A dynamical interpretation of
emergence and its consequences
John Collier
Philosophy
University of KwaZulu-Natal
Outline
1. Use of emergence concept and its historical ground
2. Some mistaken ideas about emergence; weak and
strong emergence
3. The logical conditions for emergence
4. Complex organization and emergence
5. Dynamical conditions for emergence
6. A problem with applying the dynamical conditions for
emergence to systems in general
7. Some possible solutions
8. 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.”
C.D. Broad’s notion of emergence
1. Unpredictability
The higher level cannot be predicted in principle
2. Non-reducibility
The whole is logically more than the sum of its parts
3. Holistic
The system cannot be decomposed into (additive
combinations of) its parts without loss
4. Novelty
A tricky one. No clear definition, but not merely
surprising. A new kind of property
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 apply
Conditions 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 topdown 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 independence
Nonholonomic 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 nonreducible; 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.
Ordinary
Partial
Differential
Differential
Trivial
Easy
Difficult
Easy
Difficult
Intractable
Many Parameters Intractable
Intractable
Impossible
One Parameter
Very Difficult
Very Difficult
Impossible
Very Difficult
Impossible
Impossible
Equation:
Algebraic
One Parameter
Linear
Several
Equations
Parameters
Nonlinear
Several
Equations
Parameters
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!