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CHAOS AND CRIME


Lecture 003 

The ABCs of Crime: Attractors,  Bifurcations and Chaotic Regimes

Jan, 1991
Rev., Aug., 1999


You see, there is so much energy
dissipated, that you can use it
to build something...cosmos, life,
ourselves, [and even society].
               ...Prigogine




CRIME AND CHAOS     The dynamics of our social world can not be
captured by the stable and periodic dynamics which are central to
classical mechanics. The same is true of criminal behavior.
Instead, what is seen in new findings of chaos research are
patterns of instability and change out of which come the incredible
variety in infinite complexity of actually existing natural and
social forms.  In any society, criminal behavior expands and
contracts, folds and unfolds with a richness and a discontinuity
which appear to be outside the scope of science.  
Yet the new science of complexity embodied in the work of Lorenz, 
Mandelbrot, Takens, Smale, Prigogine and others offers to reclaim the 
nonlinear dynamics of social systems to the knowledge process we call
science.  Chaos theory, by helping to map the nonlinearity in
physical and natural systems, thus reunites the social sciences
with the physical and natural sciences; this time not by forcing
the data to fit classical mechanics but rather by relegating
classical mechanics to but a few actually existing physical
systems.
     In this chapter, I want to offer the reader an exposition of
crime and chaos and to make the connections in the everyday life of
those who may engage in behavior harmful to themselves, to others,
to their society or to other societies.  There are two concepts
which are fundamental to an explication of Chaos theory and its
application to a postmodern criminology; that of the attractor and
that of bifurcation.  These concepts were introduced in Chapter 3;
we will flesh them out and explore the varieties of criminal
behavior in more detail here.
     Nonlinear dynamics produce those fuzzy, fractal structures of
social behavior called attractors; nonlinear dynamics also produce
three kinds of change at bifurcation points.  Together, these
concepts and the insights they offer may help redirect attention to
the sources and solutions to criminal behavior as we enter the 21st
century.
     The payoff from such explorations is an understanding that an
observer of criminal behavior will observe differing patterns of
crime depending upon the region of the attractor observed.  In
normal, classical mechanics, if one observed one section of a
simple system, one knew the dynamics of every other region in the
field.  Not so in the science of complexity.  In fairly stable
outcome field, a given set of parameters might produce very little
crime; with a small increase in just one of those parameters, an
outcome field is expanded and with the new, more complex dynamics,
come qualitatively and unpredictable increases in crime... that is
what nonlinearity is all about; changing patterns of crime with the
same set of variables.
     It is also possible to have one set of dynamics (crime, in
this case) in one region of an outcome field and another set of
dynamics (prosocial behavior) in another region of the field for
any given person, firm, or ethnic group without any prior or
independent change in the physiological or psychological makeup of
the persons concerned.  Chaos is not only a science of the whole
but is also a science of complexity of the whole.
     Transformations to second and third order change for the same
kind of system comes when key parameter(s) bifurcates producing two
(or more) basins of attraction to which a molecule, a person or a
firm could move.  In order to grasp this idea, think of a molecule
of water.  Without any transformation of the structure of a water
molecule, a slight change in key parameter, temperature, will offer
two basins of attraction between which a water molecule could move. 
It could be in uniform and undistinguishable motion in a fluid
state or it could be part of a much more complex snowflake.  At the
same time, the snow-flake could move easily back and forth between
states without any change in the physical structure of constituent
water molecules.  The same is true of a wide range of complex
systems; viruses, moth populations, fish populations, economics,
psychology and, perchance, crime.
     It is the fractal patterns, called attractors, produced by
nonlinear dynamics which are the object of interest for those who
practice this new science of complexity.  One collects a large set
of data in time series format, puts it through a Chaos Data
Analyzer, looks for these hidden attractors in that data set and
then manipulates the variables to find which parameters drive this
behavior.  It sounds simple and in outline, is simple.  But much is
to be done before this simple research design can be put in place. 
With such a research capacity in place there is much to be gained;
a society can begin to understand the larger social factors which,
at one setting, are beneficial to a society but which, at a larger
setting, can drive one of the many forms of crime.
     This Lecture picks up on the Second Lecture which posed three
challenges for postmodern criminology.  In this Lecture, I will begin
the challenging task of explicating the non-linear ways in which 
the life of ordinary people change such that antisocial behavior
begins to attract larger and larger numbers of people given changes
in key economic and social parameters.  We first will focus upon
the concept of the attractor and then go on to draw out the
implications of bifurcations for a postmodern criminology.
A. Attractors       In the literature on chaos, a strange attractor
is simply the pattern, in visual form, produced by graphing the
behavior of a system in phase-space.  Since a nonlinear attractor
tends to have a more--or less--stable geometric shape, it is said
to be attracted to that shape.  Since it does not fit the dynamics
of newtonian physics, it is said to be strange.  Strange attractors
are messy; they have fractal geometry rather than euclidean.   
Some attractors in an outcome basin have linear dynamics.  Some
have nonlinear dynamics.  If the dynamics are nonlinear, small
changes produce large differences.
The Torus The simplest strange attractor is the Torus.  The
word torus comes from the Latin, which means, literally, a
swelling.  In geometry, a torus is a doughnut shaped structure
in which the pathways of a system expand to encompass more
of the time-space available to it.
     The torus is very important for a theory of non-linear social
dynamics as well as for a theory of social change for it defines a
pattern of behavior qualitatively different from that which is so
highly valued in modern science and criminology.  Modern philosophy
of science holds that theories which yeild great certainty are more
valuable to the knowledge process than are theories which do not
yeild predictions which are always and everywhere confirmed.  If,
as Chaos theory suggests, all complex systems behave in self-
similar ways rather than precisely identical ways, then the quest
for theoretical propositions powerful enough to predict behavior
with such contancy and precision is a lost cause.  The better
mission of research is to identify the key parameters which produce
ever more uncertainty in the lives of animals, peoples and whole
societies.
     The torus also carries in it dynamics, resolution of the
polemics about process and structure.  One can see, in Figure 1,
that structure emerges out of process.  The tracing of the behavior
of one system over time yeilds sufficient regularity such that
other systems might adjust to it; it then has the features of a
social structure in that it sets the limits and/or guides the
behaviors of others.  In like fashion, the self-similar behavior of
a large number of systems at any given point in time serves as a
structure to which still other systems must adjust.
BECOMING A TORUS.GIF (1583 bytes)Figure 1. Becoming a torus
Self Similar Behavior  In chaos theory, sameness is replaced by self-
similarity.  In the case of the dynamics of, say, bicycle theft, for
say, a bicycle thief in New York whose work life has been very, very 
regular, still there are unpredictable variations in any given parameter.  
     1. If the first cycle in Figure 1 depicted the cycle of thefts
	over, say a year, one can imagine that more bikes are stolen
	in early summer and very few in winter time. 	
     2. If the second set of cycles represent his take over a period
	of six to ten years, one can see that a definite pattern is 
	emerging.  
     3. And over a great many years, assuming our bicyle thief is not
	much different from other bicyle theives in New York, one can
	map the cycles of bicycle theft to a nicety.
     4. Over 25 years, there has emerged enough structure for insurance
	actuaries to predict liability and set rates for bicycle insurance
	policies.  
     There are any number of key factors in his routines which
converge to affect the time he might begin his day: his alarm system, his
bathing routine, his dressing routine, his breakfast routine, his
familial and sociability routines, weather conditions as well as
his transport routine.  If we were to collect data on all such
routines, then we would have a sense of why there is self-similarity
in this form of crime but not, repeat, not sameness.
Equifinality   In like fashion, a lawyer or physician might well
bill her/his patients for legal fees most of the time but, in times
of financial stress, might over-bill for hours or in the case of a
physician prescribe simple but unnecessary operations in order to
handle budget problems.  Yet if we were to examine the outcome of
the clients of the lawyer or the patients of the doctor, and try to
find some sharp differences between those clients/patients who were
exploited and those who were not, it might be very, very difficult.
Complex systems have a way of absorbing small and large differences
such that final outcomes are about the same for clients/patients.
     The capacity for a system to ignore or absorb small
differences without any significant change in the character of the
system is, in system theoretical terms, called equifinality.  There
are any number of pathways to the same outcome.  The important
thing to note for a postmodern phenomenology is that is it human
judgement and human action which obliterates the differences in
actual, observable behavior. While the lawyer may bill for far too
many hours, still he might do an excellent job for the client. While
the doctor may prescribe an unnecessary operation for a patient, still 
the life of that patient may not be greatly affected.  The doctor knows
her patient is covered by insurance; she knows the operation is safe;
she knows the patient is in fairly good health; she knows the operation
will 'cure' the immediate complaint.  So equifinality obtains. Client
and patient are served and white collar crime goes undetected.
The Onset of Variation   In the life of most people, patterns of life
are modeled by a simple torus. Routine is the name of the game at work,
at school, at play and during vacation.  Over the year, sharp changes
are noted: at Christmas time, on anniversaries, when the school year
begins and when vacation time comes along.  Yet most of the time, patterns
of life are stable enough and uncertainties few enough for most people
to manage.
And even when great changes come along, there are social routines in
place which help a person or family or firm absorb these great changes.
In the case of unemployment, there is unemployment insurance which helps
cover household expenses for a few months.  In the case of ill-health,
there are private and public insurance plans which help reduce uncertainty.
In the case of death, there are well-known rituals which help the bereaved
cope with the terrible loss of a wife or child.  So life goes on.
For our white collar professional, life is even less uncertain.  Class, 
status and social power resources are well above that of lower working
class persons...and well above that needed to cope with uncertainties 
which are built into social life. Salaries, fees, dividends, rents and
royalties bring more than enough economic power to manage even large 
increases in interest rates, tuition hikes, or insurance rates. Old school
ties, professional associations, club memberships, friendship networks
give social power to the white collar professional not available to the
marginalized worker.  And social honor demands deference and caution when
problems come along...bosses pause before firing an engineer; police are
careful when questioning a lawyer; administrations are concerned with 
public relations at hospitals and a few thousand dollars buys good legal
service.  Class, status and power combine to protect white collar workers
from uncertainties...and even from  the consequences of crime.
Much more so than marginalized workers. And it is among marginalized workers
where we find most theft, most prostitution, most drug addiction and most
uncertainty. Theft and prostitution can help with some unexpected expenses;
drug addiction can buy relief from most anxieties...for a while.
Yet even for the solid middle-class professional, sometimes uncertainty
cannot be absorbed.  Most of the time, changing expenditures are fairly 
predictable; Christmas comes every year; new automobiles are purchased 
every two or three years; children off to college at known times; I.R.A.s 
have to be purchased annually before 15 April.  However, any number of new 
and unexpected expenses might arise which could put our white collar 
employee in a situation which income does not match expenditure and the 
choice arises between use of long term savings on the one hand [thereby
depleting retirement portfolios] and embezzlement or conversion of
property on the other hand.
Cascading Uncertainties     The appearence of two or more instabilities 
at the same time has great implications for qualitative changes in the 
incidence of crime for any given set of white collar professionals.  
That instability might come from the intersection of two factors which
strain resources for the persons in question.  A medical expense
might come at the Christmas season, a car repair might come just as
a child leaves home for college.  A new product might come on the
market just as property taxes increase.  A friend might need a bit
of help just after one bought a new television set.  All this adds
up to predictable uncertainty.  We know that one's expenditures
will fall within the geometric space of a torus but we cannot say
at any given time how a weekly or monthly pay check will be spent. 
As long as the deficit between what one has and what one spends is
within a limit circumscribed by thrift, deferral of gratification
or by just plain modesty of need, then the torus remains intact.
Chaos theory suggests that, while most people can cope with
one or two uncertainties, the interactive effects of three or more
uncertainties drive people to look for new ways of dealing with
these exigencies.  Among the new ways, some are most congenial to
the human project; others inimicable.  Among these later are, for
white collar employees and professionals, all sorts of illegal and
unethical behavior which helps the doctor or the lawyer cope with
uncertainty in his or her life but puts added stress on patients,
clients and employees who have to participate in such fraud or
corrupt activity.
     Thus, in addition to the certainty required by living expenses
and business expenses and the kind of known uncertainties mentioned
above; the white collar worker might experience a third set of
unexpected uncertainties.  If that third uncertainty arises, Chaos
theory instructs us to expect an entirely new pattern of behavior.
A torus explodes to become a butterfly attractor, i.e., an outcome
field with two basins of attraction instead of one.  One basin
remains the pro-social practice of law, medicine, or dentistry
which has always marked the life of our subject.  The second and
new outcome basin/attractor might will be periodic ventures into
illegal and/or unethical behavior in the attempt to cope with the
new exigency.
BUTTERFLY ATTRACTOR.GIF (7721 bytes)Figure 2. New Ways to Cope with Uncertainty 
Actually, one might expect a slight variations in criminal
behavior for any set of doctors, lawyers or professionals who
experience even one uncertainty in a key variable.  Slightly more
criminal behavior could be expected with a second uncertainty
interacting with the first but it is the third uncertainty that
threatens to produce large changes in the criminal behavior of a
given set of white collar workers.
     Among the exigencies which might interact to greatly expand
criminal behavior of middle and upper management employees as well
as self employed professionals are:
     1. divorce
     2. major illness, 
     3. extra-marital affairs
     4. retirement and portfolio concerns
     The situation as now defined involves a) a set of predictable
and known expenditures, b) a set of unknown expenditures which are
expected and c) a set of unknown and unexpected expenses.  The
known and expected might involve mortgage payments, wages for
employees, country club fees, college tuition, clothing and utility
expenses as well as vacation costs and retirment/savings
allocations.   We can expect that, of all employees who get
divorced, some small and unpredictable set will begin to embezzle,
solicit and take brides, set up false billing accounts or otherwise
redirect company funds to private use.  xxx
     When the regularies between cause and effect, between sanction
and behavior, between plans and successes fail, a society must then
consider other approaches to deal with the problem of crime.  For
the postmodern criminologist, Chaos theory suggest that, rather
than punishment and a narrow deterrence focussed upon and only upon
individuals, the better, more useful approach is to identify the
key parameters driving these hidden attractors and, then, institute
social policy which enables individual persons and whole social
categories to cope with life on terms amenable to the larger
concerns of social justice.
Fractal Attractors  One will recall from a previous chapter that
all natural and physical systems so far studied bifurcate when a
key parameter exceeds 3.0 times its value at a semi-stable
dynamical regime.  And if the ratio exceeds 3.44, still another
bifurcation occurs such that four outcome basins develop.  Eight
attractors develop at the critical value of 3.56 while 16 such
fuzzy patterns appear when a key parameter reaches a value of
3.569.  After four such bifurcations, the period between them
decreases precipitously such that the pattern of such bifurcations
is said to 'cascade' toward deep chaotic regimes in which pattern
and predictability are very seldom observed.
     In such a basin with two attractors (each of which can be
viewed as a torus loosely connected to each other), the geometry of
behavior becomes uncertain; one may move between antisocial and
prosocial behavior; one may be involved in both criminal and
prosocial behavior at the same time...indeed, the same act may be
criminal while the next iteration is prosocial.  The concept of
crime becomes very fuzzy while the geometry of crime becomes very
complex.  I can give two hypothetical examples which may, in real
life, actually occur.
     In the torus above, as long as need and resources remain below
a critical ratio, there is no need to develop a new source of
income.  However, a small increase in the ratio might make a new
source of revenue attractive.  Suppose the ratio between income and
extra expense seldom exceeds, say, 10% of one's total weekly or
monthly wage on the one hand and one's basic needs [real and/or
false] and, further suppose that within that ratio, one can over
time return to a balanced budget.  In any given month, one may be
behind yet over the course of a year, one's income is adequate to
one's life style.  Suppose a new situation occurs in which the
ratio of the shortfall between income and expense exceeds 30% of
one's income in two or more given months.  Chaos theory and the
Feigenbaum numbers would predict that a torus would transform into
a butterfly attractor with not one but two outcome basins.
     In order to cope with these exigencies, a person would have to
lower desire or increase income to regain the semi-stable pattern
of billing marked by the torus.  If neither is changed, or if
either variable, desire or income, changes in the wrong direction,
a second economic activity with which to augment income might be
attractive which, only yesterday, was unthinkable.  Inflated
billing routines, over-billing third party carriers of insurance,
use of unnecessary procedures, fee-splitting and a dozen other
illegal and/or unethical practices might will help regain the match
between desire and income but such activity would be qualitatively
different from legal/ethical behavior and constitute a second
pattern of behavior or, in the terms used here, an attractor.
     There are about 800,000 doctors in the USA.  Suppose their
income is stable and insurance rates double from that which is
covered by ethical/legal billing routines.  Chaos theory suggests
that even with a doubling of insurance rates, doctors would be able
to adjust other expenses and remain within the constraints of law
and ethics.  Suppose Insurance corporations triple insurance costs
to cover a great increase in claims and/or jury awards.  If so,
they would have imposed the first Feigenbaum point.  Some number of
doctors might begin to move to a form of practice in which
insurance rates are lower while other hang on a while making
adjustments in other expenditures rather than make the qualitative
break to illegal practices.
     At the same time, some number might move to a strategy in
which they use the trust within the patient/doctor relationship to
increase the number of unnecessary operations while other doctors
in the same circumstances might lower life style ambition.  While
the emergence of new attractors emerge with astonishing
predictability, the remarkable thing is that it is impossible to
predict which sub-set of physicians, out of all physicians
similarly situated might move to the new attractor comprized of
illegal behavior.
B. Bifurcations     A
bifurcation is a forking or
splitting of a parameter. 
Figure 2 shows the map of a
bifurcation process in which a
stable parameter, Y, explodes to
fill the space available to it
(Region D) after it has
undergone 3 bifurcations or
doublings of its cycles.  
     In natural or social
systems, there are moments when
a very small change in a
parameter can explode to open up
a new track for a system. 
Systems may then have two states (the limit attractor) to which any
member or any iteration may go (Region A).  If the system
bifurcates again, then a torus develops (Region B).  First Order
uncertainty creeps in after the second bifurcation.  Sameness is
replaced by self-similarity.
     It is the uncertainty which comes with each bifurcation which
one can use for a theory of exploding crime rates.  For many, crime
may be a way to reconcile the otherwise untractable parameters of
life.  Property crime, violent crime, and political crime surge
nonlinearly when critical social parameters bifurcate.  In all
complex systems such that involving crime, a person may have a
'modus operandi' in which s/he skirts the borders of criminal
behavior now and again.  When uncertainty increases qualitatively,
a new basin of attraction opens up; some may involve prosocial
behavior; some anti-social.  
Rural Crime  In the case of a given population in an pre-
dominantaly rural region, most people might engage in agriculture
as their main source of income.  One or more key parameters might
change to force some off the farm and into a factory for wages to
supplement income.  Interest rates might increase, weather
conditions turn unfavorable, food imports might increase, tax on
farm land might exceed a critical value; any one of a dozen factors
might change slightly and produce the need for different sources of
income.  Two or more forms of behavior which yeild income take the
form of a Butterfly Attractor (Region C) with uncertainty within
and between them.  If wage labor is not available or help from kin
or state welfare, some small set of farmers may turn to crime to
cope with the uncertainty in the income they do have.  
     Banditry, rustling, kidnapping and highway robbery developed
in rural areas in Europe with the advent of industrial capitalism
and all the uncertainty it entailed for agrarian peoples.  In the
USA, Jesse James, Billy the kid, Pretty Boy Floyd, John Dillinger,
Bonnie and Clyde among others were folk heroes to populist
sentiment in the 1870s to the 1930s as they 'robbed from the rich
and gave to the poor.'  In some societies, kidnappers are seen to
be heroes since they extort money from the rich.
     In his excellent study of banditry, Pat O'Malley of Monash
University in Australia found that:
     *bandits were supported by their rural community
     *bandits tended to rob class enemies: merchants and squatters
     *banditry tended to redistribute wealth downward
     *bandits are symbols of resistance against the ruling class
     More to the question of control vs. prevention of political
crime, O'Malley confirmed Hobsbawm's theses that banditry
disappears when the state ceases to act on behalf of class elites. 
Hobsbawm held that unorganized class conflict is the natural
terrain for banditry (Cited in Young, 1993:33).  When the urban and
rural poor are able to organize for political relief of
uncertainty, such crime declines.
     It is Region C which is of most interest to a postmodern
theory of crime since the causal field opens up to accept two
different patterns of behavior for the same person or set of
persons.  It is important to keep in mind that the same set of
variables are at work; the causal field expands because and only
because a small change in an existing variable (called a parameter
in Chaos work) has occurred.  And, a new kind of uncertainty has
appeared in Region C which we will call second order change since
entirely new patterns of behavior are called forth by that small
change.
     After the fourth bifurcation, uncertainty increases greatly. 
In technical terms, a system tends to fill the space available to
it rather than settle down to a point or to fluctuate between two,
four or eight basins of attraction.  But note that there are
regions of order even in deep chaos...<E>.  These regions of order
constitute third order change.  Here we might see revolutions in
which one economic formation replaces another; migrations in which
one marriage form replaces another; underground structures in which
one sexual modality is replaced or supplemented.  Of all the
emergent orderliness in deep chaos, some may be congenial to the
human project and some most hostile.  All will be called sin,
crime, deviancy, pathology, evil, or some such pejorative phrase
which privileges more traditional ways of doing economics,
politics, religion or kinship.  These implications for Deviancy
Theory are spelled out in another chapter.
Attractor Basins    In the Chaos
paradigm, systems tumble from
one dynamic state another in a
very complex pattern of
behavior.  In so doing, they
produce a fractal basin of
outcomes with any number of
attractors.  There may be two,
four, eight, sixteen or many,
many more states (attractors) to
which they are attracted.
     In Figure 3, one can see at
least seven attractors or
endstates toward which a system
or person might tend.  One
attractor state might be wage
labor, another might be kinship
support, a third, medical fraud,
a fourth might involve tax
evasion as a way to enhance
income.
xxx  If we were to translate the basin to corporate crime, given
income or cost problems, a corporation might defraud customers,
plunder retirement funds, endanger workers, violate minimum wage
laws or dump dangerous toxins in rivers, earth fills or the
atmosphere.  At times, the basin of attractors for corporate crime
explode to fill the space available.  The operative question for a
theory of corporate crime centers around those parameters which
force open a causal basin.
     The size of the basin of outcomes and its geometry are central
to a theory of crime based upon Chaos theory.  In a society with a
mixed economy and with two sets of compelling parameters (x =
parameters of desire, need, obligation or affiliation and y =
parameters of income and resources), given persons or groups may be
attracted to more than one state.  Thus one might depend upon
salary, embezzled funds, insurance fraud and income tax fraud as
well as fraudulent loans in order to expand the geometries of
income to match the geometries of life style expense.  If one is
disemployed, one might steal a little, accept state welfare
illegally, prostitute oneself occasionally, and borrow from friends
and family in order to reunite desire and demand.
     It is more than of passing interest to note that, on the lower
slopes at the intersection of any given set of x parameters or y
parameters, causality loosens and prediction (hence control) fails.
The operative point is that, given a small increase in x parameters
of desire, need or human obligation or small changes in y
parameters of wages, salaries, profits, rents, or familial aid, a
banker, a doctor, a lawyer or a teenage might move from the regions
of an outcome basin in which economic behavior is legal to other
regions, some of which are illegal.
     Given compelling need, desire, or obligation along with income
uncertainty, a person or a group may seek new ways to meet the
contingencies and exigencies of life.   Some of these pathways may
be harmful to the human project.  The challenge to criminology,
indeed to all social science, is to understand why stable systems
bifurcate.   In general terms, the question is what is it that
kicks a system into far from stable dynamics.  In social terms, the
question becomes, what is it that makes crime an 'attractive' i.e.,
normative pattern.  Generally, linear feedback amplifies variation
while nonlinear feedback tends
to promote stability.  In more
human terms, I suggest that when
differences in class, status or
power bifurcate without
restraint, both property crime
and violence pops open in a
fractal basin of social
dynamics.
xxx
Property Crime For our purposes,
the unit of analysis involved in
street crime may be a particular
person or a set of persons.
Since property crime is an economic
activity, if one wanted the full
portrait (in phase space) of the
economic attractor(s) for that
person, one would have to track
the amount of income a person
obtained from several sources,
say, from wage labor, from private charity including friendship and
kinship charity; from state welfare as well as from other unearned
income sources such as rents, interest and profits.
     In Figure 4, each Box gives two ways of tracking income
behavior.  Box A might depict the income pattern of a person as
s/he grows older; high in the middle years and tapering off to a
steady state at retirement.  Box B could depict the income pattern
of a seasonal worker; high in summer and next to nothing at other
times.  Box C represents the income pattern of, say, a real estate
sales person over four or five months; four of five years; it grows
and declines but keeps within limits.  It is Box D that is
interesting to a theory of crime increase.  The lower view shows
the butterfly pattern one could not see from traditional time
series tracking.
     One can see two distinct periods or patterns of income in Box
D.  One wing of the butterfly might be income that is generated by
wage labor.  If our subject turned to state welfare, borrowed
money, begged from parents, or provided illicit services, the
fractal would have two, three, four, five or more wings (or
regions) in it.  If our person or group invented a new form of
crime, still another region would be constructed in a basin of
outcomes.
     For property crime the question arises, what forces the
bifurcation from one source of income to two, three, four or more. 
The answer is that the same person or set of persons may have a
life style changes which pushes
the person to generate more
income that is available from
family, wage labor, charity,
welfare or other sources.
     Young people, as they move
into adulthood, undergo a life
style change.  Desire for cars,
separate lodging, fashionable
clothing, concert tickets,
jewelry or other items special
to youth culture.  Allowances
and part-time work might not
suffice.  Charity and welfare
are closed options.  Most are
too young to have unearned
income from property.  I want to
suggest that is bifurcations in
a social parameter, in this case
desire for consumer goods and
services, which destabilizes the
economic life of a young person
and opens up, nonlinearly, the possibility of property crime as an
economic attractor.  One must expand one's basin of options if one
is to participate fully in youth culture in a consumer society.
     For some, the tension between income and desire for goods
might be resolved by dropping out of school and working full time. 
For others, it might mean doing without and foregoing participation
in youth culture.  Some young people turn to petty theft as a way
out.  Young men and women shoplift in order to reconcile the
growing disparity between income and desire for commodities and
services.  Some steal from friends and family.  
     These are the lucky ones; in many cities and towns, organized
crime offers opportunity and income.  The presence of organized
crime circles which require illicit labor and offer relatively
large wages in return make crime as an economic endeavor even more
attractive.
     Organized crime offers several manageable alternatives to open
up (bifurcate) a basin of economic attractors for young people. 
One can steal and supply the demand for fenced auto parts.  One can
find work in the drug trade or in the policy rackets.  One can find
work in prostitution or pornography with which to reconcile desire
and income.  A young person would find it difficult to reconcile
other parameters however.  Demand on time would might be a problem.
     For such a person school work, part-time work, social demands
of friends, family affairs and property crime activity all make
conflicting demands on time.  Again the person might juggle school,
social life and theft for a while but if we map out the time
parameter in phase space, we would find two, four, eight or more
attractors each demanding time.
Crimes of Violence  There are several forms of power available with
which one person can shape the behavior of another.  I want to
focus on four: physical power, economic power, social power and
moral power.  The case I make here is that each form of power is an
attractor.  If we track the life of any given person, we will find
one or more of these activities.  Most of us use social power to
shape the behavior of known others.  
     Social power arise from social relationships: family, work,
church, recreation and community.  Those who are disemployed and
who are embedded in a strong and supportive network of friends,
neighbors and family often rely greatly upon social power to meet
the contingencies and exigencies of life.  Symbolic interactions
are the media of social power.
     Economic power can be used to shape the behavior of unknown
others: indeed it is bad form to use money to influence friends and
family but not clerks, owners, and tradespersons.  Given a regular
and adequate income; given levels of desire manageable by either
social power or economic power, then violence is not likely to be
used.  Legal tender are the media of economic power but sometimes
direct exchange is made.
     Ordinarily, one uses physical power only upon inanimate
objects or animate objects without the capacity for symbolic
interaction.  Absent social power or economic power; given
insatiate levels of desire, one might use physical power to reunite
desire and supply.
     Given uncertainties in resolving discrepancies between needs
and resources; given limited resources available within social
networks; given limited job opportunity; given incremental debt
burden; given continuing desire for housing, food, transport,
entertainment, clothing, and given demands by friends or family,
one might, nonlinearly, use violence to take what cannot be bought
or borrowed.  One scarcely need mention that it is minority youth
who are most often closed out of social power and economic power by
racism.  Racism is the parameter; not race per se.
     Moral power arises from shared values.  Those values are often
embedded in a religious tradition but can be secular.  Professional
ethics is a source of moral power as are laws and civil rights. 
Moral power can be a constraint on the use of social, economic and
physical power in the pursuit of desire.  In Part I, I spoke of the
bifurcations in social organization that tend to dilute moral
power.  In Part III, I will use ideas from Currie, Pepinsky,
Hulsman, Iadicola and others with which to reinforce and expand
moral power as an alternative to physical power and an adjunct to
social power in social policy.  Generally, social justice is
preferable to criminal justice as a solution to crime.
Gender Violence     There are several parameters found in American
culture which tend to promote violence against women and men. 
Patriarchy sets the stage for violence against women.  By itself,
patriarchy might not produce high levels of gender violence, but,
coupled with aggression as a solution to uncertainty, they produce
a dangerous instability.  Low level violence is normative for some
families.  When a male has a dispute with a female, he often uses
physical power to supplement social power inside the household. 
Some research suggest that, as uncertainties arise on the job or in
domestic finances, males increase the frequency and violence of
force as a pretheoretical tactic against children and partners.
     One cannot predict when a given person will move from
supportive gender relations to abusive; nor can one ascertain the
precise mix of violence and caring.  All one can say within the
Chaos paradigm is that women should be on guard when uncertainty
enters the life space of males socialized to the use of physical
power.
Warfare   Men are taught assiduously from childhood that violence
is a solution to the determination of status.  One fights with
fists, knives or guns at home until a certain stable hierarchy is
known.  Given uncertainties in social power, economic power or
physical power, violence may expand.  
     Men are taught as adults to use guns and bombs as a solution
to uncertainty in foreign affairs.  Patriotism combines with
aggression to create a culture of violence.  Again social standing
is gained, indirectly by being a proud Brit, a proud German or a
proud American.  Given uncertainties in foreign markets, access to
raw materials (oil is a case in point), or capital flow; given
fragmentation of social power or failures of economic power, one
nation may use physical power in the effort to shape the behavior
of another.  Such efforts should be futile, if Chaos theory is
correct, since causal connections between force and compliance fade
and fail as force bifurcates.
Racial Violence     Given the degradations of racism, it begins to
be acceptable to use physical force against minorities.  As social
power and economic power become uncertain, one should expect
recourse to physical power.  One might expect both declassed Anglos
as well as Blacks to use violence in their existential terror over
jobs, housing, status and local politics.  Given the covert backing
of institutional racism, moral constraints on Anglo violence are
reduced; Chaos theory would suggest unpredictable outbursts of
Anglo racial violence as uncertainty increased in two, three or
more arenas of life: jobs, politics, marriage or such.
Organized Crime     Organized crime is considered crime since it
profanes sacred supplies.  The commodification of sex, gaming,
drugs, violence and other such services continues to grow and
thrive in a market economy.  Those who provide illicit goods and
services themselves, if Chaos findings are relevant, may be caught
up in bifurcated life situations reconciled by offering such
services.  Again, if we set desire for a life style as a driving
force, then we have to think about the alternative attractor states
available for those who deal in drugs, prostitution, fencing,
extortion, gambling and other such income producing ventures.
     Many legitimate income attractor states are more or less
saturated.  Small business is very competitive.  Large business
organizes market monopolies.  Professions require credentials.  For
those closed out of such occupations, illicit markets attract both
workers and entrepreneurs.  If police and courts do not complicate
things too much; if markets are stable; if supply is available,
then organized crime is an attractive income alternative.  Racism
tends to protect established economic privileges.  For such
persons, organized crime offers growth markets for sex, gambling,
drugs and stolen goods.
     Yet if uncertain supply of drugs, uncertain supply of pushers,
uncertain enforcement by officers and courts (rather than
collusion) as well as vagaries in moral onus converge to complicate
the life of the illicit entrepreneur, s/he might well find that
there are too many variables to juggle and give over such trade. 
The person or the set of persons might try other ways to reconcile
desire and resources with which to reconcile desire.
     One must inquire about the demand for illicit goods and
services.  The essential thing about most goods and services
offered by organized crime is that these are solidarity supplies
used as pathways to the Holy in premodern societies.  Massification
of markets, schools, churches as well as their bureaucratization
together with industrialization has reduced both the realm of the
Holy and the reach of the Holy.  The privatized use of drugs, sex,
gaming, erotic literature and other psychogens, combined with the
market economy tends to desanctify these supplies.  One can then
use them for any personal or social purpose one wishes.
     Given high levels of interpersonal insecurity and given the
definition of such commodities as solidarity supplies, one learns
to reach for them when the problematics of life grow untractable. 
When authentic intimacy, sensuality and love are unavailable,
commodity love and intimacy offer short term satisfaction.  When
wages are uncertain, gambling becomes a magical way to reunite
desire and need.  When truly religious spirituality is lost to the
rationalization and formalization of the church, a certain
privatized spirituality is available through the use of alcohol or
other drugs.
Corporate Crime     Corporations thrive in a rational environment. 
If labor supply is tractable; if demand is dependable; if taxes are
manageable; if competition is congenial, retail outlets are captive
and if governments are friendly, one would not expect corporations
to commit crime.  In this case, desire for profits could be met. 
Changes in any expense parameter could affect the attractor state
for corporate income.  Labor costs, management perks, taxes,
capital equipment, raw materials, licenses, bribes, campaign
contributions, association dues are among the parameters which can
force a bifurcation.  Several can change at once and force a firm
to look for other ways to generate order.  As H. Ross Ashby once
said in his Principle of Requisite Variety, only variety can cope
with variety to generate order.  Crime offers several such options
for re-instituting rationality and predictability.
     The picture one gets from Chaos theory is that, in order to
forestall bankruptcy, to attract capital investment, to satisfy
ownership and otherwise function as a corporate entity, corporate
officers find crime an attractive alternative economic tactic.  If
workers are weak and or legislatures friendly, labor can be
exploited.  If customers are unorganized and legislators
indifferent, fraud and defective goods offer possibility for
reconciling desire for profits and expenditures.  If legislators
are carefully preselected and low income neighborhoods vulnerable,
toxic wastes can be dumped.
     If only one of these parameters is untractable, say labor
supply, then it can be managed by increasing wages.  If two are
unpredictable, say labor supply and competition, then the corporate
officer could reconcile desire for profits by increasing prices and 
seeking government subsidy.  Disorder is transferred to customers
or to the state.  Chaos theory suggests that corporate officers
might begin to consider criminal action as three or more attractors
become fractal, i.e., worker supply, competitor activity or, say,
customers become unpredictable and there are fewer alternatives
from which to seek and obtain order for the system.
     If governments become untractable, firms can exploit
dealerships, franchises, captive retail outlets and thus transfer
disorder to small business.  If governments become too untractable;
passing pollution laws, labor laws, consumer protection laws and
such, they close off the options for reconciling profits, costs and
income.  If laws are passed and if corporations cannot count upon
benign neglect, or if policing laws even becomes uncertain, the
rational thing to do may be to move to, say Mexico, Korea or
Malaysia.  
     Chaos theory teaches us that a corporation might live with two
or three unmanageable parameters but when a fourth, fifth and sixth
parameter explodes to fill the space available to it, then crime
becomes a quick and easy solution.  One either eliminates the
effects of the parameter or one turns to another parameter to
generate order.
White Collar Crime  White collar crime involves deception and
subversion of the social trust and social power by doctors,
politicians, lawyers, banker, professors and real estate brokers
not to mention small businesses which depend upon the social power
of community, fellowship and friendship with which to compete with
big business.
     If we use Chaos theory as an intellectual tool with which to
sort out white collar crime, we would for small changes in income
or in life style.  Generally professionals have three sources of
income; fee for service, rental property and investment portfolios. 
Life style demands can be very high.  Houses cost hundreds of
thousands of dollars; furnishings and maintenance tens of thousands
more.  Country club memberships, cultural affairs, vacations plans
and community benefits demand thousands more each year.  Add to
that the costs of college for the children of the professional
classes, tax burdens as well as insurance costs and one has a
demand for high and steady income sources.  
     If we put ourselves in the life of, say a physician who has an
income of two hundred thousand a year and expenses of roughly the
same, then one has a steady state that might vary even less than
the fractal in Box C above.  A small change in any one of their
parameters might destabilize the economic state of a white collar
family.  Divorce is a particularly expensive process; it forces a
sharing of income between two households both with life style
needs.  While the data suggest that income drops more for wives,
curiously, it is white collar males who tend to turn to crime; it
is they who have social positions to exploit.
     Income might drop.  Investment portfolios might fail in a
savings and loan crises.  Property income might fail if a major
corporation moved from a city.  Governments may alter third party
health care schemes and curtail sources of income.  Patients may
default on bills as wages decline or jobs disappear.  A doctor
might be able to handle one, two or three such losses but four or
more might drive her/him to crime.
     The possibilities for violation of trust are many for doctors.
They can prescribe unnecessary and expensive medical procedures. 
They can bill Medicare and Medicaid for services not rendered. 
They can massify and mechanize the clinic substituting
interpersonal therapies with drug therapy.  They can bill patients
at $40 to $100 dollars a visit when most of that time is taken up
with low paid nurses and technicians.  Doctors can exploit the
labor of employees, promising retirement plans, profit sharing, and
wage increases---then dismiss the nurse or technician without so
doing.
     Again, one must wonder why it is possible for good people to
commit crime and to escape guilt and shame.  In Part I, I suggested
bifurcations of moral responsibility are part of the answer.  In
the case of a physician, third party payment dilutes the effects of
fraud.  The putative 'victim' becomes the abstract state or the
remote insurance company.  One has less compunction robbing them
than patients directly.  But doctors do over prescribe drugs and
operations for known, trusting patients.  They tend to do so for
persons of low status.  People receiving state aid are degraded in
our health care system much more so than in Canada or Europe. 
Women are the victim of choice for unnecessary operations in a
sexist society.  Elderly persons are the victim of choice for over
prescription of drugs.
     Those forms of crime which can be done by remote or diluted
agency are preferable for those professionals who are well
socialized and who have good images of themselves.  There is less
onus for harming nonpersons than persons with full social standing. 
The same doctor who exploits the government can be very
compassionate for friends or for charity patients of his own.  The
more bifurcations of responsibility, the more attractive become the
crime.  The same is true of corporate officers above or political
criminals below.
Political Crime.    There are four generic kinds of political
crime, each of which has its own attractors and bifurcations. 
There is first the crime of a state against its own people.  When
politicians subvert the political process at home in the interests
of corporate elites, gender privilege and ethnic preference they do
much harm to women, minorities, workers, customers, residential
areas, small business and others excluded from the political
process. 
     Then there are crimes of one country against others.  All the
rich countries, as a loosely connected bloc, subvert the economy
and politics of their client states in the third world.  The kinds
of crime observed here vary from out and out warfare with pillage,
rape and murder to the bribery of political leaders.  Genocide is
a third major form of political crime.  One people may eradicate
another in order to have access to land, game, natural resources or
property.  Then too, there is the crime of citizens against their
own government.  Assassination, rebellion, treason and other forms
of crime are included in this genus.
     Chaos theory would suggest one would look at larger social
parameters, note when they change from Box C to Box D, above,
dynamics.  Then given disorder, inquire into the tactics used to
restore order.  In the sixties, students, women and minorities all
engaged in destabilizing street politics.  The antiwar movement
added a fourth destabilizing arena.  At the same time, there were
constant political attractors which were privileged.  The Nixon
government had built its legitimacy on law and order, on economic
support of business, upon a subtle appeal to racism and upon the
firm grounds of patriarchy.  Chaos theory would suggest that, while
a government might be able to manage one, two or three forms of
resistance and rebellion, they could not ignore four, five or more.
     The Nixon administration did, in fact, respond to the anti-war
movement by withdrawing from Vietnam and by moving to the tactics
of 'low-intensity' warfare in its other military operations.  This
response successfully dampened anti-war disorder.  However, Mr.
Nixon could not go back on the law and order theme; aggressive
policing of street crime masked the fact that business was being
deregulated and corporate crime overlooked as part of the Nixon
effort to keep American business competitive with Pacific Rim
nations.  
     Nor could Mr. Nixon support ERA and equal opportunity for
women since most men (and many women) accepted gender inequalities. 
The entry of women into the labor pool as auxiliary to the income
of males meant that employers did not have to pay full wages and
benefits to such 'part-time' employees.
 
     Racism offers several advantages to politicians in search of
legitimacy; it offers racial superiority in lieu of economic
democracy or social justice.  It creates a surplus labor pool with
which to drive down labor costs.  It transfers the costs of
'development' to unorganized sectors of the population.  The death
of Mr. King was a crucial, sensitive event that sent civil rights
movement in a different trajectory.
     As long as women, Blacks or workers have no political power;
as long as they are denied voting rights or their social power
fragmented by other means, such disorder is manageable by the usual
control tactics; force, fear and minor concessions.  When women,
workers or minorities have votes and are represented in law making
bodies, they may not be safely ignored.   One way to manage dissent
is for the state to go underground.  Mr. Hoover used a variety of
dirty tricks to discredit Mr. King.  Mr. Nixon was able to
destabilize Democratic party opposition by his Committee to Reelect
the President headed by John Mitchell.
     Given a set of prime attractors and the resources to do so, it
is rational to wage an underground warfare in the effort to end
destabilizing social protest.  Mr. Nixon and his administration
used illegal tactics at home and abroad with great skill.  Mr.
Reagan and his administration did more with lesser ability.
     Political crime of citizens against their own government are
commonplace.  Perhaps the most common such crime is income tax
evasion.  IRS estimates that from 30 to 50% of returns are
fraudulent.  Most of this comes from small business and
professionals since waged persons have much less room for creative
accounting.  For such crimes, one would return to an analysis of
the deteriorating income sources or unpredictable expenditures
faced by those with a middle class life style to maintain.  One can
'save' several thousand dollars by any one of a dozen illegal
tactics.
     One must note that a certain political legitimacy can be
obtained by transferring uncertainty to third world countries. 
Social justice programs which offer long term response to
inequality and uncertainty at home for minorities, women, and
workers can and often does increase social distress and disorder in
client states.  The lessons of empire learned by the British,
French, Portuguese and Germans illuminate the transfer of
uncertainty and inequality to colonies.  Crimes against other
states often stabilize and bring order with them.
     Finally, but not unimportantly, genocide is a short term
solution to inequality and uncertainty.  The surplus population of
Europe organized to slaughter Native American Indians in order to
clear the land and provide economic security to immigrants. 
Germans gained much from the slaughter of Jews in WWII.  Property
was confiscated, competition eliminated, jobs were provided in the
military, the SS, and in the prison camps, social honor was
reinforced (by claims of superiority for self and by degradations
for others) as well as some debts canceled.