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In graph Frontier

Proportionality

In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio.

At a glance

Type
scale
Disciplines 2
Mental models 1
Role in the graph
Cross-disciplinary bridge
reaches 4 discipline lenses

Key signals

Cross-disciplinary reach
Disciplines
2
  • Mathematics
  • Algebra
Evidence & development

Dependencies

What this concept builds on and what it makes possible — derived from the atlas’s dependency, causal and structural relations, not from every related edge.

Foundations · builds on

Proportionalitydepends onRatioEstablished

Open Ratio →

proportionality depends on Ratio.

Mechanism: Two quantities are proportional when their ratio stays constant — double one and the other doubles too.

Sources:

Structural role & consequence

Interpreted from the current atlas graph — what the connections mean, not just how many there are.

  • Removing this node lengthens the structural route between Form and volume and Perspective drawing from 2 to 3 steps (they stay connected — alternative routes exist).

    structural · Structural removal simulation — not a historical or causal counterfactual.

  • 67% of its relationships cross field boundaries, reaching 4 other disciplines — unusual in a discipline where most concepts stay within their field.

    structural · Structural graph analysis — not a claim of importance, causation or history.

  • Currently dark in the atlas: no key date stored · 3 of 3 of its relations lack claim-level evidence.

    atlas representation · Describes the current Thinking OS representation, not the state of the world.

  • Builds on 1 foundation (requires / depends-on / derived-from / emerges-from).

    structural · Structural graph analysis — not a claim of importance, causation or history.

67%

cross-field
1 within-field, 2 cross-field

0 of 3 relations carry evidence · concept has a verified source

Strengths & constraints

Strengths

  • Cross-disciplinary connector — 67% of its relationships cross field boundaries. structural

Constraints

  • Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
  • No dated history stored — the atlas records no key date for this concept. atlas representation

Conditions

  • Its dependency reading rests on 1 foundation relation. structural
  • Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural

Dependency radial

What this concept builds on (left) and what it makes possible (right) — derived from dependency and causal relations.

RatioProportionality◀ builds onenables ▶

Seen through each discipline

How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.

Mathematics

Through this lens it connects to Ratio.

Proportionality through the Mathematics lens

Algebra

Proportionality is studied in this field.

Proportionality through the Algebra lens

Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.

This idea also appears in…

The same structure shows up in other disciplines. These are real recurrences drawn from the graph — a starting point for asking “what carries over, and what changes?”

Scale31 disciplines · 44 concepts

Concepts

  • HierarchySystems ScienceBiologyComputer Science

    shares a mental model

  • ScalePhysicsGeographyAstronomy

    shares a mental model

  • Surface-area-to-volume ratioBiologyArchitectureGeometry

    shares a mental model

  • SymmetryPhysicsVisual ArtsGeometry

    shares a mental model

  • AtomPhysicsChemistryAtomic Physics

    shares a mental model

  • Big O notationComputer ScienceAlgorithmsComputational Complexity

    shares a mental model

Mental models at work here

The scientific picture
  • Connects 3 other ideas across 2 disciplines.
  • A cross-disciplinary bridge — its connections reach into 4 other fields.
  • Most of its connections are of the “Teaching link” kind.
  • It exercises 1 reusable thinking pattern.

Derived from the graph’s real structure — observations, not a score.

Sources