Hierarchical Concepts

The central distinction

An ultrametric hierarchy organizes states by degrees of similarity. Similarity alone does not make two different states indistinguishable: an ultrametric is still a metric. A restricted observation map is what groups states that an observer cannot tell apart.

What the note does

The MIND note gives a precise account of finite ball partitions, observation quotients, resolution towers, and an adaptive refinement index for a regular rooted tree. It also separates symmetry indices from information gain. Much of the underlying mathematics is established background; the note is framed as a correction and synthesis.

Why it matters to The MIND

Concepts often depend on resolution. At one level, many states receive the same description; a finer observation separates them. This page connects the historical ultrametric and unconsciousness theme to the more explicit observation language of ProLTs and concept differentiation.

Current boundary

The note does not formalize a complete psychology of unconscious thought or establish an empirical model of consciousness. Its claim is about mathematical observability in a specified hierarchy.