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members of the social group. Bushe and Coetzer (1995) equate appreciative inquiry with the
socio-rationalist view that social groups do not follow lawful principles and that social orders are
inherently unstable and continuously recreated, as opposed to the logical positivist view that
social phenomena are sufficiently enduring, stable, and replicable to allow for lawful tendencies
or at least probabilistic inferences. These two views of social processes are not necessarily
contradictory because lawful principles can result in continuous change including realms of
chaotic behavior which may appear to be random. In this paper we hold that social systems are
subject to the same laws and principles that govern the rest of nature, i.e., the Laws of
Thermodynamics and other general laws and principles of the sciences recognized in Energy
Systems Theory (Odum 1994). Governance by laws and principles does not exclude the central
thesis of the theory of appreciative inquiry which is that social systems evolve toward the highest
good perceived by members of the group.
Odum (1996) has proposed the Maximum Empower Principle as a 4* Law of
Thermodynamics that can be used to identify system designs that will be the most competitive in
an evolutionary process. This principle states that the criterion for success in evolutionary
competition is that empower (energy production per unit time) is maximized. Emergy is defined
as the available energy of one kind previously used up directly and indirectly to make a service
or product. Its unit is the emjoule. (Odum 1986, Scienceman 1987, Odum 1996). Emergy
normalizes the many kinds of energy flows in a hierarchical network so that they are expressed in
equivalent units. The solar emjoule, sej, is commonly used to normalize energy flows of many
kinds in environmental systems. Solar transformity is the solar energy required to make one
joule of a product or service. Its units are sej/J. Energy can be converted to emergy by
multiplying by its transformity. The Maximum Empower Principle implies that systems evolve
toward designs that generate more empower. This principle is general and it should apply to all
hierarchical levels in nature. Nevertheless, it is often difficult to see how individuals, groups,
and societies that are focused on their own self-interest can evolve toward actions, policies and
designs that will maximize competitive fitness for the whole system.
The heliotropic hypothesis (Cooperrider 1990) provides a mechanism for social change
by demonstrating how positive image and positive action form a reinforcing loop. One example
of such a positive loop has been discussed by Jussim (1986) as the Positive Pygmalion Dynamic.
This loop can exist when one social group forms a positive image of another group. This image
gives rise to affirmative cognition and affirmative treatment of the other. Affirmative treatment
results in better performance of the other or a heliotropic confirmation of the first group's
positive action. The social group observes this improved performance and reinforces its positive
image of the other. If the theory of appreciative inquiry explains the direction of social
evolution, then system designs structured with heliotropic loops should generate more empower
than designs without such loops. We tested this proposition by measuring the cumulative
empower generated by models representing six different modes of interaction between two social
groups competing for the same resources. From a comparison of the empower generated by the
models, we proposed a path for the evolution of social systems by identifying the conditions
under which different modes of social interaction lead to maximum empower for an individual
social group and for the social system as a whole.
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Methods
The six models were diagramed using Energy Systems Language (Odum 1994) and then
translated into a set of simultaneous 1* order differential equations. The constant coefficients,
forcing functions, and state variables of the models were assigned initial values based on a model
of competitive exclusion simulated by Odum and Odum (1995). The differential equations and
the model parameter values were programmed using Microsoft Quick Basic version 4.5 and
simulations were carried out on a Dell Optiplex Gxi computer.
Energy Systems Language consists of a set of mathematically defined symbols that allow
the easy representation of interactive networks. These diagrams are a kind of visual mathematics
because they can be translated directly into a set of differential equations. The Energy Systems
Language symbols used in these six models are defined as follows:
(1) External forcing functions are shown as circles.
(2) State variables are shown as a tank.
(3) Interactions are shown as rectangular arrow heads containing a mathematical symbol, e.g.
multiplication or division.
(4) Consumers are used to represent the social groups. They are shown as hexagons which
include a tank and several interaction symbols that describe the stored energy and interactions of
the group.
(5) A large rectangle defines the system's boundaries which divide the system components from
the external forcing functions.
(6) Small rectangles attached to a tank or enclosing a portion of a pathway are sensors that
supply information in the model but no appreciable energy flow.
(7) Flows along pathways are shown as black lines with arrow heads indicating the flux of
energy.
(8) Used energy no longer capable of doing work is shown by a gray line flowing from an
interaction or storage into the heat sink or ground symbol.
The model equations are constructed based on the force-flux law in a manner analogous
to Ohm's law for electrical currents. Each equation consists of a set of mathematical
expressions that include the constant coefficients, the k's, the state variables, Q, and Q2 for the
social groups, and IMQ and/or IMQ2 for the image that Q2 forms of Q and the image that Q
forms of Q2, respectively. Each social group was assigned the same value for the k governing a
process, e.g. the maintenance cost of storage k3 for Q and k4 for Q2 are assigned the same value
of 0.05 (Figures la - 6a). The only difference between the two social groups is that Q processes
the available energy more efficiently than Q2, e.g. k5 is 0.08 for Q but k6, the equivalent
coefficient for Q2, equals 0.06. The coefficients k5 and k6 represent the net increase in
production for Q and Q2, respectively. Values for other k's govern the cost of building and
maintaining images of the other and the effect that those images have on the production process
of the other. These values were kept similar in each of the six models so that the cumulative
empower generated by a model would be an accurate indicator of the relative competitiveness of
the system designs representing different modes of social interaction. The initial values for the
energy source, I, the energy state variables, Q, Q2, IMQ, and IMQ2, and the solar transformities
of the sources and state variables were the same for all model configurations. The model
equations are shown within boxes on Figures la- 6a. The values for the constant coefficients,
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state variables, and forcing functions are written on the model diagrams and can be keyed to the
equations because a set of common symbols is used in both the diagram and in the mathematical
expressions that comprise each equation.
The diagrams and equation boxes in Figures la and 2a demonstrate the method for
simulating changes in emergy production and use in the models. The emergy calculations are not
shown for the models in Figures 4-6, because the same rules are used to calculate emergy from
energy flows and storages in all the models and because showing the emergy calculations on
these diagrams would make them unnecessarily complicated. The emergy change, dEm/dt, is
calculated by multiplying the energy inflow or outflow from an energy storage by the appropriate
solar transformity, the ST's. Emergy is not decreased by the maintenance cost of storage as long
as the stored energy is increasing. When energy losses exceed energy gains for an energy
storage the stored emergy also decreases. The stored emergy was not allowed to increase if the
increase in stored emergy was less than 0.01 of the emergy stored.
Models
Six models were structured to answer the question "Do modes of social interaction based
on heliotropic loops result in more empower production than some other kinds of social
interaction?" Since social interactions have evolved in a milieu of competition for scarce
resources the six models were built using two consumers competing for a common resource base.
Social groups interacting under these conditions are the source of some of the bitterest rivalries in
the modern world. For example, the present conflicts between Israelis and Palestinians, Hutus
and Tutsis, and the Protestants and Catholics of Northern Ireland have all developed in
environments where both groups must share the same resources. In building the six models we
have assumed that, before an interaction is possible, a social group must first form an image of
the other. These images are stored energy that represents the costs of building and maintaining
the information that forms the basis for one social group's image of another. Information decays
quadratically (Odum 1994); therefore, a considerable amount of the energy available for growth
must go into building and maintaining the image. There is a strong evolutionary reward for
forming such images because they can result in the survival of a group that might otherwise be
eliminated.
The diagram in Figure la represents two social groups focused on their own well-being
without direct positive or negative interaction with each other. Of course, these two groups
interact indirectly by exploiting a common pool of resources. This mode of interaction represents
the competitive exclusion model familiar in biology which always results in the more efficient
group eliminating the less efficient group (see Figure Ib). In the second model (Figure 2a) the
less efficient social group forms a negative image of the more efficient group and this image
inhibits production of the more efficient group in proportion to its magnitude. The third mode of
social interaction has both social groups forming a negative image of the other (Figure 3a). The
fourth model (Figure 4a) shows an interaction in which the more efficient social group develops a
positive image of the less efficient group and reinforces the productivity of the less efficient group
in proportion to this image. This model formulation assumes that a connection has been
established between the less efficient group, Q2, and the production function of the more efficient
group, Q. This connection must be established to complete the positive feedback loop. The fifth
model is the converse of the fourth, because it shows an interaction in which the less efficient
group forms a positive image of the more efficient group. Once again a connection between the
-------
more efficient group, Q, and the production function of Q2 must be assumed. We will further
consider this assumption in the discussion. In Figure 6a, both social groups invest energy in
forming positive images of the other. In this case the connections between groups are both
supported by an image. The social interactions diagramed in Figures 4a, 5a, and 6a all have
positive interactions that are governed by heliotropic loops as discussed by Cooperrider (199Q).
For example, in Figure 5a IMQ, the positive image of Q, controls k8*Q2*IMQ*Q*R, an
affirmative action or positive feedback from Q2 to Q, which in turn results in heliotropic
confirmation or improved productivity of Q as demonstrated by increased energy flow on the
pathway governed by k5. This improvement in productivity is detected by Q2 and results in an
increase in its positive image of Q along the pathway governed by kl 1.
Simulation Results
The competition between social groups without direct interaction (Figure Ib) results in the
elimination of Q2, the less efficient group. This process is called competitive'exclusion in
ecology. Figure Ib shows that the emergy of social groups, Q and Q2, follows the pattern
established by the energy levels of these groups. If the less efficient group, Q2, invests the energy
to form a negative image of Q, the efficiency of Q decreases to the point where Q2 becomes the
more efficient competitor (Figure 2b). The negative image of Q formed by Q2 persists long after
Q has been reduced to a very low level. When both social groups invest in negative images of
each other either one can prevail depending on the values chosen for the coefficients. If the cost
of creating and maintaining the images and the effectiveness of their negative feedback are the
same for both groups, the more efficient group, Q, is again able to eliminate the less efficient
group, Q2 (Figure 3b). The negative image that the dominant group, Q, has of the other, Q2, does
not decay over time even though Q2 exists at a very low level (Q2 is prevented from going to
zero). In contrast, the negative image that Q2 holds of Q is gradually lost. In the model
formulations with no feedback or with negative feedback, one social group always loses in
competition with the other.
If at least one social group is able to develop a positive image of the other, both groups are
able to survive. Figure 4b demonstrates this result when the more efficient group, Q, forms a
positive image of the less efficient group, Q2. For the parameter set simulated, Q2 is able to
maintain a higher emergy level that Q. Q is able to reach higher emergy levels if its feedback to
Q2 is less effective in enhancing Q2's productivity. On the other hand, Q2's emergy level can be
increased by contributing more to the productivity of Q. If the less efficient group, Q2, forms a
positive image of the more efficient group, Q; Q eventually reaches a higher emergy level than
Q2. However, in the short run Q2 has higher emergy than Q (Figure 5b). The converse of this
pattern is observed in Figure 4b where Q has formed a positive image of Q2.
The system with social interactions governed by a double positive image could not be
supported by the original resource base, 1=5. However, when available resources were doubled,
1=10, the resource base was able to support this system design. Figure 6b shows that the emergy
levels attained by Q and Q2 are more equal when both social groups have positive images of each
other. The positive images of the other are robust and persist in time at emergy levels that are
greater than those developed by a single positive image. The proportion of the available emergy
that went into image building was greater for the interaction mode with two positive images than
-------
for the modes with only one positive image.
The cumulative empower developed by the models for each mode of social interaction are
compared for the original resource base (Figure 7a) and for double the original resources (Figure
7b). Systems designs in which social interactions develop a positive image produce more
cumulative empower when time - 320 than system designs with no interaction or designs which
develop negative images. The mode of social interaction in which the less efficient group
develops a positive image of the more efficient group develops the most empower for the low
resource base. The smallest amount of empower is generated when the less efficient group has a
negative image of the more efficient group. No interaction between the social groups generates
more empower than is produced by creating a negative image, but this design generated less
empower than designs with positive images. When the available resource base is doubled the
system design iu which social interaction leads to the development of two positive images can be
supported. This design develops the most cumulative empower from this resource base. An
interesting feature of the cumulative empower comparison when the resource base is doubled is
that the mode of social interaction with two negative images generates the most empower in the
short run. This system design generates the second most empower through the 200* time unit,
and only falls decisively behind the two designs with a single positive image near the end of the
simulation.
Discussion
Our comparison of the cumulative empower generated by the six models of social
interaction demonstrates that system designs containing single heliotropic loops generate more
empower than designs with no interaction or designs with negative interactions for the low
resource scenario. The system design with two positive images could not be supported on low
resources but it generated the most cumulative empower when the resource base was doubled.
These results support our hypothesis that systems which develop heliotropic loops develop more
empower than the other designs tested. The development of a single positive image of one group
by the other allows both social groups to survive with reasonable levels of emergy attained by
each group. Thus, heliotropic designs have an advantage over the other modes of interaction both
in producing more cumulative empower and in allowing the survival of both social groups as
significant contributors to the system.
The models and simulation results shown in Figures 1-7 can be used to think about the
evolution of social interactions. One scenario in which social interactions may have evolved is
represented by a system design with two social groups competing for the same resources. Taken
together these six models can be used to represent a logical path for social development under the
above scenario. This path should proceed from designs with lower empower production toward
designs with higher empower.
As mentioned earlier the system design without interaction between the groups (Figure 1)
is the classic competitive exclusion model in ecology that always results in the more efficient
group eliminating the less efficient group. This system design may change because survival must
be the primary concern for any rational social group. Therefore, the less efficient social group
has a strong impetus to develop a negative image of the more efficient group (Figure 2). The
development of a negative image by the less efficient group leads to its survival because it acts to
decrease the productivity of the more efficient group. In this case survival, and therefore empower
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production, at the lower hierarchical level of the social group has taken precedence over empower
at the higher level of the system. This situation, however, is not stable because the more efficient
group now has a strong incentive to survive by developing a negative image of the less efficient
group.
System designs with two negative images generate more empower than those with only
one negative image and thus the evolution of social interaction should proceed in this direction.
In addition, both social groups have a chance to survive depending on the coefficient values.
Evolution toward & system design with two negative images explains how a connection can be
established between each social group and the production function of the other when they
compete for the same resources. Recall that this kind of connectedness is a prerequisite for the
development of a single image heliotropic loop. Once these dual connections have been
established it is possible that an intended negative action of one social group might result in an
increase in the productivity of the other due to natural variations in the factors controlling
production. Such a scenario is one way to explain how a heliotropic loop can get started. A
heliotropic loop can not be initiated directly from a design with the no social interaction because it
is evident that any attempt to enhance the productivity of the other without a reciprocal
connection will hasten the elimination of the altruistic group. A dual positive connection
between social groups might also arise if the resource base being exploited was sufficiently
different to allow trade to develop. However, this scenario violates our initial assumption that the
two social groups are evolving in competition for the same resources.
It is significant that empower production by the system design with two negative images
overlaps the empower produced by systems with a single positive image for the high resources
scenario. This implies that in our modem high energy world, conflict may be preferable to the
unilateral development of positive images of the other e.g., in Northern Ireland, Palestine and
perhaps Rwanda. It is also clear that empower production on the larger resource base is decidedly
greater for a design with two positive images. Social interactions should evolve toward designs
with mutual heliotropic loops when sufficient resources are available. In a lower energy world, a
single positive image results in more empower than conflict or no interaction e.g. the early
colonial relationships between Great Britain and her colonies in places such as India, Jamaica, and
Hong Kong. A positive image of the more efficient group resulted in greater empower generation
for the low energy scenario, but this result was reversed when resources were doubled.
Maximizing empower production for the whole system implies that the evolution of social
interactions should proceed from negative to positive interactions guided by images of the other.
The imperative for group survival under competition for the same resources leads from
indifference to the other toward negative images of the other that may result in the survival of the
a less efficient group. However, conflict generated by negative images is not the ultimate goal of
social evolution if it is guided by maximizing empower. Maximum empower for a system
appears to result from designs that include heliotropic loops based on positive images of one
group for another.
The initial evolution of social interactions toward a lower empower state for the system
can be explained by considering empower production at the level of the individual group. At first
such a movement seems to contradict the Maximum Empower Principle but this principle is
completely general and to understand its workings we must consider all hierarchical levels. The
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inclusion of an autocatalytic feedback loop (the double arrows surrounding k5 and k6 in the
consumer symbol used to represent each social group) implies that each group possesses a
positive image of itself and will work toward maximizing its own empower. The positive image
that a social group holds of itself explains the initial development of a negative image of the other
because empower for the first group is maximized. Thus, a single negative interaction develops to
maximize empower for the less efficient social group. The first development of a single positive
image might be explained by the fact that initially the group that forms the positive image has a
higher emergy level than the other (Figure 4b and 5b). Therefore, at the level of the individual
social group, the development of a positive image of the other is favored in the short run because
empower for the group forming the image is greater than it is when the other first forms a positive
image.
If the evolution of social interactions is guided by the progressive development toward
designs that maximize empower for the whole system, system designs with heliotropic loops will
eventually develop because they produce more empower than the other designs tested. The two
opposing views of social evolution mentioned in the introduction can be reconciled, if the socio-
rationalist interpretation of appreciative inquiry is understood as a chaotic choice generator within
a deterministic system. This method of searching for knowledge effectively identifies alternative
modes of social interaction, i.e. those that include heliotropic loops. These new normative
visions for society point the way to the changes in system design that will allow the group to
realize its vision. The new social designs are then tested in evolutionary competition and those
that lead toward more empower survive.
Acknowledgments
We wish to thank H. Walker for early review and discussion of the central idea of this paper. We
also thank H. Walker, S. Hale and W. Davis for internal review of the paper. This paper is
contribution number NHEERL-NAR- 2011 of the USEPA's National Health and Environmental
Effects Laboratory, Atlantic Ecology Division. The opinions expressed are the authors' own and
do not necessarily reflect the views of the USEPA.
References
Bushe, G.R., and G. Coetzer. 1995. Appreciative Inquiry as a Team-Development Intervention: A
Controlled Experiment Journal of Applied Behavioral Science 31 (1): 13-30.
Cooperrider, D,L. 1990. Positive Image, Positive Action: the Affirmative Basis of Organizing,
pp.91-125. In Appreciative Management and Leadership. S. Srivastva and D.L. Cooperrider eds.
Jossey -Bass Publishers San Francisco.
Jussim, C. 1986. Self-Fulfilling Prophecies: A Theoretical and Integrative Review. Psychological
Review 93(4):429-445.
Odum, H.T. 1986. Enmergy in Ecosystems, p. 337-369. In Environmental Monographs and
Symposia, N. Poulin ed., John Wiley& Sons, New York.
Odum, H.T. 1994. Ecological and General Systems: An Introduction to Systems Ecology.
University Press of Colorado, Niwot, CO 644 p.
8
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Odum, H.T. 1996. Environmental Accounting: Entergy and Environmental Decision Making.
JohnWiley&Sons,NY,370p. .
Odum, H.T. and EC. Odum, 1995. Environmental Mini-models &Simulation Exercises. Center
for Environmental Policy, Environmental Engineering Sciences, University of Florida,
Gainesville, 273 p.
Scienceman, D.I987. Energy and Emergy, pp. 257-276. In Environmental Economics, Q. Fillet
and T. Murota eds. Roland Leimgruber, Geneva,Switzerland.
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ST1
Energy equations:
(l)dQ/dt = k5*Q*R-k3*Q
(2) dQ2/dt = k6*Q2*R - k4*Q2
(3)R = I/(l+kl*Q+k2*Q2)
Emergy calculations:
(1) dEmQ/dt = STE * kl*Q*R - STl*k3*Q,
where STl*k3*Q =0, if STE*kl*Q*R>=STl*k3*Q
(2) dEmQ2/dt = STE*k2*Q2*R - ST2*k4*Q2
where ST2*k4*Q2 =0, if STE*k2*Q2*R >= ST2*k4*Q2
Figure l(a) An energy systems diagram of two social groups, Q and Q2 competing for
the same resources, I, without direct interactions. The initial values for the pathway
coefficients, storages, and the ernergy source used in the equations are shown on the
diagram. ST indicates solar transformity, Em emergy, and a gray line energy no lon^;r
able to do work.
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200
150-
>
E>
O
HI
0100-
0)
c
LU
50-
-Emergy of Q
Stared energy In Q
-Emergy of Q2
Stored energy In Q2
320
Figure 1(b) Stored energy (light line) and emergy (heavy line) of the two social groups, Q and Q2, in
competition for the same resources without direct interaction. The legend lists model outputs in
order of their magnitudes at time = 320.
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0.002
Energy equations:
(1) dQ/dt = k5*Q*R*(l-kd*Q2*IMQ) - k3*Q, where kd = 0.05
(2) dQ2/dt = k6*Q2*R - k4*Q2 - k7*IMQ*Q2 - k8*Q2*Q
(3) dIMQ/dt = k8*Q*Q2 - k9*IMQ2
(4) R = I/ (1 + kl*Q*(l - kd*IMQ*Q2) +k2*Q2)
Emergy calculations:
(1) dEmQ/dt = STE*kl*Q*R*(l -kd*IMQ*Q2) -STl*k3*Q,
where STl*k3*Q =0, if STE*kl*Q*R>=STl*k3*Q
(2) dEmQ2/dt = STE*k2*Q2*R - ST2*k4*Q2 - ST2*k7*IMQ*Q2 - ST2*k8*Q*Q2
where ST2*k4*Q2 =0, if STE*k2*Q2*R >= ST2*k4*Q2
(3) dEmQI/dt = ST2*k8*Q*Q2 - ST3*k9*IMQ2
Figure 2(a) An energy systems diagram of two social groups competing for the same
resources, I, when the less efficient group Q2 has a negative image of the more efficient
group, Q. The initial values used in the equations are shown on the diagram. ST
indicates solar transformity, Em emergy, and a gray line energy no longer able to do
work.
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200
150 i
S>
-------
Energy equations:
(1) dQ/dt = k5*Q*R*(l-kd*Q2*IMQ) - k3*Q - k8*Q*IMQ2 - k9*Q2*Q
where kd = 0.00001
(2) dQ2/dt = k6*Q2*R*(l -kd*Q*IMQ2) - k4*Q2 -k7*IMQ*Q2 - kl 1 *Q2*Q
(3) dIMQ/dt = kll*Q*Q2 - k!2*(IMQ)2
(4) dIMQ2/dt = k9*Q*Q2 - klO*(IMQ2)2
(5) R = I/(1+ kl*Q*(l - kd*IMQ*Q2) +k2*Q2*(l - kd*IMQ2*Q))
See Figures 1&2 for the method of calculating emergy.
Figure 3(a) An energy systems diagram of two social groups competing for the same
resources, I, when each has a negative image of the other. The initial values used in the
equations are shown on the diagram.
-------
200
150-1-
B>
0)
UJ
100-1-
504-
EmergyofQ
^ Emergy of Q2
Emergy of the image of Q
Emergy of the image of Q2
80
160
Time
240
320
Figure 3(b) Stored emergy produced by the two social groups, Q and Q2, and their negative images
of each other in competition for the same resources.
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Energy equations:
(1) dQ/dt = k5*Q*R*Q2 - k3*Q - k7*k8*Q2*Q2*R - k9*Q2*Q*R
(2) dQ2/dt = k6*Q2*R*Q*MQ2 - k4*Q2 - k8*Q2*R*Q
(3) dIMQ2/dt = k7*k8*Q2*Q2*R - klO*(IMQ2)2
(5) R = I / (1 + kl*Q*Q2 + k2*Q2*IMQ2*Q)
See Figures 1&2 for the method of calculating emergy.
Figure 4(a) An energy systems diagram of two social groups competing for the same
resources, I, when the more efficient group, Q, has a positive image of the less efficient
group, Q2. The initial values used in simulating the equations are shown on the diagram.
-------
200
S>
0)
LU
150-1-
1004-
504-
Emergy of Q2
-Energy of Q
- Emergy of the Image of Q2
80
160
Time
240
320
Figure 4(b) The emergy of the two social groups, Q and Q2, when the more efficient group.Q, has a
positive image of the less efficient group, Q2.
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_JL._
Energy equations:
(1) dQ/dt = k5*Q*R*Q2*IMQ - k3*Q - k9*Q2*Q*R
(2) dQ2/dt = k6*Q2*R*Q - k4*Q2 -k8*Q*R*IMQ*Q2 - kll*k9*(Q2)2*Q*R
(3) dIMQ/dt = kl l*k9*(Q2)2*Q*R - k!2*(IMQ)2
(4) R = I / (1 + kl*Q*IMQ*Q2 +k2* Q2*Q)
See Figures 1&2 for the method of calculating emergy.
Figure 5(a) An energy systems diagram of two social groups competing for the same
resources, I, when the less efficient group, Q2, has a positive image of the more efficient
group, Q. The initial values used in simulating the equations are shown on the diagram.
-------
200
o>
UJ
150
100 -
50
Emergy of Q
Emergy of Q2
Emergy of the Image of Q
-t-
80
160
Time
240
320
Figure 5(b) The emergy of the two social groups, Q and Q2, when the less efficient group,Q2, has a
positive image of the more efficient group, Q.
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Energy equations:
(1) dQ/dt = k5*Q*R*Q2*IMQ - k3*Q - k9*Q2*Q*R*IMQ2
- k7*Q2*k8*Q2*R*IMQ
(2) dQ2/dt = k6*Q2*R*Q*IMQ2 - k4*Q2 - k8*Q*R*Q2*IMQ
- kll*(Q2)2*k9*Q*R*IMQ2
(3) dIMQ/dt = kll*(Q2)2*k9*Q*R*IMQ2 - k!2*(IMQ)2
(4) dIMQ2/dt = k7*Q2*k8*Q2*R*IMQ - klO*(IMQ2)2
(5) R = I / (1 + kl*Q*Q2*IMQ+ k2*Q2*IMQ2*Q)
See Figures 1&2 for the method of calculating emergy.
Figure 6(a) An energy systems diagram of two social groups competing for the same
resources, t when each has a positive image of the other. The initial values used in thi
equations are shown on the diagram.
the
-------
200
0)
LU
EmefoyoiQ2
Emergyof Q
Emergy of tto!m>goofQ2
""""Emergy of ttw Image of Q
320
-------
Positive Image of the more efficient group
Positive Image of the less efficient group
No Interaction
Two negative Image* Q wins
One negative Image Q2 wins
Time
Figure 7(a) The cumulative empower of social groups, Q and Q2, produced by alternative system
designs using available resources, I =5. The legend lists model outputs in order of their magnitude at
time = 320.
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Two positive Images
Positive Image of the Ins efficient group
Positive Image of the more efficient group
Two negative Images
Negative Image of the more efficient group
Time
Figure 7(b) The cumulative empower of social groups and their images produced by alternative
system designs when available resources are doubled. The legend lists model outputs in order of
their magnitude at time = 320.
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