finding

active

finding:the-nearly-identical-detailed-sub-symmetries-and-sub-sub-symmetries-on-all-six-arms-of-individual-snow-crystals-are-not-explained-by-any-present-diffusion-aggregation-model

The nearly identical detailed sub-symmetries and sub-sub-symmetries on all six arms of individual snow crystals are not explained by any present diffusion-aggregation model.

Key finding establishing a gap in current morphogenetic explanation that Alexander's principle addresses

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Claims (2)

claim

The nearly identical detailed structure on all six arms of a single snow crystal is not explained by any present diffusion-aggregation model, implying non-local coordination.
restatessupports
Alexander's use of snowflake arm symmetry as evidence that something beyond local mechanics is required in morphogenesis
The principle of unfolding wholeness is a new principle, not automatically given by non-linear dynamics, catastrophe theory, or bifurcation theory, necessary to explain the appearance of living structure.
supports
Alexander's central assertion that existing frameworks are insufficient and a genuinely new principle is required

Concepts (1)

concept

Diffusion-Aggregation Model
associated_with
Computational models of crystal growth that produce rough overall symmetry but fail to explain the detailed identical sub-symmetries on snowflake arms

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.

Local symmetries are pervasive in nature (sun, trees, crystals, bodies) and are associated with minimum energy and least-action principles.claim0.783
Approximate calculations with symmetries gave accurate experimental results for architectural wholeness (Book 1, appendix 6).finding0.756
Empirical validation of the theory of centers in architecture.
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 effectiveclaim0.754
Interpretation of the experimental finding: overlapping local symmetries are the hidden structural feature that creates perceived wholeness
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 brutalclaim0.743
Claim distinguishing the deadening effect of large-scale neoclassicist symmetry from the vitalizing effect of numerous overlapping local symmetries
Echoes of similar proportions and angles appear throughout any natural system due to uniform underlying processes, giving a consistent character to different parts.claim0.739
In nature, unfolding often consists of a process that establishes local symmetries one by one.claim0.738
Connects biological morphogenesis to architectural process.
Schechtman and colleagues discovered naturally occurring metallic alloys with long-range orientational order and no translational symmetry — quasicrystals — confirming Penrose's tiling patterns in nature.finding0.738
Empirical discovery cited as evidence that non-local geometric order appears in physical matter
Glide-reflections appear to be less-favored symmetries in Islamic geometric patterns compared to other isometries.claim0.737

Restated by (1)

cosine ≥ 0.90

Other entities that say roughly the same thing. May be merge candidates or independent restatements across papers.

claim
The nearly identical detailed structure on all six arms of a single snow crystal is not explained by any present diffusion-aggregation model, implying non-local coordination.