Tree vs Semilattice

Two ways a whole can be made of parts. In a tree, any two units are nested or disjoint. In a semilattice, units overlap, and each overlap is itself a unit. Living things are semilattices, but the mind can only hold a tree at once (Alexander — A City Is Not a Tree).

Why it matters

• Richness: on 20 elements, a tree holds at most 19 units; a semilattice holds over 1,000,000.
• Cognition: "In a single mental act you can only visualize a tree." People strip overlap out of what they perceive, and planners strip it out of cities. This is Willingham's comprehension narrowing from the structural side (Surface vs Deep Structure).
• Not all overlap counts: "A garbage can is full of overlap." Structure needs the right overlap.

In this wiki

• The wiki is a semilattice, its folders a tree. A page lives in one folder but in many link neighbourhoods. Syntheses are recorded overlaps. That's Method Reflection T2, now grounded.
• Which links earn their place: a link should mark a real shared unit (a mechanism, a claim, a tension). One that just repeats a shared word is garbage-can overlap (The Borges Map).

For the front door

You can't show a semilattice whole, and the global graph "hairball" is exactly that failure. Show several trees over the same semilattice and let the reader switch between them, the way the orange/football example alternates groupings. The LATCH views are those trees (Legibility in the Lens, Not the Land).

Connections

• Legibility — imposing a tree on a semilattice is the legibility failure in built form.
• LATCH — five standard trees to lay over one body of knowledge.
• Living Structure — Alexander's later theory of what makes overlapping centers alive.

Sources

• Alexander — A City Is Not a Tree