Social-Psychological Harmonic Oscillators in the Self-Regulation of Organizations and Systems:

Quantum Informatics for Cognitive, Social, and Semantic Processes: Papers from the AAAI Fall Symposium (FS-10-08)
Social-Psychological Harmonic Oscillators in the Self-Regulation of
Organizations and Systems: The Physics of Conservation of Information
William F. Lawless1 and Donald A. Sofge2
Paine College, 1235 15th Street, Augusta, Georgia, USA, wlawless AT
Naval Research Laboratory, 4555 Overlook Avenue SW, Washington, DC,
donald.sofge AT
understand the intelligent behavior of humans, animals and
machines (Ying, 2010).
Our prior research (Lawless et al., 2010b) has established
that cooperation is required for organizational effectiveness,
especially as organizations trade growth in size for reduced
instability to gain market control, but the tradeoff means
that increased cooperation reduces an organization's ability
to innovate. However, in a system (Lawless et al., 2010a),
such as the European Union, Haiti, or China, forced
cooperation increases corruption and reduces effectiveness
in responding to emergencies (e.g., earthquakes). From
other research (Ostrom, 2009), we know that self-regulated
systems are more effective than centrally controlled or
privately owned systems, except when self-regulation
compromises social welfare such as corrupting the practice
of science (Lawless et al., 2005). We also know that if an
algorithm exists to run an organization perfectly (Conant &
Ashby, 1970), the organization emits zero information
(Conant, 1976), making a perfectly run organization appear
to be dark to outsiders but also itself (Lawless et al.,
2010b), accounting for the negligible associations between
managers and the performance of their firms (Bloom et al.,
2007). Inversely, the turmoil in a competitive society
produces more “lightness” from additional information than
darkness from its absence, a paradox involving tradeoffs
underlying the physics of the conservation of information
that must be resolved for systems composed of humans,
machines and robots to be able to computationally regulate
Presently, the conventional model of interdependence is
provided by game theory, ineffective for several reasons
that include its static nature even when used in repeated or
"dynamic" games (Lawless et al., 2007); its inability to
predict (Sanfey, 2007); and its unsatisfactory modeling of
interdependence problems (Schweitzer et al., 2009). In our
search for a better model of interdependence, we noted
Feynman (1996) postulated that conventional models of
entanglement were inefficient, an observation that we had
also made about existing theories of interdependence
(Lawless et al., 2007).
Using computational intelligence, our ultimate goal is to
self-regulate systems composed of humans, machines and
robots. Self-regulation is important for the control of mixed
organizations and systems. An overview of self-regulation
for organizations and systems, characterized by our solution
of the tradeoffs between Fourier pairs of Gaussian
distributions that affect decision-making differently, is
provided. A mathematical outline of our solution and a
sketch of future plans are provided.
Tradeoffs invoke a differential uncertainty principle for
organizations and systems between four interrelated
bistable variables: the possible location of a planned event
and its spatial frequency; associated energy and time
expenditures; action and self-reports of that action; or plans
and their execution (Lawless et al., 2010b). We have found
that as certainty increases in one factor socially
interdependent with another, uncertainty increases in the
other. The physics of these tradeoffs have different impacts
whether the focus is on an organization or system of
organizations. In this paper we lay out a conceptual path to
the solution we have found for the tradeoffs in selfregulating organizations and systems.
We have previously established theoretically that
computational intelligence can exist to control
organizations, systems, and systems of systems (Lawless et
al., 2010b). Less-well developed are the mathematical
proofs to support control, which we briefly sketch in this
paper. It is an important problem for several reasons.
Success will not only help to understand organizations and
systems, but also to control organizations and systems with
computational intelligence. This fits with the two goals of
Artificial Intelligence: to build intelligent machines; and to
Copyright © 2010, Association for the Advancement of Artificial
Intelligence ( All rights reserved.
Further, Rieffel (2008) concluded that quantum
information theory has benefited quantum and classical
theories, especially entanglement and control (in the social
context, we use “classical” to mean traditional). Working
with Rieffel's theme, similarities exist between social
interdependence and quantum entanglement. Both
interdependence and entanglement are fragile, quickly
breaking down when interacting with an external
environment (e.g., quantum "decoherence" and social
interference). Unknown states for both are impossible to
copy (e.g., quantum's "no cloning theorem"; and a movie of
human behavior requires a long development: the 2009
movie Avatar took 16 years to finish). Both produce
powerful computational effects (e.g., entanglement reduces
computations from exponential to polynomial time; and
interdependence is central to social problem solving on
juries, scientific journals, entertainment, etc.). Both defy
classical descriptions; e.g. "intuition is dangerous in
quantum mechanics." (Gershenfeld, 2000, p. 253), while
classical interpretations of interdependent social states
commonly produce two incommensurable or irreconcilable
stories in every social situation, the touchstone of juries,
trumpeted by Aeschylus in his play Oresteia; in modern
jurisprudence, incommensurability in the competing views
between a prosecutor and defense attorney are required for
justice (Freer & Purdue, 1996).
That interdependence produces incommensurable stories
is not only the foundation of game theory, but also the first
mathematical solution to the Prisoner's Dilemma Game,
known today after Nash (1951), its discoverer, as Nash
equilibria (NE). However, Axelrod (1984) characterized
NE solutions as pernicious to social welfare, recommending
that with evolution, society should replace individual "selfinterests" with cooperation. Simon (1990), too, construed
cooperation as altruism. Simon concluded that altruism and
bounded rationality were acceptable to Darwinian models
of evolution. But from our perspective based on
organizational and system tradeoffs, the replacement of
self-interest with altruism and bounded rationality reduces
the likelihood of innovation and evolution in human affairs
(Lawless et al., 2010b).
We believe that our approach with the conservation of
information (more or less variance in the tradeoffs by
managers choosing among interdependent Gaussian
distributions) is high-risk research. Deriving a theory of
complementarity to produce uncertainty in tradeoffs among
conjugate variables, as suggested by Bohr for action and
observation, was considered by Von Neumann &
Morgenstern (1953, p. 148), the developers of game theory,
to be "inconceivable". Nonetheless, guided by Bohr, our
discovery transforms game theory (Lawless et al., 2010b).
The mathematics we envision eventually will provide a
system, and the organizations within it, the ability to selfregulate using computational intelligence. But for this
paper, we focus on self-regulation in the physics of the
tradeoffs between cooperation and competition.
To develop interdependence theory, we adapted Cohen's
(1995) interpretation of classical uncertainty principle for
signal processing.
Our research project began with trying to understand the
mismanagement of U.S. military nuclear wastes (Lawless,
1985). Lilienthal (1963), the first leader of the U.S. Atomic
Energy Commission (AEC) recognized that AEC's selfregulation would compromise the practices of its scientists.
AEC management determined the priorities for its scientists
that it chose to receive funding, independent of merit,
allowing AEC's (and ERDA's and DOE's) management to
manipulate its scientists, control the data that was collected,
and determine the results that were published. In contrast,
and with the first ever prediction with the physics of the
conservation of information (Lawless et al., 2005),
competition driven by independent scientific peer review
has had a positive impact of the practice of science by DOE
scientists by reducing the influence of DOE management
on its scientists.
But all organizations prefer self-regulation, including
commercial ones. The U.S. Federal Reserve Board, the
European Union, and the Roman Catholic Church are
examples. But in these cases, self-regulation depends on
their determination of "transparency" to meet its objectives.
Can self-regulation ever work? Not for commercial or
private enterprises according to Hardin (1968), who
believed that a common resource had to be regulated by a
central authority with enforced cooperation or privatized to
sustain the resource. However, Ostrom (2009), a nobel
laureate in economics for 2009, demonstrated that a
resource commons can be successfully self-regulated by an
association of users. She challenged the conventional
wisdom that the management of property common to
multiple users conflicts with individual self-interests had to
be poorly managed. In these cases failure means the likely
loss of a resource (e.g., salmon in the Pacific Northwest).
And yet Ostrom found that outcomes are often better than
predicted by Hardin. She found that successful resource
users frequently managed its self-regulation.
Ostrom's characterizations of successful community
associations are: self-governance: clearly defined group
boundaries; rules matched to local needs; individual
responsibilities proportional to benefits; users participating
in rule modifications; community rights respected by
external authorities; and a graduated system of sanctions
used by community members with low-cost conflict
consumption. From our perspective, the key characteristic
is the establishment and maintenance of interdependence
between resources and users who share the benefits and
costs (Lawless et al., 2009).
scientists). Adopting a system to reduce this uncertainty
was the first recommendation, leading to the eIRB system
now installed at E-MDRC (an IRB is an Institutional
Review Board required to conduct research on humans and
animals; eIRB is an electronic or web-based IRB.). But in
overcoming fragmentation by enforcing cooperation across
its system, the MDRCs must not adversely impact its
practices of science.
Specific to DOE or the military MDRCs, top-down
(minority) control is desired to optimize its operations in a
way that fulfills its mission in the field. However, minority
control encumbers the practice of science, which depends
on NE (e.g., challenges to prevailing scientific theories). In
organizations, reducing the existence of internal centers of
conflict (NE) is often the goal of management. But
suppressing NE makes the practice of science inefficient or
ineffective, creating a paradox (exceptions exist, such as
IBM). Thus, for optimal performance, scientists conducting
research within an organization should be governed by its
chain of command (e.g., achieving its mission), whereas to
produce top-notch scientific research in a system, scientists
must be governed by internal and external NE, a paradox.
Since DOE and the MDRCs have the specific missions of
being knowledge generators, this paradox should not be
resolved. Instead, construing the paradox as a source of
tension helps to conceptualize the dual role of system
scientists, where individual tension can be exploited to both
power mission performance and to change its vision in a
way that revitalizes the organization and the system over
Collecting information from well-defined networks or
organizations for social network analysis (SNA) is
relatively straightforward. But even when the information is
readily available, the signals collected from social networks
have not led to valid predictions about their actions or
stability (NRC, 2009; Schweitzer et al., 2009). For "Dark"
social networks (DSNs), comprised of illicit drug gangs or
terrorists (Carley, 2006), uncovering information to
compute an SNA is orders of magnitude more difficult.
This failure with SNAs, game theory, and organizations in
general (Pfeffer & Fong, 2005) has led to a wide request for
new social theory to better understand the effects of
interdependence in social networks and organizations
(Jasny et al., 2009; NRC, 2009). For example, Barabási
(2009) concluded that room needs to be made for a new
theory "to understand the behavior of the systems … [and]
the dynamics of the processes ... [to] form the foundation of
a theory of complexity." (p. 413)
COI predicts that organizations with unified commands
are more stable than those under dual or shared commands
(i.e., fragmented; Lawless et al. 2007); larger organizations
are more stable than smaller ones; and that, unlike systems,
the best run organizations have a clear mission under a
central chain of command but with minimum bureaucracy.
These findings buttress the theory first proposed by Conant
(1976) that optimal organizational performance requires
effective communication and lines of communication
(channels), effective coordination (management) with
minimum blocking processes (bureaucracy), and with
minimal generation of internal noise.
In addition to COI, we have proposed that two
complementary processes operate in an organization or a
system. First, restorative forces act via negative feedback to
meet a business model or worldview (e.g., missions,
baselines, or standards such as "best business practices").
Second, inductive forces act via positive feedback to
progressively change the current operational procedures
Based on field results, we postulated that system
fragmentation characterizes the existence of non-cohesive
work cultures and practices. For an organization,
fragmentation impedes the execution of an organization's
business model (Lawless et al., 2007). In our case study of
the military's system of Medical Department Research
Centers (MDRC; MDRC is an acronym for a fictitious
name to represent the system in order to keep the real
organizations, one of seven, anonymous. By extension, EMDRC is one of the seven sites in the system) designed to
teach research methods to its physicians, we found that by
increasing inefficiency, fragmentation increased the
difficulty of executing its mission, or even knowing the
effectiveness of the system at any point with a desired
degree of confidence. Fragmentation was reflected by an
increase in the uncertainty in the knowledge about MDRC's
publication rates, publication quality (scientific impacts),
and scientific peer status (the comparative quality of its
Mathematical Model
We have postulated that information about an
organization's market size forms a Gaussian distribution
coupled to its Fourier transform as a multiplicative Fourier
pair that ideally equals or exceeds a constant, producing
COI (Rieffel, 2007). We have identified four sets of Fourier
pairs that describe interdependence in the tradeoffs for
organizations or systems. First, larger organizations are
more stable (lower stock market volatility) or "darker" than
smaller organizations, motivating organizations to grow in
size with mergers and acquisitions (Andrade et al., 2001).
Second, even for well-known organizations, the more
skilled they become, the "darker" become the signals of
their presence to observers and to themselves (Landers &
Pirrozolo, 1990; Lawless et al., 2000), in effect, hiding their
presence; in contrast, system effectiveness requires
information from NE. Third, as certainty in one factor
grows, uncertainty in its Fourier paired cofactor grows,
creating tradeoffs between conjugate variables (i.e., an
exactness in two conjugate variables cannot occur
simultaneously). Illustrating this for self-reported and
interview data, the meta-analysis by Baumeister and
colleagues (2005) found that self-esteem, often studied in
psychology, was negligibly correlated to academic and
work performance. Fourth, the more focused an
organization's operational center-of-gravity, the more able
it is to replicate its business model or plan geospatially
(Lawless et al., 2009).
By studying the fluctuations an organization or system
daily experiences across these four pairs of interdependent
cofactors, COI suggests that it is possible to reverse
engineer them from the information they produce in
response to perturbations. But to complete our theory, we
need in addition a mechanism to measure the effects of an
NE on social welfare across a system or between two
organizations from a methodologically social perspective.
For that we use Lotka-Volterra type equations to produce
limit cycles (May, 1973; see Figure 1).
Conservation of Information, NEs, and SPHOs
A Hilbert Space (HS) is an abstract space defined so that
vector positions and angles permit distance, reflection,
rotation and geospatial measurements, or subspaces with
local convergences where these measurements can occur.
That would allow real-time determinations of situated,
shared situational awareness in localizing the center of
gravity for a target organization or system, σx-COG, to
represent the standard deviation in the shared uncertainty,
and σk to similarly represent the standard deviation in
spatial frequencies of its patterns across physical space
(e.g., the mapping of social-psychological or organizational
spaces to physical networks). As an NE, it establishes an
"oscillation" between orthogonal socio-psycho-geospatial
operators A and B such that
L-V Notional Chart
N, in population
[A,B] = AB - BA = iC ≠ [B,A]
This type of oscillation defines a social-psychological
decision space embedded within an organization or system.
It is called an "oscillator" because decision-making occurs
during sequential or turn-taking sessions that "rotate"
attention for the topic under discussion in the minds of
listeners or deciders first in one valence direction (e.g.,
"endorsing" a proposition) followed by the opposite (e.g.,
"rejecting" a proposition) to produce an oscillation or
"rocking" back and forth process for a social-psychological
harmonic oscillator (SPHO), like the merger and
acquisition (M&A) negotiations between a hostile predator
organization and its prey target.
Considering discrete Fourier transforms, that these
operations are incommensurable suggests that social
knowledge is only derived from non-commutative
orthogonal operators (i.e., the eigenstates of a Hermitian
operator are orthogonal if their inner product is zero, as in
<ψm|ψn> = 0). Pure oscillations are unrealistic
("frictionless"; May, 1973) and possibly driven by illusions
(endless discussions of religion, or risk perceptions
common to cooperation processes). We have found that
these are more likely from enforced cooperation under
consensus than majority rules (i.e., the "gridlock" between
DOE Hanford and its consensus citizens board, rather than
accelerated cleanup at DOE SRS pushed by its majority
rule board), because consensus rules, at least in DOE,
specifically reject science as a determinant (Bradbury et al.,
The lack of an SPHO identifies decisions made by
minority (consensus) or authoritarian rules (e.g., decisions
common to military, authoritarian government or CEO
business decisions; cf. Lawless et al., 2007). Unlike an
organization's central command, a democratic space could
be defined for a system as a space where decisions
characterized by SPHOs are made by majority rule (e.g.,
jury, political, or faculty decisions).
The key to building the abstract representations
necessary to construct an SPHO is to locate opposing
clusters of the shared interpretations of concepts
Time, units
Figure 1. Instead of a limit cycle (N1 versus N2; in May,
1973), the data are displayed with N over time, t. Arbitrary
parameters produce "frictionless" oscillations from an NE.
We interpret N1 and N2 to be in competition at time 1 (and t
= 3.5, 6 and 7). The public acts at time 2 (and t = 3, 4 and
5) to produce social stability.
Figure 2. Despite the arbitrary nature of the data in the
Figure 1, the 2010 campaign for Senator in Illinois captures
the limit cycle on the left from about the end of January
2010 to the end of April (at the far left, the Democrat is on
top, but falls beneath the Republican by the end; for the
contest between Obama and Clinton in 2008, see Lawless et
al., 2010b).
geospatially across physical space or via a sociopsychological network anchored or mapped to physical
network space. SHPOs should generalize to entertainment;
e.g., Hasson and his colleagues (2004) found that a Clint
Eastwood movie engages an audience's attention with this
rocking process. This insight suggests that the reverse
engineering of forcibly darkened organizations (e.g.,
terrorists, Mafia) is possible (Lawless et al., 2010b).
The disturbance of a system oscillating between
conjugate bistable states |ψ> by an operator Xn produces an
observable xn with probability |an|2, causing eigenfunction
|ψ> to collapse into an eigenstate |n> unless |ψ> is already
in one (i.e., a classical image or interpretation). an is a
coefficient of an orthonormal basis. Thus, |an|2 is
According to Bohr (1955), complementarity actors and
observers and incommensurable cultures generate conjugate
or bistable information couples that he and Heisenberg
(1958) suggested paralleled the uncertainty principle at the
atomic level. Our model tests their speculation and extends
it to role conflicts (Lawless et al., 2009). Even for mundane
social interactions, Carley (2002) concluded that humans
become social to reduce uncertainty. Thus, the information
available to any human individual, organization, or system
is incomplete, producing uncertainty. More importantly,
this uncertainty has a minimum irreducibility that promotes
the existence of tradeoffs between any two factors in an
interaction (uncertainty in worldviews, stories or business
models, ΔWV, and their execution, Δv; uncertainty in
centers of gravity ΔxCOG and spatial frequencies, Δk; and
uncertainty in energy, ΔE, and time, Δt).
Given [A,B] = iC, and the difference δ A = A - <A>,
where <A> is the expectation value of A, and its variance is
<δ A2>, then [δ A,δ B] = iC; further, <δ A2><δ B2> > ¼
<C2>, giving the Heisenberg uncertainty principle ΔAΔB
>1/2<C> (see Gershenfeld, 2000, p. 256). The uncertainty
relation models the variance around the expectation value
of two operators along with the expectation value of their
The uncertainty in these oscillations can be reformulated
to establish that Fourier pairs of standard deviations
σ Aσ B > ½
pilots and book-knowledge of air combat maneuvering
(Lawless et al., 2000); and captures the discrepancy
between game-theory preferences and actual choices made
during games (Kelley, 1992). It must allow rotation vectors
as a function of the direction of rotation. It must permit
measurements between vectors and rotations. And a model
of interdependence must enable a mathematics of
interdependent (ι) bistability where measurements disturb
or collapse the ι states that occur during socialpsychological interactions in physical space.
Up to this point in time, we have simulated equation
(2) for organizations. In the future, we plan to finalize the
mathematics and simulate it for a system. Two operators A
and B are community interaction matrices for an NE that
locate ι objects in social space (shared conceptual space)
geospatially. ι states are non-separable and non-classical;
disturbances collapse ι states into classical information
states. Two agents form an NE, one as Einstein and the
other as Bohr, and meet in Copenhagen to discuss the
implications of conjugate variables in quantum mechanics,
the two exchanging incommensurable world views that
profoundly disturb science and society even today (e.g.,
Frayn's 1998 play Copenhagen), together generating
bistable social perspectives that drive competition,
moderated by a neutral audience that exploits it to solve its
problems. Cooperation may make an organization work
better, but competition and conflict across a system of
organizations produce classical interpretations of social
reality that generate the unending debates that underlie
technological innovation and social evolution. This
conclusion, based on physics, significantly advances our
understanding of human organizations and systems.
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