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.

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• The geometry of the physical world has the most profound impact on human inner freedom and sense of life.claim0.836
  Central thesis of the chapter.
• If living structure impacts inner freedom, then the physical world has impact on the most precious attribute of human existence.hypothesis0.832
  Stated early in the chapter as a conditional.
• 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.claim0.826
  Synthesis of geometry and life.
• What is the impact of living structure on human life?question0.820
  Opening question of the chapter.
• 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.claim0.820
  Alexander's strongest ontological claim: living structure is not probabilistically improbable but mathematically necessary given the principle of unfolding wholeness
• Buildings and objects with living structure enlarge our capacity for relatedness; those without deaden it, even in nature.claim0.814
  Practical consequence for architecture and urbanism.
• Living structure is enormously susceptible to minor changes, and accuracy of detail is necessary for success.claim0.807
  Warning that the recursion of centers requires extreme precision.
• The geometry of living structure is markedly different in kind from the geometry of design done on a drawing board or on a computer.claim0.805
  Fundamental distinction between generated and static geometry.