The Theory

Some thoughts do not fit into sentences. The relationship between five interacting components is hard to describe verbally but trivially clear in a diagram. A mathematical proof is more precise as an equation than as a paragraph. Code is not just a way to instruct computers — it is a way of thinking, of forcing yourself to be absolutely unambiguous about every step. Diagrams, formal languages, prototypes, and physical models are all cognitive externalization media that offer something text cannot: spatial organization, formal precision, or tangible manipulation. Larkin and Simon proved formally that diagrams are sometimes computationally more efficient than words for reasoning — not just prettier, but actually faster to think with.

What the Research Found

Larkin and Simon provided a mathematical proof that diagrams can be computationally superior to text for reasoning because they preserve spatial relationships that text must reconstruct sequentially. Novak developed concept mapping as a tool for making conceptual relationships explicit and manipulable. Wing defined computational thinking as a fundamental cognitive skill — formalizing problems into algorithmic steps. Knuth proposed literate programming, where code and explanation are woven together as a thinking medium. Papert showed that building external artifacts (constructionism) is itself a form of learning. Hostetter connected gesture to simulated action, showing that physical externalization is grounded in embodied cognition.

How We Use It

Question D1 option (c) — "I grab paper and pen and draw a diagram, a map, a chart" — maps to diagrammatic externalization (dimension value 4.3). Option (d) — building a prototype or model — maps to physical externalization (value 4.4). Option (e) — writing pseudocode, equations, or formal language — maps to formal externalization (value 4.5). D2q mirrors these for communication contexts. D3q(d) — externalizing for systems via prompts or code — and D5q(c)/(d)/(e) capture which of these media you would miss most. If you instinctively reach for a whiteboard, a prototype, or a code editor when thinking, your externalization medium is non-verbal.

Related Articles

D4 Thinking Out Loud: When Your Voice Becomes Part of Your Mind D4 Writing as Discovery: How the Page Thinks With You D1 Thinking in Pictures: The Mind's Eye as a Cognitive Engine

References (7)

  1. Larkin, J. H. & Simon, H. A. (1987). Why a diagram is (sometimes) worth ten thousand words. DOI
  2. Novak, J. D. & Canas, A. J. (2008). The theory underlying concept maps and how to construct and use them.
  3. Papert, S. (1991). Situating constructionism.
  4. Wing, J. M. (2006). Computational thinking. DOI
  5. Knuth, D. E. (1984). Literate programming. DOI
  6. Hostetter, A. B. & Alibali, M. W. (2008). Visible embodiment: Gestures as simulated action. DOI
  7. Levi-Strauss, C. (1962). La pensee sauvage.