concept
active
concept:local-symmetriesLocal Symmetries
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
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Papers (1)
paper
Thinkers (2)
thinker
- A. M. Turingassociated_with
- Hermann Weylstudies
Frameworks (4)
framework
- Fifteen Properties of Living Structureassociated_withimplementsThe set of geometric properties that appear in all living structure: levels of scale, strong centers, boundaries, echoes, gradients, deep interlock and ambiguity, local symmetries, roughness, inner calm, not separateness, and others.
- The system of fifteen specific transformation types, each corresponding to one of the fifteen properties, that together constitute all structure-preserving transformations.
- Wholeness as Nested System of CentersimplementsAlexander's quasi-mathematical definition of wholeness as a recursively nested system of living centers displaying local symmetries, approximating the overall gestalt of a configuration
- Coherent entities at the scale of rooms and bays — roughly halfway between building volume and smallest elements — whose existence and beautiful pattern of arrangement is essential for profound building order; first noted by Ingrid King
Communities (2)
community
- Fifteen Propertiesassociated_withmembers_of
- Christopher Alexandermembers_of
Concepts (13)
concept
- Local Symmetries Transformationrelated_toA structure-preserving transformation: introducing symmetries within a center, not globally, to strengthen local order.
- Local-Symmetry Transformationassociated_withrelated_toA transformation that strengthens a center by giving it an internal axis of symmetry, local to the center.
- LOCAL SYMMETRYrelated_toOne of Alexander's fifteen properties; appears in birthday table, handshake, and namaste examples
- 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.
- Morphogenesisassociated_withProcess by which cellular collectives generate large-scale structure and form; presented as a collective intelligence problem.
- Living processusesA generative process that repeatedly applies the fundamental process to create uniqueness and belonging in the environment
- Strong Centersassociated_withThe property that living structures contain centers that are not merely blobs but strong, field-like centers that organize the space around them; every strong center is made of many other strong centers recursively
- Levels of Scaleassociated_withThe property that living structures contain centers at a beautiful range of sizes at well-marked levels with definite jumps, where each level helps the next; jumps should not be too great (ideally 2:1 to 4:1, less than 10:1)
- Good Shapeassociated_withThe property that a good shape is a center made up of powerful intense centers which themselves have good shape; built up from elementary figures with high internal symmetries, bilateral symmetry, a well-marked center, compactness, and closure
- feeling-symmetry principleassociated_withThe design criterion that among possible new local symmetries, one introduces the symmetry that most intensifies the feeling of the whole.
- Natural system of symmetriesextendsA hierarchy of approximate symmetries that is balanced, comfortable, and characteristic of life; the specific balance that distinguishes living from dead structure.
- Alhambra Planassociated_withThe plan of the Alhambra palace, used as a key example of local symmetries without overall symmetry—wildly asymmetrical overall yet full of local symmetries at many levels, creating organic wholeness adapted to site
- Binding Energy in Crystal Growthassociated_withThe mechanism by which incoming molecules preferentially attach to corners with greatest binding energy, perpetuating plane faces and preserving crystal wholeness
Chapters (6)
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- Chapter 20: Summation: The Morphology Of Living Architecture: What We May Call Archetypal FormintroducesmentionsFinal chapter of Vol. 3, synthesizing the morphology of living architecture, introducing archetypal forms, and distilling the core invariant structure.
- The working unit chapter that presents Alexander's method for generating large public buildings through living process, illustrated by six major projects.
- The chapter that catalogs and analyzes the fifteen recurrent geometric properties found in systems that have life, connecting them to the deeper theory of centers and wholeness
- Always Making CentersmentionsChapter 10 of The Nature of Order, Vol 2, describing the process of creating living centers through differentiation and the fundamental process.
- The chapter from which all other entities are extracted; it explains how living process, applied repeatedly in exterior space, generates the distinct morphology of gardens.
- Belonging And Not-BelongingmentionsChapter 1 of Volume 3, introducing the concepts of belonging and not-belonging in the built environment
Related by similarity (8)
cosine ≥ 0.65 · no typed edgeEntities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.
- Interpretation of the experimental finding: overlapping local symmetries are the hidden structural feature that creates perceived wholeness
- 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
- Sum of windowed Hamiltonians with same window length; a key construct introduced in the paper to model local interactions on graphs
- Prior assumption that high-level variables align with disjoint groups of neurons in standard basis; contrasted with distributed representations.
- Movement in a given direction through a given distance; all frieze patterns possess this symmetry by definition.