Emergent Intelligence: The Brain as a Complex Adaptive System
December 4, 2013
1
Complex Systems
At various points in our young lives, we come to the realization that neither our parents nor our teachers know everything, that people in charge make all kinds of mistakes, and that many powerful entities decidedly do not have the best
interest of the people nor the planet at heart. In short, we learn that the world is not a well-oiled machine.
For the most part, things normally just work out, though no laws can guarantee it. For sure, there are plenty of laws,
but there is no master plan to maximize much of anything: happiness, economic growth, traffic flow, environmental
sustainability, etc. In reality, the world works due to a complex combination of imposed constraints (e.g. traffic laws)
and individual interactions (e.g. drivers swerving to avoid those who occasionally forget them).
From all of this, large-scale patterns and systems emerge, ones that are rarely considered optimal or well-oiled, but that
generally work well for at least a sizeable fraction of the people. The eye-opening fact that the world works without
excessive global manipulation, and without many guarantees, may initially disappoint us, but the understanding of
how predominantly local interactions produce sophisticated global results can turn that childhood dismay into adult
fascination.
The field of complex systems or complex adaptive systems (CAS) specializes in these intriguing feats of self-organization
in a variety of systems as diverse as the planet itself: rainforests, termite mounds, traffic jams, epidemics, global
economies, climate, the internet, immune systems, politics, migration patterns, stampedes, stock markets, bacterial
colonies, retail distribution chains, brains, languages, metabolic pathways, and ancient civilizations.
As described by various authors [11, 7, 8], complex systems typically consist of many interacting components (or
agents) and exhibit several of the following properties:
1. Distributed control - nothing oversees or manages the components and their interactions.
2. Synergistic - The sophistication or complexity of the gestalt greatly exceeds the summed complexities of the
components.
3. Emergent (Self-Organizing) - The global structure arises solely from the local interactions, often via positive
feedback.
4. Autopoietic - The global structure is maintained by local interactions, often via negative feedback.
5. Dissipative - The system is far from equilibrium (and thus in a low entropy state), yet stable.
6. Adaptive - The system can modify its own structure and/or behavior in order to maintain other aspects of itself.
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Precise definitions of complexity abound, but have little formal agreement. Within particular disciplines, such as
computer science or physics, formalizations of the term aid in intra-disciplinary assessments; but over-arching characterizations to, for example, compare the complexities of a sorting algorithm to that of a steam engine do not exist, and
seem somewhat ludicrous.
However, a few cross-disciplinary generalizations are in order. Complexity rarely depends upon the number of components, nor their individual intricasies, but on their interaction protocols. Though individual humans seem infinitely
complex on their own, the mind-boggling complexity of society stems not from the many billion individuals, but
from the billions (or trillions) of interactions between them, many of which are (even in complete isolation) highly
unpredictable.
Typically, complex systems defy the prediction of global behavior from cursory analyses of components and their
interactions. Surprises are commonplace, and in many cases, the only way to avoid them is to observe the system
itself or run very large-scale simulations. In fact, Bedau [2] defines a weakly emergent system in terms of explanatory
incompressibility: the only way to ascertain the system’s behavior is to run a complete simulation of it; no shortcuts,
such as analytically model solutions or slick heuristics will do the trick.
Finally, emergence and self-organization are the two words most synonymous with complex systems, while many of
the other adjectives, such as nonlinear and autopoietic, have straightforward ties to these anchor terms. For example,
emergence and its inherent surprise often result from synergistic interactions, where the global sophistication greatly
exceeds the sum of the individual agent complexities; and this super-additivity is the hallmark of a non-linear system.
Similarly, self-organization and autopoiesis are often co-occuring complements: self-assembly and self-maintenance
typically require one another.
A common element to discussions of emergence is that the self-organizing global structure provides constraints upon
the local structure, thus biasing component interactions in ways not immediately predicted by the local behaviors. This
leads to a useful working definition of emergence:
The transition of a multi-component system into a state containing high-level properties and relationships:
1. whose causal origins involve a non-linear (and often unpredictable) combination of other component’ properties
and relationships , and
2. that often add further constraint to the low-level interactions.
For example, convection cooling of water on a pond’s surface produces vertical flows wherein warm water masses rise,
are cooled, and then sink. These large-scale flows emerge from the local properties of water molecules that lose energy
and are simply displaced from the surface by higher-energy molecules from warmer water. As small vertical streams
form, their molecules may collide with nearby molecules, imparting vertical momentum and gradually broadening the
stream. This constitutes positive feedback and leads to the rapid cooling of water.
Since water is most dense at 4◦ C, any cooling below that temperature produces lower density surface water, which
then halts the convection stream and reduces cooling to a (much slower) conductive process. Below 0◦ C, ice formation
begins and further reduces the cooling rate of the remaining liquid. Thus, the local properties of water (i.e., it’s
maximum-density and freezing points) support the emergence of the light upper layer and then ice, both of which have
a negative feedback upon the vertical streams and thus upon water temperature, which they help stabilize.
In sum, one emergent structure, a convection current, accelerates the cooling rate via positive feedback. The other
emergent structure, ice, provides a negative feedback to maintain water temperatures (near freezing) despite much
colder air temperatures.
An often-cited example of emergence comes from the renowned neuroscientist, Roger Sperry[15]. As shown in Figure
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1, the round wheel pattern enables a rolling motion, which imparts circular momentum upon the individual wheel
molecules. Though an elegant example of top-down constraint, this fails to illustrate the actual self-organization of the
global wheel form.
Tumbleweed more convincingly exemplifies emergence. As the plant dries out and dies, it disengages from the root
and is easily blown around. Being dry but still malleable, the dead plant attains a rounder form via repeated contact
with the ground and the bending and breaking of individual stems. Eventually, the accumulated deformations round
the weed to the point of being able to roll and impart top-down rotational momentum upon its molecules. Upon
reaching a wetter area, the tumbleweed absorbs water and mechanically opens up, thus imparting another top-down
momentum upon its molecules.
Figure 1: Roger Sperry’s example of a wheel and the top-down effects of global structure upon the motions of individual molecules.
As a more practical example of emergence, consider the work of Spears et. al. [14] in which purely local information
guides the movements of agents (representing military vehicles), which then self-organize into target global patterns,
such as hexagonal and square lattices. As shown in Figure 2, a hexagonal pattern emerges when all agents follow the
simple rules of a) repelling all agents located closer than R units to themselves, while b) attracting all agents outside of
that circle. For instance, on the left of the figure, agent B is pushed to the right by A and pulled upward by C, yielding
a resultant force vector that moves it in a northeasterly direction, while agent C is pulled to the southwest, and agent
A to the north. Together, these forces drive the agents into a stable triangular pattern. With many agents, this becomes
a hexagonal grid.
C
C
A
A
B
B
Figure 2: Emergence of a hexagonal lattice from simple attraction-repulsion behavior among agents (dots). Dashed
circles denote borders between attraction and repulsion. (Left) All interactions between 3 agents are shown. These
lead to the formation of a triangle, in which the resultant force vector on each agent vanishes. (Right) Sketch of some
interaction forces among a larger group of agents, which eventually lead to a hexagonal lattice.
To form square lattices, the authors introduce two types of
√ agents differentiated by their spin values, either up or
down. The preferred radius for dissimilar agents is R, and 2R for similar. Squares then emerge among groups of 4
agents, two of each type, with√alternating types along the perimeter (with edges of length R) and like types in opposite
corners (a diagonal distance 2R apart). In addition, by allowing agents to occasionally change spin, they facilitate
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an ingenious method of self-repair, as detailed in [14].
2
Chaos and Complexity
Complex systems are frequently characterized as those exhibiting a mixture of order and disorder; and the complex
regime of a dynamical system is often defined as the edge of chaos: an area in state space between order and disorder/chaos. So an understanding of complexity requires one of chaos as well.
The trademark of a chaotic system is Sensitive Dependence upon Initial Conditions (SDIC). Assume two separate runs
of a system, one in which it begins in state s0 and another in s0 ∗, where the two states are distinct, but extremely (even
infinitesimally) close in state space. The two runs of the system cause a transition through T states, ending in sT and
sT ∗, respectively. SDIC entails that these two final states are not close: the two trajectories of the system diverge in
state space. Figure 3 shows SDIC for a fictitious 2-variable system.
s*T
X2
s0
s*0
sT
X1
Figure 3: Simple illustration of SDIC in a system composed of two variables: X1 and X2 . Though initial states s0 and
s0 ∗ are very close, the trajectories from each quickly diverge.
The problem with chaotic systems is that they are nearly unpredictable, since the accuracy of the initial state can rarely
be assessed to more than a few significant digits. The mathematical beauty of chaos is that very simple, completely
deterministic, non-linear systems can exhibit it. One such model is the logistic map of equation 1, one of a few
classic examples of chaotic systems, and one that has applications in a wide range of fields, such as ecology, medicine,
economics and neural computation.
xt+1 = rxt (1 − xt )
(1)
The gist of the model is simple: the next value of x is the product of a rate constant, r, the current value of x, and one
minus that value. x0 is assumed to be between 0 and 1, and the model insures that x never goes outside those bounds.
The choice of r strongly influences the trajectory of x in the following manner:
• r < 3 - the system quickly transitions to a value that remains stable from timestep to timestep, a.k.a. a point
attractor.
• 3 ≤ r ≤ 3.57 - the system transitions to an infinite loop between k different values, a.k.a. a periodic attractor of
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period k. When r = 3, k = 2; as r increases, the system goes through various bifurcation points, where k doubles.
The frequency of occurrence of these points increases as r approaches 3.57.
• r > 3.57 - the system never settles into a discernible attractor and SDIC arises.
In short, small values of r produce an ordered state, while those above 3.57 produce chaos. To illustrate SDIC in this
state, Figure 4 shows two trajectories that begin with a mere one millionth separation but gradually diverge. Also note
that both trajectories are non-repeating.
Rate=3.9000
1.0
0.6
0.6
X
0.8
X
0.8
0.4
0.4
0.2
0.2
0.00
Rate=3.9000
1.0
20
40
Time
60
80
0.00
100
x0 = 0.7
20
40
Time
60
80
100
x0 = 0.700001
Figure 4: Two applications of the logistic map (with r = 3.9) using initial values differing by only one millionth. The
trajectories diverge after approximately 30 timesteps.
Values of r near 3.57 represent the complex regime or edge of chaos. Many studies have shown that within this regime,
a system is best able to perform computation: the storage, transmission and modification of information. Others
indicate that systems often transition (or evolve) naturally to this regime.
This natural transition is best exemplified by Bak’s sandpile [1]. Imagine dropping single sand grains onto a pile,
always from the same point above the pile, and always just one grain at a time: the external perturbation to the pile
is both small and constant. Initially, each grain will just fall to the table, but eventually the pile will develop a peak
with steep slopes. At this point, the addition of each new grain can potentially cause avalanches, of various sizes (i.e.
displacing varying numbers of sand grains). But when the sizes of those avalanches are plotted, it turns out that the
vast majority of perturbations cause small avalanches, while an exponentially decreasing number of larger avalanches
occur. Still, some very large avalanches do occur. This exponentially declining frequency curve is known as a power
law distribution, and it is an often-cited signature of a system in a critical state.
Figure 5 gives the plot of a typical power-law curve (left) along with a cartoon example of a distribution of avalanche
sizes for a sandpile as described by Per Bak. For this and many other systems formally deemed complex, the frequency
distribution of values for some important system variable is the basis for the power-law distribution expressed in
equation 2.
f (x) = cxk
(2)
As long as the perturbations are small and constant, then the occurrence of a power-law distribution over the internal
effects of the disturbances is often grounds for the following type of claim:
Most perturbations lead to small changes in the system, indicating that it is predominantly stable or
ordered. But occasionally, a small perturbation can produce a large change, indicating a more unordered
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Power-Law
1.0
0.8
Frequency
of
Occurrence
f(X)
0.6
0.4
0.2
0.00
10
20
X
30
40
50
Avalanche Size
Figure 5: (Left) Plot of the function f (x) = cxk with c = 1 and k = -2, a standard example of a power-law curve. (Right)
Sketch of a power-law distribution for the avalanches of a typical sandpile.
or chaotic situation. The mixture of the two, order and chaos, with the former dominating, is a strong
indicator of complexity in the system.
In addition to formalizing the critical state, Bak argued that many systems will naturally transition to it of their own
accord, with only minor external assistance (such as the dropping of sand grains onto a pile): they are emergent in the
same way that a convection current emerges from a) the internal physicochemical dynamics of water, combined with
b) an external temperature perturbation. The term self-organized criticality (SOC) [1] expresses both the emergent and
edge-of-chaos aspects of this important phenomenon.
An important mathematical construct for assessing order, chaos and complexity is the Lyapunov exponent, λ in equation 3, where 4x0 and 4xt are the initial and final separations, respectively, between two trajectories of a system.
4xt = 4x0 eλt
(3)
Intuitively, when λ < 0, the trajectories converge; the system is ordered. Similarly, when λ > 0, the systems diverge,
indicating SDIC and chaos. The complex regime is that (often narrow) band of parameter space where λ = 0 and
trajectories neither diverge nor converge. For systems with large state-space vectors, this would seem to be a nontrivial band to find, although influential complexity theorists such as Stuart Kauffman [8] support Bak’s view that
many systems will almost inevitably approach this edge-of-chaos area.
Throughout this book, you will see examples of systems that appear to inhabit the complex regime as evidenced
by a mixture of orderly and chaotic behavior, where order dominates but chaos has just enough presence to support
adaptation.
3
Levels of Emergence
Some of the more thorough philosophical investigations into emergence come from Terrence Deacon [4, 5], who describes three different levels, ranging from basic multi-scalarity to those invoking notions of self and memory/representation.
Related to these levels are synchronic and diachronic aspects of emergence, where the latter involves global pattern
formation over time, while the former involves changes of spatial scale without temporal progression. For example, temperature emerges synchronically at the macro level from energetic molecular interactions at the micro level;
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this emergence does not unfold over time but merely becomes evident to the outside observer in the shift of spatial
perspective and equipment: from the microscope to the thermometer. Conversely, pond freezing exhibits diachronic
emergence through the temporal sequence of conduction, convection, conduction and ice formation.
Deacon’s 3 levels or orders of emergence are more elaborate. First-order emergence is primarily synchronic and
involves aggregates of low-level interactions that produce higher-level properties. Temperature from molecular interactions, color from molecular light-absorption properties, and weight from atomic mass are all examples of first-order
emergence. This type of emergence is often devoid of surprise, with high-level properties being easily predicted from
a statistical analysis of the underlying micro properties and events. Stochastic perturbations of first-order systems tend
to average out at the macro level, as opposed to being magnified by positive feedbacks; and the global patterns exert
no obvious constraints upon local dynamics.
Although this is a fairly mundane type of emergence - essentially a base case - it exhibits some degree of explanatory
complexity in that global patterns do not follow from local interactions by simple causal arguments: tools such as
statistical mechanics, which average over the micro events, are needed for the logical derivation of global effects from
aggregated local causes.
With 2nd-order emergence, the fun begins! In these scenarios (as sketched in Figure 6), stochastic micro-level perturbations (a.k.a. asymmetries) can become amplified into global patterns in a diachronic manner. A recurrent causal
architecture also comes into play as these global structures bias local behaviors. These systems are both self-organizing
and autopoietic, and they involve a significant mix of bottom-up and top-down causality. These systems are dissipative
in that material and energy may flow through them (i.e., they are far from equilibrium), but the global structure (i.e.
the low entropy formation) is recirculated, amplified, and often eventually stabilized. This stability of form engenders notions of self : some hallmark of the system or system class that is created and maintained. Most examples of
emergence in the popular complex-systems literature are of this type.
At the top of Figure 6, notice that individual components begin with many degrees of freedom. This entails a large
search space of possible actions, a space that gradually constricts as the global pattern emerges. Although activities
such as the Brownian movement of molecules rarely evoke notions of search, when system components are cellular or
multicellular, the metaphor begins to fit.
In 3rd-order systems, the emergent high-level structures are imprinted into another structure: the memory or representation, which can function as a seed for another round of 2nd-order emergence, producing another, similar, high-level
structure. Essentially, this facilitates reproduction and evolution of the self. This seeding is a re-presentation of the
memory to the lower-level dynamics, which catalyzes 2nd-order emergence.
Third-order emergence involves a synergy between self-organization and representation. The latter implicitly houses
a memory of the self-organizational process, which, in turn, can create new representations. These representations
may be disseminated and subjected to differential selection pressures (via different micro-level environments) and the
resulting heterogeneous replication frequencies. Thus, 3rd-order emergence facilitates evolution by natural selection,
where the representation is obviously analogous to DNA.
Furthermore, any adaptations of the system to the environment will involve changes to the dynamics, some of which
may be reflected in the emergent global pattern and thus encoded in the representation. In this way, the representation
becomes an implicit memory of a history of environments (via the adaptations necessary to survive in them). For example, any animal’s genome serves as a history of its adaptations, a reflection of a long chain of salient environmental
factors - ambiguous, noisy, and woefully incomplete, but a history nonetheless.
Figure 7 illustrates the basic process, wherein the representation is built in parallel with the global structure. Then,
when transferred to an unordered environment, i.e. one where the local interactions have few constraints, the memory
provides a bias leading to both a) the rejuvenation of a high-order pattern, and b) the biasing of the low-level dynamics.
Since this new situation may not be identical to the original, the representation may also change to more accurately
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Time
Symmetry of Local
Interactions
Global
Structure
Global
Structure
Asymmetry
Amplified
Asymmetry
Figure 6: The essence of 2nd-order emergence. From predominantly unbiased (a.k.a. symmetric) local interactions, a
small amount of bias arises randomly. Positive feedback accentuates this bias, forming a global pattern that provides
significant constraint upon the low-level behaviors (i.e., increasing asymmetry). Negative feedbacks eventually kick
in to stabilize the local dynamics and global structure. Arrows denote degrees of behavioral freedom of low-level
components
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reflect the new scenario.
The representation acts as information in the formal, information-theoretic sense that, when added to a system of
relatively unconstrained (i.e., high entropy) local interactions, it provides a strong bias, thereby promoting structure
and reducing entropy; information content equates with induced entropy reduction (as detailed in a later chapter).
Global Structure
Memory-1
Memory-1
Amplified
Asymmetry
Global Structure
Memory-2
Memory updated
to include
recent
history
Amplified
Asymmetry
Figure 7: Essence of the re-presentation process underlying Deacon’s 3rd-order emergence, where a memory structure
arises as an additional result of 2nd-order emergence. It then serves as a seed for regenerating the global pattern in a
new environment.
Deacon illustrates 2nd- and 3rd-order emergence with an abstract biochemical system called an autogen, which is
probably inspired by Varela et. al.’s earlier model of autopoiesis [6]. As shown in Figure 8, an autogen consists of an
autocatalytic loop (AL) surrounded by a membrane. The loop and membrane are symbiotic: a by-product of the loop
are membrane building blocks (M). The membrane prevents chemical constituents of the loop from dissipating into
the environment. Though many components of the AL are produced from other AL constituents, a few raw material
chemicals (e.g. X and Y) are also required to perpetuate operation.
The autogen’s structure emerges through a 2nd-order process in which various compounds come into contact and begin
producing other compounds, including M and other molecules of the AL. Positive feedbacks include a) the ability of M
molecules to partially restrict the movement of the AL compounds, thus helping to prevent their immediate dispersal,
and b) the eventual formation of the complete AL loop, allowing compounds A-D to produce one another (in the
presence of X) and M (using Y).
Once the complete membrane and AL have formed, negative feedbacks help to stabilize the structure. For example,
since X and Y are only consumed (not produced) by the AL, their internal concentrations will wane without periodic
resupply, which turns out to be an emergent property of the autogen. As the AL loop begins to slow down, production
of M cannot keep pace with natural deterioration of the membrane, and gaps appear. These allow X and Y to flow into
the cell, thereby restimulating the AL, producing more M, and mending the membrane.
In short, the positive feedbacks involving AL and membrane lead to self-organizing autogen formation, while the
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Y
X
M
M
M
A
X
X
X
D
Auto-catalytic
Loop
Y
B
Y
C
M
M
X
X
Y
Figure 8: The basic structure of Deacon’s autogen, with an autocatalytic loop (AL) that requires raw materials (X and
Y), and is surrounded by a membrane, whose building blocks (M) are produced by AL.
negative feedbacks insure autopoiesis (self-maintenance).
Furthermore, if the membrane splits in two places, creating pieces M1 and M2, then each piece may usurp enough of
A-D, X and Y to have a private AL, which will then generate a complete new membrane for each, thus producing 2
copies of the original autogen. So reproduction can also be a 2nd-order emergent phenomenon!! Conceivably, an AL
could become modified - for example by replacing compound D with E. If this produced a more efficient AL, possibly
one requiring less raw materials to produce the same amount of membrane, then it might have a survival advantage in
terms of having less frequent membrane tears. Of course, more tears could lead to faster reproduction, so an inefficient
AL might actually be a more prolific copier. Either way, the roots of evolution are already evident in this 2nd-order
emergent system.
Y
X
M
M
A
X
X
M
X
D
Y
B
Y
C
M
M
X
Y
X
Figure 9: Re-supply of X and Y via gaps in the deteriorating membrane.
Deacon’s autogen exhibits 3rd-order emergence with the addition of a representation in the form of a chemical template. In general, chemical reactions are enhanced by mechanisms that increase the proximity of their reactants.
For example, by elevating the odds that A and X molecules meet in Figure 10, production of B should increase. If
molecules A* and X* exist, and bind to A and X, respectively, and if A* normally binds to X*, then the presence of
an A*-X* compound should promote A-X proximity and B production. Thus, A* and X* serve as building blocks for
a template that a) promotes AL formation, maintenance and productivity, and b) embodies a memory of the AL such
that the infusion of a well-mixed chemical soup with the template can greatly accelerate autogen emergence. The information embodied by the template greatly biases the low-level dynamics of the chemical soup, producing structures
(i.e., autogens) much faster than they would normally emerge.
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Third-order emergence requires that the representation emerges as well. Although many of the building blocks may
arise naturally in the chemical milieu, there is a decided selective advantage to any autogen whose AL produces some
or all of them. For example, the AL of Figure 10 produces 4 of the 7 template blocks. Clearly then, autogens that
produce templates should have an increasing frequency in the population compared to purely 2nd-order species, and
each template modification that improves AL efficiency should give a selective advantage to these representations,
whose relationship to DNA should now be obvious. Hence, 3rd-order emergence introduces the genotype-phenotype
distinction.
Templates, like other representations, are structural embodiments of the dynamic processes that underlie self. They
play the informational role of catalyzing activities that reduce entropy.
W*
B*
Z
M
A
X
D
Auto-catalytic
Loop
Y
B
W
C
X*
A*
Template
X*
A*
B*
W*
Z*
D*
Y*
X
A
B
W
Z
D
Y
Figure 10: Use of an auto-generated template to promote spatial proximity of the reactants of the autocatalytic loop.
These three levels of Deacon will serve us well as we investigate emerging intelligence across the three levels of
adaptivity: evolution, development and learning. As shown in later chapters, the two systems turn out to be more
orthogonal than they may appear on the surface. For example, Deacon’s third level not only applies to evolution itself,
but, in some cases, to learning.
4
Emergence and Search
Have you ever wondered why migrating birds often fly in a V formation? The explanation is classic emergence. We
begin with an important fact of physics: when a bird flaps its wings downward, it pushes air downward, creating a low
pressure region above one of higher pressure (due to the added air). A split second after this happens (and the bird
moves forward), this pressure difference produces a small updraft. A second bird, trailing behind and to the side, can
use this updraft to lift its own wing, thus saving some energy. In addition, if birds prefer seeing the horizon ahead of
them, instead of the backside of another bird, then they will naturally seek out locations in the moving flock that both
save energy and provide an unobstructed view. When all birds have these motivations, the group self-organizes into a
flying wedge.
As illustrated in Figure 11, from the perspective of a single bird looking for an optimal location, the initial, unorganized
phase affords many options (starred locations). These comprise a broad, unconstrained, private search space for the
bird. However, as the global V pattern emerges, it embodies a top-down constraint, operationalized as a restriction of
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the bird’s search space. So whereas the bird can (quite literally) wing it and randomly choose among many options in
the unorganized state, its moves become forced as the wedge materializes.
?
?
Figure 11: The emergence of a V pattern in flying birds (arrows), each of which creates pockets of uplifting air behind
and to each side. Stars denote unused (by a trailing bird) pockets with an unobstructed view, while circles represent
unused pockets with a poor view. (Left) Prior to V formation, many unobstructed pockets exist, which entails many
options for the focal bird (drawn with an open arrowhead). (Right) In the V, the only optimal options for the focal bird
are at the edges, and these promote extension of the V, a positive feedback.
As shown in Figure 12, this transition from an open to a restricted search space is even more obvious for schooling fish,
which conserve energy by swimming directly behind another and appear to follow a few local behavioral guidelines:
head in the same direction as your neighbors while avoiding collisions. The same basic idea pertains to human
scenarios as well, such as swimming in crowded pools, driving in congested freeway traffic, and finding your favorite
concession stand at halftime of a football game. The important point is that the decisions, which may appear quite
intelligent, involve no sophisticated knowledge or planning; they are merely reactions to an emerging set of largescale constraints, which often make the correct movement choice patently obvious. In short, as situations accumulate
constraints, even the most intelligent of beings exhibits little more problem-solving wizardry than Simon’s [13] ant on
the beach.
Figure 12: Emergence of schooling in fish. (Left) In the unorganized state, a focal fish (open arrowhead) has many
movement options (stars). (Right) The organized state offers few degrees of freedom.
Emergence in systems of decision-making agents can therefore be viewed as an interaction among parallel search
processes. The initial trial-and-error dynamics of each such process enables the system to jiggle into configurations
(e.g. short diagonal lines and small wedges) where positive feedbacks commence (e.g. forcing the moves of birds near
these patterns) and allow the small patterns to grow into large-scale constraints, which then exert natural restrictions
on every individual search process. Without the trial and error, there is no jiggle, and the system can quickly stagnate
in a highly ineffective state. Imagine what happens if every bird, fish or human simply choosse a movement sequence
ahead of time and sticks to it, come hell or high water!
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From an observer’s global viewpoint, the group as a whole might appear to be searching for an efficient pattern, though
no over-arching goals nor instructions guide such a transition. Still, the system gives the impression of trying different
alternatives and eventually becoming attracted toward particular stable configurations. A similar interpretation pertains when we observe populations of non-cognitive agents, such as neurons. Each does have a repertoire of possible
behaviors, which become constrained by the behaviors of other neurons, but the neuron obviously has no awareness
of these options.
Despite the lack of cognizant deliberation by molecules or neurons, and by the aggregates that they form, the search
perspective provides useful insights and predictions when analyzing such systems. Of course, at the highest levels,
the brain itself performs cognitive acts, but the choices that organisms make are not explicitly about neural patterns;
i.e. there are not specific target patterns of neural firing toward which organisms explicitly strive. Yet, from the
perspective of an outside observer examining patterns of neural firing, the system can appear to naturally transition
to certain attractive states, cycles or semi-recurring patterns. Just as in physics, where systems are often described as
seeking a low-energy state, the search metaphor provides useful explanatory leverage in any population of interacting
entities, each of which has several degrees of freedom. Then, in cases of emergence, these degrees may change as
global patterns form and evolve, giving the outward appearance of a system seeking a particular ordered state.
In emergent systems, individual agents make local choices, thus affecting a small subset of the global situation. However, unlike many localized design decisions in AI search, those in emergent systems are not tested in isolation but in
vivo: in direct interaction with other system components. Emergent systems do not deal in partial states with expected
completions, but in complete states with expected transitions. Through an understanding of the interaction topologies
and behavioral repertoires of the agents, as well as the changing constraints, one can begin to attach probabilities to
these expectations and to differentiate between situations in which strong constraints force agent choices and those in
which agents possess a legitimate freedom to explore.
It turns out that this exploratory freedom of individual agents is the foundation of natural adaptivity - a foundation
composed of an extremely malleable substrate, but one that tends to bend without breaking. As we will see, the
ability of living systems to modify themselves to accommodate external change relies heavily on the ability of their
components to exhibit fairly explicit trial-and-error behavior. As the basis of adaptivity, parallel search among multiple
agents is pivotal in the emergent complexity of life and intelligence.
For example, the development of the nervous system is a highly adaptive process in which brain hooks up to body, not
by carrying out a genetically-specified topology-building plan (i.e. connect neuron A to neuron B, then B to C and D,
etc.), but by individual neurons performing various search processes, such as sending out axons in search of dendritic
targets. Those that find a dendrite to synapse onto may survive, while failure to connect can spell death. Similarly,
during cell mitosis, a pair of centromeres send out exploratory microtubules searching for chromosomes with which
to attach. Those that hook up will form part of the mitotic spindle; the rest will wither away. This is exploration,
trial-and-error search within individual cells, that enables the centrosomes to find all the chromosomes, wherever they
lie within the cell. The cell adapts to random chromosome locations because the centrosomes can search/explore, in
the same way that the nervous system adapts to varied locations of muscle cells via the exploratory axons of motor
neurons.
5
Emergent Intelligence
Although many different properties of complex systems have already been discussed, Melanie Mitchell’s formulation
[10], motivated by a network perspective, seems very relevant for the emergence of intelligence. She provides four
basic characteristics of complexity:
1. Global information is encoded as patterns over the component states.
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2. Stochasticity abounds, and is often magnified by positive feedback.
3. Parallel exploration and exploitation at the level of individual agents is ubiquitous.
4. Top-down and bottom-up interactions co-occur continuously.
The brain exhibits these in many different ways, though one example of each suffices for now. First, neural representations are commonly believed to involve population coding: concepts such as tumbleweed are encoded by large
combinations of active neurons, not the individual cells alone. Second, random neural activations occur continuously
in the brain, and these often employ positive feedback to illicit large-scale firing patterns, such as the synchronous
activity common to brain oscillations, such as theta and gamma waves, which are critical for memory formation and
retrieval [3]. Third, during development, neurons grow axons that independently explore the environment for other
neurons with which to connect. In this search for efferents, links to already well-connected neurons have a selective advantage, since this exploitation of proven networkers enhances the new neuron’s chances of participating in
active circuits and thus surviving. Finally, the brain’s interpretation of sensory information relies on a healthy mix
of bottom-up (sensory-driven) signals that interact with top-down (expectation-driven) signals from higher cortical
regions.
Most popular accounts of complex systems, such as Mitchell’s [11], include the brain in their list of examples, with
intelligence touted as an emergent result of billions of interacting neurons. Unfortunately, intelligence is a rather
vague concept, and certainly not one easily described by a particular global pattern - although, as discussed in later
chapters, scientists have attempted to define concepts such as consciousness in terms of information-theoretic metrics
and the neural activation patterns that satisfy them. However, a detailed analysis of the many neural structures and
mechanisms (along with their origins) that underlie intelligent behavior reveals a parade of self-organizing systems.
These span the three primary levels of adaptation, and at each level, emergence relies heavily upon a search process.
From an evolutionary perspective, brains have emerged along a million-year timescale via the gradual expansion of
a very distant ancestral genotype (by duplication and modification of successful genetic components). Evolution has
devised ingenious developmental recipes for converting genotypes to phenotypes. Although evolution is often characterized as random by laymen who either lack a solid biological background or have various religious agendas, the
concept of selection pressure and its ability to steer evolution via genotypic adaptations normally suffices to convince
open-minded people that evolution has the ability to craft complex organisms that purely random processes could
never achieve. In short, evolutionary search is highly biased, favoring some genetic and phenotypic variations over
others.
However, even many biologists view the processes by which variations arise (prior to selection) as random, with
selection then separating the wheat from the chaff. Conversely, the popular new theory of facilitated variation [9]
indicates quite the opposite: the processes that generate variations are also highly biased. Essentially, millions of years
of evolution have hit upon complex combinations of genes, and versatile genotype-phenotype relationships that greatly
improve the odds that random mutations will produce viable phenotypes, thus giving selection a very high-quality pool
of applicants. It seems that the DNA representations of natural 3rd-order emergence are both extremely informative
and robust. Clarifying the source of this robustness can both a) enhance our general understanding and appreciation for
evolution as a designer, and b) suggest feasible strategies for artificial evolutionary searches for intelligent algorithms.
This permits an interpretation of the evolutionary search process as, in fact, quite well informed and strongly biased to
choose routes that history has pre-selected by virtue of the constraints gradually molded into the genotype-phenotype
mapping.
Developmental processes themselves exhibit considerable self-organization, as a multitude of embryonic cells send
and receive chemical signals, many of which strongly affect behavior and lead to the formation of global structures.
As discussed later, exploratory search, involving real physical molecules and cells, along with their connective tubing
and wiring, plays out in many parts of the body and brain. Without this developmental search and the grow to fit
assembly paradigm that it engenders, the genome would become more a blueprint than a recipe, and lose most of its
robustness along the way. An examination of the 2nd-order emergence in developmental search helps explain how
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instances of apparently improbable simultaneous coevolution of many traits are actually the modification of one trait
followed by a host of phenotypic adaptations to that perturbation, all made possible by the flexible search processes
implicitly encoded by the genome. Development is one of the most impressive emergent phenomena in existence, as
the complex global structure of the organism arises from an intricate interplay among a wide variety of cells.
Postnatal modifications are often considered examples of phenotypic plasticity, with classic examples being the increase of muscle mass via weight lifting, the increase of red-blood-cell count by moving to higher altitude, and the
modification of synaptic strengths in the brain (often equated with learning). Whereas development lays down the
main components and their connections, plasticity/learning involves smaller, more local, tweaks to that infrastructure.
In the brain, development involves the formation of large populations of neurons, along with the extensive axonal and
dendritic networks linking them, whereas learning typically involves synaptic formation and/or tuning but may include
the addition of new neurons to established populations (and their linking up to others), although only a few areas of
the mammalian brain appear to support post-natal neurogenesis [12].
Learning also has many emergent aspects, again resulting from processes often characterized as search. For example, synaptic tuning in supervised-learning scenarios is commonly modeled as a gradient-descent search for a vector
of synaptic weights that reduces the total error of a neural network’s input-output mapping. Classic AI supervisedlearning algorithms are not particularly emergent, due to the presence of externally-provided control signals and complex algorithms with a highly non-local flavor. However, some brain circuitry exhibits more decentralized supervised
learning from which the mature, fully-functioning network gradually arises. Other brain networks display emergent
reinforcement learning involving global chemical broadcasts but certainly nothing ressembling global hands of god
steering the process (as in classic AI methods of reinforcement learning). Finally, unsupervised learning is a common
brain mechanism capable of crafting complex topological maps from purely local interactions. Here, both natural
and artificial versions of the algorithm exhibit considerable self-organization. In addition, the dynamic progression
of networks tuned by unsupervised learning is often modeled as a search process in the space of neural-activation
patterns.
Compared to development, the self-organizing global structure of learning is less impressive for its physical differences from the original (simpler, less-organized) state but more recognized for its accentuated informational content,
behavioral intricacy or functional ability. In many cases, to fully appreciate the emergence within a learning system,
one needs mathematics (e.g. information theory) instead of a microscope or phylogenetic tree.
Indeed, intelligence is emergent, and just as imperfect as Mom, Dad, tax laws and the United Nations. Still, the
neural machinery is oiled well enough to perform many impressive feats. The full extent of this phenomena goes well
beyond examples of sophisticated coordination arising from individual decisions, such as the ability of 5 basketball
players to weave intricate patterns from only individual movement principles, or of jazz musicians to produce lively
entertainment with band members whom they’ve never met before, or of fireflies to blink in synch. The true beauty
of emergent intelligence is spread across the three adaptive mechanisms and Deacon’s three levels. And it’s all about
search and neurons.
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