Roughness arises inevitably when a regular order is forced into three-dimensional constraints, producing adaptive irregularities like those in corn cobs, crystal dislocations, and radiolarian shells.

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• Color variation (roughness) brings color to life by preventing flatness; the interaction of slightly different hues creates a shimmering unity.claim0.775
• Roughness is an essential structural feature without which a thing cannot be whole; it is not a residue of technically inferior culture or hand-craft inaccuracyclaim0.774
  Claim that morphological roughness arises from paying attention to what matters most and letting go of what matters less, making it more precise than rigid regularity
• This geometric substance that I call the brutal order comes, in fact, from the need to allow a certain regular rhythm of members to arise within an irregular envelope, because it is fitted to irregular circumstances.claim0.767
  Defines brutal order as the intersection of regular structural rhythm with irregular contextual fitting
• Roughness can never be consciously or deliberately created; to make a thing live, its roughness must be the product of egolessness, the product of no willclaim0.766
  Claim that genuine roughness comes from abandon and freedom, not from contrived effort to appear interesting; artificial roughness is merely contrived
• 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.hypothesis0.759
  Extends the brutal geometry thesis beyond architecture into all creative and social domains; acknowledged as not yet confirmed with certainty
• Their actual roughness, and the visible soft morphological character they have because of this roughness, are of the essence of the fact that they are living.claim0.747
  Asserts that roughness is an essential quality of living structure, not merely a sketch artifact.
• Echoes of similar proportions and angles appear throughout any natural system due to uniform underlying processes, giving a consistent character to different parts.claim0.747
• The intricate and context-specific adaptation that shapes every detail differently is a necessary structural feature of all life.claim0.746
  Foundational claim about the necessity of adaptation for life in structures.