sequence diagram for three levels of model construction processes used by S2, and the resulting sequence of models. The row labeled Level 3 uses the letters G, E and M to show the Generation, Evaluation, or Modification phase of the GEM Cycle described earlier in Figure 1. The cycle is seen here as generating an alternating pattern of Evaluations and Modifications. The row labeled Level 2 shows the Tactical Heuristic Processes that helped to evolve the model in each of the above phases. These are seen as subprocesses for each phase at Level 3, as indicated by the thick black downward arrows, which mean ‘Utilizes the Subprocess’. The bottom row in the figure does not show reasoning processes or a process level, but rather the progression of new models resulting from the processes above it, as indicated by the thin blue downward arrows from Level 2 to the models underneath. The top row shows major Model Construction Modes to be discussed later, including a Model Competition Mode for deciding whether bending or twisting is the dominant model for deformation in the spring.

FIGURE 5

Maxwell’s development of E&M theory via analog models. Below, specific tactical heuristics appear in lower case bold and model construction phases of the GEM cycle appear in capitalized bold letters. Starting from Faraday’s ‘lines of magnetic force’ around a magnet, the (simplified) reasoning processes for Maxwell are: (1) Model Generation (via using an analogy): He imagined that the magnetic field is like a fluid with vortices (B) rotating in the same direction around each of the magnetic lines of force (A - Nersessian’s rendition). This qualitative model, along with incorporating a continuum mechanics theory of fluid flow (applying a schema) inspired an initial mathematical model for basic magnetic phenomena, as summarized in Table 3. (2) Model Evaluation (by evaluating internal incoherence via running the model): Mentally simulating the above system, Maxwell believed adjacent vortices would die out because of friction generated between vortices, just as gears turning in the same direction will jam if they touch (C). This cast doubt on the initial model and became a constraint. (3) Model Modification (by analogy and adding a model element): Maxwell transformed his model by adding small vortices between the larger vortices, analogous to ‘Idle wheels’ between gears, to enable the vortices to rotate without jamming or creating friction (D). He makes the simplifying assumption that fluid vortices are inelastic and do not deform. This provided a way to model electromagnetic induction (the principle of the generator) and electric current in a wire. (4) Model Evaluation (by identifying a gap in the model): Maxwell found a gap in the above model in not being able to account for static electricity and other phenomena when running the model in a mental simulation. (5) Model Modification (by altering a model element): He transformed the model again by adding elasticity to the vortices, yielding a way to model the above phenomena. (6) Model Evaluation (by running the model to predict new Evaluatory Observations): Mental simulation allowed him to predict the propagation of electromagnetic waves through space (also from equations). Confirmation of this prediction after Maxwell’s death by Hertz’s discovery of radio waves was a sensational contribution to confirming Maxwell’s theory (see summary in Table 3). (From Nersessian, 2008 p. 138, © 2008 Massachusetts Institute of Technology, by permission of The MIT Press).

FIGURE 6

Modeling Processes Framework with four levels of reasoning processes. The framework represents a process hierarchy. Higher levels are hypothesized to contain larger tasks at longer time scales. Horizontal arrows show possible sequences. Arrows between levels mean ‘Can utilize subprocess’. A subprocess can contribute to a larger goal/process above it. For example, S2’s episode 2 in Table 2 is an episode of Model Evolution at Level 4, implemented in part by Evaluate Model at Level 3, which is in turn implemented by the subprocess Ask if Model Explains Relevant Observations at Level 2, implemented via a Mental Simulation comparison at Level 1. The GEM cycle at Level 3 can be envisioned as accessing and alternating between processes on the left and right sides below it at Level 2. At Level 2, within each set (such as those under ‘Evaluate Model’). the processes are not shown in any necessary order. All processes in the figure are heuristic in being not guaranteed to work, although ‘Tactical Heuristic Processes’ is used to name Level 2 because items at that level are historically most associated with the term ‘heuristics’. Initials under each process indicate fields where it was seen in this paper: M, Mechanics (S2); E, Electromagnetism (Maxwell); G, Genetics. The great majority of processes occurred in more than one field; this provides an initial indication that those are field-general processes (others may turn out to be as well). Note that at: Level L4: Only Model Evolution processes at Level 4 are unpacked in this diagram. Level L3: Evaluation, for example, can be implemented by any of the seven subprocesses it is pointing to, in any order, singly or with more than one being used. Level L2: L2 subprocesses for Model Evaluation at L3 are a different subset from the others at L2, indicating more structural guidance in the framework. Each Level 2 process is shown as a subprocess for only one process at Level 3, except for Analogy, Simplifying Assumption and Applying a Schema, which were found to occur with either Generation or Modification here (indicated by arrow originating from the dotted box at Level 3). Level L1: Similarly, the downward arrow from a dotted box at Level 2 to Level 1 indicates that the Level 2 processes within that box can each utilize the Level 1 strategy as a subprocess (to avoid drawing a profusion of arrows).