finding

active

finding:weighted-symmetry-measure-by-segment-length-correlates-less-well-with-coherence-than-unweighted-local-symmetry-count

Weighted symmetry measure (by segment length) correlates less well with coherence than unweighted local symmetry count

Finding that giving extra points to longer symmetrical segments reduces correlation with experimentally measured coherence, showing large symmetries contribute little extra; what matters more is the number of smaller local symmetries

Neighborhood — ranked by edge-count

Claims (1)

claim

Overall symmetry in a system, by itself, is not a strong source of life or wholeness; local symmetries create coherence while overall symmetry is often naive and even brutal
supports
Claim distinguishing the deadening effect of large-scale neoclassicist symmetry from the vitalizing effect of numerous overlapping local symmetries

Methods (1)

method

Subsymmetries Experiment
associated_with
Experimental method using 35 black-and-white strips of 7 squares each (3 black, 4 white) with multiple cognitive tasks (description, memorization, tachistoscopic recognition, subjective simplicity rating) to measure perceived coherence and correlate it with number of local symmetries

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

Number of local symmetries correlates almost perfectly with perceived cognitive coherence across 35 strip patternsfinding0.803
The key experimental finding: the number of subsymmetries (locally symmetrical connected segments) in a pattern predicts its perceived coherence; most coherent strips have 9 subsymmetries, least coherent have 5; the measure correlates almost perfectly with combined experimental rank order
Configuration coherence can be measured by counting locally symmetric sub-configurations; this measure shows strong agreement with cognition and perception experiments.finding0.796
Quantifiable measure linking structural properties of configurations to human perception, supporting the mathematical reality of wholeness.
c_symm (Symmetry-based Coherence Measure)method0.758
A mathematical measure that assigns life=1 to connected symmetrical subsets and 0 otherwise, used as a first approximation for wholeness.
Perceived coherence of patterns is an objective measure, not idiosyncratic or subjective—people agree on relative coherence regardless of experimental taskfinding0.746
Finding that relative coherence rankings remain constant across different people and across different cognitive processing tasks (description, memorization, tachistoscopic recognition), establishing coherence as an objective feature of cognitive processing
Local symmetries act as a kind of glue which holds space together; the more glue there is, the more the space is one, solid, unified, coherent—and the symmetrical segments must overlap for the glue to be effectiveclaim0.738
Interpretation of the experimental finding: overlapping local symmetries are the hidden structural feature that creates perceived wholeness
Determining whether or not a pattern has glide-reflection symmetry can be challengingclaim0.731
Author's methodological note about subtlety of glide-reflections
Glide-reflections appear to be less-favored symmetries in Islamic geometric patterns compared to other isometries.claim0.729
Local symmetries are pervasive in nature (sun, trees, crystals, bodies) and are associated with minimum energy and least-action principles.claim0.727