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Emergence of Emergence


To initiate a living roadmap/taxonomy of Organizing Principles of Emergence, with examples and links to external resources.

Applications/Potential uses

  • Educational/Outreach
  • Common meta-language for inter-field communication
  • A hub for researchers wanting to publicize their research (mention/link)
  • Fodder for funding agencies

Format (Data structure)

Two main possibilities

  • Directed acyclic graph (DAG) of concepts (from more general to more specific)
    • Pro: easy to navigate and learn from
    • Con: may be too restrictive; structuring as such will require significant effort
  • ad-hoc graph (pages and links, a la Wiki)
    • Pro: unlimited flexibility
    • Con: hard to get a full picture or learn from; not a taxonomy

Knowen default format is DAG. Every page has to have one or more parent pages.

Rules of the project

  • Every participating author can invite additional authors
  • Don't hesitate to edit, but try to be prompt, since while you are editing other will not be able to.
  • Every edit is recorded in history, and can be commented on
  • General comments on a page can be made from history view of the page
  • When a page gets too large, consider keeping only generalities in it, and splitting details into descendant pages.


The initial material was collected during meeting at the Aspen Physics Center on July 18, 2017. Participants included Ehud Altman (Berkeley), Colin Benjamin (Bhubaneswar), David Campbell (BU), Lincoln Carr (Mines), Adrian Del Maestro (U Vermont), Clifford Johnson (USC), Stefan Kehrein (Goettingen), Ivar Martin (Argonne), David Pines (Santa Fe Inst), Jörg Schmiedmayer (Vienna), Sarang Gopalakrishnan (CUNY).
The product of the meeting was a list of (i) Common Features (principles?) of Emergence, (ii) Examples of emergent behaviors or systems, (iii) Big questions.

Concepts/Principles of Emergent behavior

  • Nonlinearity [fluids, chaos, integrable systems]
  • Complexity [simple rules, complex behaviors: fractals, bifurcations, Cellular automata]
  • Collective behavior

  • Universality [phase transitions, same crystals of different atoms]
  • Appearance of nearly conserved quantities [cold gases]
  • Renormalization group/C-theorem
  • Scaling, self-similarity [roads, blood vessels]

  • Networks [gene regulation, social]
  • Patterns, Motifs [genes]
  • Modularity [particles, animals, planets, galaxies]

  • Frustration
  • Natural selection
  • Trade-offs
  • Diversity
  • Robustness, Adaptivity
  • Synergy/cooperativity
  • Game theory

  • Fractional derivatives
  • Fractional geometry
  • Fractality/multifractality

  • Quantum to classical transition
  • Interactions
  • Entanglement
  • Emergent locality
  • Dissipation

  • Dualities
  • Effective theories

  • Non-Gaussian statistics
  • Central Limit Theorem
  • Highly structured probability spaces [DNA, proteins]

Examples of emergent behaviors or systems

  • Brain
  • Memory
  • Senses
  • Evolution
  • Last Universal Common Ancestor

  • Cities
  • Geology, hydrology
  • Flocks/colonies

  • Sand dunes
  • Entropy
  • Arrow of time
  • Dissipation
  • Entanglement

  • Superconductivity
  • Solids, liquids, gases
  • Phonons
  • Quasiparticles

  • Localization
  • Integrability
  • Solitons

  • Big Bang
  • Space-time
  • Standard model
  • AdS/CFT
  • T-duality

  • Reductionism :)

Big questions

  • What constitutes an organizing principle? Would we know it when we see it?
  • Are the principles the same, from quantum to bio?
  • How many organizing principles are there? (10-20, or $10^6$?)
  • Are there predictive principles?
  • Can the principles be (made) quantitative?

  • Does emergence mean appearance of simple behaviors despite complex constituents?

  • Is complexity equivalent to algorithmic complexity?
  • Are there common ways to identify complex systems, to tell apart soup from hidden order?