My claim in Book 2 is that the intricate and beautiful structure of living centers comes about naturally, and most of the time without effort, as a result of the repeated application of structure-preserving transformations to the wholeness which exists.

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

• The intricate and beautiful structure of living centers comes about naturally, and most of the time without effort, as a result of the repeated application of structure-preserving transformations to the wholeness which exists.claim0.945
  Central interpretive claim of the chapter, asserting that living structure is an effortless natural outcome of structure-preserving transformations.
• Structure-preserving transformations that continually modify wholeness slowly cause space to be filled with unfolded I-like centers.claim0.853
  Proposition 3 of the Mid-Book Appendix; the claim linking the mathematical process of unfolding to the emergence of I-likeness in natural and built structures.
• In nature the principle of unfolding wholeness creates living structure nearly all the time. Human designers, who are not constrained by this unfolding, can violate the wholeness if they wish to, and can therefore create non-living structure as often as they choose.quote0.843
  Encapsulates the distinction between natural and human-made order, central to Alexander's critique of contemporary architecture.
• The structure of living centers appears in natural things — snowdrops, waves, clouds, mountains, foxes, grains of sand — and these too resemble the human self, requiring that there be a deep connection under the surface.claim0.842
  Alexander's argument that self-likeness in natural forms cannot be explained by artistic intention alone, requiring Proposition 2 for theoretical coherence.
• Life and living structure will appear in the world inevitably because the mathematical way space gives rise to structure necessarily reinforces wholeness as part of its most normal evolution.claim0.841
  Alexander's strongest ontological claim: living structure is not probabilistically improbable but mathematically necessary given the principle of unfolding wholeness
• The profound wholeness of living structure, almost every time it has been done most profoundly, has been done in a mystical‑religious context.claim0.836
  A sweeping historical observation that grounds the claim that mystical context is a near‑universal condition for the highest living structure.
• Nature always produces living structure because it follows a process of unfolding wholeness; human designers can create non-living structure by violating this process.claim0.833
  Core distinction between natural and designed configurations, explaining why properties are ubiquitous in nature but rare in bad design.
• The key thing about all LIVING sequences is that they generate centers in an order which lets each center unfold naturally from the centers laid down before.claim0.833
  Defines the essential structural property that a sequence must have to be living.