The precise number fifteen is not significant, but the order of magnitude of the number is significant—there are not five and not a hundred, but about fifteen

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

• Everything is vague to a degree you do not realize till you have tried to make it precise.concept0.746
  Epigraph motivating the necessity of precise semantic specification in programming
• The fifteen properties are the very simplest things which can possibly be used as a basis for assembly of a living thing, and it is from simplicity that they ultimately derive.claim0.734
  Justification for using the fifteen transformations as a foundation.
• For a given task, the number of all sequences which work is tiny by comparison with the huge number of all possible sequences; less than a trillionth of all 6 × 10^23 possible sequences actually work well enough.claim0.733
  A combinatorial argument that good sequences are astronomically rare, emphasizing the difficulty of discovery.
• The fifteen properties are not independent; they overlap, and each property is partly defined in terms of the other fifteen propertiesclaim0.730
  Meta-claim about the logical structure of the properties: the more carefully each is defined, the more it relies on the others, revealing their common origin in the field of centers
• The fifteen properties emerge directly and inevitably from the unfolding of the whole; it is these fifteen properties that guide all differentiations during development.claim0.729
  Alexander's claim that living structure properties are not incidental but are the operative mechanisms of wholeness-preserving transformation
• Each of the fifteen transformations designates one way in which a structure may be transformed into another structure, while increasing its life.quote0.728
  Defines the role of the transformations in generating living structure.
• Why do the fifteen properties occur in nature?question0.726
• Levels of scale is not a mechanical thing requiring merely a wide range of sizes; it arises properly only when each center gives life to the next one and the detail actually does something to create life in larger centersclaim0.724
  Clarification that levels of scale fails when detail is merely present but not doing anything—as in machine-made doors with superficially many panels that have no real life