Like many young physicists in spe, there was a period in which I got really into the idea of emergence – a notoriously slippery idea. It is something like the idea that a complex system (complex as in a network of interacting elements, not as in complicated) can have properties that can not be attributed to any of its constituents. Classic examples span an enormous range of ideas:

The patterns a flock of starlings make (emergent behaviour in the system of interacting birds) Superconductivity (emergent behaviour in the system of electrons interacting in a lattice) Consciousness (emergent behaviour in the system of interacting neurons(?))

It has often been summarised by the aphorism “more is different”, after the title of the legendary essay by Phil Anderson.

Sure, more is different, but different how?

Something about the new phenomenon has to be different in an exciting way to deserve such a pretentious word as emergent. That is the source of many discussions, and misunderstandings.

Since we can put different thresholds on how exciting the phenomenon should be, a hierarchy of emergence, ehm, emerges, that generally describes not very exciting things as weakly emergent, and very exciting things as strongly emergent. Even if excitement isomorphic R, it’s probably useful to talk about some discrete classes:

- very weak emergence: "The principle that whole entities exhibit properties which are meaningful only when attributed to the whole, not to its parts. Every model of a human activity system exhibits properties as a whole entitity which derive from its component activities and their structure, but cannot be reduced to them."" (Checkland 1999)
Checkland mentions two important things: 1. A single unit can not show emergent behaviour. Only a property of multiple things can be called emergent. 2. In the example of a human activity system, he mentions that the behaviour can be derived from the components and theit structure. That places his interpretation firmly in the weak emergence camp, as the defintion of strong emergence later will hopefully illustrate. What makes this level *very* weak is that there is no lower bound on the excitement we should feel upon observing the phenomenon. Any property that can only be defined on a complex of units qualifies. Even pretty mundane things like a distance between two objects, or a centre of gravity, will do. This is not the type that got me excited. 
  • weak emergence:

  • strong emergence: There is no way to dedce the phenomenon from the units, or a description of their interactions. Basically, it is incomputable from facts. It gets very close to another slippery idea: qualia (, escept for the fact that qualia generally make no reference to complexity (AFAIK).

Better quantifier: efficiently computable. like how we this about possible transitions in thermodynamics.