Ultrametric Model of Mind, I: Review

TL;DR

This paper develops an ultrametric mathematical model based on hierarchical clustering to represent Matte Blanco's principles of symmetric and asymmetric being, linking psychoanalytic concepts with formal topology.

Contribution

It introduces an ultrametric topology as a novel mathematical framework for modeling the structure of symmetric reasoning in psychoanalytic theory.

Findings

Ultrametric topology models hierarchical structure in text data.

The model captures symmetric reasoning processes.

Foundation for analyzing conscious and unconscious thought processes.

Abstract

We mathematically model Ignacio Matte Blanco's principles of symmetric and asymmetric being through use of an ultrametric topology. We use for this the highly regarded 1975 book of this Chilean psychiatrist and pyschoanalyst (born 1908, died 1995). Such an ultrametric model corresponds to hierarchical clustering in the empirical data, e.g. text. We show how an ultrametric topology can be used as a mathematical model for the structure of the logic that reflects or expresses Matte Blanco's symmetric being, and hence of the reasoning and thought processes involved in conscious reasoning or in reasoning that is lacking, perhaps entirely, in consciousness or awareness of itself. In a companion paper we study how symmetric (in the sense of Matte Blanco's) reasoning can be demarcated in a context of symmetric and asymmetric reasoning provided by narrative text.