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FAQ: Reading the Knowledge Graph

Understanding concepts, relationships, and how ideas connect

What is a Knowledge Graph?

A knowledge graph represents ideas as nodes (concepts) connected by edges (relationships). Instead of reading Ashby's books linearly, you can explore how ideas connect—seeing that "Law of Requisite Variety" derives from "Variety," or that "Ultrastability" generalizes "Stability."

Each concept has a definition, a formal statement, and often an intuition (a plain-language explanation). Relationships show how concepts depend on, extend, or constrain each other.

Why These Relationship Terms?

Our vocabulary is grounded in Gordon Pask's Conversation Theory. Pask—who studied under Ashby—developed the concept of entailment meshes: networks showing how concepts necessarily lead to other concepts. We use Pask's terminology so the same relationship vocabulary works across Ashby, Pask, Beer, Whitehead, and other thinkers on this platform.

Relationship Types

We use seven relationship types. Each has a specific logical meaning. Read them as sentences: "Concept A [RELATIONSHIP] Concept B"

ENTAILS Logical Implication

Meaning: If A is true/present, then B necessarily follows. A logically implies B. You cannot have A without B being true.

Core term in Conversation Theory. Entailment is the logical relation where one topic necessarily leads to another.
A → ENTAILS → B
"A entails B" = "If A, then necessarily B"
Example
Stability ENTAILS Equilibrium
If a system is stable, it necessarily has equilibrium states. You cannot discuss stability without equilibrium being part of the picture.
DERIVES_FROM Prerequisite / Dependency

Meaning: To understand or define A, you must first understand B. B is a prerequisite for A. A derives its meaning from B.

The reverse of entailment. In an entailment mesh, if B entails A, then A derives from B. This is how you trace prerequisite chains backward.
A → DERIVES_FROM → B
"A derives from B" = "To understand A, you need B first"
Example
Law of Requisite Variety DERIVES_FROM Variety
You cannot understand the Law of Requisite Variety without first knowing what "variety" means. The law derives its meaning from the concept of variety.
GENERALIZES Abstracts / Extends

Meaning: A is a more abstract, general, or developed form of B. A builds on and goes beyond B. A takes B to a higher level.

In entailment structures, topics exist at different levels of abstraction. Generalizing moves up to more encompassing concepts.
A → GENERALIZES → B
"A generalizes B" = "A is a more abstract/developed form of B"
Example
Ultrastability GENERALIZES Stability
Ultrastability isn't just stability—it's a higher-order form that includes self-reorganization. It takes the stability concept to a new level.
PARTICULARIZES Instance / Specific Case

Meaning: A is a concrete example or specific instance of B. A demonstrates B in practice. A makes B tangible and specific.

The reverse of generalization. Moving down the abstraction hierarchy to concrete cases that exemplify the general concept.
A → PARTICULARIZES → B
"A particularizes B" = "A is a specific instance of B"
Example
Homeostat PARTICULARIZES Ultrastability
The Homeostat is a physical machine that demonstrates ultrastability. It's a concrete, particular instance of the abstract concept.
CONSTRAINS Limits / Bounds

Meaning: A places limits on B. A restricts what B can do or be. A defines the boundaries within which B operates.

A → CONSTRAINS → B
"A constrains B" = "A limits or bounds what B can achieve"
Example
Channel Capacity CONSTRAINS Transmission of Variety
You cannot transmit more variety than your channel capacity allows. The channel's capacity sets an upper bound on what can flow through.
ENABLES Makes Possible

Meaning: A creates the conditions for B to exist or occur. Without A, B wouldn't be possible. A is a necessary enabler.

A → ENABLES → B
"A enables B" = "A makes B possible"
Example
Double Feedback ENABLES Self-Reorganization
Without the second feedback loop (through step-mechanisms), self-reorganization couldn't happen. Double feedback is what makes it possible.
CONTRASTS Differs From

Meaning: A and B are different in important ways. Understanding the contrast between them illuminates both.

A → CONTRASTS → B
"A contrasts with B" = "A and B differ in important ways"
Example
Direct Regulation CONTRASTS Indirect Regulation
Direct regulation specifies everything genetically; indirect regulation delegates to learning. They're two fundamentally different strategies.
ANALOGOUS_TO Structural Similarity

Meaning: A and B share structural or functional similarities, often across different domains. They work the same way despite being different things.

Pask emphasized analogy as a key relationship—recognizing shared structure across domains is how knowledge transfers between fields.
A → ANALOGOUS_TO → B
"A is analogous to B" = "A and B share structural similarities"
Example
Thermostat ANALOGOUS_TO Homeostasis
A thermostat and biological homeostasis work the same way—both use feedback to maintain a variable within limits. Same structure, different domains.

Summary Table

Relationship Read As Direction
ENTAILS "A necessarily implies B" A → B (forward implication)
DERIVES_FROM "A needs B as prerequisite" A ← B (trace backward)
GENERALIZES "A is more abstract than B" A ↑ B (up abstraction)
PARTICULARIZES "A is a specific case of B" A ↓ B (down to instance)
CONSTRAINS "A limits what B can do" A bounds B
ENABLES "A makes B possible" A supports B
CONTRASTS "A differs from B" A ≠ B (bidirectional)
ANALOGOUS_TO "A works like B" A ≈ B (bidirectional)

How to Use Relationships for Learning

Finding Prerequisites

Follow DERIVES_FROM chains backward. If you don't understand "Law of Requisite Variety," look at what it DERIVES_FROM ("Variety"). Learn that first, then return.

Going Deeper

Follow GENERALIZES forward to see more developed forms. Once you understand "Stability," see what GENERALIZES it ("Ultrastability") for the next level of sophistication.

Finding Examples

Follow PARTICULARIZES to find concrete instances. If "Ultrastability" seems abstract, look for what PARTICULARIZES it ("Homeostat") to see it in action.

Understanding Limits

CONSTRAINS relationships show what bounds or limits a concept. "Channel Capacity" constrains "Transmission"—this tells you where the hard limits are.

Frequently Asked Questions

Q: Why Pask's vocabulary?

Gordon Pask was Ashby's student and developed Conversation Theory, which provides a rigorous way to think about how concepts relate. Since this platform will include Pask alongside Ashby, Beer, and Whitehead, using a unified vocabulary grounded in Pask makes the whole system coherent.

Q: What's the difference between DERIVES_FROM and ENTAILS?

They're inverses. If A ENTAILS B (A implies B), then B DERIVES_FROM A (B needs A). We keep both because the direction matters for learning: DERIVES_FROM helps you find prerequisites; ENTAILS helps you see consequences.

Q: What's the difference between GENERALIZES and ENABLES?

GENERALIZES means A is a more abstract/developed form of the same idea.
ENABLES means A makes B possible—they may be quite different things.

Example: "Ultrastability GENERALIZES Stability" (same family, more advanced). "Feedback ENABLES Error-Control" (different concepts, one makes the other possible).

Q: Are these relationships symmetric?

Only CONTRASTS and ANALOGOUS_TO are symmetric (if A contrasts with B, B contrasts with A). All others are directional—the arrow matters.

Q: Where do these relationships come from?

They're extracted from careful reading of Ashby's texts. Each relationship has "evidence"—a citation to where Ashby makes the connection. The extraction aims to capture Ashby's own logic, not impose external interpretations.