The geometry of space plays an enormous role in the presence or absence of deep human life: centers in space either support or hinder the evolution of free life.

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

• The geometry of the physical world has the most profound impact on human inner freedom and sense of life.claim0.861
  Central thesis of the chapter.
• The deep nature of space appears to be so profound that just the geometric unfolding, when done properly, leads to results which make sense from an engineering point of view.claim0.849
  The mystery that beautiful geometry often yields good structural behavior is acknowledged but not yet fully explained mathematically.
• Space becomes more deeply functional and well-organized as it begins to resemble more deeply the human person; life in a center means the space begins to resemble the human selfclaim0.835
  Extraordinary structural claim: functional organization converges on resemblance to the human self
• The impact of the geometry of the environment—its living or not-living structure—has a trace-like, catalytic effect on emotional, social, spiritual, and physical well-being.claim0.826
  Analogy to trace elements and enzymes.
• 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.claim0.810
  Alexander's strongest ontological claim: living structure is not probabilistically improbable but mathematically necessary given the principle of unfolding wholeness
• Life occurs in space not as an attribute of living organisms but as an attribute of space itselfclaim0.809
  Radical ontological claim that life is a property of spatial configuration itself, not limited to biological organisms; the degree of life depends on the coherence of centers
• The deep order which produces life in buildings is a direct result of the physical and mathematical structure that occurs in space.claim0.809
  Points toward the scientific/mathematical foundation promised later in the book.
• The option space of beings enables us truly to see life for the first time, in the absence of standard phylogenetic relationships.claim0.807
  Epistemological claim about the role of novel organisms.