From Community Dynamics to Topological Beauty
A Comparison Between Davis & Schübeler and Ron Atkin
Sungchul Ji and J. J. Joshua Davis
Introduction
What makes a community harmonious and beautiful?
The article “A Simulation Model to Explore Community Dynamics Based on Resources and Quality of Space” by Jeffery Jonathan Joshua (ישוע) Davis and Florian Schübeler (2019) offers one answer: the emergent harmony of a community arises from soft variables such as kindness, inner peace, and the “quality of space” (QOS), as much as from tangible resources.
Ron Atkin’s topological measure of beauty, by contrast, suggests that harmony and beauty emerge when the complexity of a system matches the cognitive structure of the observer. Using tools such as simplicial complexes and q-analysis, Atkin developed a mathematical lens to quantify aesthetic and structural balance.
By comparing these two frameworks using a 6-Dimensional Venn-type Comparative Analysis (6VCA) [1] as shown in Table 1, we uncover how system dynamics (time-based evolution) and topological resonance (structural beauty) can complement one another in the study of peace and harmony.
Shared Principles (C(S))
Despite their different languages—system dynamics for Davis & Schübeler and algebraic topology for Atkin—both frameworks share a profound principle:
Peace and harmony emerge when relationships (social or structural) are organized in a way that resonates with human perception and values.
In Davis & Schübeler’s model, quality of space (QOS) drives collective well-being, much like topological resonance drives the perception of beauty in Atkin’s measure.
Both highlight the interplay of order and complexity—too little structure leads to stagnation, while too much leads to chaos.
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6VCA: Community Dynamics vs. Atkin’s Measure of Beauty
Complementarity (C(C))
The two models are complementary:
Community Dynamics Model (A): Focuses on how harmony evolves over time—simulating growth, oscillations, or collapse based on resources, population, and Quality of Space.
Atkin’s Topological Measure (B): Focuses on how harmony is perceived structurally, capturing the balance of order and complexity at a single moment.
Together, they offer a time–structure complementarity: A tells us “how peace grows,” while B tells us “why peace feels beautiful.”
Unique Contributions (D(A) and D(B))
Davis & Schübeler (A): Offers a practical simulation tool for intentional communities, emphasizing actions of kindness and soft variables often neglected by traditional economic models and mainstream science.
Atkin (B): Provides a universal, mathematical language for describing beauty, harmony, and cognitive resonance, applicable beyond social systems (e.g., art, music, science).
Conclusion
The Community Dynamics Model and Atkin’s Q-analysis illuminate two complementary dimensions of harmony:
One is dynamic, temporal, and experiential.
The other is structural, topological, and abstract.
By integrating these perspectives, we can better understand how communities function and evolve, and also why they feel beautiful and peaceful when conditions align.
References:
[1] Ji, S. (2025). A 6-Dimeniosnal Venn-type Comparative Analysis of a pair of Opposing Views on Contemporary Theoretical Physics.