The deep order which produces life in buildings is a direct result of the physical and mathematical structure that occurs in space.

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• It is this injection of definite, strong, geometrical order that allows the profound depth of the made thing — the building in the land — and it is from this that the order must and will arise.claim0.837
  The geometric injection is the causal source of the building's profound depth
• The kind of order that occurs in living structure has a complexity not usually describable by drawings or by architectural images.claim0.818
  Emphasizes the non-pictorial, process-dependent nature of living order.
• 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.claim0.813
  The mystery that beautiful geometry often yields good structural behavior is acknowledged but not yet fully explained mathematically.
• It is only when engineering and architecture work together from the very first day that deep feeling or life can be attained in a building.claim0.811
  Assertion about the necessity of early engineering integration for living quality.
• 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.claim0.809
  Synthesis of geometry and life.
• 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.claim0.804
  Alexander's strongest ontological claim: living structure is not probabilistically improbable but mathematically necessary given the principle of unfolding wholeness
• The deepest living structure in buildings is not attainable without some new understanding, without a new faith based on a new physical and intellectual grasp of the nature of the material universe.claim0.802
  A strong conditional: the creation of the highest living structure requires a cosmology that reunites self and matter in terms consistent with modern science.
• We cannot create living order only by concentrating on appearance; we must characterize the geometry that comes from living process.claim0.797