Stefan Geier's Diploma Thesis and James Deese's Butterfly Experiment: transition probabilities and triangular-tetrahedral-hexagonal cognitive-neuronal structures and artificial intelligence and neurophysiology

Stefan Geier's Diploma Thesis (LMU Munich, 1987) and James Deese's Butterfly Experiment:Transition probabilities, triangular-tetrahedral-hexagonal cognitive-neuronal structures, artificial intelligence, and neurophysiology.
(A first look)

Stefan Geier's Diploma Thesis (LMU Munich, 1987) can be compressed into one central scientific statement: cognitive structures are scale-dependent. Associative near terms and concepts are best described by transition probabilities. Distant terms and concepts in Geier's analyses of James Deese's butterfly field are best described by a triangular-tetrahedral(-hexagonal) structure, featuring Nature as the superordinate apex and Fauna, Seasons/Sun, and Colors/Sky forming the basal triangle. The hexagonal extension is a necessary consequence of the triangular, near-equilateral basic structure of the cognitive map and its geometric representation.

The thesis recognizes a completely different regime for closely associated terms. Near terms, such as bee, flower, insect, fly, bird, wing, moth, and cocoon, are not best described solely by undirected distances. Instead, they form a local, directed association field. The correct model for this is a transition probability: from stimulus i to reaction j, how often does the transition occur?

Remake of the Schoenpflug & Schoenpflug (1983, p. 138) transition-probability network, as cited and used by Geier (1987, Fig. 5.3, p. 71 ff). The remake is qualitative and didactic, not a numerical recovery.

The importance of transition probabilities is not the only structural result; a tetrahedral structure with near-equilateral trinagles is also a basic feature of human associative cognitive structures:

Table of the six semantic edges from page 75

Edge	Wording on page 75	Geometric reconstruction	Interpretive note
D1	"nature" - "bees" - Fauna	Nature to Fauna	Apex-to-basal edge; bees functions as bridge.
D2	"nature" - Jahreszeiten & Sonnenschein	Nature to Seasons/Sun	Apex-to-basal edge.
D3	"nature" - "flower" - "yellow" - Farben & Himmel	Nature to Colors/Sky	Apex-to-basal edge via flower/yellow.
D4	Fauna - Farben & Himmel	Fauna to Colors/Sky	Basal edge A-C; must be straight in the reconstruction.
D5	Fauna - Jahreszeiten	Fauna to Seasons	Basal edge A-B.
D6	Farben & Himmel - "yellow" - "sunshine" - Jahreszeiten	Colors/Sky to Seasons/Sun	Basal edge C-B via yellow/sunshine.

The edge list is not a minor detail. It is the central semantic code of the tetrahedron. Edges 1, 2, and 3 are explicitly nature-conditioned; edges 4, 5, and 6 connect the other three concept regions. This is the strongest textual reason to place Nature at the special D vertex and to place Fauna, Seasons/Sun, and Colors/Sky on the basal triangular face.

 

Summary of the consequences of Stefan Geier's Diploma Thesis:

Scale	Best description	Why
Associative near terms	Directed transition probabilities p(j | i)	Local associative motion can be asymmetric; arrow direction and strength matter.
Distant concept regions	Triangular-tetrahedral-hexagonal geometry	Separated clusters require a global relational map with vertices, faces, and edges.
Modern AI implementation	Probability plus embeddings plus attention	Large models combine local prediction with high-dimensional relational geometry.

This distinction is highly scientific. It prevents a category error. Near association is dynamic and probabilistic; distant semantic organization is geometric. A good cognitive theory needs both. Stefan Geier's thesis contains both and therefore is a basic work for artificial intelligence (AI), neuronal networks and neurophysiology.

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