Navigating the landscape of learning, where multiple routes can deepen rather than dilute understanding.

A Clearing

In the foyer of the ÀNI Art Academies Waichulis, there is a poster that I am quite fond of, titled “Navigating the Learning Process.” It illustrates mechanisms of learning within two broad categories: those often associated with rote learning (repetition, chunking, fluency, acronyms) and those associated with meaningful learning (metaphor, representation, communication, and problem-solving). The background for this poster is a graphic depicting layers of trees, intended to suggest a forest. That background is not simply an aesthetic choice; rather, it is a nod to a metaphor I often use to communicate how learning “happens”. Over time, I have come to call that metaphor the cognitive forest.

The explanation goes a little something like this…

Imagine standing in a small clearing in a vast, dense forest. Everything in that clearing belongs to a concept you have already developed. Let us say the clearing concerns the idea of a brick wall. Within that space are the basic features of the idea: bricks, mortar, arrangement, load, proportion, structure, and function. You understand that bricks and mortar can be combined in a certain way to make something that stands or functions in a certain way. You may also understand that the wall’s integrity depends on the relation between its parts. Too little mortar can cause the structure to fail, while too much mortar can compromise it in another way. If someone references a brick wall, you can “go” to that clearing and find enough there to navigate the idea successfully.

In cognitive terms, this clearing resembles what researchers often call a schema: an organized structure of prior knowledge that helps us interpret, remember, and learn new information (Van Kesteren, 2013; Brod, Werkle-Bergner, & Shing, 2013). It is not a perfectly bounded container, nor a little picture stored somewhere in the brain. It is better understood as a functional organization of associations, such as features, relations, memories, expectations, perceptual patterns, and possible actions that can be recruited when a situation calls for them. That brick-wall clearing did not appear from nowhere. It was cultivated and established through and from earlier clearings: experiences with objects, weight, stacking, construction, stability, failure, enclosure, and so on. Some of those experiences are personal and developmental (what we might call ontogenetic). Others depend on perceptual and neural capacities that are part of our inherited biological equipment (what we might call phylogenetic). We are not born with a mature concept of a brick wall, but we are born with nervous systems already prepared to detect patterns, edges, surfaces, objects, spatial relations, regularities, and consequences. Those early capacities provide some of the first footholds from which later learning, or clearings, can proceed.

This matters because comprehension or understanding usually requires some available place to emerge from; something it will often remain attached to. For example, when I was first learning about the makeup of oil paint, I remember being told that the relationship between pigment and vehicle (a drying oil) was like the one between bricks and mortar in a wall. Too much oil or pigment in the mix can compromise the strength and longevity of the paint film. That analogy did real work. It was a path from an existing clearing (schema) to the creation of a new one that I labeled “paint film”. I could import what I already understood about proportion, binding, structure, and failure in one domain to begin understanding another. In more academic language, this is a case of analogical transfer: using relational structure from a familiar domain to reason about a less familiar one (Gentner, 1983; Day & Goldstone, 2012). Without that brick-wall clearing, I would have needed to approach the new idea through some other route. Perhaps food, glue, suspension, sediment, or another familiar structure. The point is that I would still have to reach an understanding from somewhere.

This is why I often cringe a bit when I hear the flashy instruction to “forget everything you know.” The sentiment may sometimes point toward something legitimate: a student may have a bad habit, a faulty assumption, or an unhelpful framework that needs to be revised. But taken literally, the advice collapses almost immediately. There is no clean slate waiting to receive fully formed concepts. Understanding and comprehension depend on the association, modification, differentiation, and reorganization of what is already present. Meaningful learning, as psychologist David Ausubel famously argued, is strongly shaped by what the learner already knows (Ausubel, 1968). When there are fundamental issues in a particular field of learning, the task is not to “erase” the forest, but to prune, redirect, and cultivate it.

Now, some of you may already be thinking about a potential regress problem here, and it is worth addressing. What I mean is that some of you may be wondering, “If each new clearing depends on prior clearings, where do the first ones come from?” The answer is not that infants arrive with fully formed concepts of color, space, painting, or brick walls. Rather, early learning begins with biologically available perceptual systems and developmental experience. The nervous system is already organized in ways that make some distinctions, regularities, and associations easier to form than others (a phylogenetic contribution). Experience (ontogenetic) then strengthens, weakens, and reorganizes those patterns over time. This is why prior knowledge can powerfully shape later memory and learning, and why learning is often described as linking new information to existing knowledge structures (Brod et al., 2013; Van Kesteren, 2013).

So when I speak of the cognitive forest, I am not using the forest as a loose metaphor for “all of cognition.” I mean something more specific: the developing terrain of concepts, schemas, associations, and routes by which one idea becomes accessible through another. A clearing is a usable schema or region of understanding. A path is a mechanism, such as an association or analogy, that enables movement and dynamism between regions. A route is a chain or relevant network of connected clearings. A new clearing arises when experience is organized into a usable structure of understanding that can be revisited, reconfigured, expanded, and connected to others.

And, of course, as you, the reader, have probably already realized, I am doing the same thing here. To explain learning, I am asking you to begin with a forest; something far more familiar to most readers than the technical machinery of schema theory, analogical transfer, or associative learning. From that familiar clearing, I am attempting to cut a path (via metaphor) toward a new one. With any luck, this clearing can become useful enough to grow, branch, and lead elsewhere.

Rote Tools and a Meaningful Network

In education, it is common to distinguish between what is often called rote learning and meaningful learning. The distinction is not new. In the 1960s, Ausubel described rote learning as the acquisition of information without integration into existing knowledge structures, and meaningful learning as the process by which new information becomes anchored to what the learner already understands (Ausubel, 1962; 1968). Within the cognitive forest, these two modes of learning operate in fundamentally different ways.

Rote learning is usually defined by memorization without meaningful integration. It often involves repetition, drill, and memorization strategies, including some mnemonic devices, that prioritize recall over understanding, elaboration, or semantic integration. It uses mechanical repetition to create fast, automatic recall. As such, rote equips the learner with tools to cut through terrain. Repetition, some forms of chunking, fluency strategies, and acronyms can be highly effective for information access, reducing the immediate burden on working memory and helping to stabilize fragile knowledge during early stages of encoding and consolidation. But what they often produce, by themselves, is not yet a rich pathway or clearing, but a tool that can help establish one. More specifically, in our cognitive forest, they function more like an axe, chainsaw, or machete, allowing you to more effectively and efficiently establish your way to a specific destination.

Rote learning mechanisms can be absolutely invaluable and even downright necessary in many cases. They can be extremely reliable, and in many scenarios, that reliability depends on stability. A mnemonic device like “Every Good Boy Does Fine” does not need to evolve as your understanding of music deepens; rather, it can remain fixed, and that invariance is precisely what makes it useful. However, that stability comes with a limitation. What is built through rote processes tends to remain locally bound unless it becomes integrated with other knowledge. It can be accessed and applied in familiar contexts, but it does not readily reorganize or extend itself when the terrain shifts. If a problem arises in which the required information is displaced from a familiar context or the entry point changes, you may find yourself reaching for the same tool without a clear way to adapt it.

By contrast, knowledge developed through meaningful learning becomes integrated into a broader network of relationships. As new experiences accumulate, earlier understandings can be reinterpreted, refined, and sometimes fundamentally restructured through processes such as reconsolidation and schema modification. These changes need not remain isolated. They can influence related ‘clearings’ across the network. They can propagate, altering related “clearings” across the network. This difference is reflected in research showing that information learned through rote processes is less likely to support transfer unless it becomes meaningfully connected to existing schemas, whereas integrated knowledge structures are more flexible and adaptable across contexts (Shuell, 1986; Kember, 1996).

When learners engage through metaphor, representation, communication, or problem-solving, they begin to establish new routes and clearings that can be revisited, extended, and recombined. These processes do more than store information; they reorganize it. In cognitive terms, they support the integration of new material into existing schemas through elaboration, abstraction, and analogical mapping (Ausubel, 1968; Day & Goldstone, 2012). Over time, these routes become more stable and more numerous. The learner is no longer limited to a single point of entry or a single way forward. If one path is blocked, another can be taken. The terrain becomes navigable to an increasingly adaptable traveler.

This is where flexibility emerges. A learner who relies primarily on rote tools may perform very well under narrow, familiar conditions but struggle when asked to adapt. A learner with a more developed network of connections can adjust more readily, not because they have memorized more, but because they have more ways to get there. None of this is to suggest that rote tools are of lesser value. A saw or machete is very often necessary when trying to form a path or a clearing in a forest. In fact, early in learning, when the terrain is dense and unfamiliar, these tools can provide critical access. From the perspective of cognitive load theory, strategies that reduce immediate processing demands can make the difference between engagement and overload (Vogel-Walcutt et al., 2011).

The Mistake of the Single Map

As some of my readers here may have experienced, there is a persistent tendency (particularly in technical and educational circles) to seek or promote a single, optimal representational system. And this is not an unreasonable stance. Accuracy and precision are incredibly valuable in many, many situations. And of course, consistency matters. I would not be one to argue that higher-resolution models cannot preserve or reveal more information. But when these things are paired with the idea that knowledge is best organized within a single, maximally accurate framework across all contexts, we may quickly find a disconnect with how cognition actually operates.

Research in learning and cognitive science shows that understanding is often supported by the use of multiple, well-coordinated representations rather than a single dominant one. Different representations highlight different aspects of a concept, support different inferences, and provide alternative routes for access and application (Ainsworth, 2006; Rau & Matthews, 2017). In complex domains, no single representation is generally sufficient to support flexible understanding across the full range of relevant contexts. Instead, learners benefit from coordinating across multiple frameworks, each with its own strengths and limitations.

Within the cognitive forest, relying on a single “map” is like insisting that every movement through the terrain must follow one fixed set of coordinates. This may work under controlled conditions, but it does not reflect how navigation typically occurs. Movement through the forest depends on a range of resources—paths, landmarks, regions, and prior routes—each contributing in different ways depending on the situation.

A highly precise system can be invaluable, particularly when fine distinctions are required. But precision alone does not guarantee accessibility, flexibility, or transfer. In many cases, coarser or more intuitive frameworks provide critical entry points, helping learners establish initial connections that can later be refined or reorganized. The issue, then, is not only whether one system is more “correct” than another. It is whether a system contributes meaningfully to the development of a connected, navigable landscape of understanding.

In fact, one measure of a deepening understanding may be the number and quality of routes by which a concept can be reached. A clearing that can only be accessed from one direction may remain fragile. If that route is blocked, the learner may be unable to proceed. But when a concept can be approached through formal description, metaphor, practical examples, perceptual experience, analogy, and problem-solving, it becomes more stable, flexible, and readily usable. The point is not to multiply representations for their own sake, but to cultivate meaningful paths that converge on, refine, and strengthen the clearing.

Model Granularity and Cognitive Utility

Across many domains, we find that the same phenomenon can be described with different models at multiple levels of detail. Each one can be evaluated by purpose, assumptions, scale, predictive power, explanatory usefulness, tractability, and fit to evidence. In computational neuroscience, for example, models of the neuron range from highly simplified logical abstractions, such as the McCulloch–Pitts model, to far more biologically detailed formulations, such as the compartmental modeling approach developed by Wilfrid Rall (McCulloch & Pitts, 1943; Rall, 1959/1962; Segev, 2018).  These models are not necessarily in competition in the way one might assume. Each is constructed with a particular purpose in mind, and each affords different kinds of insight depending on the task at hand.

The McCulloch–Pitts model, for instance, treats the neuron as a simple threshold unit that produces a binary output, analogous to “firing or not firing”, based on its input. It ignores most biological detail, but in doing so, it makes it possible to model large networks and reason about logical structure and computation. By contrast, Rall-type models incorporate far more considerations, such as spatial structure, membrane properties, and signal propagation along neuronal components called dendrites. These details make them far more useful for understanding the physiological behavior of real neurons, but also far more computationally demanding and less tractable for large-scale abstraction. The question, then, is usually not which model is “true” in any absolute sense, but which level of granularity is appropriate for what one is trying to do.

This same principle applies well beyond neuroscience. In painting, we see something similar in the way color is organized and communicated. The Munsell system offers a highly structured, three-dimensional model of color space with fundamental dimensions of hue, value, and chroma (Munsell, 1905). This model is designed to organize color according to perceptual dimensions and to support relatively precise specification and comparison of colors. It is an extraordinarily powerful system when fine discrimination, calibration, or consistent communication is required.

But alongside it, we find much simpler frameworks, such as the Itten color wheel, that persist in both teaching and practice. These systems do not attempt to map color space with the same perceptual precision. Instead, they illustrate basic categorical relationships among hues, especially for teaching contrast and the concept of complementarity, and offer a very general view of how the hues of colorants may seem to behave in many subtractive mixing contexts. They compress the complexities of color into a more abstract form, even if that compression introduces distortions relative to more formal models.

The persistence of simplified abstract models despite the availability of more formal, higher-resolution systems is not difficult to explain. Simpler systems reduce the complexity of the domain to a level that is easier to manage in real time, often amid complex tasks where working memory resources can become heavily taxed. They foreground certain relationships while compressing or omitting others, sometimes at the cost of precision. In doing so, they can support rapid judgment, general communication, and effective decision-making in contexts where the full precision of a higher-resolution model may be unnecessary or even impractical. A painter making quick adjustments on a palette, or a student trying to grasp basic color relationships, may benefit more from a system that is immediately accessible than one that is maximally precise.

This is not a matter of one system replacing another, but of different systems offering different affordances.

As I have argued elsewhere and often, many of the stronger claims surrounding these devices do not withstand careful scrutiny (Green, 1995; Palmer, Schloss, & Sammartino, 2013).  In some cases, additional detail can make a system more difficult to use without providing a proportional benefit for the task at hand. Lower-resolution models can preserve enough of the underlying structure to remain effective, particularly when they serve as entry points for learners or as tools for quick, situated decisions.

Within the cognitive forest, this distinction is easy to recognize. Not every movement requires a fully detailed map of the terrain. There are times when a high-resolution representation is indispensable, and others when a simple marker, a familiar route, or a coarse boundary is more than sufficient to move forward. The issue, once again, is not which representation is most complete. It is the representation that allows the learner or practitioner to navigate effectively within the constraints of the situation.

The Case for Warm and Cool Colors

A recent discussion with a colleague brought this topic to the forefront for me. The debate over the utility of “color temperature” as a color descriptor or pedagogical device in art illustrates this tension clearly. Critics of warm and cool distinctions often point out that they are inconsistently defined, culturally variable, and largely redundant when compared to more structured systems such as hue, value, and chroma. In one sense, these criticisms are not without merit. Warm and cool do not function as precise technical dimensions. They do not map cleanly onto a single axis of color space, nor do they offer the kind of consistency that more formal systems are designed to provide.

But stopping the analysis there misses what these distinctions are actually doing.

Warm and cool operate less like coordinates and more like associative frameworks. They draw on recurring perceptual, ecological, and pictorial experiences, such as firelight, sunlit surfaces, shade, atmosphere, proximity, and distance, and use those associations to organize visual information in an immediately accessible way. These associations are not wholly arbitrary, even if their boundaries are not rigid. They reflect regularities in how humans often experience, interpret, and pictorially organize visual environments.

In this sense, warm and cool function as a kind of context-sensitive embodied heuristic. They provide a way to group and compare colors that supports rapid judgment, communication, and decision-making, particularly in contexts where formal analysis may be too slow or unnecessarily complex. Their variability is not simply a flaw; it is partly a consequence of their flexibility as context-sensitive tools. Importantly, they are not replacements for precise descriptors of hue, value, and chroma. They do not attempt to serve the same function. Rather, they offer an additional pathway, another way of moving through the cognitive forest. And when that pathway is properly connected to others, it can deepen rather than dilute understanding. A painter might understand the precise hue relationships within a passage while also recognizing a broader warm–cool shift that organizes the image at a different level.

To reject warm and cool entirely on the grounds that they are imprecise is to apply the wrong criteria. It assumes that all useful frameworks must operate with the same level of formal definition. But as we have seen, cognition does not depend on a single, perfectly specified system. It depends on the availability of multiple, overlapping representations that allow for flexible access, interpretation, and action. From that perspective, the question is not whether warm and cool meet the standards of a formal color model. It is whether they contribute to the development of a more connected, navigable understanding of color. And for many learners and practitioners, they absolutely do.

But What is a Continent? 

In a recent conversation about practical and pedagogical utility, ÀNI president Jeremy Sinsimer mentioned another very useful case study for understanding the utility argument, namely, how we navigate certain aspects of geography. Believe it or not, there is no universally agreed-upon definition of what constitutes a continent (Lewis & Wigen, 1997; Encyclopedia Britannica, 2026). Depending on the tradition, the world may be divided into six or seven continents, with certain landmasses grouped or separated for historical, cultural, and practical reasons.  Boundaries such as that between Europe and Asia are not strictly determined by clear geological separations, but are instead shaped by historical, cultural, and practical considerations. Such separations can be difficult to justify on purely physical grounds.

And yet, in ordinary communication and education, the concept of continents remains nearly indispensable.

Why?

Because it enables efficient communication. It is often far more practical to refer to “Asia” than to specify a set of latitude and longitude coordinates. The term immediately provides a coarse but functional sense of location, context, and relation. It allows people to orient themselves quickly within a complex system. Continents are not precise. They are not scientifically uniform categories under a single fixed criterion. But they are cognitively useful abstractions; tools that compress complexity into a form that supports navigation, communication, and understanding.

Devices like the Itten Color Wheel and warm-cool color distinctions function in a similar way. They do not divide color space with the precision of a formal system, nor do they maintain strict consistency across all contexts. But they provide an accessible way to group, compare, and communicate relationships within a complex visual field. Like continents, they offer a level of abstraction that is often more useful in practice than a fully specified coordinate system.

The value, in both cases, lies not in definitional purity but in functional utility.

Separating Fact and Fiction

At this point, an important clarification is necessary. To defend the utility of abstractions and heuristics is not to suggest that all of the claims associated with them, or even born from them, are legitimate. For example, the Itten Color Wheel is often associated with the idea that red, yellow, and blue are universal primaries in all contexts. They are not. Others infer from the Farbkreis that the colors within the illustration are exact predictions of mixtures in terms of hue, value, and chroma. They do not (Kirchner, 2023). They do not. The wheel may still provide a useful way to organize and communicate certain hue relationships, but that utility does not validate every claim attached to it.

Something similar occurs with color temperature. Some connect the warm-cool distinction to the rule that warm colors advance and cool colors recede. Within certain ecological or pictorial frameworks, especially those involving atmospheric or aerial perspective, this may often be useful. But it does not mean that colors will behave that way perceptually in all contexts. A cool color can advance; a warm color can recede; and factors such as value, chroma, contrast, edge sharpness, scale, placement, and surrounding context can easily alter the effect. That fact does not invalidate the concept of warm/cool colors. It only shows that the heuristic should not be mistaken for a universal law.

The same distinction applies to compositional devices such as golden-ratio armatures, the rule of thirds, and dynamic symmetry. As I have argued elsewhere and often, many of the stronger claims surrounding these devices do not withstand even the most modest of scrutiny. They do not, by themselves, demonstrate hidden causal principles of aesthetic success, nor do they validate the more mystical or post-hoc narratives often attached to them. But that does not mean that the armatures themselves are useless. Used within an appropriate framework, they can provide organizational advantages: they can help divide a field, generate constraints, compare proportional relationships, scaffold decisions, or provide a shared language for discussing visual arrangements. The error lies not in using such devices, but in mistaking their organizational utility for proof of aesthetic and communicative causal necessity.

In the language of the cognitive forest, the distinction is between a useful path and an overextended map. A path may help us move through the terrain, but it does not follow that every sign placed along that path is accurate, or that the path leads everywhere. Some heuristics provide genuine access to structure while also accumulating claims that exceed their proper scope. The task is not to reject the path, but to understand where it is useful, where it ends, and what terrain it actually helps us navigate.

The Forest Revisited

We can now return to the forest with greater clarity.

The cognitive forest is not chaos. It is a structured landscape of connected and sometimes overlapping representations. Some are precise, formal, and highly differentiated. Others are compressed, intuitive, and more immediately accessible. Some preserve important relationships while omitting detail. Others may be useful in one way, but are otherwise buried in claims that exceed what they can actually support. What matters is not simply whether a representation is complete, but what kind of work it allows the learner or practitioner to do and what they hope to build upon it.

Within this landscape, different tools serve different functions. High-resolution systems, such as Munsell, support precise specification, fine discrimination, and consistent communication when those demands are present. Compressed, mid-level frameworks, such as warm-and-cool distinctions or simplified color models, organize experience in ways that can support rapid judgment, intuitive grouping, and flexible application. Other devices, such as compositional armatures, may help to organize space and generate advantageous constraints, even when most of the functional claims attached to them are not justified.

Like continents, these are not rigid categories so much as functional distinctions. Their value depends on how they operate: what they preserve, what they omit, what they distort, and whether they support effective navigation through the domain. A tool does not need to describe the entire terrain in order to be useful. But neither should its usefulness be mistaken for universal authority. Effective learning and performance depend on the ability to move within this layered environment. Experts do not often rely on a single representation. They move fluidly between levels, using precision when required, relying on more compressed or intuitive frameworks when sufficient, and translating between systems as context demands. This capacity is often described in cognitive science as a form of adaptive expertise, in which knowledge is not only well developed but also flexibly applied across situations (Hatano & Inagaki, 1986; Carbonell et al., 2014). This flexibility is not a weakness or a compromise in any way. It is the foundation of expertise.

Excellence and the Plurality of Paths

In a culture that often equates rigor with reduction, there is a persistent temptation to eliminate anything that appears vague, inconsistent, or difficult to define with precision. The impulse is understandable. Clear systems, clean definitions, and tightly bounded frameworks offer a sense of control and certainty. But excellence does not emerge from the elimination of all ambiguity. It emerges from the ability to work with it carefully and selectively, with an understanding of where it is appropriate and where it is not.

Within the cognitive forest, this means recognizing that different tools serve different functions. Some offer precision and stability. Others offer accessibility and speed. Some compress real structure into usable form. Others must be qualified, limited, or rejected when the claims made on their behalf exceed what they can actually support.

The task is to hold these systems in relation: to recognize which tools are useful, understand their limitations, and deploy them within a broader, interconnected framework of knowledge. Moving effectively through a complex domain requires more than accuracy in isolation. It requires judgment; an ability to select the right level of description for the situation, to shift between representations when needed, and to remain sensitive to the structure of the problem at hand.

More Than One Way Forward

In this forest, we cannot simply drop into a new clearing. We must travel. And the more viable paths we have, the more effectively we can navigate. A forest with only a single route is fragile, as any obstruction can bring movement to a halt. A forest with many connected paths allows for adjustment, redirection, and continued progress.

The same is true of learning.

Deep levels of understanding do not usually emerge from a single representation, a single level of description, or a single perfectly specified system. It develops through connection: linking new material to what is already known, moving between precise and compressed frameworks, and choosing the level of description that best serves the task at hand.

Simplified models, like some of the color models discussed here, can be seen as akin to the idea of continents. They are not failed models merely because they are not maximally precise. They are adaptations to the realities of cognition: ways of organizing complexity into forms that can be used, shared, revised, and built upon. They do not replace more formal systems, nor are they intended to. They exist alongside them, offering additional ways to access and structure experience.

That does not mean every heuristic deserves equal trust, or that every claim attached to a useful device is justified. Some paths follow the terrain closely. Some are rough but serviceable. Some are temporary routes that help a learner begin. Others become misleading when treated as more authoritative than they are. The value of a framework depends on what it preserves, omits, and distorts, and whether it supports meaningful movement through the domain.

To discard useful abstractions merely because they are imprecise is not necessarily to advance understanding. It may instead constrain it, limiting the number of ways a learner can connect, interpret, and act. Precision matters. But precision is not the only cognitive virtue. Accessibility, flexibility, transfer, and communicative usefulness also matter.

The cognitive forest demands discernment. Not every path is equally valid, and not every map is trustworthy. But neither is a single, “perfect” map sufficient for every journey. What matters is the ability to recognize which paths follow the terrain, which tools are appropriate to the task, which claims exceed their evidence, and how to move between representations as conditions change.

The forest cannot be mastered by reducing it to a single path. The real discipline in the pursuit of understanding and expertise is learning how to move through it.