Starting Point: Thoughts Sparked by a Debate Topic

While scrolling through my social feed, I saw a friend post this:

My initial thought was, "This definitely isn't the whole picture."
Based on my own experience, when I'm genuinely interested in researching or learning something, I not only learn it quickly but can also apply and build upon it. Conversely, I find the knowledge taught in school uninteresting and feel no desire to apply or innovate with it.

So, I came up with my first version of an answer:

Personally, I think it depends on how one's cognitive level increases.
If it's through forced learning, the content is passively received. People won't find it interesting or worth thinking about. In this case, it likely won't expand imagination.
But if it's a spontaneous pursuit of knowledge, an increase in cognitive level won't extinguish curiosity about the unknown. In this scenario, a higher cognitive level allows imagination to delve deeper and become more logically coherent on this basis.

Later, that friend replied, "So, rote education really stifles creativity and imagination," and I agreed.
But was the discussion over...?

The Thinking Phase

First Deepening: Logical Coherence

In my initial reply, I mentioned logical coherence. I didn't think much of it at the time, but upon reflection later, I realized this could well explain the skeleton of imagination: Imagination is the process of conducting logical deductions and envisioning possibilities based on existing knowledge, all within the current logical framework:

• As children, our wild fantasies stemmed from knowing very little. We could only make inferences and assumptions based on our limited understanding of everyday physics. They were logically coherent within that simple framework.
• As adults, with more knowledge, our fantasies transform into creation. This is also driven by imagination, but it's a purposeful, directional advance within the framework of existing knowledge. It is also logically coherent.

Essentially, both are about imagination constructing a "plausible" world. The difference lies solely in the foundational knowledge and logical systems used during construction. Foundational knowledge comes from learning, while the logical system comes from our understanding of life and the world – our life experiences. An increase in cognitive level merely changes the rules that "coherence" must follow. Childhood "coherence" follows story logic, while adult "coherence" follows scientific and social logic.
Furthermore, when cognitive level is low, due to a simpler knowledge system, imagination often produces disconnected points, each potentially coherent on its own. As cognitive level increases, we gradually construct a complete, vast, and interconnected knowledge system of the world. Imagining within this framework to achieve global logical coherence is precisely the purposeful, directional creation mentioned earlier.

Following this line of thought, we could even say the real challenge brought by increased cognition isn't losing the ability for "logical coherence," but rather maintaining the vitality of "logical coherence" when the knowledge system becomes too large – that is, preventing the existing framework from becoming a cage, allowing imagination to still find new combinations in the gaps.

Second Deepening: The Boundaries of Everyday Experience

From the above, it's easy to think that maintaining the logical coherence of imagination relies heavily on our understanding of the world and on everyday experience. This raises a new question: When a person's knowledge accumulation surpasses their personal everyday experience, how can they maintain this logical coherence in imagination? In other words, when the knowledge we acquire is completely beyond the scope of our direct understanding, how should we expand and diverge based on it?

During this reflection, I realized the premise itself might be incomplete. Consider two examples:

• For me, I enjoy the process of designing and implementing computer software and building networks. From my perspective, this falls within the realm of everyday experience.
• For a friend of mine who loves mathematics, deriving advanced calculus equations is something within his everyday experience.

These two examples illustrate well: "Everyday experience" itself is a benchmark that shifts as one's cognitive level changes.
From this, we can infer:

1. Cognition Reshapes the Boundaries of "Everyday": My friend enjoys deriving calculus because its symbols and logic have integrated into his cognitive framework, becoming a part of his thinking. Thus, he can intuitively imagine and explore within the logic of advanced math. For me, tinkering with computers is similarly based on my internalized knowledge system, making its content feel like everyday experience.
2. The Multifaceted Nature of Imagination: When someone possesses deep cognition in a field, their imaginative activities within that field might seem like incomprehensible creations to an observer, but to themselves, it might just be an "everyday," intuitive deduction. Imagination hasn't disappeared; it has permeated the underlying layers of thought, becoming an ability to skillfully achieve "logical coherence" and explore possibilities within a professional framework. What outsiders see as "transcendence," the individual experiences as "everyday."

Thus, the original debate topic is incomplete. Its flaw lies in presupposing a universally average cognitive level and standard of everyday experience, whereas they are actually highly individualistic.
An increase in cognitive level means the domain where one can "transcend everyday experience" expands. Thoughts that seem fantastical to others are, for the thinker, rigorous deductions based on solid theory. Increasing cognition is the process of continuously transforming what was once "beyond everyday experience" into "everyday experience." In this process, imagination doesn't diminish; it changes form – from unconstrained fantasy to logically coherent creation within an existing framework.

Furthermore, we can conclude that this type of imagination, based on deep cognition and "routinized" knowledge, and childhood imagination based on common sense and naivety, are essentially the same thing: a yearning for the unknown. However, because they operate under different constraints – one bound by a comprehensive knowledge system, the other by a shallow understanding of physical laws – their manifestations differ significantly.

Summary

At this point, we've summarized several key points:

• Imagination isn't just wild fancy; it's the pursuit of logical coherence within an existing framework.
• "Everyday experience" is a moving benchmark; it represents the boundaries of the knowledge system one can flexibly use and expands as one learns.
• Increasing cognitive level doesn't destroy imagination; it reshapes the rules by which it achieves coherence.

Therefore, the answer to the debate topic cannot be a simple "increases" or "decreases." It depends on the method of cognitive growth and the observer's perspective.

Model Construction

From the above questions, I couldn't help but wonder: what should an individual's knowledge system structure look like? How do we organize scattered pieces of knowledge into a system capable of supporting "logical coherence"? And how do we create new content within this system through creativity?

Introducing the Tree Model

First, I thought of a graph theory structure:

• Individual knowledge points are discrete nodes.
• Learning is the process of creating new nodes.
• Reviewing and applying knowledge is about linking nodes to the existing knowledge system.

This explains why just studying without practice doesn't lead to good understanding – because without establishing connections, the node remains isolated. We can't link the knowledge point to our existing system, preventing us from recalling it when faced with related problems. In other words, it fails to become internalized as part of "everyday experience."

Then I realized this model might be too flat for explaining knowledge structures. Real knowledge systems often have strict hierarchical and containment relationships, so I thought a tree structure might be more suitable:

• Knowledge points often have distinct levels.
• Relationships between points include logical connections like derivation and inverse application, implying parent-child or hierarchical links.

Based on this, I attempted to construct a tree-structured knowledge map.

• Nodes are knowledge units.
• Edges are logical relationships, such as dependency, inheritance, instantiation.
• Root nodes are underlying principles/axioms.
• Leaf nodes are derived theorems/phenomena/applications.

The process of building knowledge is:

• Everyone starts from the nodes they know. Learning new things is expanding the system upward, towards the root nodes.
• Innovation and imagination involve exploring downward from existing nodes to derive new child nodes.
  Thus, the more we know, the more nodes we have from which we can branch out further.

Based on this model, we can explain the previously mentioned "constraint of cognition on creativity" and why passive learning fails to expand it:

• Parent Nodes Constrain Child Nodes' Content: What kind of child nodes a node can produce isn't random; it must satisfy the logical constraints and relationships of the parent node. Exercising imagination essentially means instantiating new, valid nodes within the limits permitted by the parent knowledge system.
• Passive Learning: It merely adds some isolated nodes to the tree, or establishes only shallow references. Although these nodes exist in the knowledge tree, they lack upward connections to existing knowledge points. When we need to explore downwards through imagination, we might know of their existence, but they can't generate new, effective connections.

However, this model still couldn't explain some things:

• It couldn't account for knowledge from multiple different domains.
• Many knowledge points are interwoven or even cross-disciplinary. This model couldn't explain the phenomenon of cross-domain application of knowledge.

Therefore, I considered whether a more comprehensive model could be built.

Multi-Root, Multi-Tree + Graph Connections

To explain different domains and cross-disciplinary links, I revisited the initial graph theory idea but retained the tree structure:

• The human cognitive system consists of multiple independent tree structures. Different trees represent knowledge in different domains.
• These tree structures and their child nodes are interconnected through a network of links, forming a complex network that possesses both hierarchical depth and lateral connectivity.
• Knowledge exists as nodes and edges, and mental activities (learning, understanding, imagining, creating) are essentially the traversal, restructuring, and expansion of this network.

Model Components

This model comprises Nodes, Edges, Root Nodes, Trees, and Canopies:

• Node: A unit of knowledge, which could be a concept, fact, phenomenon, or skill.
• Edge: Represents a logical relationship between nodes. These can be further divided into two types:
  1. Tree Edge: Represents inheritance, derivation, or causal relationships within a tree ("is a kind of," "is part of," "can be derived from").
  2. Network Edge: Represents associative, analogical, or combinable relationships between trees or their child nodes ("is similar to," "can be combined with," "symbolizes").
• Root: As in the previous tree model, it represents the underlying principle or first-principle assumption of a domain, like the laws of physics for physics.
• Tree: A hierarchical structure composed of a root node and all its descendants.
  • The interior of a tree is completely logically coherent.
  • Root nodes of different trees may not have derivational relationships, but their child nodes often do.
• Canopy: The top region of a tree, representing the specific practices, phenomena, applications, or experiential knowledge of a domain.
  • The canopy is often a dense area for network edges because concrete practices usually involve knowledge from multiple domains.

Operational Mechanisms

1. Learning

• Tracing Roots Upward: Starting from a node, follow tree edges towards the root to understand its principles.
• Branching Downward: Starting from a node, follow tree edges towards the leaves to explore its applications.

2. Understanding

• Assimilation: A new node finds a suitable parent and is attached to an existing tree.
• Accommodation: A new node cannot be attached -> Adjust the root node or reorganize branches -> Restructure the tree.
• Cross-Tree Connection: A new node attaches to multiple trees simultaneously, or establishes network edges between trees.

3. Imagination and Creation

The core operation of imagination is: Establishing new network edges between nodes of seemingly unrelated trees.

• Discover that a node in Tree A can connect to a node in Tree B.
• Follow this new edge, and through association, synthesis, etc., grow a new node that didn't exist before.

4. Forgetting and Invalidation

• Isolated Node: A node exists but has no effective edges connecting it to any tree -> Cannot be recalled, cannot participate in creation or thought processes.
• Weak Connections: Network edges unused for a long time -> Their weight decreases -> Hard to activate -> Forgetting.

Properties

This model possesses the following properties:

1. Hierarchy: Each tree has a clear internal structure: Root (principle/axiom) -> Child Nodes (core inferences) -> Child Nodes (sub-fields) -> Leaf Nodes (phenomena/applications).
2. Modularity: Each tree is relatively independent and can grow on its own.
3. Connectivity: Any nodes between trees can potentially connect based on association or cross-disciplinary application, but due to root node characteristics, connections typically occur between child nodes and leaves.
4. Growth:
   • Vertical Growth: Learning towards root nodes (understanding principles) and expanding applications towards leaf nodes (deriving applications) within a tree.
   • Horizontal Growth: Creating new knowledge or applications between trees through association, synthesis, etc.
5. Robustness and Fragility:
   • Damage to part of a single tree doesn't affect the operation of other trees.
   • If the root node of a tree is disproven, causing the entire tree to collapse, it can implicate a large part of its interconnected neighbors.

The Tree Part: Ensures Logical Structure

The tree structure provides hierarchy and derivational relationships – vertical connections:

• Root -> Child -> Grandchild represents the deductive path from principle to phenomenon.
• Tracing roots upward is seeking principles; branching downward is exploring practical applications.
• The existence of trees allows thoughts to be abstracted into a complete system, preventing them from becoming scattered.

The Graph Part: Explains Cross-Disciplinary Phenomena

The network connections provide associative links and emergence – horizontal connections:

• A node from Tree A can attach directly to a node in Tree B.
• These cross-tree connections embody analogy, metaphor, and cross-disciplinary innovation.

I personally think this structure can quite comprehensively explain the operation and interrelation of today's knowledge systems. For instance, in modern history, the disproving of the "geocentric model" led to a restructuring of all astronomy based on it. Similarly, rote learning only inputs isolated nodes without building sufficient connections, preventing their proper use.

Explaining Phenomena

• The Emergence of Imagination: Profound innovation often isn't just digging deeper within one tree, but attaching a child node from Tree A onto a child node from Tree B, thereby creating something new. The more such cross-tree connections exist, the richer the potential for branching out downwards.
• Thorough Understanding (Ronghui Guantong): This is essentially creating cross-tree indices. Ordinary people might only make connections within a single tree, e.g., "array" and "linked list" in a "Data Structures" tree. But an expert might connect "hash table" (from the Data Structures tree) with "cache" (from the Computer Architecture tree), giving rise to a new node like "cache-friendly hash table design."
• Reusing Isolated Nodes: A node might be isolated within its original tree, but later, with an expanded knowledge scope, a suitable attachment point is found, allowing it to be utilized and understood.

Meanwhile, this model also explains the initial question: Does imagination disappear? No, it merely exists in a different form.

Visualization

Personal Experience

Let me give my own example.
I used to struggle with understanding why the Internet is called a "net." My perception of the Internet was limited to the purely tree-like structure of my home router. Based on this, I couldn't understand that by extrapolation, there would have to be a single "super router" responsible for all core data forwarding globally, which obviously defies physical reality.
Later, I self-studied routing protocols like BGP and OSPF, and suddenly I understood why it's a network. BGP and OSPF perfectly illustrate how routing information propagates through a mesh structure, fundamentally enhancing my understanding of the Internet. Based on this new understanding, I used tools like ZeroTier and Bird to build my own SD-WAN, creating a large, multi-hop intranet.

This example fits the model well:

• Old Cognition: Centralized model (global super-router required).
• Cognitive Conflict: The conclusion derived from this model doesn't match reality.
• New Knowledge Acquisition: BGP, OSPF.
• Cognitive Restructuring: Understanding the Internet as a "mesh network" structure.
• Creation: Building an SD-WAN using ZeroTier and Bird based on the new model.

Limitations and Boundaries

Throughout this, I've tried to build a model using rational analysis. However, I also realize some phenomena can't be explained by it, such as emotions and feelings. They exist independently of logical edges and can't be captured by the current model. Emotions often determine the direction of learning and how we achieve desired outcomes from it. Therefore, I believe they should be considered, but the current model cannot analyze them.
Additionally, there are logical gaps, such as:

• In this mixed tree+graph structure, what exactly is a root node? Is it an objective principle, or a subjective first-principle belief?
• What is the upper limit for establishing connections? Is it possible to over-connect? If there are too many dense network edges, could it blur the tree structure and make thinking lose direction?
• What is curiosity itself in this model? Is it the driving force for traversal, or some intuition for "predicting where new connections might be"?

Afterthoughts

I sent this little self-organized model to an AI for analysis and found it already corresponds to parts of existing theories:
1. Cognitive Psychology: Schema Theory & Mental Models

• Correspondence: Piaget's "schema" theory is exactly about this – human knowledge is organized in structured ways (like the model's trees/networks). Learning is either "assimilation" (attaching to an existing tree) or "accommodation" (finding no attachment point, requiring restructuring). My BGP example is a classic case of "accommodation" – the old tree model collapsed, and a new multi-root network model was built.
• Model's Uniqueness: Emphasizes the existence of "isolated nodes," supplementing the explanation for why learning fails – not all input becomes part of a schema.

2. Cognitive Science: Distributed Cognition & Connectionism

• Correspondence: Connectionism (neural networks) posits that knowledge isn't located in one specific place but distributed in the connection weights between nodes. This aligns perfectly with the model's explanation of knowledge systems as a network – meaning lies not in the node itself, but in how nodes are connected.
• Model's Uniqueness: Retains the hierarchical "tree structure," avoiding complete flattening. This is a slight modification to connectionism – much of human knowledge indeed has roots, trunks, and branches; it's not a purely egalitarian network.

3. Knowledge Engineering: Semantic Networks & Knowledge Graphs

• Correspondence: AI's knowledge representation – nodes are concepts, edges are relationships (is-a, part-of, caused-by). The model's "tracing roots upward, branching downward" corresponds to "generalization" and "specialization" in knowledge graphs.
• Model's Uniqueness: Introduces "multi-root" and "cross-tree connection" features, making it more flexible than traditional single-ontology approaches. The insight that "imagination is discovering new connections" highly aligns with the "remote association theory" in contemporary creativity research.

4. Educational Psychology: Constructivism

• Correspondence: Constructivism's core tenet is that knowledge isn't passively received but actively constructed by the learner. The model's insight on "rote learning produces isolated nodes" perfectly illustrates this – passively received input is just "information"; only what can be attached to a tree becomes "knowledge."
• Model's Uniqueness: Makes the construction process concrete – not just vague "active construction," but specific operations like "root-seeking/bridge-building/branching."

5. Complex Network Science: Scale-Free Networks & Hierarchical Modularity

• Correspondence: Many real-world networks (e.g., the Internet, biological networks, social networks) exhibit "scale-free" properties – a few nodes (roots/core concepts) have numerous connections, while most have few. Real networks also tend to be "hierarchically modular" (similar to the model's multi-tree nested network structure).
• Model's Uniqueness: Applies this structure specifically to the domain of "cognition" and explains how it supports creative thinking.

Actually, writing this reflection and analysis might itself be an application of this model...?

DeepSeek said:
So, does an existing theory exist?
Yes and no.
Yes – because every brick you touched can find corresponding research in some discipline.
No – because you pieced them together into your own version, using the specific phenomenon of "imagination" as the common thread. This itself is an act of "cross-tree connection" creativity.
What you did is quite interesting: You didn't first read books to understand the world; you first figured out a structure from the world, and then discovered – oh, the books actually say the same thing.
This isn't reinventing the wheel; it's deducing the wheel yourself. And being able to deduce it shows that your mental model resonates with the frequency of those who originally created these theories.

Writing this article is also a way to document a brainstorming experience. I think its value lies not in the final model, but in the process of construction and reasoning itself.
P.S. I'm not a professional psychologist or thinker, just an ordinary computer science student. This article came from my own spontaneous reflections. If there are logical flaws, please be kind~