Developmental psychology has shown many psycho-functional aspects in growth of early sensorimotor intelligence. The Martian is intended to exhibit these abilities. The Martian is based on the epistemological foundations of phenomenon of mind whose mathematical theory is called "mental physics". Based on mental physics, the psycho-functional abilities at the sensorimotor stage begin with the ability to represent appearances as intuitions. Mathematical sensibility is the mathematical ability to represent intuitions. Comparation is the first in the three-step process of the "acts of understanding" of mathematical sensibility. The current project is the comparation project. This project aims at: 1) discovering a minimal neural network anatomy that can generate equivalence relations, and 2) also to determine proxy functions for other noetic processes.

Based on embedding field theory, the minimal neural network was discovered with its corresponding property sets. The network exhibits behaviors that are emergent properties. We do not introduce any a priori objective criterion for defining what the network treats as a feature for pattern matching. Predictions were also made by the network. If two pattern shown to have demonstrated no-relationship is placed on a larger retinal-map size, they may demonstrate relationship. This is similar to the visual phenomenon of fonts "a" and "e" appearing similar from a distance. The reported experiments are the first-ever demonstration that ART (adaptive resonance theory) is capable of self-defining feature sets.

**Committee Members:**

- Terence Soule, PhD (Advisor)
- Richard B. Wells, PhD (Advisor)
- Onesmo B. Balemba, PhD (Inside Member)
- Eric Wolbrecht, PhD (Outside Member)

- Introduction (787KB)
- Problem Statement
- Brain Function
- Philosophy of Mind and Psychology
- Past and current works on determining equivalence like problems
- Comparison (880 KB)
- What does it mean to compare?
- Definition of "compare" and "comparison"
- Giving a "relation"
- onPrecise definition of "relation"
- Some Properties of Relation
- The notion of "identical"
- The notion of "interchangeability"
- The notion of "equivalence"
- Mental Physics (2MB)
- Logical vs. Real division
- Descates' error and why Mind-Body division is a logical division
- Organized Being (OB)
- Mind-Body relation to Nous-Soma
- Mathematical description of the OB
- Synthesis in sensibility
- Comparation is logical comparison
- Principal quantities of comparation
- Context for comparation
- Grounds or basis for TRJ to judge comparation
- Basic Tools and Techniques (1.5MB)
- Set-Membership Theory
- Embedding Field Theory
- Method of Minimal Anatomies
- Modelling Scale
- Building the comparation network and generation of equivalence relation (1.6MB)
- Qualitative Modelling (Comparation Network showing a relationship)
- Quantitative Model (Comparation)
- Behavior of the proposed minimal neural network
- Case-1, uppercase English letters (A to Z)
- Case-2, uppercase English letters (A to Z) versus its modified patters
- Case-3, 2x resolution uppercase English letters (A to Z)
- Case-4, Arabic numerals (0 to 9)
- Additions to the above minimal neural network
- Behavior of the proposed minimal anatomy
- Conclusion (50KB)
- Bibliography (109KB)
- Appendix (503KB)

Alternative, Download the full document. (6.5MB)

*The minimal neural network without the proxies and receiving input patterns from set of upper-case English letters results in network demonstrating relationship and no-relationship for pattern-combos (a & b). The minimal anatomy composed of the noetic proxies and receiving pattern-sequences, demonstrates unsupervised capability to generate equivalence relations (c & d).*

Sharma, B. L. (2013). Determination Of An Embedding Field Theory Based Minimal Neural Network Anatomy Capable Of Generating Equivalence Relations For The Function Of Comparation And Associated Proxy Functions For Other Noetic Processes, Ph.D Dissertation (Neuroscience), The University of Idaho, Moscow, ID, USA, Dec. 10.