Local Symmetries Transformation

A structure-preserving transformation: introducing symmetries within a center, not globally, to strengthen local order.

Neighborhood — ranked by edge-count

concept

Local Symmetries
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The property that living wholes contain many interlocking and overlapping local symmetries rather than overall symmetry; local symmetries act as glue holding space together, and their number predicts cognitive coherence
LOCAL SYMMETRY
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One of Alexander's fifteen properties; appears in birthday table, handshake, and namaste examples
Local-Symmetry Transformation
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A transformation that strengthens a center by giving it an internal axis of symmetry, local to the center.
Structure-Preserving Transformations
uses
Chapter 2 of Volume 2 of The Nature of Order, introducing structure-preserving transformations as the mechanism by which living structure arises naturally through unfolding wholeness.

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.

Local symmetries are pervasive in nature (sun, trees, crystals, bodies) and are associated with minimum energy and least-action principles.claim0.782
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 effectiveclaim0.781
Interpretation of the experimental finding: overlapping local symmetries are the hidden structural feature that creates perceived wholeness
Spatial Transformationconcept0.781
Local Hamiltonianconcept0.751
Sum of windowed Hamiltonians with same window length; a key construct introduced in the paper to model local interactions on graphs
Natural system of symmetriesconcept0.749
A hierarchy of approximate symmetries that is balanced, comfortable, and characteristic of life; the specific balance that distinguishes living from dead structure.
Levels-of-Scale Transformationconcept0.743
A transformation that introduces intermediate-sized centers to fill out the hierarchy of scales, strengthening larger centers.
Boundary Transformationconcept0.741
A transformation that develops a thick boundary zone around a zone to intensify its coherence.
Translation Symmetryconcept0.738
Movement in a given direction through a given distance; all frieze patterns possess this symmetry by definition.