Half a dozen sequences taken together can have a very big effect on the environment and show a wholly new way of conceiving space.

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

• 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.claim0.814
  A combinatorial argument that good sequences are astronomically rare, emphasizing the difficulty of discovery.
• Roughly 2,000 long sequences, each containing ~20 smaller snippets, thus about 40,000 short sequences could completely transform the built environment.claim0.810
  Quantitative estimate of the scope of the gene pool needed for a living world.
• 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.claim0.802
  Defines the essential structural property that a sequence must have to be living.
• Less than a trillionth of all the 6 × 10^23 possible sequences actually work well enough to allow smooth unfolding.quote0.799
  Alexander's striking quantification of the rarity of good sequences, underscoring why finding the right order is so difficult and precious.
• Each living center has life to the extent it is linked to other centers; likewise, sequences generating living centers are interdependent.claim0.794
  Establishes the necessity of the network of sequences.
• If the evolution of the natural world follows a step-by-step process in which each step is structure-preserving, then the fifteen properties will appear more and more often, and the degree of life in the wholeness will increase steadily.hypothesis0.790
  Conditional statement linking smooth unfolding to the progressive emergence of the fifteen properties and increased life.
• It is reasonable to expect that sequences, with their inherently far greater power, will have a greater effect than static patterns.claim0.773
  Asserts that dynamic, process-oriented sequences will outperform the earlier pattern language approach.
• We hypothesize that a similar 'brutal' and purely geometric process always occurs somewhere in other kinds of unfolding that generate living order — in poetry, dance, social structure, planning, and family relationships.hypothesis0.772
  Extends the brutal geometry thesis beyond architecture into all creative and social domains; acknowledged as not yet confirmed with certainty