article summarizes Stuart Kauffmans book At Home in the Universe.
All of the principles that are discussed concerning complex systems are
his, or if attributed to others, may be found in his book. The conclusions
drawn with respect to venture management and transition management in
organizations are a mixture of mine and Dr. Kauffmans. The models
from the Taylor Modeling Language are copyrighted, of course, by MG Taylor
Part I: Selection, Self-Organization,
Part III: Coevolution
on Coupled Fitness Landscapes and Patch Theory
for Order in Emergent Systems
We know a little bit now about how systems become autocatalytic. But consider
the autocatalytic set of molecules once more. Imagine that there are new
molecules entering the pool and also realize that some random, uncatalyzed
reactions can create new molecules as well. These new entrants may enter
the autocatalytic set or they may inhibit one or several reactions in
the set. Either way, the products of the set change, and in this way the
set can vary over different generations. However, there must be a balance
between stability and change in the autocatalytic set. If stability dominates,
then the set becomes frozen and cannot evolve. If change dominates, then
chaos sets in.
Were looking for another phase transition here,
one between order and chaos in a systems behavior. The presence
of the autocatalytic set is a manifestation of order. All of the reactions
are occurring in a very deterministic fashion that we can map. There is
no variation in the behavior of the set unless it is changed by the addition
of random molecules in some way. This type of homeostasis is good! Translated
to the business world, it means that consumers can trust that when they
take a stereo system out of a box and plug it in, it will work. The autocatalytic
set that created the stereo is a representation of the ordered regime
of behavior. But without some variability in the equation, wed all
still be listening to Victrolas instead of CD players.
To uncover the requirements for order, Kauffman uses a
model called an NK network. Heres how it works.
N = the number of nodes in the network.
K = the number of inputs to each node (coming from other nodes in the
network, not from outside of it).
P = the rules of logic governing how each node decides what its next state
will be, given the state of the inputs from other nodes to which it is
further that each node is a light bulb that can be on or off. We can represent
this with a 1 and a 0. Whether a node is on or off is a function of the
K inputs it receives. An input is the state of the node that sends the
input. So imagine a piece of a network consisting of just three nodes,
N1, N2 and N3. Lets say that N2 and N3 are both inputs to N1 (and
conversely, N1 is an input to N2 and N3--in these networks, the connections
run both ways simultaneously). At a certain time we look at the network
and see that N1 is "off", N2 is "on" and N3 is "off".
The inputs to N1 at that time are "on" (N2s output) and
"off" (N3s output). The result is that N1 is "off",
so there must be a rule governing N1 that says "when N2='on' and
N3='off', the state of N1 will be 'off'."
The functions, or rules that nodes use to determine whether
they will be on or off are known as Boolean functions and are logical
gates like AND, OR, IF NOT IF, and so on. The particular rule that N1
is using in the preceding paragraph is an AND gate, meaning that both
N2 and N3 have to be "on" for the state of N1 to be "on".
There are several key things to remember about this "toy
- There are a bunch of nodes, N in the network
- The nodes are connected to each other by K connections
- A connection means that the two nodes at opposite ends
of any given connection send each other information concerning their
current state (on or off in the case of light bulbs)
- Each node uses a function or rule to govern its behavior
based on the inputs it receives from the other nodes its connected
- Therefore, when a node provides input to another node
that determines its behavior, its acting like a catalyst.
In computer simulations of NK networks, inputs between
nodes are assigned randomly. Rules of behavior for each node are assigned
randomly. The initial state of every node in the system is assigned randomly.
Then the system is started to see what will happen. At first a set of
twinkling lights appears. After a while one of several behaviors emerges
for the entire network. The number of cycles it takes for the system to
settle down into a "solution" or order is called the state cycle.
If the state cycle is too long, the network will maintain the appearance
and behavior of a chaotic system.
The lights never stop twinkling; in other words, they never settle down
into a pattern. This is the chaotic regime of behavior. In the chaotic
regime, random changes (mutations) in the state of individual nodes
can cause cascades or avalanches of change to sweep across the network
in a phenomenon called divergence. This propagation of change hints
at the influence of positive feedback loops.
The lights stop twinkling; some remain on and some remain off in set
patterns that never change after the system settles down at the end
of its state cycle. This is the ordered regime. Once a system has reached
the ordered regime, small, random changes (mutations) in the state of
nodes in the system are usually damped out in a process called convergence
and the network returns quickly to its previous, ordered state. The
damping out phenomenon is reminiscent of the negative feedback loops
found in cybernetics.
EDGE OF CHAOS
Most of the lights stop twinkling but there are islands where the lights
twinkle continuously in a fixed pattern. This is the complex regimetenuously
connected islands of variability in a sea of order. In this regime,
random changes made in the ordered portion will be damped out but random
changes in the islands will tend to propagate from island to island,
allowing the network to adapt.
If stability of the network is most important, the ordered
regime must be discovered quickly; searching for types of networks whose
state cycle is short. When continued evolution of the network takes priority,
we seek the edge of chaos regime where islands of variability are connected
to one another across the larger sea of order. What adjustments to N,
K or P yield networks that adapt?
TUNING NETWORK BEHAVIOR: IMPLICATIONS FOR TRANSITION
First, K, the number of inputs to each node may be tuned. Networks with
high K values exhibit more chaotic behavior. This is easy to understand.
If the current state of everything depended upon the behavior of everything
else, nothing would settle down to a solution. This is one of the problems
with consensus, by the way. There are too many conflicting demands on
each node, and the rule that each node uses says that youve got
to placate all of the conflicting demands. And every node is trying to
do the same thing! What a mess.
In Kauffmans toy model, the complex regime emerges
when K=2 (the ordered regime exists where K=1). Thats kind of surprising
at first glance but intuitively understandable. Consider matrix management
style organizations where each worker reports to a functional boss and
a project boss at once. Now imagine each employee reporting to a third
or fourth boss. Chaos erupts out of the conflicting demands. Im
not claiming that all people in all organizations should only have two
catalytic connections to other people or artifacts in the enterprise.
Such a proposition is clearly nonsense, but it is interesting to think
of bureaucracies, participative management, and DesignShop®
events in the light of the K=2 phenomenon. At
some point in traditional organizations the number of connections between
nodes--the number of other people, things, processes, environmental changes,
whose behavior has a direct influence on someone's behavior--crosses some
threshold and the individual or business unit at the focal point of this
high density of catalytic connections will flip from being deeply ordered
(never changing) to being intensely chaotic (never settling down).
But what if K is greater than 2? We each must be connected
to dozens of other nodes whose behavior can cause us to reevaluate our
current course of action and change our own state. Can such chaotic networks
be tuned as well to behave in the complex regime? Yes. To do so the P
variable must be adjusted--the rules of logic that each node uses to transform
its inputs to outputs. Rules can be selected which allow the control of
the ratio of nodes that are "on" or "off" in the network.
This adjusts the amount of chaos present in the network. Such Boolean
functions are called canalizing functions, meaning that "at least
one input has a value that by itself can completely determine the response
of the node." In effect, the node can substantially ignore the other
inputs. Canalizing functions remove conflict for the nodes in question.
What does this mean to organizations? Assume that the
P variable in enterprises is the amount of uniformity demanded based on
the rules that nodes use to do their work. (This is a VERY loose analogy,
by the way.) A wide range in variability of the rules AND a high number
of catalytic connections results in chaos. To keep the number of catalytic
connections in the network high, the variability in the rules is attenuated.
This has implications on the latitude of freedom that network members
have in choosing information that determines how they accomplish their
jobs. In densely catalytic networks, too much freedom in the influence
of different inputs may inject so much conflict in the system at each
node that the network will never settle down out of chaotic behavior.
Too much attenuation of the P variable will cause the
network to sink out of the complex regime into the ordered regime. When
the company policy manual or the corporate culture restricts nodes in
the enterprise from engaging in decision
by design, the enterprise loses its ability
By tuning the number of connections and removing some
conflict in the rules that nodes use to calculate their behavior (based
on the behavior of other nodes), the network may steer itself into that
zone of complexity to optimize both order and adaptability.
Other Comments on Transition Management and Requirements
- The more inputs required for decision making, the more
conflict in the system, and the more chaos
Traditional hierarchy gets around this by enforcing strict rules on
who can talk to whom. Matrix management attempts to relieve the constriction
through a controlled system of expanding the number of connections per
node. Ad-hoc arrangements, such as the modular system of delivering
a DesignShop reconfigure the network and its connections based upon
the work at hand, thus offering a more flexible response.
- A warning for participative management and consensus
management styles: trying to resolve too many conflicting inputs creates
- A warning for strict hierarchical and bureaucratic
organizations: eliminating too many inputs or restricting the decision-making
process stops adaptation and innovation.
- Steering complex systems:
- To increase order, decrease dependent connectivity
(where one node relies upon information concerning the state of
a number of other nodes in its decision making process)
- To increase adaptability, increase connectivity
- To reduce conflict, many individuals automatically
tune out the effect of most of the input they receive from other
nodes so that they can make faster decisions: they take charge of
tuning their own P variable.
- To reduce conflict, many organizations add layers
of rules, policies and procedures which serve to override input
from multiple sources. If too many policies are instituted,
the organization may enter the deep ordered regime from which attempts
to adapt will prove fruitless.
- To increase order, add more rules to reduce options at the node
- To increase adaptability, allow more decisions to emerge from
interaction between nodes.
Evolution of Living Systems on Correlated Fitness Landscapes
"Evolution is a process of attempting to optimize
systems riddled with conflicting constraints."
How does selection work? Imagine two types of bacteria, red and blue.
Imagine further that they are present in equal numbers in some vat with
adequate food available. Assume
that the red bacteria expresses a gene that allows it to undergo cell
division every 10 minutes, while the blue bacteria does not express that
gene, and it divides in 20 minutes, or double the time. Over a short period
of time, the red bacteria population will grow to vastly eclipse that
of the blue bacteria. The red bacteria is not "selected" in
any ordinary sense of the word. No one is doing the selection. The genetic
makeup of the red bacteria, and the capabilities this makeup bestows on
the organism allow it to eclipse, in some manner, the presence of other
bacteria who lack a competitive genetic makeup.
But by what process does an organism become more successful
or more fit in its niche? Certainly not all changes in the genetic code
allow for an increase in fitness. Genes work with one another in a sort
of network like that described in the previous section. They have the
ability to turn one another on and off. In such networks circumstances
like the density of connections and the rules for decision making may
lead to chaos or to order or to the complex regime at the edge of chaos.
If the genetic code is a sort of program, then what effect are mutations
likely to have on it? Think about the applications programs like the HTML
editor this article was composed upon. Imagine that Microsoft Front Page
were suddenly subject to random mutations in the lines of its code. The
application rapidly turns to garbage. Theres no redundancy in the
system to offer continued stability.
Redundancy is one of the first lessons of evolving systems
that should be applied to organizations. This has applications in theories
concerning continuous improvement and reengineering. If you try to make
the enterprise too efficient, then its response to evolutionary pressures
will be collapse.
Biologists have long used the metaphor of a landscape to describe the
march of a species toward fitness. Imagine a terrain like the Appalachians
or the Alps. The peaks represent high points of fitness, where an organism
is highly compatible with the demands of its niche. Evolution is a process
of moving from the valleys to the peaks.
But fitness is rarely dependent on the state of one isolated
gene. It depends instead on the coupling between genes, known as epistatic
coupling. This coupling, when diagrammed, looks like a network where each
node is a gene and the connections between them are inputs to the genes
behavior. This sounds familiar. Indeed, the familiar NK network may be
employed to expose some of the parameters that influence fitness. Remember
that N is the number of nodes and K is the number of inputs that determine
each nodes behavior.
tune the K value to see what happens. If K=0, and none of the nodes are
connected, there is a single peak on the fitness landscape and it takes
N/2 steps to attain the peak. So if there are 100,000 genes, it will take
50,000 generations on average to reach the peak. Once there, theres
nowhere else to go. This is the ideal of gradualism in evolutionary thinking.
Small changes in the genome over time lead species inexorably upward in
a gradual way to well-defined peaks. This doesnt sound unreasonable
until the landscape has a tendency to deform due to the interaction of
other species in the ecosystem.
look at the other extreme. Suppose K=N-1. In other words, suppose each
node is connected to every other node except itself. The resulting landscape
is a surrealistic nightmare of many impossibly steep peaks, cliffs, and
valleys. An adaptive walk on this landscape to a local peak can be accomplished
in only a few steps. It also turns out that the fittest peak on this landscape
is only half the height of the single peak on the K=0 landscape. More
connections don't lead to better solutions. And theres no telling
whether any particular peak is the most fit or not.
K is tuned from a value of 2 through a value of 8 the zone for the higher
peaks is revealed (not as high as the K=0 option, though). Selection seeks
good landscapes to evolve on. An interesting feature of the K=2 through
K=8 landscapes is that there are far fewer peaks than in the K=N-1 landscape
and the peaks tend to be clustered together. Once on a peak, chances are
other good choices for greater fitness lie close at hand. This means that
the highest peaks can be scaled from the greatest number of initial positions,
particularly in the K=2 landscape.
How quickly these different peaks can be scaled depends
upon the mutation rate and the number of nodes in the network. If either
the mutation rate or the number of nodes becomes too large, the population
tends to disperse rather than converge on local peaks. Its behavior becomes
more frenetic. This is called error catastrophe.
At the beginning of this section I used Kauffmans
blue and red bacteria example. Bacteria multiply by dividing; there is
no sex involved (in general). So bacteria depend mostly upon random mutation
as a mechanism for moving uphill to local fitness peaks. Once on a peak,
there is no mechanism to move down (well there is, but lets assume
there is not, because the mechanism in question will not help our organizational
theory much). All things being equal, organisms cannot devolve in order
to climb successive peaks. The devolved individuals would no longer be
as fit as other members in the population and would die out. Why would
it be important to move down? Because the peak an organism or an enterprise
or a species or an industry finds itself on may not be the highest peak
on the landscape. It may be the lowest peak on the fitness landscape instead.
So how can a population on one peak move downhill in order to climb an
adjacent higher peak? Or, more accurately, how can a population of organisms
get a higher view of the whole terrain?
is where sex, or more specifically, the recombination of DNA, plays a
role. Imagine a herd of turtles on a fitness landscape (yes, a herd of
turtles--just checking to see if you made it this far. . .). The father
is on one peak and the mother is on another, distant peak. They wish to
explore the terrain between them. By mating and sharing their DNA, their
offspring will inhabit a spot on the terrain in-between them. This spot
may be more or less fit than either of the parents, but its the
only way to find out what the terrain is like there. If the terrain is
not so good, chances are that offspring will not be selected for further
experiments. But even if the offspring is selected as a future mate, then
there will be an opportunity to explore yet more terrain.
It might seem that long jump strategy is the best one
to use in a search procedure on fitness landscapes. Find two parents who
are far apart from each other on the landscape so that the space equidistant
between them may be explored. This is a good strategy, but only under
certain conditions. The reason has to do with the correlation of the landscape.
If Im hiking in the Appalachians I know that the next step I take
will be roughly correlated with the elevation I am currently on. Of course
there are occasional cliffs, but for much of my walk on the mountains,
a step in either direction takes me down some small amount or up some
small amount. This is what is meant by a correlated landscape. K=2 to
K=8 landscapes are correlated landscapes. Even if I hop out four or five
steps, most of the time, Im a little higher or a little lower than
I was before. But what is the elevation a mile from where I am? There
is little correlation. I could end up a good deal higher or a good deal
lower in elevation.
Right after a catastrophe or at the birth of a new innovation,
thats the time to use the long jump strategy. Chances are that the
organization is not too high on the landscape to begin with, and a long
jump has a better chance to increase its elevation than plodding up the
hill out of the marshes. This is a period of rapid, dramatic, successive
innovations in a variety of directions--borrowing each other's ideas,
people and methods. But after all of the players have moved up some degree
in fitness, they may not think its wise to risk losing what theyve
gained. So in the middle game, smaller steps are more reasonable. Its
also a feature of fitness landscapes that as an organization climbs up
each step, finding the next step up after that becomes exponentially harder.
In the end game, once a high peak is attained, its best stay there.
Why? Well, all small steps lead inevitably back down. And long jumps have
an overwhelming probability of taking you far down in fitness level because
there are only a minuscule number of peaks in all of state space. Your
chances of landing on one higher than the one youre on are infinitesimal.
IMPLICATIONS FOR TRANSITION MANAGEMENT
Living systems must have redundancy in them to dampen out the effect
of miscellaneous, random mutations. Removing redundancy makes the system
more efficient, but less able to adapt to changing demands or evolve
with its larger ecosystem.
Choosing a Good Landscape by Tuning the K Variable
Selection seeks good landscapes to evolve on. Think of the K inputs
per node as conflicting constraints. Then, to create the best advantages
for finding good peaks, manage these conflicting options.
- A minimum of dependencies between nodes minimizes
conflict, but yields overall mediocre performance.
- Too many dependencies between nodes maximizes conflict,
leading to multiple, suboptimized standards of performance.
- A medium number of dependencies between nodes "structures
the landscape" so that it's easier to find and migrate to relatively
high levels of performance.
Watching the Rate of Mutation
It is possible to try to change an organization too quickly
in too many ways. This can happen by adding too many nodes or increasing
the rate of mutationthat is, adding new ideas to the pot too quickly.
The resulting error catastrophe will cause the organization to wander
all over its fitness landscape instead of moving toward local peaks.
Change and acquisition must be balanced over time.
Exploring Large Areas of Terrain on the Fitness
Landscape Requires Finding a Mate
The way to explore broad areas of the terrain is to find a
mate and combine the "DNA" from the two organizations. This
can mean partnerships and alliances. But it also means that the alliance
should have a specific product, perhaps an organization all to its own,
something that can be called an offspring, otherwise the partnership
will simply involve one organization ingesting another.
Different Strategies For Different Parts of
Immediately after a major innovation, it pays to make wild jumps across
the landscape in search of higher terrain. This can be done with spin-offs,
partners, skunk works, broad-based hiring, or acquisitions. Once an
organization has established itself on the slope of a high peak, the
strategy should begin to shift to shorter hops and finally to single
steps in improvement in order to attain the peak. Once the organization
has reached the peak, it should stay there unless the mutation rate
increases (in which case it will drift along ridges) or the landscape
deforms (see the next section). Fortunately, all landscapes deform due
to couplings with other organisms and species in the ecosystem, so no
one will be "king of the hill" for long.
Increasing Complexity Attenuates Finding Radical
The more complex the organization, the harder it is to find radical
improvements in fitness through drastic changes in its genes. Complexity
here is a function of the number of nodes and the number of connections
per node. Large, highly integrated organizations simply cannot make
radical, innovative leaps. Not because they wouldnt like to, but
because its a function of their properties. This is why such organizations
resort to skunk works, divestitures, and acquisitions to feed their
demand for innovation. Its also why if the acquisitions are done
too thoroughly, the innovation rapidly dies out. Theres too much
complexity to sustain it.
concepts concerning complex adaptive
systems come from Stuart Kauffman's book At Home in the
Universe, 1995, Oxford University Press
application to organizational theory copyright © 1997, MG Taylor Corporation.
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