The first objective of this paper is to assemble a collection of reasoning strategies or processes that were used during scientific model construction in the three case studies. Due to space, I will necessarily leave out a number of strategies, but I will include important ones that played a role in the most innovative, successful discoveries.

A second objective is to ask whether the processes are organized some way, such as in a series or cycle. The organization question has had proponents on both sides. An anarchistic view with little structural organization for theory construction processes stems from Feyerabend’s (1975) book Against Method. Diametrically, in an influential book, Langley et al. (1987, 2006) believed they had demonstrated via AI programs that scientific discovery could be achieved using highly organized algorithmic methods. However they did not focus on the invention of new qualitative theoretical representations or the abduction of visualizable explanatory models, which will be foci here. The types and degree of organizational structure is a difficult question that will certainly not be settled in this paper, but I hope to develop a framework that can shed some light on the issue.

A third objective is to ask whether any of these expert scientific reasoning processes can be embodied or grounded in the perceptual and/or motor systems by examining descriptions in two of the books of the possible role of perceptual/motor imagery and mental simulations in modeling at the lowest level of the framework, also drawing on a think-aloud study by Trickett and Trafton (2007).

I need to begin by identifying some large scale parallels between the three book authors. First, each agrees that mental strategies used by scientists are embedded or situated in larger material, social, cultural, and environmental systems that play an extremely important role in what Gruber (1974) called their ‘network of enterprise.’ But in the three works of interest here, and much of their history, these authors have chosen to concentrate on a variety of poorly understood cognitive strategies, as a way of focusing their energy on a central part of the problem. I will have the same focus in this paper.

Secondly, each of the authors has an approximately 40-year history of work on strategies used in science, and there is a central common finding that each of them converged on long ago. Each author describes the evolution over time of a scientific model that goes through a series of evaluations and revisions. I will describe this as a Model Construction Cycle– a pattern of Model Generation, Evaluation, and Modification (abbreviated: GEM cycle). The form of the cycle is described in the caption for Figure 1, basically indicating that a model can be constructed iteratively by an initial generation process, followed by a sequence of evaluations and modifications under constraints, unless there is a fatal flaw or major breakthrough that dictates starting over. Although this ‘GEM’ cycle is simply described, its power and centrality is supported by the fact that all three of the authors converged on its basic iterative form as central to model construction, despite working from quite different sources and using slightly different names for the three phases. [Darden (1991) describes this cycle as “(1) searching for new ideas, (2) assessing them, and (3) improving them” (p. 21), and Nersessian (2008) as a cycle of (1) Model construction, (2) Evaluation, and (3) Adaptation (p. 184). This illustrates one kind of consolidation in settling on compatible terminology that I needed to do for the consolidation.] Model construction cycles in science have also been discussed elsewhere, e.g., Shapere (1980), Nersessian (1984, 1992), Holland et al. (1986), Darden and Rada (1988), Goel and Chandrasekaran (1989), Forbus and Falkenhainer (1990), Gentner et al. (1997), Millman and Smith (1997), and Gorman (2006); and by Miyake (1986) and Clement (1989) for protocols.

Thirdly, I would characterize the three authors as analyzing detailed historical examples or protocol observations as significant constraints, to hypothesize reasoning patterns that could have produced those examples or observations. Qualitative case studies in psychology are not intended to report on data from large numbers of subjects, but the approach has considerable value in the early stages of a field area, especially in an area with highly complex or nested, interacting processes where qualitative theoretical mechanisms are sparse or uncertain (Newell and Simon, 1972; Cronbach, 1975; Campbell, 1979; Strauss and Corbin, 1998; Dunbar, 1999; Weisberg, 2006; Jaccard and Jacoby, 2010; Tweney, 2012; Ylikoski, 2019), including for in-depth psychological microanalysis studies with single subjects (e.g., Gruber, 1974; Anzai and Simon, 1979; Tweney, 1992; Gentner et al., 1997). The first desired outcome for this paper in the ‘hypothesis and theory’ category of this journal is to construct a qualitative theoretical framework or ‘field map’ of important scientific reasoning strategies for model construction, and major interconnections between them, on the basis of detailed case studies of scientific events.

To anticipate, as an advanced organizer, after reviewing strategies identified in the three case studies, a modeling processes framework describing a partial organization of the modeling strategies will be proposed at four nested levels:

The plan for the paper is to describe: (1) strategies from the three case studies at levels L3 and L2 first since level L3 is central; (2) the proposed larger framework organization; (3) strategies assigned to levels L4 and L1; (4) grounding at the lowest, and then possibly higher levels; (5) possible benefits of this organization and grounding; (6) possible directions for future versions of the framework.

A first set of strategies at Level 2 that implement the central Model Construction Cycle strategies at Level 3 can be obtained from Darden’s (1991) case study of the early history of genetics. It covers an approximately 30-year period of theory construction, from the rediscovery of Mendel’s work in 1900 to the 1930 version that is used in textbooks today. I can only describe a simplified portion of the heuristic strategies she identified here. Darden described her book as hypothesizing strategies that could have produced the historical changes she observed in the historical record. Table 1 illustrates three GEM cycles in column 3. Darden categorized each Level 2 strategy in column 2 (e.g., analogy) as one of the three GEM types in column 3 (e.g., ‘Model Generation’).

In what follows below, the more general model construction phases of the GEM cycle are capitalized in bold letters, while more specific heuristic strategies used appear in bold lower case (for those unfamiliar with the biology, the gist of the GEM cycle in column 3 of Table 1 and supporting tactical heuristics in column 2 are the most important findings here).

As shown in Table 1, Model Generation was initiated by Mendel in his research involving unitary, separable characters of pea plants, such as color and height. In expounding and clarifying Mendel’s theory, de Vries’ made explicit the simplifying assumption of the one to one relation between a visible character and the inferred underlying unit.

Mendel’s concept of a ‘character’ of the organism was eventually recognized as deficient because it did not include a mechanism explaining how characters are transmitted. This Evaluation of the model is described by Darden as identifying a gap in the model. It motivated researchers to propose the idea of a ‘factor’ (an early nascent version of the concept of the gene) that could be segregated, independently assorted, and associated with a germ cell that was transmitted to the daughter organism (I will use the more modern term ‘gene’ from this point on). The Modification process in this case was the addition of a model element. So far this provides a simple example of one round of the G-E-M cycle.

Mendel had also observed and explained 9–3–3–1 inheritance ratios for two traits of offspring from dihybrid crosses with independent assortment in peas. In the next cycle shown in Table 1, Bateson and others Evaluated the theory by finding cases with linked traits and anomalous ratios that deviated from the expected 9–3–3–1, exposing failures in predicting new observations. In response, Bateson and Punnett Modified the theory by adding model elements: their Reduplication Hypothesis specified differential duplication of some of the germ cells, producing unequal numbers of types of gametes, accompanied by elaborate diagrams of duplication patterns. As shown in Table 1, The Reduplication Hypothesis did explain the initial anomalies, but was eventually Evaluated as unsuccessful, in part because the prediction of differential cell division at early stages was never observed. In addition Morgan discovered coupled characters with other anomalous ratios exposing failures to explain relevant observations. He also argued that the necessary modifications to Bateson and Punnett’s reduplication theory to account for them would be so convoluted as to violate refined criteria for theories such as simplicity, extendibility, and avoidance of ad hocness.

In item 8 Morgan Generated his own, remarkably innovative, competing theory in response to the prediction failures in item 5 in Table 1. Utilizing the Exploratory Observations (observations not motivated by theory evaluation) from research on chromosomes in cytology, he hypothesized that linked genes were on the same chromosome, like the analogy of beads on a string, and that strings of linked genes on the same chromosome assort during meiosis rather than individual genes. Darden cites this as an example of also using interrelations with another field, here the previous observations of pairs of chromosomes in cytology. In addition he hypothesized that crossing over could occur with chromosomes able to exchange a portion of their chain of genes to explain partial coupling. This theory was Evaluated positively as having more explanatory adequacy than Bateson’s for explaining relevant observations of anomalous ratios of offspring types. Morgan also predicted observing that chromosomes break and rejoin at crossing-over points; cytologists eventually confirmed this visually in the 1930s.

In summary, we see an interesting variety of tactical heuristics used in column 2, Table 1. The overall pattern in column 3 of Table 1 shows a Modeling Cycle: a cyclical repetition of model Generations, Evaluations and Modifications which correspond to Figure 1. Darden describes such GEM cycles as central, and lists each of the smaller tactical heuristics within one of those three categories in her book summary¹.

In Clement (2008) experts were videotaped working on unfamiliar explanation problems using think-aloud procedures (Ericsson and Simon, 1984). They were professors or doctoral students who had passed comprehensives in a variety of technical fields. One task used was the target problem in Figure 2. The reader may enjoy generating ideas on it, including informal ones, before reading further. I will focus here on the solution of a single subject S2, who produced the most productive solution and explanation for the spring problem, because it eventually will enable me to illustrate all four levels of the framework compactly. In the protocol, S2 not only predicts correctly that the wide spring stretches more, but also confirms that and answers ‘Why?’ by inventing a model for how a spring wire deforms during stretching and how it provides a restoring force back in return. He initially thinks that the spring wire is bending, but then detects a serious problem with that model. He eventually experiences an Aha! event and improves the model by hypothesizing that the wire is twisting when it is stretched. That discovery represents a conceptual change in identifying a new hidden variable and causal mechanism for stretching. It is also a marked conceptual breakthrough because the subject was stuck in the bending model for a considerable period of time, suggesting that he had to overcome an idea fixation or set effect. Twisting of the wire and the resulting torsional strain is in fact the most important source of stretching and restoring force recognized by engineers (Appendix I in Supplementary Material contains an introduction to the concept of torsion).

The sequence of models generated by S2 is shown in Figure 3, and the caption describes how they emerge from phases of the GEM cycle and the smaller strategies used for each phase in it. A corresponding, condensed transcript is shown in the first column of Table 2. As the reader reads down the transcript there, items in bold in the Level L2 column show the tactical heuristics used to implement the model construction cycle in the Level L3 column (similar to the cycle in Table 1 for genetics). Levels L1 and L4 will be discussed later.

Figure 4 shows a summary of three of the levels of reasoning processes (strategies) used by S2. The rows labeled Level L3 and Level L2 show several Model Construction Cycles as the initial bending model was Generated, then thrice Evaluated and Modified, until it included twisting as well. The thick downward arrows in Figure 4 also show the sense in which the more specific Tactical Heuristic Reasoning Processes at Level 2 can be considered subprocesses for the more general Modeling Cycle Phases at Level 3; each subprocess at Level L2 contributes to the larger process above it. Later the subject distinguishes between confidence in his answer to the spring problem, which has been high, and confidence in his understanding of it, and estimates that his torsion idea has increased his understanding of the system from “way, way down” up to “like, 80%.”

In conclusion we see that for levels L2 and L3, S2 is using several of the same strategies identified in the genetics episodes in Table 1, including the three parts of the GEM cycle, plus Analogy, Simplification, Addition of a model element, and evaluation of whether it Explains relevant observations. These and other Tactical Heuristic Reasoning processes enabled him to make a conceptual breakthrough in an Aha event and to reconceptualize his explanatory model for the spring system².

A similar model construction cycle was described by Nersessian in the case of Maxwell. I will not go into his mathematical results, but outline the series of qualitative mechanical models he used since that is the focus here and for Nersessian (2008). Nersessian’s book weaves together historical analysis and a survey of previous psychological research on mental modeling, mental simulation, analogy, and thought experiments, analyzing how those processes work together for creative reasoning and conceptual change.

The Figure 5 caption describes a progressively more complex series of qualitative analogical models constructed by Maxwell on his way to developing his final equations. The sequence in Figure 5 represents three passes through a cycle of model evaluation and modification, as summarized in Table 3, right-most column. Notably, Nersessian shows how tracking and accumulating constraints is important. Negative evaluations often provide constraints for the next modification process, not just disconfirmation. This is especially important for Nersessian in dealing with Maxwell’s case, because the mechanical models suggest abstract constraints that he can reflect in his mathematical models, via a Generic Abstraction process, even though he must in the end give up most or all concrete aspects of the mechanical models he used. Another strategy is Apply Schema(s) to a Model. This refers to accessing and applying one or more schemas that have not been applied to the phenomenon before. Maxwell adapting ideas from the new science of continuum mechanics to E&M theory is one example. Nersessian also finds many parallels between processes she identifies in one of the Clement (2008) protocols and Maxwell’s processes; this is also seen in Tables 2,3³. In sum, even though Maxwell’s objective was to reach a quantitative theory at an extremely high level of abstraction, Nersessian argues that his development of the theory, remarkably, depended on a series of visualizable qualitative models generated by a GEM cycle.

Thus far a consolidated set of important modeling strategies from the three authors has been examined at Levels L3 and L2 in Tables 1–3, as follows:

The importance of the strategies was indicated by their significant participation in episodes of insightful model construction and conceptual change. I can now propose the Modeling Processes Framework in Figure 6, which depicts an organizational structure for the above strategies at levels L3 and L2 and more, as described in the caption. The framework is constrained by the historic and protocol events analyzed in this paper from the three books, and it outlines a set of 24 processes that could produce them, drawing on the three authors’ hypotheses wherever possible. Again, all 24 are considered processes, strategies, and heuristics, so those terms are used more or less interchangeably here. The four levels shown were introduced in the “Abstract” and the “Introduction” sections.

As a starting point the GEM cycle shown at Level 3 in Figure 6 (abbreviated from Figure 1) represents a major convergence between the three authors. Additional structure can be added by hypothesizing that heuristics come in several different task ‘sizes’ and can be placed in corresponding levels. Craver (2007) and Wright and Bechtel (2007) note that the term ‘levels’ has been used in many ways. Here I use downward arrows to signify that larger processes at a higher level of organization are implemented via smaller subprocesses at a lower level (as in Figure 4). For example, the arrows from a process at Level L3 to Level L2 in Figure 6 indicate ‘subprocesses to try’ at Level L2, any one of which may or may not be sufficient, as ways to implement the process at level L3. Higher level processes are also hypothesized to typically take more time (Newell, 1990; cf. Nathan and Alibali, 2010). The figure also shows that the great majority of processes occurred in more than one field (see caption), providing an initial indication that those are field-general processes. Interestingly, the L2 strategies serving Evaluation at L3 are separate from those serving Generation and Modification. Thus, with many unordered subprocesses, the framework depicts a partially organized structure for heuristic modeling processes. It focuses on the processes identified in Tables 1–4 and certainly does not attempt to describe all processes used in science. From here I will use the shorthand L1 to L4 to designate levels. The framework builds on a smaller subprocess hierarchy framework for L1, L2, and L3 described in Clement (2008, p. 479). Two-level organizations at L2 and L3 were described in Nersessian (p. 184–5) and more broadly in Darden (1991, Chapter 15). All of the authors make the point that more than one L2 process can sometimes be involved in achieving a goal within a single L3 phase (as seen in Tables 1–3). Although none of the three books proposed a separate Level 4, each of the authors described most of the processes that I have shown there, to be discussed in the next section, followed by Imagistic Processes at Level 1.

Lindley Darden and Nancy Nersessian were kind enough to critique a draft of this paper, and approve of the summaries of important strategies from their work as sources contributing many items to the framework in Figure 6, while understanding that I necessarily could only represent a condensed portion of their analyses in the space allowed here (e.g., Figure 6 does not include the additional strategies listed for each author in footnotes to their summaries above). Any remaining errors are of course my responsibility.

Figure 6 shows several large-time-scale modes of scientific modeling hypothesized to operate at Level 4. So far I have considered only the Model Evolution Mode, which, as the main mode focused on in this paper, is the only mode that is unpacked in the framework at the lower three levels. For that reason the other four modes at Level 4 are only briefly described in Table 4 with examples. These modes are:

Once a qualitative model has support, a modeler can pursue any of the processes to the right of Model Evolution at L4 in Figure 6, until they reach a level of satisfaction that fits their purposes at hand. Adding the last two modes in the list above yields three possible (nested) cycles in the framework: the GEM cycle at L3, operating within the larger ‘Degree of Precision’ and ‘Level of Explanation’ cycles at L4 (Clement, 2008). This means the GEM cycle and processes below it are hypothesized to still be important as mathematical precision is increased, but with parameter manipulation and deduction (and recently computer simulation) becoming increasingly important at L1.

The downward arrow from a dotted box at L2 to L1 in Figure 6 indicates that the L2 processes within that box can each utilize the L1 process below it as a subprocess. I first describe these L1 processes and then summarize arguments that they are imagistic processes.

In posing this question I noted that the terms ‘embodied’ or ‘grounded’ have come to have many potentially confusing meanings (Wilson, 2002). Here I will focus on one meaning– that a cognitive process can utilize the perceptual and/or motor systems in the brain as a componential part of its operation. I will use the term ‘perceptual-motor grounding’ or ‘grounded’ for short with this meaning to help avoid confusion here with other meanings of ‘embodied.’ My focus on it fits the sources I am analyzing, and it is not at all to deny the importance of others investigating other embodiment and ‘4E’ issues.

There is now widespread agreement that visual imagery is grounded in the sense that it uses the perceptual systems in the brain, based on considerable evidence as reviewed in Kosslyn (1994), Kosslyn et al. (2001), Svensson and Ziemke (2004), and Ganis and Schendan (2011). Schendan and Ganis (2012) conclude that “direct neural evidence reveals that top-down processes of mental imagery sustain an imagistic representation that mimics perception well enough to prime subsequent perception and cognition.” Reviews by, e.g., Jeannerod (1994, 2001), Decety (1996, 2002), Gre‘zes and Decety (2001), and Kilteni et al. (2018) provide similar conclusions for motor imagery as vicarious motor actions that can participate in mental simulations. Together these studies conclude that perceptual and motor imagery involve and make substantial use of largely the same perceptual and/or motor regions in the brain as used in real perception and action.

The above findings imply that when the Mental Simulation and Structural Transformation processes utilize imagery (perceptual and/or motor), they are grounded in the sense of utilizing the perceptual and/or motor systems in the brain. These two processes shown at L1 in Table 2 occur throughout S2’s protocol segments in conjunction with multiple types of imagery indicators. On the basis of this and other protocol data in Clement (2008), I concluded that these two L1 processes can utilize imagery, and we have substantial evidence from those cited above that imagery is grounded. Nersessian (2008) argued that Maxwell used these two imagistic processes, and Trickett and Trafton (2007) argued that scientists from six other fields were using dynamic, visualized mental simulations in data analysis tasks. Thus there are reasons for believing that the L1 reasoning processes of mental simulations and structural transformations can be grounded in the perceptual and/or motor systems of expert scientists. This conclusion, if true, is very much at odds with older traditional computational accounts of cognition, in that at least part of the knowledge representations are imagistic and modal, rather than consisting of amodal, language-like symbols, and that these are analog in preserving at least rough, schematic correspondence relationships to the spatial forms or behaviors of the entity being represented. In addition, reasoning can be conducted by dynamic processes such as mental simulation that coordinate imagery of actions or events that unfold over time, as opposed to reasoning via discrete logical operations or rules on static symbols. An implication is that the cognitive system does not always operate independently from the perceptual and motor systems, but rather can be closely intertwined.

One might ask whether the above argument is pre-empted by Barsalou’s all-encompassing theory that implies that all concepts may be grounded, modal ‘simulators.’ However, Barsalou states that his theory is controversial and in need of evaluation, especially with respect to advanced, abstract concepts or reasoning processes, and although I resonate in spirit with much of it, I have not wanted to take it as an assumption here. Rather, I want to see what positions are suggested independently by the case studies with regard to reasoning processes in science. Thus it was not just assumed from the outset here that L1 processes involve modal imagery and are grounded; hence the attention to Nersessian’s, Trickett’s and my own findings that support that. And although much of the research on grounded cognition has focused on the nature of knowledge concepts used in everyday conversation or activities, e.g., Barsalou (1999, 2009), the focus here has been on proposing that expert scientific reasoning that is capable of generating novel scientific models and inferences, can be grounded. One can also ask whether L2 or higher processes can be grounded, and this question will be examined in the discussion.

A broader related issue of situated or extended cognition is the role of external spatial representations, such as diagrams. Larkin and Simon (1987) described several possible advantages for using diagrams during problem solving, including supporting perceptual recognition, inferences, and order of search clues. They also speculated that these might also be advantages of internal imagery representations. All three book authors plus Trickett and Trafton (2007) hypothesized that diagrams can be an external support for modeling.

Darden (1991) included “Introduce and Manipulate a Symbolic Notation,” including diagrams, as a model generation strategy. Nersessian (1992, 2008) noted that Maxwell’s papers contained key diagrams, and remarkably, that his readers were instructed by him as to how to mentally animate them. Diagrams do not show animation and sometimes other features directly, and for S2 I have inferred that internal imagery was used, when evidenced by related action gestures animating a diagram like that of the hexagonal coil (protocol section 4), or by the subject’s speaking of relevant invisible features in a diagram. These both also indicate that the diagrams were insufficient on their own for representing certain relevant features.

Hegarty et al. (2003) studied students learning from diagrams about a device and found that learning was enhanced by asking them to make predictions about the behavior of its components, suggesting the importance of mentally animating static diagrams. In Trickett and Trafton (2007), spatial diagrams of observation patterns were provided as the main data sources for scientists to work from, and they detected scientists’ mental simulations of models, many of which were mentally projected onto the presented diagrams. Comparing via an internal simulation placed over an external image, is one species of what Trafton et al. (2002) and Clement (2004, 2008, 2009a,2018) termed an ‘alignment,’ or ‘overlay simulation,’ respectively, and since it is a possible method for evaluating an imagistic fit between an analogy and a target, or between a theoretical model and observations, it represents a very interesting form of extended cognition (cf. Vankov and Kokinov, 2011). See additional work on diagrams in, e.g., Hegarty et al. (2003), Gooding (2006), Craver and Darden (2013), Tversky (2015), Bechtel (2017), and Chandrasekharan and Nersessian (2017).

Regarding theoretical aspects of the framework, so far an attempt has been made to consolidate processes (strategies) and build on the GEM cycle identified by the three authors, introduce explicit levels in Figure 6, hypothesize greater size and time scales at higher levels, interpret the connections between levels as subprocess relations, move some larger processes the authors identified into a fourth Level 4, and hypothesize two other types of cycles there. I have also attempted to clarify the distinction between simulation and transformation processes at Level 1, and argue that these processes can be imagistic and grounded in the perceptual-motor systems, on the basis of think-aloud and neurological studies. The framework may also be viewed as a working typology of heuristics by different levels.

The hypotheses above were formed under many important constraints. Figure 6 partly serves as a record of 24 functionally diverse processes consolidated from the case studies in that each item in it corresponds to a process type derived from the books, shown in Tables 1–4⁴. The vertical and slanted arrows in Figure 6 also correspond to the types of L3–L2–L1 connections between processes that were indicated one or more times in Tables 1–3. Thus the framework is constrained for now by showing only the processes and vertical connections documented in the tables, plus the GEM cycle pattern there, and those framework components and structure have a basis in that sense. But the framework is expandable. Figure 6 suggests that most of the heuristic processes are field-general rather than field-specific. This complements the significant heuristics identified in Langley et al. (1987), many of which were field-specific or topic-specific (though some may be generalizable).

A first result is that scientists use a considerable number of modeling processes–more than one might think– (at least the 24 indicated in Figure 6, with more in the books), complementing other studies that go into depth on a few heuristic processes. Most were field-general in appearing in more than one study. A major advantage for science is having multiple processes to try, important since heuristics can fail to work. For example, the framework presents a broader view than blind variation or prior concept combination alone being fundamental for creativity: e.g. combinations can arise from repeating the “Apply Schema to Model” or “Analogy” processes at L2; and non-blind variations can arise from “Altering Model Elements within Constraints” at L2 (cf. Chan and Schunn, 2015a, who provide evidence for the advantages of conducting improvement cycles in addition to conceptual combinations in product design).

In summary, the modeling processes framework in Figure 6 contains a consolidated set of important, mostly field-general reasoning processes used during episodes of innovative theory construction. Since its heuristic processes are only sometimes useful with uncertain utility individually, possible strengths of the framework have been proposed that may help explain how such processes can work together to produce successful and innovative scientific models. These include its wide range of processes to try, its flexible, organizational structure via cycles and hierarchical subprocess relations that provide partial guidance and allow it to balance sources of divergence and convergence for creativity, and the hypothesized benefits of grounded imagistic processes at L1. These strengths may begin to explain how the framework can function as a relatively powerful coalition of processes for constructing innovative scientific models even though each process has uncertain utility. By continuing to investigate how heuristic processes can be organized, we may add clarity to their purposes, structure, and functioning.

For reasons of focus this paper concentrates predominantly on reasoning processes. Knowledge representations for models, observations, cases, sources, and constraints have not been addressed except to say that imagery can be heavily involved, and I will briefly steer the reader toward questions raised and work by the three authors on this issue.

In future modeling the framework may need to be ‘softened,’ to account for other phenomena such as those in Clement (2008) that seem less controlled, e.g., the generation of multiple divergent ideas at ‘brainstorming’ points; ‘off task’ remindings, or the sudden new application of a knowledge schema. These could be explained by spontaneous spreading activations (perceptual or verbal) to knowledge schemas, as could S2’s Aha! in section 5 of Table 2 involving the sudden activation of twisting and torsion schemas from running the newly created hexagonal coil model.

But the latter insight also involves an interruption of the subject’s current reasoning process, as he suddenly switches from examining the bending model to evaluating the twisting idea. Combined with the problem of how unordered subprocesses in the framework are selected, these phenomena also imply less control over reasoning strategies and more flexibility than a more strictly programed hierarchy. One can speculate that to explain these phenomena, future versions of a modeling framework should include: (1) spreading activation of knowledge schemas; (2) parallel activation of alternative strategy units in the framework, with a number of sources influencing which strategy becomes activated most strongly and implemented. This would allow for competition resolution mechanisms for decisions between unordered substrategies, and opportunistic interruptions of a process (cf. flexible, hierarchical, competitive activation networks for actions in Norman and Shallice, 1986; Anderson, 1993; Thagard and Millgram, 1997; Cooper and Shallice, 2000; Hommel and Wiers, 2017). These features could be combined with the present framework in Figure 6 as properties of connections and strategy units that bias and incline but not always require the scientist to activate and use the subprocesses and sequences shown, in what one might term a ‘soft hierarchy.’ Allowing interruptions from spontaneous activations of schemas would add variation and divergence to idea generation in the framework, moving the framework somewhat further from the ‘sighted’ end of Simonton’s (2018) scale of degrees of sightedness. One could also include redistribution of activations after negative feedback from model evaluations (Ohlsson, 2011), plus process preconditions, utility and cost estimates, and bounded rationality limitations such as limited working memory resources for goals, plans, imagery, and verbal processing (Altmann and Trafton, 2002; Jilk et al., 2008). The collective features above could contribute to explaining the above phenomena indicating less control but greater flexibility.

Another implication, partially analogous to parallel activation across levels in Cooper and Shallice’s (2000) and Cooper’s (2019) multi-level action hierarchies, is that one could envision a connected subprocess string of three processes at L3, L2, and L1 (e.g., model modification via adding an element via an imagistic structural transformation in Figure 6), each staying activated in parallel to some degree during their operation, with the L3 and L2 processes each ‘monitoring’ the results from those below them for completion. All three processes might also be attending to an imageable model representation simultaneously. This would suggest the alternative possibility of a more direct form of ‘entrained’ parallel grounding of L2 and possibly L3 processes rather than only the serial form of componential grounding of ‘calling’ a grounded subprocess at L1. Indeed, in instances like episodes 7B-C in Table 2 the L1–L2–L3 relationship appears to be so simultaneous, tightly coupled, and entrained, and the dynamic perceptual-motor imagery appears to be so central to the L2 and L3 processes, that it could support referring to their ‘entrained grounding.’

These indicate some possible directions for future research. Because of the similar patterns in the three book studies and the Trickett and Trafton (2007) paper reviewed here, I have proposed the partial serial, cyclical, and hierarchical levels organization of the processes in the framework in Figure 6 as a first order model, while recognizing that similar patterns of connections in future models may take the form of activation contributions amidst bounded capacities. This may relate to those advocating pluralistic models of serial and parallel processes (e.g., Jilk et al., 2008; Trafton et al., 2013), with higher levels in a hierarchy involving more sequential control over longer periods, and lower levels involving faster, parallel processing of imagined perception and action.