1. 1 Emergence Alex Ryan alex.ryan@dsto.defence.gov.au M. C. Escher, Moebius Strip II (Red Ants)

2. 2 Key Points Provides an alternative to level-based accounts of emergence (Scope, Resolution, State) Shows the Möbius strip has emergent properties Gives precise definitions for emergent properties and emergence

3. 3 The Level-based Explanation Emergent property at one level is meaningless at a lower level Flocking (macro) of a single bird (micro) Consciousness of a neuron

4. 4 Scope = {elements within the system boundary (space)} X {moments (time)} elements boundary system time

5. 5 Resolution = Smallest possible distinction of elements (space) & moments (time)

6. 6 State Microstate Macrostate The information that distinguishes between alternative system configurations up to some resolution at one moment in time Ideal Gas

7. 7 Macro to Micro Relationship The macrostate has either a lower resolution or a greater scope, or both.

8. 8 Novel Emergent Property A property is a novel emergent property iff it is present in a macrostate but it is not present in any microstate, where the microstates differ from the macrostate only in scope.

9. 9 Emergence of One-sidedness Component i Emergent Properties One sided One edged Non-orientable

10. 10 Defn: Emergence Emergence is the process whereby the assembly, breakdown or restructuring of a system results in one or more novel emergent properties.

11. 11 Summary Emergence is coupled to scope, not level A novel emergent property is a difference between global and local structure Emergent properties can be modelled, emergence cannot Emergence does not need to be complex, adaptive, or self-organising