Deborah Duong's 1991 Master's thesis, published "as is" in
Behavioral Science, Volume 40, 1995, pp. 275 - 303.
A SYSTEM OF IAC NEURAL NETWORKS
AS THE BASIS FOR SELF-ORGANIZATION
IN A SOCIOLOGICAL DYNAMICAL SYSTEM SIMULATION
by Deborah Vakas Duong and Kevin D. Reilly
University of Alabama, Birmingham
This sociological simulation uses the ideas of semiotics and symbolic
interactionism to demonstrate how a simple associative memory in the
minds of individuals on the microlevel can self organize into macrolevel
dissipative structures of societies such as racial cultural/economic
classes, status symbols and fads. The associative memory used is
the IAC neural network. Several IAC networks act together to form
a society by virtue of their human-like properties of intuition and
creativity. These properties give them the ability to create and
understand signs, which lead to the macrolevel structures of society.
This system is implemented in hierarchical object oriented container
classes which facilitate change in deep structure. Graphs of general
trends and a historical account of a simulation run of this dynamical
system are presented.
KEYWORDS: Neural Network, Self-Organization, Object-Oriented
System, Container Class, Sociological Model, Dynamical System, Semiotics,
Symbolic Interactionism
INTRODUCTION
Neural Networks, Object Oriented Programming, and Dynamical
System Simulation
Neural networks are self organizing dynamical systems reputed
to represent meaning better than other Artificial Intelligence methods.
An Interactive Activation and Competition (IAC) neural network is
an associative memory which has the human capacity to understand new
situations and make generalizations. It is by virtue of these traits
that IAC networks have another human property when many of them interact
together: they create symbols which have shared meaning. These symbols
are a source of order for the system as a whole. This simulation
is a larger self organizing dynamical system made up of smaller IAC
networks interacting. It represents a society, and the orders that
the IAC networks develop among themselves represent structures that
exist in societies.
To achieve such order, the architecture of individual IAC networks
has to be changeable. Traditional IAC models do not have this capability.
Object oriented programming with container classes facilitates dynamic
network architecture in this system. Thus, this program not only
demonstrates how the individual IAC networks can develop order among
themselves, but also serves as an example of the value of object oriented
programming with container classes in changing deep structure. It
demonstrates the value of this implementation method in the modeling
of dynamical and self organizing systems in general.
Semiotics
The science of semiotics tells us that human beings continuously
search for meaning in signs, and that social life is a system of those
signs. Perhaps this is so because of the limitations of biology:
we can not see truth directly, but guessing at it through our senses
is a matter of survival. We associate people's observable physical
features with meaning instinctively, just as we associate words with
meaning. Yet, just because we perceive a sign as having a particular
meaning and have learned this meaning on our own
doesn't mean we are correct, even if we are in agreement with
others. Racial prejudice is one such mistake. While race is not
a true indicator of ability, we subconsciously classify others on
its basis.
This simulation is about the creation of signs, about how symbols
come to have meaning to people. It is about people classifying each
other and themselves based on outer characteristics. It is a self
organizing system: with only a simple neural associative memory in
each person and goals "programmed in", properties of society such
as racial class and status symbols emerge. The people of the society
do not communicate to each other with words, but develop opinions
in synchrony from their similar experiences. As a dynamical system,
their opinions often develop from "accidents of history": accidents
which determine the future of the society. The people in the simulation
always look for signs, often choose false signs, and attempt to trick
each other by putting false signs upon themselves.
Symbolic Interactionism and Self Organization
As a demonstration of how ideas create societies while societies
create ideas, this simulation is an inquiry into the sociology of
knowledge. Baert and Schamphliere (1987) pointed out the similarities
between the theory of self organization from physics and symbolic
interactionism originating in sociology. In symbolic interactionism,
man is not only a reactor to society but a creator of it as well.
According to G.H. Mead, because man has a self, he is able to put
himself into the perspective of other participants in an interaction
and act only after he has predicted the outcome based on past experiences.
People "reconstruct" society by virtue of their capacity to observe
and change themselves. That is exactly what happens in this simulation.
Employers try to hire talented workers based on their observable features
while workers modify these features, if they can, based on their perceptions
of whether employers will hire them or not. As in Mead's ideas, this
self organizing system goes beyond external/algorithmic determinism
and environmentalism: change is not predicted but comes from the
individual actions of persons. As the workers change themselves
and the employers change their opinions of the workers, properties
of societies emerge.
Workers put the history of their traits and whether they were
employed or not into an IAC associative memory. This self organizing
neural network represents Mead's "me" aspect of the self by incorporating
the employers attitudes into the self. There is stochasm in the employers'
choice of employees and in the workers' choice of traits representing
the unpredictability of the "I" response to the community. Both
the stochasm and the self organization of the IAC allow for novelty
in the system and for status symbols and classes to emerge without
being directed to. This simulation differs from symbolic interactionism
in that there is an objective truth: an actual amount of talent each
worker has. It is just judged by those whose capacity to judge is
limited.
Simulation Purpose
The purpose of this simulation is to demonstrate that a simple
associative memory is sufficient to explain the development of social
signs, status symbols, racial prejudice and racial class. The individual
actions of workers on the microlevel create the structures of society
on the macrolevel: the sum of their actions is greater than the parts.
In this simulation, there are two types of macrolevel order:
structures of belief and social structures. We have a unique opportunity
to look into quantified belief because we use neural networks. Possible
belief structures of employers are belief in status symbols and prejudice.
An employer believes in status symbols if he has a relatively higher
opinion of people having items purchased with social rewards. In
this simulation, money is the social reward for talent. There is
some truth to the belief that status symbols are a sign of having
desired qualities, more than belief in items which can be acquired
freely by anyone or belief in traits such as skin color which no one
can change. In this simulation, prejudice occurs when all employers
hold a lower opinion of one race than another, even though the members
of each race have the same degree of talent. Workers with similar
traits may come to have similar beliefs because they are treated the
same. This formation of cultural classes by self-fulfilling prophecy
is another macrolevel belief structure.
Possible social structures are racial economic classes, the purchasing
of status symbols, and fads. Racial economic classes form when one
race persistently has more money, material possessions, and higher
levels of employment than another. We know status symbols are being
purchased when expensive items are purchased more than can be expected
by chance by those who can afford them. Fads, in this simulation,
are the simultaneous acquiring of traits which cost no money. Social
structures result from belief structures while belief structures result
from social structures: they co-evolve together.
METHODS
<note: the next paragraph appears in the thesis but not the paper>
In this system, three employers take their turns laying off employees
and hiring replacements from a pool of fifty workers. Each employer
has ten employees, making the over-all employment rate 60%. They
lay off 70% of untalented workers randomly, and 20% of all workers
randomly. With these percentages, it is likely that all the employees
that an employer has in any particular cycle will be laid off before
five cycles of firing/hiring. Employers hire on the basis of an estimation
of the workers' talent, which they can not observe until after employment.
They make this guess by an association of workers' traits and talents
that they have seen in the past. The first employees are hired randomly.
After employees are dismissed, they are not recognized by the employer
when they re-apply: he still has to guess their talent.
The three observable worker traits are a fad, a suit and a skin
color. The only difference between these three traits is the ease
with which they may be acquired by the workers. A fad is free and
may be changed to any one of three values. Although one of the suits
costs nothing, the other two must be bought with money earned from
employment. Their prices are 0 dollars for suit 0, 6 dollars for
suit 1 and 9 dollars for suit 2. All workers start with suit 0.
One dollar is earned each round that a worker is employed. Skin color
is a trait which the worker can not change. It has two possible values:
black and white. The proportion of talented persons of each skin
color are equal (less than two percentage points difference). The
workers' unobservable trait, talent, comes in two values: talented
and untalented. Skin color, fad and talent are all assigned randomly
at the beginning of the simulation. Once a worker is hired, an employer
knows his talent for the purposes of laying off and to update his
associative memory.
Workers who are unemployed re-decide what they should be and
change their traits, if necessary, in an attempt to impress the employers.
Even if they decide to keep the suit they have, they must pay for
it again. They change their traits to (or keep them at) the combination
which they can afford that they associate most highly with employment.
Every time they are judged by an employer, they add knowledge of the
result to their associative memories.
The IAC
The IAC neural associative memory holds and processes the knowledge
in the simulation. Each person in the simulation has a separate IAC
network. Neural networks are good models of human decision making
because they process knowledge in the same way that human beings do:
they capture meaning with models of human neurons. The IAC network
in this model has the same behavior as that described by McClelland
and Rummelhart (1989) with the additional property that nodes may
be added and deleted as necessary during the simulation, so that memories
may be added as new knowledge is learned and deleted as old knowledge is forgotten.
"Interactive activation and competition" is a descriptive
name for the IAC network's architecture. This network is divided
into several pools of nodes, each node having inhibitory connections
with other nodes in its pool. These inhibitions put the nodes in
competition with each other: the stronger one node is activated, the
more it is able to turn other nodes in the same pool off. Every node
in each pool is also connected to a node in a special pool with no
intrapool inhibitions, the instance pool. The activation is interactive
because the bidirectionally excitatory connections provide the route
by which what is going on in one pool influences (while it is influenced
by) what is going on in the other pools.
This architecture serves as an inductive associative memory:
it can arrive at a general conclusion based on specific examples.
The pools represent "traits" : in this simulation they represent
the traits of fad, suit, skin color and talent in the employer's memory.
In the worker's memory, they represent fad, suit, and whether the
worker was employed or not. The nodes in the pools represent values
of traits. For example, in this simulation there are three nodes
in the suit pool representing suits 0, 1, and 2. Each instance pool
node connects a single set of associations in the pools. In this simulation,
instance nodes represent people, and they have excitatory connections
to the values of that person's traits, at most one in each pool (see
figure 1). In the employer's memory, each instance node represents
a different individual while in the worker's memory, each instance
node represents himself at a different point in time.
Intuition and Creativity
To estimate how talented an applicant is, the employer activates
the nodes in the pools that represent the applicant's traits and sees
how strongly the node representing talent is activated compared to
the node representing lack of talent. The answer that he will get
will not be a precisely correct logical one, but a more "intuitive",
even "creative" answer. Energy flows back and forth through the
network fifty times: it goes from the activated traits to the people
(represented by instance nodes) who had them, to their traits and
to the people who had them while it is being inhibited in the pools,
so that each pool has a node activated more than the others. That
node, in the talent pool, is the answer.
In this simulation, the amount of talent a person is
judged to have is the activation of the node
representing talent less the node representing lack of talent in the
talent pool. It is a real number. It is an answer which is holistic,
using all of the knowledge. It is intuitive because even if the black
people that the employer knows are as talented as the white people
he knows, it won't give an answer based on that, but on the other
traits that those black people had, and the talent of the people who
had those traits, and the talent of the people who were like those
people, etc.
Every cycle adds another level of recursion to the answer.
It is intuitive because you can not quite pin down how the answer
is arrived at, but it isn't by reasoning. It is almost like a "feeling"
about a person. Why don't people use logic instead of this intuition? Perhaps
it is just another biological limitation. Our neurons (without the
assistance of a paper and pencil and a statistics text book) have
difficulty in holding and processing all of the information needed
to make a precise answer. If they did, like expert systems, they
would not be able to deal with new information because the data to
base it on would not be there. If a few examples were there, then
the answer would be based on those few examples instead of the whole
body of data, leading to an insignificant answer.
In contrast, the IAC network can easily deal with new combinations
of trait values it has never seen before and even trait values it
has never seen at all using the fact that a new trait value is something
other than the trait values now present in the trait pool. If all
the trait values in a pool are associated with lack of talent,
meaning an employer is dissatisfied with them, then not activating
them may lead to a higher estimation of talent in some cases, so that
the employer will be willing to try something new.
This creative ability to understand new situations is essential to human beings
both in this simulation and in real life. Even though the worker's
IAC represents Mead's "me", the values of the culture, it is still
creative in imaging what other people (or employers) might think.
A Choice Function
Mead's "I", the decisions made based on information from
Mead's "Me", does not follow strictly the output from the association,
but has an element of stochasm as well. When an employer chooses
an applicant to fill a position, he uses his IAC to measure the talent
of each unemployed worker , and then puts all of these values into
a choice function which chooses one of them based on a decision parameter.
Possible values of the parameter are from -1.0 to 1.0. If 1.0 is
given, the choice function chooses an applicant from the list randomly.
If 0 is given, the values of talent (after normalization) are interpreted
as a distribution from which a random variate is picked. The applicants
with higher talent have more chance of getting picked. If -1.0 is
given, the person with the maximum talent value is chosen.
Other values between -1.0 and 1.0 result in a decision that
varies smoothly between these extremes. A new distribution is mapped
from the given set of values. The decision parameter actually represents
a percentage used in this mapping. For example, decision parameter
-0.5 will let the maximum talent value take up its given percentage
of the distribution, as when zero is the decision parameter, plus
50% of the remaining space, the unassigned portion of the new distribution.
The other values are mapped on in descending order: the next value
takes on its proportion plus 50% of the remaining space, and so on.
If there is not enough space for the given percentage of an applicant,
it is then cut off. Of course, 1.0 gives the maximum value 100% of
the space.
If the decision parameter is 0.5, the minimum amount of space
that any value in the new distribution may take is 50% of 1/n of the
total space, where n is the number of applicants. The smallest values
are apportioned first, so that values larger than 50% of 1/n are calculated
based on the remaining space. Of course, if the decision parameter
is 1.0, each of the n applicants gets 100% of 1/n of the space, making
a uniform distribution (see figure 2).
The decision parameter may be thought of as representing self-doubt.
If you are absolutely sure of your intuition, then you pick the one
you feel the best about every time: this would be represented by a
decision parameter of -1.0. If you want to give close seconds a chance
sometimes, your decision parameter is a negative number greater than
-1.0. If you have little confidence in your ability to decide, you
may chose more randomly with a positive decision parameter less than
1.0.
We used a single decision parameter per simulation, usually negative
for the employers and slightly negative for the workers, but it is
also possible to vary the parameter during simulation, producing a
"simulated annealing" effect. This could be useful, for example,
to simulate decision making in people through their development.
Teenagers are known to try different things before they have much
experience, but this gives them experience with which to stabilize
their ideas about the world and about themselves. We could represent
their decisions with a positive decision parameter to the choice function.
As people gain experience, they gradually become more confident in
their decisions and may even become so set in their ways that they
no longer give new things a chance. We could represent this by making
their decision parameters more negative. According to physics' annealing
theory, this is an optimal way to make use of all the facts. Individual
points of view are not settled upon before sufficient exposure, and
those within a generation come to have similar views in synchrony.
The decision function may be thought of as analogous to
the "activation rule" of the nodes of a neural network, persons
and employers as analogous to neurons, and the society as analogous
to a neural network. As nodes are connected to each other through
synapses, so are employers connected to workers by employment. Just
as the network dissipates to a solution after many cycles, so does
the society as a whole after its cycles. The solutions at the society
level are the dissipative structures of racial class, fads, and status
symbols.
Container Class Organization
We are able to ask questions about micro-macro interrelations
- the relation between the node's state and the network's state, or
the relation between the network's state and the society's state -
by virtue of the object oriented container class organization of the
system. The program is implemented in object-oriented C++. Each
entity of this and any other object oriented system is an object of
a class. The data and functions which act upon the data are encapsulated
together into a class, representing the attributes of an entity and
its behavior. Objects are individuals of a class: for example, "dog"
would be a class while "Rover" would be an object. A container
class, in object oriented programming, is a class which has other
classes in its composition (see figure 3).
Container classes are convenient because they are modular and
you know just where to make a modification to ask a question: for
example, to ask how a worker's behavior affects the network we know
we must change one of the functions in his class. They are important
tools in demonstrating how a change in the number, the interrelations
among, or even the type of micro-entities a macro-entity is composed
of affects the macro-entity. Container classes can do this because
the list of objects an object contains may vary in length and in terms
of which particular objects they are composed of on-line. Also, inheritance
classes may be used to represent variations in the type of object
contained object on-line. Possible questions to ask are "How
do the number of workers affect the opinions of the workforce as a
whole?" or "How do different compositions of the workforce in
terms of variation in worker behavior affect the system as a whole?"
In this simulation, container class organization enabled the arrangement
of memories in the networks to vary and enabled employers to delete
and add employees. Because of this we could ask how changes in the
micro-entity brains affect the macro-entity society and how the brain
is affected in turn.
Model runs, however, use lots of time and space.
By simulating the actual entities themselves instead of using differential
equations to represent them in aggregate as in most dynamical system
simulations, we have gained the ability to change deep structures
on-line, but we have lost the convenience and efficiency of the differential
equations. The program has over 2000 lines of code and takes 50 hours
of CPU time on a Sun 3/50 workstation. Over 30,000 inquiries to IAC
networks are made by the workers and employers. Employers pay, lay
off, and hire employees 200 times.
Hierarchy
This simulation is hierarchical, but not in the sense we usually
think of when we think of hierarchy in neural networks or in inheritance
classes. Its container classes are hierarchical: each class represents
a different level in the hierarchy, and may be modified to see the
effect on other levels (classes) in the hierarchy.
There are 13 classes in this simulation. From the lowest level
to the highest level they are synapse, axon, node, pool, IAC network,
trait, memory (characteristics), workforce, employee, employer, companies
and society. As depicted in figure 4, the higher levels contain the
lower levels.
A society contains a workforce and companies. A workforce
contains a linked list of worker-objects, and the companies-object
contains a list of employer-objects. Both the worker and the employer
contain an IAC network. Additionally, the employer
contains a list of employee-objects and the worker contains a characteristics-o
bject which contains a list of traits. Each employee-object points
to a worker in the workforce, so that the companies contain a subset
of the workers that the workforce contains. This is one way interrelations
may form: when two objects contain the same object they may influence
each other through it. The IAC network, which is the brain in both
the workers and the employers, contains a list of pools. The pools
contain a list of nodes, and the nodes contain a list of synapses
and axons. The axons contain synapses of other nodes, creating a
connection. From synapse to society there are ten levels of hierarchy.
Reverberation
A change in one of the lowest levels, perhaps in the activation
function of the nodes, could reverberate up to the highest hierarchical
levels and cause change on the societal level. That is why hierarchical
classes are particularly good for asking questions about micro-macro
interrelations. The central question of this simulation, "How
do people's associations of each other affect society as a whole and
how are their associations affected by society?" is really quite complex.
To answer it, we might start with changes on the axonal level, the
connections in the IAC network, which change when employers and workers
learn new sets of associations. We observe those changes reverberate
up ten levels of hierarchy to the societal level and back down ten
levels to change the associations represented in the axons once again.
Or, we might start with changes on the employer level in the employer
relationship and watch them reverberate down the hierarchy to the
axonal level and back up again. It doesn't matter where we start
because perceptual structure co-evolves with social structure: they
cause each other.
Data Encapsulation
Change occurs between each level and the next: a change in one
level can not change levels further up or down the hierarchy without
changing the level next to it (containing or contained by it). This
is a trait of natural hierarchies: its simulation is facilitated by
the data encapsulation of the container classes. In object oriented
programming, data encapsulation means that the data a class is composed
of can only be manipulated by the procedures of its class. In our
model, each class contains procedures which manipulate only its data,
and since the classes are container classes, the data is the next
lower level of hierarchy. For example, procedures of class workforce
call procedures of class worker to manipulate the worker-objects in
its list. Procedures of class worker call procedures of class IAC
network to manipulate the IAC network it contains. Every level manipulates
the next by calling its procedures, down to the nodes which call procedures
of the synapses and axons. Each procedure call is a reverberation
to the next level of hierarchy. A class such as synapse or node will
contain a pointer to the object which contains it, facilitating change
in structure so that reverberations may go back up the hierarchical
levels.
Dynamics
We now have enough information to talk about how change
is implemented in the simulation. In every cycle, after paying his
employees, one of the employers dismisses a random 70% of his untalented
employees and 20% of his remaining employees. His linked list of
employees decreasesas a result of this action.
Then, he hires the same number back again from
the pool of fifty workers, not recognizing the ones that he just dismissed.
His IAC judges each worker's talent and his choice function chooses
a worker based on these measures, one at a time. As workers are hired,
the memory of each one's traits and talent is added to the employer's
network. If an individual was hired by the employer in the past, his
representation in the employer's mind is updated.
Memories in the IAC network are updated
by the deletion of old nodes and the addition of new ones to
the list of nodes representing persons in the instance pool and the
creation of axonal connections between the instance nodes and the
nodes in the trait pools representing the values of personal traits.
As each worker is either accepted or rejected by an employer, he puts
this new set of associations between his traits and his employment
into his network. If there are ten sets of associations or memories
in his network already, he deletes the earliest memory by deleting
its instance pool node and its axonal connections to the traits in
the pools. He then adds a new instance node and connections to the
traits in the pools for the new memory. Keeping only ten memories
saves computer memory space and processing time, at the same time
it keeps the workers' ideas more or less current. In both the employer's
and the worker's IAC networks, new nodes are added to trait pools
if none of the memories present have a new memory's trait value and
old nodes are deleted in the trait pools if the memory being deleted
is the last one to have that trait.
As the workers are hired, the employer's linked list of employees
increases. The other two employers repeat this process of laying
off and hiring. Then, the unemployed workers all update their traits,
one at a time. Each combination of traits which the individual worker
can afford is judged by his IAC network in terms of its employment
value, then one of these combinations is chosen by his choice function
and bought.
These are the changes that occur to the societal connections
of the simulation, the employment relations, and the perceptual connections
of the simulation, the associations in the IAC. Statistics on each
employer's perceptions of the 18 different combinations of worker
traits are collected every five frames, along with the numbers and
percentages of workers who have those traits. Employment rates for
the races and talent rates for each suit are also collected This
is done for 200 cycles.in the simulations reported in this paper.
RESULTS
Structure vs. History
Because this is a dynamical system, the results are difficult
to report. As Peter Allen, one of the originators of self-organizing
social system simulation said, "The richness of human systems,
produced by layers of mutual adaptation and initiative and framed
by historical circumstances makes each situation `unique'. Case studies
may accumulate, but on what principles can general conclusions be
drawn?" Graphs of averaged trends, although they do give a good idea
of what is happening in a system, do not give a good idea of why it
is happening.
Social scientists from Durkheim to Marx, to the dismay of historians,
have seen general trends as laws to which specific situations must
conform. What happens to an individual is not important: it is determined
by laws. What they did not know was that if individuals act on their
own, they will drive the general trends while they are influenced
by them, causing structure in the general trends to appear even without
laws. Under different accidental circumstances, the structure will
be different: the particular structure itself is not a law.
This is the idea of self-organization. Nobel Prize winning physicist
Ilya Prigogine proposed the idea of dissipative structures which self
organize. Peter Allen, Prigogine's co-worker for twenty years, left
statistical mechanics to use this idea in social systems. Classical
social scientists were influenced by the immutable "laws"of physics
of their time, and came to be at odds with historians, who had traditionally
believed that men and accident could change the course of history.
Prigogine is said to have inserted history into physics: in doing
so, he inserted it into sociology as well. So, in reporting results,
we will give both graphs of general trends and a historical account
of a simulation run. Æ(
Chaos <Çrvqna?CVPDF Å!#0 '!7 KH s!vkynb! te ´o"wxe&s[ ™!vkEt7!O T N "A K J ˜ig#Kunb*
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ulašhmm0r}odas= †d"pymsmG AL‡sgiedab/a(Figure 5 shows the trends of prejudice against black people in
a society with three employers having decision parameters of -0.5
, and with 17 blacks and 33 whites having talent in equal proportions.
This society has racial class: a hypothesis test for the difference
between the black employment rate and the white employment rate on
typical cycle 180 showed a significant difference at the a = 0.01
level .
Figure 6 shows the same society with a decision parameter
of 0 in the employer's choice function. There is no significant difference
between the employment rates of white and black (a=0.05) at typical
cycle 180: this society has no racial classes. We might be tempted
to form a rule, since all else was the same, that the more stochasm
there is, the less prejudice and racial class there is. If the world
was linear, it would be true. But it is non-linear: When an even
more stochastic parameter .15 is used, prejudice and racial class
return. It may not even be because of the parameter, but because of
the different random accidents that happened in their simulation as
a result of a change in the parameter. In another set of simulations
using the same parameter but a different set of random numbers and
different initial conditions, prejudice occurred with the -0.5 parameter
and no prejudice with either the 0 or the .15 (stochastic) parameter.
Thus, we are not talking about what must happen, but what is
possible. Even that can be informative, or even surprising. We will
concentrate on what happened in the simulation of Figure 5, with a
decision parameter of -0.5. We will call this "run 1" and will
give both its general trends and its history.
General Trends in Run 1
The first interesting thing about this simulation is that the
employers' perceptions of the various traits are synchronous even
though they do not tell each other what they believe. They each come to
their perceptions through their own experiences alone. The workers,
although they do not communicate, also behave in synchrony within
their skin-color and even economic classes, because of their similar
experiences.
Figures 7 through 13 show the three employers' views of how talented
persons having each trait are, comparatively. They all exhibit synchrony:
Their opinions go up and down more or less together. The total of
the measures of talent for all values of a trait for any employer
is 1.0, and the value least associated with talent among the values
of one trait is always zero, even if it is highly associated. Values
are normalized for comparative purposes.
The synchrony of the perceptions of suits in figures 7 through
9 is not at all surprizing. After all, suits (other than suit 0)
are correlated with talent because a worker can only buy them with
money obtained from employment, and the untalented are laid off in
greater proportions than the talented. Each employer may have observed
these facts about suits independently. How might the synchrony of
the perceptions of fads in figures 10 through 12 be explained? A
fad is free and can be changed as easily by those with talent as by
those without it. Perhaps a correlation between the fad and the suit
could develop in the case where employers prefer a particular fad
in a particular suit and disapprove of the same fad in another suit.
Then a correlation between fad and talent could emerge in a self-fulfilling
prophecy. Figure 12 is a particularly good example of synchrony.
In looking at these, one may be tempted to propose that fads by nature
rise and fall quickly, but we have another simulation in which all
employers and employees avoided a fad for the entire run.
What is surprising is the synchrony of the employers' opinions
about skin color in figure 13. Prejudice against black is more persistent
than fad preferences. It was lifted and reinstated in the employers
in synchrony. These perceptions are clearly wrong: we know for a fact
that black and white have the same proportion of talented persons.
We can't claim that it is simply because they are a minority: we have
other simulations in which prejudice is against the majority. Figure
14 gives the average perception of white people, which, because of
normalization, is just the average perception of black people inverted.
Notice that the perceptions of the three employers did not cancel
out, but averaged into a wave of high amplitude because they were
synchronous.
Synchrony occurs because the employers all change and are changed
by the same pool of workers. The traits of the workers are the only
communication between the employers, and are an effective one. To
know why the synchrony occurred, refer to the details about how color
is perceived as being related to other traits, and how it comes to
be related to the other traits in a self-fulfilling prophecy, that
is given in the historical account.
Figures 15 through 20 illustrate the workers' response to the
employers. They contain the three employers' responses to a trait
averaged together and the percentage of all workers having that trait.
In figures 15 through 17, the workers respond to the employers preference
for fads but it is delayed, perhaps because employed workers are not
required to change their traits or because the workers who do change
base their choices on their past ten experiences with having their
traits judged by an employer.
Figures 18 through 20 show the average employers perception of
each suit as well as the actual percentage of each suit that are talented.
They are correct in their perceptions: The perceptions of suits rise
and fall with the percentage of talented persons wearing those suits.
The rising curve for expensive items shows belief in status symbols.
The percentage of persons wearing the suits follows the employers
preference as well. This shows the purchasing of status symbols.
We know that fads and suits have become symbols with shared meaning
because the workers respond to the employers' perceptions of them.
The employers adapt to the workers, and the workers adapt to
the employers: as they do, society unfolds. But something is missing
from these averaged descriptions of society's unfolding. It is the
complexity: the relations between the traits are left out. This is
important: for example, a particular fad could be favored in a black
person wearing a particular suit but disliked in a white person wearing
the same suit. Black people could use this fact to open the door
to employment and change the employers' mind about them. Trying to
understand a complex system by looking at an averaged graph of each
of its components alone is almost like trying to understand a paragraph
by looking at graphs of the average number of each word. Important
information about the interrelations of the components is missing.
Without the details, the causes are missing.
The following historical description of the simulation gives
some causal information, but is by no means complete. We have only
snapshots of what is happening every five cycles, and do not know
what is happening between the cycles. Nor can we pinpoint which accident,
had it happened slightly differently, could blow the entire society
to a different state. We can never understand "why" something
happens in any complex system perfectly, but must be content with
general impressions and guesses.
The History of Run 1
At cycle 5, we already see prejudice. 35% of blacks are
employed while 72% of whites are, although at this early stage employers
think fads are the most important factor. By cycle 10, all employers
prefer white for everything, and fads are no longer important to them.
Employer 0 has decided that he likes suits, and despite his prejudice
hired a talented black wearing suit 1. It was a lucky accident that
there happened to be a black in a suit when there was no other whites
in the same suit to get the position, and fortunately he was talented.
Perhaps this lucky accident started a trend so that by cycle 15 employer
0 prefers black for most suits (by suit, we refer to suits which cost
money, suits 1 and 2).
Employers 1 and 2 still preferred white for suits, however.
They did not hire blacks at all. Employer 0's preference for blacks
in suits over whites was a window of opportunity for black, but because
he was not hired by the other 2 employers, he did not have enough
money to buy any suits. By cycle 20, the window had closed: employer
0 preferred white again for most combinations of suits and fads.
This is an example of how synchrony was enforced: employer 0 could
not change his prejudice because employers 1 and 2 did not. Black
still made do with what he had: two out of three employers preferred
him for the combination of suit 0 and fad 1. Seven out of thirteen
applicants responded by presenting this combination and five were
employed. This is more than expected by chance because there are
always between 3 and 9 possible combinations of traits any individual
can choose. This is an example of class cultural structure because
white did not present this trait disproportionately. Luckily, they
were talented: the few blacks that were hired were representative
of their race in the employers' minds, and because they were talented,
they opened the door for the rest.
By cycle 25 blacks had 70% employment and whites had only 54%.
Employers 0 and 1 preferred blacks for most combinations of suits
and fads. Six out of nine blacks present the suit 0 fad 1 combination
which is still preferred by employers 0 and 1. Again five were hired,
but this time the lot was rather untalented. Perhaps this is why
by cycle 30, only 11% of blacks are employed again. Employer 0 no
longer prefers him for suit 0 fad 1, and employer 1 does, but now
fad 1 is less popular with him. Black does what he was previously
awarded for: he presents more of the suit 0 fad 1 combination than
any thing else, and contributes to his downfall in doing so. Employer
1 hires whites with more popular fads instead.
In cycle 35, blacks are preferred for suits in 2 out of 3 employers,
but they again can not afford the suits because of the 17% employment
rate. By cycle 40, all employers have learned that suits are a good
indicator of talent. This is so when black has an 11% employment
rate and very few suits. He is only preferred in an unpopular fad
in suit 0, which he presents in greater proportion, but is rarely
chosen.
Apparently employers are becoming dissatisfied with untalented
whites' ability to buy suits, and they become disillusioned with suits.
In cycle 55, employer 2 preferred black for a popular fad and hired
three of them, so that they were more popular with everybody by cycle
60. By cycle 65, blacks employment rate had grown to 29%, while he
is preferred in most categories in employers 1 and 2. Correlation
between suit and talent hits an all time low because of prejudice:
60% of suit 0 are talented while only 20% of suit 1 and 40% of suit
2 are. As black gains to 41% employment by cycle 70, the correlation
between suit and talent returns. But that doesn't matter to black:
the employers haven't relearned the suit correlation yet, they just
want to employ black. Black gains to a high of 88% employment by
cycle 95, compared to only 15% white employment. White is preferred
for some suits, and because of his past experiences knows that he
should buy them, but he can not afford to. Black is doing well, but
never in his history has he been rewarded for buying suits, so he
does not buy them.
First employer 2 relearns the value of suits. Then by cycle
100, all employers know the value of suits. Maybe they have learned
that just because someone is black doesn't mean they are talented,
either. By cycle 105, black employment is reduced to 64%, which is
even with white employment. But these figures can not remain constant:
even though black has more money than white, only 17% of blacks buy
suits while 45% of whites do. As a class, white has learned to buy
suits while black has not. White is preferred slightly across the
board.
At cycle 110, black has 41% employment and begins to learn about
suits. Unfortunately, he will lose in the end because the suit he
prefers is too expensive for him. He has 29% suit 2's, which is quite
a lot considering how expensive they are. Employers are now preferring
him for suit 2. In cycle 120, 58% of blacks were employed, but white
out did him in buying 33% suit 2's compared to black's 11%, so that
white regained preference in most categories by cycle 125.
By cycle 135, black is 41% employed and is buying suits disproportionately
higher than whites with his fewer funds, but white is still preferred
for suit 1. Despite low employment, black continues to buy suit 2
which he is preferred for. In cycle 150, 4 black people are employed,
three of which have expensive suit 2. Black is unable to gain in
this and eventually loses to white who can better afford suit 2.
By cycle 180, 29% of blacks are employed. White is preferred
in suit 0 across the board except that black is preferred by two employers
for suits he can no longer afford. In cycle 190, black employment
is at 35% and he is liked a little more. He uses all his funds to
buy all suit 2's and no suit 1's, because he used to be preferred
for suit 2. However, he is no longer preferred for suit 2. Perhaps
a few did get in, because in cycle 200, two of the employers who liked
him before in suits show some preference for him in some fads of suit
0 as well.
In summary, black was caught in a vicious circle: he was discriminated
against because he did not have a suit, and could not afford a suit
because he was discriminated against. Black was called upon to prove
himself with suits, but often did not know the correct strategies
to take because of past prejudice. Sometimes he was lucky enough
to gain, but lost in the end to whites money and experience in buying
suits. Suits reinforced prejudice, but this was self limiting because
prejudice lowered the correlation between suit and talent.
DISCUSSION
Emergent Order
The results from run 1 show every type of macrolevel order mentioned
in the introduction: belief in status symbols and prejudice in employers,
cultural class beliefs in workers, racial economic classes, purchasing
of status symbols and the existence of fads. We have achieved the
objective of macrolevel social structures from microlevel associative
memory, even though the simulation does not include many important
factors in real societies.
A likely objection to this simulation is that it is unrealistic
and too simple. Employers do not really throw out a quarter of their
workforce in turn. Talent doesn't come in only two values. The real
world is much more complex. With so many things not taken into account,
just what does this simulation prove? Even if it were possible to
take into account all the complexity of the real world, it could not
predict what would happen next because it would be sensitive to initial
conditions.
The point is not to predict, but to understand how societal structures
may result from individual decisions, even if they are unrealistic.
This simulation does not tell how prejudice comes into being as much
as it tells how, once it is there, it might be "recreated" with
the help of status symbols. It shows how status symbols can become
a sign of what a society values (in this simulation, talent) and develop
a rough correlation with their signified value even though the symbol
itself has nothing to do with the value. It shows how what is perceived
as a different class of persons actually becomes a different class
of persons with members that develop different understandings of the
world and how to deal with it because they are treated differently.
It shows how shared meanings develop. It shows how all of these things
can come from simple associative memory.
Semiotics
This simulation can do all of this despite its differences with
real societies because it has one important thing in common with them:
it treats people's traits like a set of symbols in a language. Like
a language, the meanings of the symbols are common to all persons
of the same society, but each member learns it on their own, by experience.
Which language, or societal structure, comes to be meaningful can
not be predicted, but we know that people's traits will come to have
shared meaning. Unfortunately, when traits that can not be changed
become a sign of the negative, the injustice of prejudice results.
This model also instructs us about the nature of prejudice. Perhaps
prejudice is so hard to change because it is a "gut level" feeling.
Prejudice originates in the primitive levels of subconscious association:
even the most liberal white woman in American society will fear a
black man in inexpensive clothes that she passes in a dark alley at
night. Prejudice is part of the systems of meaning that everyone
learns in a society. A prejudiced person feels (correctly) that he
has come to his opinion on his own and feels (incorrectly) that since
others agree with him he must be right. Like language, prejudice
in this simulation and in real society self organizes and recreates
itself.
The Observable and the True
The use of employers in this simulation is not essential:
we could have developed symbol systems with only people interacting,
as long as they have goals and rewards. Still, one could object to
the use of intuitive associative mechanisms in explaining employment
practices because there are "objective" assessments of ability
on which basis employers may hire. In making such an objection, we
forget that subjective appearance is the only information we usually
have access to. We assume the signs we use are true only out of convenience
and necessity, not because they actually point to the truth. For
example, when a woman applies for a job, all the information an employer
usually has to judge her with is her resume and her appearance and
mannerisms during an interview. Suppose the resume says that she
received good grades in school. This is not objective information,
because the employer does not know if she received them through conscientious
effort or if her teachers, knowingly or unknowingly accepted a false
representation of her ability as true (with the teacher shortage,
the latter is likely). Nor does the employer know the politics involved
in her recommendations. Getting good grades can be like buying an
expensive suit: they prove you had enough ability to earn them, but
not getting them doesn't prove that you don't have ability or that
you haven't learned. Buying an expensive suit proves that you have
enough money to buy it and perhaps that you were useful enough to
society to afford it, while not buying it doesn't prove you don't
have enough money or are not useful. Both good grades and a new suit
are rewards for having done what society values. The suit in this
simulation which may be bought with social rewards may represent good
grades as well.
Even though many things that we take for granted as being objective
are really subjective, we are not lost: correlations do develop between
the observable and the true. People in this simulation and in real
life learn to "show off": to get those good grades (even at the
sacrifice of their learning) so as to display their abilities. If
they possibly can, they buy suits and other status symbols to communicate
their talent and social power, even though suits inherently have nothing
to do with talent. Yet, these correlations will never be perfect:
most likely they will be far from perfect. There will always be many
who gain by making false representations of themselves and many who
lose because they are unable to play the game, namely, the lower class.
Another objection that may be raised is that if we are so limited
in our ability to perceive truth, are not even the categories we frame
our social science inquiries into, including in this simulation, themselves
prejudiced? Is not all social science doomed to failure, reflecting
opinion more than truth? The answer is that it is not a law that
there can be no good signs of objective truth and that we must be
trapped by our senses or by the web of meanings of our culture. It
is a fact of life we can seek methods to overcome. The natural sciences
and mathematics have succeeded in making useful indicators of what
is objectively true, even if truth is only revealed in the jumps of
Kuhnian scientific revolutions. One thing which has the ability to
reveal truth is a model that works. A model which can produce one
known phenomenon from another has explanatory power which transcends
our human limitations. Computer simulation is an excellent tool for
developing such "models that work".
Computer Simulation, Determinism, and Dynamical Systems
Some sociologists believe that the use of computer simulation
in sociology implies a strict determinism and lack of free will in
human beings (Muir 1986). This may be true of single - outcome equilibrium
simulations, but it is not true of self organizing simulations which
are sensitive to initial conditions: their entire future may be changed
at the bifurcation point by the smallest individual decision. Dynamical
systems are deterministic, but because of their fractal basin boundaries,
what develops during the simulation depends upon the exact arrangement
of every atom of the system. Thus, if our "free will" can do
so much as blow an atom from one unpredictable quantum state to another,
it can change the course of history. Dynamical systems are deterministic
yet unpredictable because we can not know the state of every atom.
If chaos and self organization are good models of society, then the
individual is not just the pawn of the environment.
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(Manuscript received September, 1993)