RESEARCH NOTES

Shape cognition in mental maps

2024-03-26 · Alun @Atopos
#CogSci#Spatial

Chapter 1: What does a drawn shape reveal?↗

Ralph A. Sanders and Philip W. Porter’s Shape in Revealed Mental Maps (1974) examines how people draw Africa from memory and which distortions recur in those outlines.

The intuitive question is what happens when a geographical shape is “stored” and later “retrieved” through drawing. But there are two tasks here: recalling the shape and getting the hand to reproduce it. The authors explicitly say their design cannot separate errors from these two sources. A drawn map is memory expressed through a drawing process, not a direct screenshot of an internal representation.

A second problem is easier to overlook: the analyst introduces error when superimposing a sketch on a reference map. The study uses different overlay methods and factor analyses to distinguish patterns associated with misalignment from those associated with the drawings.

Chapter 2: Findings worth noticing↗

  1. Measure the analysis procedure’s own error. Changing the overlay center can change the measured boundary deviations for the same drawing. Displacement introduced by the method cannot simply be attributed to the person’s cognition.
  2. Outlines tend toward regularity and roundness. Both groups produced patterns of excessive symmetry, an elongated northeast–southwest axis and a shortened north–south axis. The authors interpret these as a tendency to organize complex outlines through simpler geometric forms, an interpretation of drawing performance.
  3. Similar errors do not mean equal accuracy. The Tanzanian sample drew outlines closer to the reference overall, while the groups shared several kinds of distortion. Similarities between two student samples do not establish a universal mechanism across cultures.
  4. Local indentations can disappear. The authors identify insufficient indentation along the western coast between Angola and Cameroon, as well as misrepresentation in the north and northwest. “More regular” therefore refers to identifiable changes in the outline. (Original paper, pp. 266–267.)

Chapter 3: Turning an outline into analyzable data↗

3.1 Collecting the drawings↗

The study compared 26 upper-level undergraduates at the University of Minnesota with 44 students at the University of Dar es Salaam. Students imagined rotating a globe until Africa faced them with north at the top, then drew the coastline. The Tanzanian group was also explicitly told to use the paper’s edge as a north reference.

These convenience samples provide material for comparison. Publication does not establish that student samples are sufficient for every question of this kind, or rule out differences in familiarity, instruction and drawing experience. (pp. 258, 261.)

3.2 Adjusting area and orientation↗

Each sketch’s area was measured three times with a polar planimeter and averaged. The drawings were then resized to the reference map’s area. The linear scaling factor can be written as:

si=ArefAi,Ai>0.s_i=\sqrt{\frac{A_{\mathrm{ref}}}{A_i}},\qquad A_i>0.

Here, AiA_i is drawing ii’s mean area and ArefA_{\mathrm{ref}} is the reference area. Multiplying lengths by sis_i multiplies area by si2s_i^2. Equalizing area does not correct every local position; orientation follows the task’s north-up instruction. (p. 261.)

3.3 Overlaying maps: the center is a choice↗

Rather than visually searching for the best fit of each outline, the authors compared four reproducible centers and superimposed the corresponding points:

Table 1. Four overlay centers from the paper: a methods summary, not new results
Overlay center Definition Qualification
Circumscribed Center of the smallest enclosing circle Describes the overall envelope
Inscribed Center of the largest contained circle May not be unique; the paper chooses the candidate closest to the circumscribed center
Midpoint Midpoint of the two circle centers Still depends on the inscribed-center choice
Intersection Intersection of north–south and east–west axes constructed by the paper’s rules Adapted to Africa’s outline, without guaranteed applicability to arbitrary shapes

Like control points in georeferencing, these centers establish a correspondence. They are not equivalent, however: each is derived from its own outline and need not identify the same real geographical location. A reproducible center does not guarantee an unbiased overlay. (pp. 261–262, 266.)

3.4 Measuring error along sixteen directions↗

A sixteen-direction compass rose was placed at each center. Boundary deviations were measured along matching rays. In this note’s notation:

Δrij=ri(θj)−rref(θj),j=1,…,16.\Delta r_{ij}=r_i(\theta_j)-r_{\mathrm{ref}}(\theta_j),\qquad j=1,\ldots,16.

The two radial distances, rir_i and rrefr_{\mathrm{ref}}, run from the shared center to the sketch and reference boundaries. Positive values place the drawn outline outside the reference; negative values place it inside. Each drawing therefore yields 16 directional variables. The Tanzanian drawings were also sampled after rotating the compass rose by 11.25∘11.25^\circ, allowing comparison across sampling directions. A finite set of rays still does not preserve the entire coastline. (pp. 262–263, Fig. 4.)

3.5 From correlations to factor interpretations↗

The authors first used principal components analysis (PCA), then principal axes factor analysis (PAFA), with Varimax rotation to obtain more interpretable loadings. Opposite-signed changes on opposite sides can indicate an overall overlay displacement; changes in neighboring directions help locate regional outline distortions.

Factors describe how measured variables vary together. They do not automatically identify psychological mechanisms causing the errors. The paper acknowledges that loadings depend on modeling and rotation choices; recurring patterns across groups and overlay methods provide an important basis for interpretation. (pp. 264–267.)