So how is self-organization related to beauty? A thing is beautiful if it is paradoxical. Beauty has or contains the following features:
Complexity within Simplicity
Digital-Analog (particular individuals that can coordinate their actions)
Emergent from Conflict
Evolutionary (changes over time)
Generative and Creative
Hierarchical Organization
Play (a nonserious thing done seriously)
Reflexivity or Feedback
Rhythmicity
Rule-Based
Scalar Self-Similarity
Time-Bound
Unity in Multiplicity
These are also features of self-organizing processes. Christian Fuchs lists the following features as aspects of self-organization:
Emergence
Complexity
Cohesion (digial-analog)
Openness
Bottom-up Emergence
Downward Causation
Non-Linearity
Feedback Loops, Circular Causality
Information
Relative Chance
Hierarchy
Globalization and Localization
Unity in Plurality (Generality and Specificity)
And for Emergence, he lists the following aspects:
Synergism (productive interaction between parts)
Novelty
Irreducibility
Unpredictability
Coherence/Correlation
Historicity
If we compare the lists, we can see the correlation between self-organizing complex systems/processes and beauty. Each have the same attributes. "Cognition, co-operation and communication are phenomena that can be found in different forms in all self-organizing systems. Information is a relationship that exists as a relationship between specific organizational units of matter (Fuchs). All beautiful objects are information-generating processes, and all successful firms are, in the broadest definition of the term, information-generating processes (if you inform something, you give it form -- and giving things new forms is what any business does). And to the extent that something is a self-organizing process, it is beautiful. Thus, understanding the nature of beauty helps one to understand whether or not you have a healthy, productive, profitable firm.
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