A dynamical interpretation of emergence and its consequences

John CollierPhilosophy

University of KwaZulu-Natal

Outline

1. Use of emergence concept and its historical ground2. Some mistaken ideas about emergence; weak and

strong emergence3. The logical conditions for emergence4. Complex organization and emergence5. Dynamical conditions for emergence6. A problem with applying the dynamical conditions for

emergence to systems in general7. Some possible solutions8. Identifying and managing emergent systems

18th Century use of emergence concept and its historical ground

• Epistemological emergence and model oriented approaches• Origin of the concept

– G. H. Lewes in 1875: something that is incommensurate with its components and not reducible to their sum or their difference

– J. S. Mill (A System of Logic, Bk.III, Ch.6, §1, 1843) does not use the word: “All organised bodies are composed of parts, similar to those composing inorganic nature, and which have even themselves existed in an inorganic state; but the phenomena of life, which result from the juxtaposition of those parts in a certain manner, bear no analogy to any of the effects which would be produced by the action of the component substances considered as mere physical agents. To whatever degree we might imagine our knowledge of the properties of the several ingredients of a living body to be extended and perfected, it is certain that no mere summing up of the separate actions of those elements will ever amount to the action of the living body itself.”

1. UnpredictabilityThe higher level cannot be predicted in principle

2. Non-reducibilityThe whole is logically more than the sum of its parts

3. HolisticThe system cannot be decomposed into (additive combinations of) its parts without loss

4. NoveltyA tricky one. No clear definition, but not merely surprising. A new kind of property

C.D. Broad’s notion of emergence

Some mistaken ideas about emergence

• Mystericism (separate substances, vitalism, causal independence, and ungrounded teleology) “If you can understand it, it isn’t emergent.”

• Emergence is a purely epistemological phenomenon.• Emergence is a property of our models of the world, not of

the world itself.• Emergent computation is more than merely a simulation of

emergence (game of life, chaos models). – Computation that terminates is by definition computable

and hence reducible. As a corollary, numerical models of strongly emergent systems are necessarily not emergent themselves, and thus are potentially misleading.

Emergence trivialized• Emergence is a result of complexity alone, e.g., (Bar-Yam 2011): “In

conventional views the observer considers either the trees or the forest. Those who consider the trees consider the details to be essential and do not see the patterns that arise when considering trees in the context of the forest. Those who consider the forest do not see the details. When one can shift back and forth between seeing the trees and the forest one also sees which aspects of the trees are relevant to the description of the forest. Understanding this relationship in general is the study of emergence.”

• He goes on to give an example: “Consider a key. A description of a key's structure is not enough to show us that it can open a door. To know whether the key can open a door, we need descriptions of both the structure of the key and the structure of the lock. However, we can tell someone that the function of the key is to unlock the door without providing a detailed description of either.”

Weak versus strong emergence

• Useful distinction to make between properties (or systems) that must be understood as a whole, including their large scale interactions but are reducible (weak emergence) from those that are not reducible (strong emergence).

• Distinction originates with myself and Scott Muller (1998), Mark Bedau (1997), David Chalmers (the last only for mental properties, so not the same idea, 2006)

• Paul Humphreys and “fusion” as a causal property creating a new, fused, system. Both weak and strong emergence are fused, and hence subject to being confused.

Broad’s conditions hard to applyConditions 1-4 are hard to detect and hard to distinguish from epiphenomenal properties. However there has been some progress:• Humphreys: fusion as a necessary but not sufficient condition (fused

system is a different one from the old system), though dynamical.• Robert Rosen (1991): systems with analytic but not synthetic models

– Synthetic models are a sum of their parts and pairwise relations, or can be analyzed fully in terms of their inputs and outputs

– Analytic models need not have any corresponding synthetic models. If so, they cannot be reduced to their parts or input-output relations.

– There are many more analytic models than synthetic ones (Gödel).– Logical condition on models, not systems themselves. But the logic of

a good model, on Rosen’s account, must mirror the causal connections of its object. Nonreducibility shows up in closed causal loops in complex organizations (nonlinearities).

• Wimsatt (2007): non-aggregativity – closer to a dynamical view, but not much different from Lewes and Mill.

Computational aspects of emergence• Non-reducibility: A property is nonreducible if it cannot be computed from

additive (or subtractive) combinations of the properties of its parts (Lewes, Rosen).

• Non-predictability: the trajectory of a system is predictable if and only if there is a region η constraining the initial conditions at t0 such that the equations of motion will ensure that the trajectory of the system will pass within some region ε at some time t1, where the region η is chosen to satisfy ε. For indeterministic systems, the values are determined to the extent determined by the probabilistic factors in the laws. Otherwise it is non-predictable. All holonomic trajectories are predictable for an arbitrarily long time using Taylor series (there is a convergent solution).

• Connecting to dynamics: So, non-holonomicity is required for emergent systems with emergent properties (Pattee). The state taken by such systems depends on the path taken. All traditionally studied Hamiltonian systems are holonomic or nearly holonomic (conservation of energy).

Complex organization and emergence (phenomenology)

• The basic idea of an organized system is that it is interconnected in complex ways, so that there are both local and non-local effects.

• Complex organization – involves neither summation nor

top down control, but shows an interaction of bottom-up effects and top-down effects

– Complexly organized systems cannot be decomposed

• Thus they show the characteristics of emergent systems

Interactions of boundaries and system laws (nonholonomic systems)

• Conrad and Matsuno– Differential equations provide the major means of describing the

dynamics of physical systems in both quantum and classical mechanics. The indubitable success of this scheme suggests, on the surface, that in principle it could be extended to a universal program covering all of nature. The problem is that the essence of a differential equation description is a separation of itself from the boundary conditions, which are regarded as arbitrary.

• We cannot do this, in general, for non-holonomic systems.• The problem is not that we cannot separate laws and boundary

conditions, but rather that the systems itself does not allow this sort of solution. We can still understand the system in terms of laws and boundary conditions, but this does not allow us to give full solutions for its behavior.

Failure of the independenceNonholonomic systems, in which boundary conditions are time dependent, by definition:

– Energy is not conserved, e.g., dissipative systems, so stepwise changes of the system dynamics must take finite time.

– Boundary conditions and system laws cannot be separated in principle, except in ad hoc ways.

– Near holonomic we can approximate by step functions at one end, or by perturbation theory at the other. This is the standard methodology. (e.g., phase changes, planetary dynamics)

– Radically non-holonomic systems don’t allow these approximations. If the dissipation rate is comparable to some global property perturbations may grow and the trajectory is path dependent, depending on changing boundary conditions.

Dynamical conditions for emergence

1. The system is nonholonomic, implying the system is nonintegrable (this ensures at least incomplete reducibility)

2. The system is energetically (and/or informationally) open (boundary conditions are dynamic)

3. The system has multiple attractors (alternative divergent paths that arbitrarily close to each other in some region)

4. The characteristic rate of at least one property of the system is of the same order as the rate of the nonholonomic constraint (radically nonHamiltonian)

5. If at least one of the properties is an essential (individuating) property of the system, the system is essentially non-reducible; it is thus an emergent system

Deriving the logical conditions

• Unpredictability: path dependence, divergent solutions (can’t use Taylor series)

• Nonreducibility: laws plus boundary conditions are not adequate to compute trajectories (see unpredictability). Piecewise dynamics of parts and their combinations do not allow computation of trajectory. Trajectory is noncomputable (in principle).

• Holistic: Behaviour of system cannot be localized.• Novelty: New kinds of behaviour become possible.

Examples of likely emergent systems

• Mercury and the Sun (I.I. Shapiro- 3:2 rotation to revolution periods, not 1:1 like the Moon)

• Bénard Cells (must assume cells form to show how cells form – self-reference, impredicativity)

• A wheel starting to skid (nonholonomic and surprising)• Cell differentiation (Rosen, Collier and Banerjee)• Ant behaviours (nest building, foraging, etc.)• Non-selective sympatric speciation (Collier)• Living systems (the original prototype for strong emergence)• The mind, social systems, behavioural economics

Generalizing the dynamical conditions for emergence

• My characterization of emergent systems uses concepts from physics that are clear in that realm.

• However, as some of the examples show, emergent systems are often not easy (or perhaps possible) to be characterized in terms of physical equations.

• We need other ways to characterize emergence dynamically for systems that are not obviously physical.

Two possible approaches

1. We can look at most systems from the perspective of forces and flows in networks. This is a dynamical representation. If the laws governing the forces and flows interact then we have a candidate for emergence.

2. Many higher level systems (biological, mental) can be characterized in terms of information. If information is dissipated in the system at a similar rate to the rates of one of the properties on which it depends, then the property is likely to be emergent. E.g., sympatric (same locale) speciation, genetic information dissipated.

3. Combination of the two approaches works best.

Identifying and managing emergent systems

• Aside from the previous two methods, systems with a certain degree of mathematical complexity will not have general solutions (see next slide).

• Such systems will show unpredictability and path dependent behaviour, so we have to be very careful how we approach their management – the problem is often called the problem of unintended consequences.

Equation: Algebraic Ordinary

Differential

Partial

Differential

One Parameter Trivial Easy Difficult

Linear

Equations

Several

Parameters Easy Difficult Intractable

Many Parameters Intractable Intractable Impossible

One Parameter Very Difficult Very Difficult Impossible

Nonlinear

Equations

Several

Parameters Very Difficult Impossible Impossible

Some notable consequences of dynamical emergence 1

• A whole system is emergent if its individuating property, what makes it what it is, is emergent.

• Without this property the system would not exist. • All systems, though, are embedded in larger systems

with more general dynamics. • We can ask, then, what the region is within the larger

system emergent systems are likely to form.• This involves questions of stability and possible

bifurcation that are well known to chaos theorists.• A mathematical “zoo” of attractor kinds is useful.

Some notable consequences of dynamical emergence 2

• In general for systems that meet the criteria for dynamical emergence there will be regions of stability, transitional zones between stable zones, and regions of instability. Thus properties may be reducible within some regions and not in others.

• This is important for engineering purposes (whether physical, biological, mental or social engineering) for two main reasons.

• Sometimes we want to design systems with regions of stability in which performance is predictable and non-emergent within required operating parameters.

• Other times we want to design systems that will show emergent but stable properties.

• Knowing the likely behavior of the system throughout these regions and nearby in phase space will help with these goals.

A plea for better management practices

• The other major engineering problem is dealing with given complexly organized systems with emergent properties in order to intervene as required for various management purposes, whether it is to control and prevent disasters, restore from disasters, or (in human endeavours) to encourage novelty and creativity.

• It is necessary to work with the systems and not try to assert too much control in order to get good results.

• The most obvious ways to control are not often the best ones to get results in such systems (require excessive energy, have unpredictable consequences.

Facilitation rather than control

• The general form of management I recommend for complex systems is best called facilitation. It encourages their natural tendencies rather than trying to control them from the top, or permitting anarchic local control. Interactions between parts or subgroups should be managed the same way. In emergencies more top down control may be required, but in non-emergency situations it is both expensive and detrimental.

• Interestingly, a management determined to control might reasonably stimulate a situation of or appearance of crisis in order to justify its efforts at control. This is unlikely to happen with facilitation.

Thank you for your attention

Now for questions!