Center Bryn Mawr College | ||
March 26, 2003 and April 2, 2003
Rob Wozniak
A Developmental Psychologist Among the Emergenauts; Or, a Few Preliminary
Reflections Made upon Observations Recorded during the Course of a Six-Month
Voyage of Discovery Aboard the H.M.S. Emergence
One Very
General Question
“Are there general ‘laws
of emergence’? Or is the nature of
emergence system or system class dependent?”
A Number
of More Specific Questions
Self-Organization
Emergence
is closely related to self-organization. Although
self-organization has been variously defined, most definitions involve some
variant of the following claim: In self-organizing
systems, global order (i.e., complex aggregate structure/behavior) results (emerges)
from the local behaviors of simple agents following simple rules specifying
conditions under which those agents act (interact) in such a way that the results
of the agents’ actions are fed back as input to the operation of the rule system
at some future time step.
Q1. Emergence (of global order from local interactions)
would appear to be criterial for self-organization
so defined. But is self-organization
so defined criterial for emergence?
Q2. Must the rules of self-organizing systems be
simple? How simple? How much less complex than aggregate behavior
(of brains, cities, families, economies) does the rule
system defining the behavior of individuals have to be?
Self-organization
appears to depend on some minimum number of agents, many (but not necessarily
all) of whom are operating in parallel (i.e., following the same rules under
the same conditions). As
Flake (1998) puts it: “Complex systems with emergent properties are often highly
parallel collections of similar units. Ant colonies owe much of their sophistication
to the fact that they consist of many ants...A parallel system is inherently
more efficient...Parallel systems that are redundant have fault tolerance...some
ants die...similar ants can substitute...and subtle variation among the units
of a parallel system allows for multiple problem solutions to be attempted simultaneously”
(p. 4).
Q3. Are there limitations to massive parallelism
with increases in rule system complexity, as for example, in biological systems. While cells,
for example, carry a complete copy of the genome, gene expression is a complex
function of a given cell’s local environment.
Even ants, whose behavioral rule system may be less complicated than
the genome, presumably act on only a subset of those rules as a function of
their local environment. Cells and ants,
in other words, are functionally differentiated in ways that seem to violate
the principle of massive parallelism; or are they?
Q4. Could it be that the general rule in complex biological
systems is something like “provide each agent with a full lexicon of rules but
allow the subset of active rules to be determined by local information and to
change over time as local conditions change?” Are simple rule systems (e.g., Game of Life)
just limiting conditions on this complexity or is this a principled distinction?
Randomness, Complexity/Criticality,
Chaos
Resnick (1994) cites the following claim: “the study of
self-organizing systems is, in some ways, the ‘related opposite’ of the study
of chaos: in self-organizing systems, orderly patterns emerge out of lower-order
randomness; in chaotic systems, unpredictable behavior emerges out of lower-level
deterministic rules” (p. 14).
Q5. What exactly does it mean for a system to be
complex?
Q6. What is the relationship between randomness,
complexity, and chaos? Between complexity and criticality?
Q7. In what sense, if at all, does randomness underlie emergence in self-organizing systems
(in termites there is an element of randomness, but Langton’s
ant and boids seem to be completely deterministic)
Q8. Isn’t aggregate behavior in a complex, self-organizing
system just as “unpredictable” from knowledge of local rules as it is in chaos?
Q9. Is all complexity a function of perturbations in
systems that have self-organized to criticality?
Q10. Are emergence and complexity just two sides
of the same coin?
Levels of Organization
(Hierarchical Structure)
Employing
the example of a standing wave produced by a boulder in a flowing stream, Holland
claims that emergence “usually involves patterns of interaction that persist
despite a continual turnover in the constituents of the patterns” (p. 7) and
that “persistent patterns at one level of observation can become building blocks
for persistent patterns at still more complex levels...At each level of observation
the persistent combinations of the previous level constrain what emerges at
the next level” (pp. 7-8). Ants, though
they may be following simple rules, are themselves complex organisms whose rule
following is presumably a pattern emerging out of local interactions among populations
of neurons, etc. Indeed, systems of any
level of complexity at all would seem to be composed of sub-systems that are
themselves composed of subsystems, etc. etc. Yet much of the discourse about emergence seems
to be two-leveled, focusing on agents as units whose interactions yield complexity
at the next-higher aggregate level. Indeed,
even Bak seems to fall prey to this tendency.
In describing that canonical example of self-organized criticality, the
sand pile, he argues that as the pile begins to self-organize, “there is no
global communication within the pile...just many individual grains of sand...[whose]
addition...[transforms] the system from a state in which the individual grains
follow their own local dynamics to a critical state where the emergent dynamics
are global” (p. 51).
Q11. How do we take the existence of multiple (not
just two) levels of organization into account in conceptualizing/modeling emergence?
Q12. Does emergence usually involve patterns of interaction
that persist despite turnover in the constituents of the patterns?
Q13. Aren’t small changes (local dynamics) in Bak’s sand pile locally catastrophic? Is it reasonable to talk about local criticality
for components of the sand pile?
Q14. Could local catastrophes (occurring in subsystems
with their own states of self-organized criticality) constitute the self-organizing
process that brings the sand pile as a whole to global criticality, at which
point the size of landslides is limited only by the size of a grain of sand
at one end and the total pile at the other (i.e., is scale-free)?
Holism/Nonreduction
Almost
everyone who comments on emergence argues that it is a case of the whole being
“more than the sum of its parts” or as Paul put it earlier in the year (and
I’m paraphrasing), properties of elements allow more than one outcome when elements
interact, hence the behavior of the whole cannot in principle be understood
solely in terms of properties of the elements.
Or again as Bak put it in discussing his sand-pile,
once criticality has been reached, “the avalanches form a dynamic of their own,
which can be understood only from a holistic description of the properties of
the entire pile rather than from a reductionist description
of individual grains...” Emergent phenomena,
in other words, cannot be understood in terms of agents operating in isolation;
one must take into account both the agents and interactions among agents.
This
appears to introduce a non-reductive element into the “science of complexity”.
Some like Holland, who describes a checkersplaying
program as “fully reducible to the rules (instructions) that define it, so nothing
remains hidden; yet the behaviors generated are not easily anticipated from
an inspection of those rules” (p. 5) attempt to save reductionism by redefining
it in terms of the transparency of the laws governing the system; but this seems
to miss the point. It isn’t just the rules, it’s the rules and the interactions
among rules (as well quite possibly as constraints placed on the rules by specifics
of architecture and by the environment within which the system operates, see
below) that lead to unanticipated behavior.
Q15. Do the rules governing agent behavior in a complex
system interact in a principled fashion, i.e., can interactions among rules
be described by meta-rules or are all such interactions in principle idiographic
(in which case the “science” of emergent phenomena may be little different from
any other purely historical enterprise)?
Q16. Once phenomena have emerged at a higher level
of analysis than that of individual agents, won’t theoretical concepts and terms
(e.g., “flock,” “neighborhood,” “temperature”) be required to describe the higher-level
that do not have meaningfully exact counterparts (e.g., a group of birds, a
group of residents, mean kinetic energy of molecules) at the lower level.
Another way of saying this is to ask whether theoretical meaning in higher-level
terms and concepts depending on interactional phenomena
at the higher-level won’t always, de facto, introduce a non-reductive element
into a science of complexity.
Unpredictability
Last
week, Mark nicely described one sense of the term “unpredictable” when he suggested
(and this is an approximate quotation) that “emergence involves aggregate phenomena
that can not be intuited from the rules obeyed by individuals.”
This too is a common refrain in the literature.
As Bak says of the indicators of criticality “Zipf's law as well as the other three phenomena [the power
law, 1/f noise, fractals] are emergent in the sense that they are not obvious
consequences of the underlying dynamical rules." (p. 26).
Q17. Is the unpredictability of emergent phenomena merely
in the “eye of the beholder”? Who is
to say that a more powerful intellect than ours might not, in fact, be able
to intuit the nature of aggregate phenomena from an inspection of local rules?
Q18. Is unpredictability merely a practical (even
if principled) limitation as implied in the following passage from Bak: “In hindsight one can trace the history of a...[catastrophic
change] in narrative language, using the methods of history rather than those
of physics...[but] to predict the event, one would have to measure everything
everywhere with absolute accuracy, which is impossible. Then one would have to perform an accurate computation
based on this information, which is equally impossible” (p. 61).
Q19. Would emergent phenomena cease to be emergent
if the relationship between aggregate phenomena and local interactions were
completely understood?
A
much stronger sense of the term “predictable,” that does not depend on the eye
of the beholder, asserts that for a systemic outcome to be predictable, the
system’s state or at least the probability of the system’s being in a given
state at time n must be deducible in principle from some initial state at time
1 and the laws describing the behavior of the system’s components. Demonstrating that prediction in this strong
sense is impossible in principle would provide a strong sense of unpredictability,
immune to future epistemic advances.
Q20. Is the relationship between aggregate phenomena
and local interactions theoretically incomprehensible (i.e., the strong form
of unpredictability)? Is this what is
meant by a system’s being “provably computationally universal” (i.e., no analytic
solution, no adequate closed-form mathematical formulation)?
Q21. Does theoretical incomprehensibility define
the class of systems for which phenomena are emergent (i.e., is this a defining
principle related to complexity)? And
if not, is “unpredictability simply an eye-of-the-beholder phenomenon?”
Top-Down Control vs. Bottom-Up
Self-Organization
Craig
Reynold’s famous simulation of the motion of a flock
of birds (“boids”) as a self-organizing system of
autonomous agents (see Flake, pp. 270-275) assigns to those agents three simple,
weighted rules: a) avoid (move away
from boids that are to close to reduce the probability
of mid-air collisions); copy (fly
in the general direction that the flock is moving by averaging the other boids’ velocities and directions); and center (minimize exposure to the flock’s exterior by moving toward
the perceived center of the flock). The
result is “coordinated” movement within and of the flock as a whole that is
said to “emerge” from the behavior of individual agents following locally applied
rules.
Q22. Don’t the copy and center rules of “boids,” which imply that an individual boid-as-agent
is given information about the behavior of the flock as a whole (at least the
flock minus self) before its individual velocity vector and hence position at
the next time step is calculated, violate the principle of higher-order complexity
emerging out of purely local interactions?
Q23. Is there something about the type of emergent organization
in boids (in which properties of the whole partly
determine the behavior of individual agents) that distinguishes it in principle
from that in instances such as termites and Langton’s
ant?
Resnick, Johnson (2001) and others present the contrast
between bottom-up self-organization and top-down authority imposed organization
in what is largely an either/or fashion.
Yet in the most complex systems (cities, brains, economies) both principles
appear to be operative in some sort of interactive process (e.g., the interplay
of zoning decisions with the global phenomena arising out of local neighborhood
interactions, the interaction between systemic inhibitory effects of frontal
cortex and phenomena arising out of the local behavior of neurons in motor cortex,
the relationship between decisions made by central banks and the effects of
purchasing decisions made by individuals, etc.).
Q24. Won’t models of complex systems need eventually
to represent not only both top-down and bottom-up effects but the rules governing
their interactions; or will these rules of interaction themselves emerge from
the interplay of the separate (and lower-order) top-down and bottom up rule
systems?
Environment
Earlier
in the year, if I recall and understood him correctly, Paul discussed “context”
as that which creates change. It is,
in other words, simple interactions among simple things occurring in a context
(e.g., the size of the playing field in the game of life) that generates global
order. Context is, in effect, any relevant
influential factor(s), each of which may follow its own rules of interaction, that lie outside the rules governing the simple
elements on which we focus. Note that
this idea seems closely tied to levels of analysis in that aspects of context
so-defined and the original simple elements may themselves serve as a local
elements in a higher-order complex system. Indeed,
hierarchical emergent systems are those in which emergence generates patterns
that themselves become the basis for further emergence (as in biological evolution
from inorganic to organic single-cell to multi-cellular organisms, etc.).
Q25. Where is the environment (context) in models
or even in discussions of self-organizing systems? Ant colonies aren’t operating in a vacuum, neither
are populations of neurons or neighborhoods. Can the tendency to ignore a system’s environment
be traced to inability to conceive of systems within systems so that emergent
properties at more than two levels are simultaneously being taken into account?
Adaptation
As
just indicated, ant colonies, brains, neighborhoods, etc. don’t exist in isolation
from a broader environment. Indeed, their
“success” presumably depends directly on their ability to adapt to their respective
environments. Indeed, Johnson suggests
that inasmuch as negative feedback is “a way of indirectly pushing a fluid,
changeable system towards a goal,...[it is]...a way
of transforming a complex system into a complex adaptive system” (p. 139). Yet just as context seems to be largely lacking in discussions of
“internal” principles of self-organization, so too does the problem of adaptation
seem to be primarily given lip-service.
Q26. If negative feedback pushes a system towards
a goal, how is the goal set?
Q27. How much does self-organization depend on internal
principles such as feedback loops between individual agents and how much on
need to adapt to a more global environment?
Q28. In complex biological
systems, from ant colonies to brains, where does evolutionary selection operate?
On the local rules in the individual ants or neurons, which are presumably
determined by genes, or on emergent systemic behavior?
Architecture
Q29. What is the role of architecture (i.e., spatial/anatomical
connections among agents) vs. the role of rule-governance (e.g., fire/don’t
fire; pick-up/don’t pick up) in emergence?
Q30. In what ways do architectural constraints and/or
external input add to complexity of the system or influence emergent outcomes?
Q31. Is architecture simply reducible to density
of interconnection and therefore probability of establishing a local feedback
loop or must architecture itself (e.g., the anatomical architecture of the brain)
be described in terms of higher-level principles?
Q32. Are cities more like brains or like ant-colonies.
Nature and Mechanisms of
Change
Catastrophism/Nonlinear change. Bak claims that “because of
their composite nature, complex systems can exhibit catastrophic behavior, where
one part of the system can affect many others by a domino effect” (p. 12).
Q33. How does catastrophic change necessarily reflect
the composite nature of complex systems?
Developmental vs. Hierarchical
Emergence.
Q34. Is it reasonable to distinguish between two
different domains of emergence, one developmental—as in catastrophic change
in which novelty emerges over time—and the other hierarchical—in which novelty
is a property of higher-levels of organization (i.e., in which “change” per
se seems less relevant)?
Historicity.
Q35. Under what circumstances can present states
be fully described in terms of present characteristics without reference to
history; and when is history not only relevant but necessary?
Stigmergy (Collective Representations/Distributed Cognition). Johnson argues that among other things, “cities...possess
a kind of emergent intelligence: an ability to store and retrieve information”
(p. 100). This would seem somewhat analogous,
albeit on a very different time scale, to the system of pheromone tracks laid
down, reinforced, etc. by individuals in an ant colony.
In both cases, local behavior following local rules creates relatively
enduring changes in the environment that store information about certain aspects
of collective behavior and make it available for use by (i.e., feedback to)
other agents. Resnick, in describing
StarLogo, points out that patches allow turtles to
communicate indirectly. By changing the
environment, i.e., altering the state of a given patch, they are able to alter
the behavior of other turtles and leave behind reminders for themselves.
“The idea, he suggests, of making use of objects in the environment,
rather than creating new internal representations, is an example of what is
sometimes called ‘distributed cognition’” (p. 34).
Q36. Is stigmergy a necessary
characteristic of self-organizing systems? Are collective representations of this sort in effect themselves emergent characteristics of the system?
Q37. Have I overdone it with the questions already?
Bibliography
Bak, P. (1999). How Nature
Works. The Science
of Self-Organized Criticality. NY: Springer Verlag.
Flake,
G. W. (1998). The Computational Beauty of Nature. Computer Explorations of Fractals, Chaos, Complex Systems,
and Adaptation.
Johnson, S. ( 2001). Emergence, The Connected Lives
of Ants, Brains, Cities, and Software.
Resnick, M. (1994). Turtles, Termites, and Traffic Jams. Explorations
in Massively Parallel Microworlds.
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