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.           (          
Chaos 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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Duong, Deborah Vakas and Kevin D. Reilly.  "Neural Network and Self-Organizing 
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Muir, Donal E.  "A Mathematical Model/Computer Simulation of Adaptive 
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Reilly, Kevin; Hayashi,Yochi;Duong,Deborah; and Krishnamraju,Penmatcha.  
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(Manuscript received September, 1993)