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Article

The Symmetry of Interdependence in Human–AI Teams and the Limits of Classical Team Science

Department of Mathematics and Psychology, Paine College, Augusta, GA 30901, USA
AppliedMath 2025, 5(3), 114; https://doi.org/10.3390/appliedmath5030114
Submission received: 12 June 2025 / Revised: 18 August 2025 / Accepted: 19 August 2025 / Published: 1 September 2025

Abstract

Our research goal is to provide the mathematical guidance to enable any combination of “intelligent” machines, artificial intelligence (AI) and humans to be able to interact with each other in roles that form the structure of a team interdependently performing a team’s tasks. Our quantum-like model, representing one of the few, if only, mathematical models of interdependence, captures the tradeoffs in energy expenditures a team chooses as it consumes its available energy on its structure versus its performance, measured by the uncertainty (entropy) relationship generated. Here, we outline the support for our quantum-like model of uncertainty relations, our goals in this study, and our future plans: (i) Redundancy reduces interdependence. This first finding confirms the existence of interdependence in systems, both large and small. (ii) Teams with orthogonal roles perform best. This second finding is the root cause of humans, including scientists, being unable to appreciate the role of interdependence in “squeezing” states of teams. (iii) Cognitive reports may not equal behavior. The last finding allows us to tie our research together and to account for the absence of social scientists from leading the mathematical science of teams. In this article, we review the need for a mathematics for the future of team operations, the literature, the mathematics in our model of agents with full agency (viz., intelligent and interdependent), our hypothesis that freely organized teams enjoy significant advantages over command decision-making (CDM) systems, and results from the field. We close with future plans and a generalization about squeezing states to control interdependent systems.

1. Introduction

The value of this study is to initiate a means of measuring a team’s performance in the field, regardless of whether teams are composed of humans, robots, machines or artificial intelligence (AI). Without mathematics, humans have operated in teams for eons. But machines, robots and AI need a mathematics to know how well they are performing. We begin by applying Noether’s theorem and symmetry to the science of teams. But, we will argue that humans intuitively manage human teams with Bohr’s quantum complementarity (e.g., [1]). A table of acronyms is included at the end.
Noether’s theorem [2] predicts that conserved quantities reflect symmetries found in nature. For example, time translation symmetry gives conservation of energy; space translation symmetry gives conservation of momentum; and rotation symmetry gives conservation of angular momentum. We shall apply symmetry to the classical social science of teams and appeal to Dirac to limit determinancy in classical social science.
To apply Noether’s idea to a team’s function, we take liberties with the complex flow of energy through a team at any instant: we avoid a focus on getting energy into a team, on dividing it among team members to perform roles, and on concerns about each team member’s state (e.g., we assume that at the moment of interest, each member ably performs an assigned role). We also ignore losses due to friction, etc.
We assume that the energy available to a team can be expended on the team’s structure, its performance, or both, creating a tradeoff in the conservation of energy. We consider the advantages and disadvantages of a team in a state of interdependence; how to maintain interdependence (indirect control), and topical questions that may be addressed by our findings. In particular, with AI (machine learning, automatons, etc.), one claim today is that AI is potentially dangerous [3]. Specifically, we ask, “Are the advantages afforded by interdependence in human–machine teams able to offset existential threats” (e.g., AI agency; in [4])?
To capture the phenomena of teams mathematically, our argument accounts for the limits of team science, social science, collective logic, and generative AI. In future research, we sketch team decision-making; debate and competition between teams; and compromise between choices offered to two teams versus majority rule (symmetry breaking) or consensus-seeking rules (minority control rule). We are not focused on building a team, but “teamness”, valuable because indicators based on individuals (beliefs, skills, etc.) have failed.

1.1. Background of the Problem

We borrow Dirac’s (p. 15, in [5]) idea of a superposition intermediate between states to focus on the confounds that obscure the interactions in teams. From Dirac, symmetry between dependent states indicates superposition, but degrees of freedom indicate independence. In Dirac’s view, superposition and interference at the quantum level create states unlike anything in classical physics. Generalizing to human teams to explain the cognitive failures we later review, the internal interactions of a team cannot predict whether a team experiences additive or destructive interference, whether to join or leave a team, or knowing whether an agent’s skills fit or not; members of a team are shifting rapidly between actor–observer roles as they coordinate actions, characterized by Bohr [1], especially if problems arise, the interference promoting or reducing support for a team’s actions, even as its dependencies [6] obscure an outsider’s view of what is occurring (National Academy of Sciences, p. 12, in ([7]).
Our goal is to develop the mathematics of interdependence to operate human–machine–AI teams. With it, we have generalized to new findings [8]. To exemplify generalizing interdependence, if inside of a team of machines, a machine, A, depends on a second machine, B, and B is dependent on another machine, C, and the results are mutually dependent on each other (i.e., A, B and C), physical interdependence performs a team’s actions satisfactorily (e.g., ref. [9] reported that its interdependent chem-labs have been crafting new materials for lasers). Current interdependent machines are ignoring communicating with words about their status, situation, or context. Generalizing interdependence in the future should advance with synchronous behavior, internal cognition and spoken words among all members of human–machine–AI teams.
Achieving interdependent communication and behavior is our goal (viz., speaking and acting interdependently by machines and humans). However, today, the Wall Street Journal [10] reported that machines cannot manage each other or humans:
“Some traditional warehouse roles have proved too difficult for Amazon to fully automate … Humans [but not robots] can easily look into a storage container packed full of goods, identify a particular item and know how to pick it up and handle it …”
Humans are more competent than machines, AI or robots. Classical social science has failed to develop an integrated science of teams [11]. But a science of interdependent cognition and behavior for humans does not exist. Thus, we focus on human–human systems to advance a science of teams.
Still, interdependence is a challenge. For almost three decades (Jones, 1998, p. 33; in [12]), social scientists had come to conclude that controlling interdependence for a team of humans in the laboratory is bewildering.
Consider cognitive concepts for individuals. Classical social science has been unable to construct valid concepts; for instance, self-esteem was found to be invalid in 2005 [13]; implicit racism invalid in 2009 [14]; ego-depletion invalid in 2016 [15]; and honesty invalid in 2021 [16]. The result was a crisis identified by Nosek in 2015 [17]. To address this situation, Nosek and leading social scientists developed new methods that would provide guidance for others to follow. It was submitted to Nature but then retracted after the editors became concerned about its methods [18]. Thus, replication remains a problem. From Psychology Today [19]:
“The vibrations of the “replication crisis” continue to be felt throughout the social sciences, and particularly within psychology.… Rather than effectively scrutinize this foundation, it has been more convenient… to push the narrative that it was founded on scientific rigor.”
From our perspective of interdependence, the loss of information in the interaction is a quantum-like superposition [11], accounting for these failed concepts. A similar problem has occurred in behavior research (e.g., [20]) and in the logic of collective decision-making in the field or when facing conflict [21]. These problems with social science and logic support our theory and the conclusions drawn earlier by Jones [12].
Furthermore, the problems with social science and collective logic not only support Jones [12], but also the consensus report by the National Academy of Sciences [7] which stated that the interaction cannot be fully examined:
The “performance of a team is not decomposable to, or an aggregation of, individual performances…”
In our research, however, we view these problems as fundamental to a science of teams: In plain sight, the loss of information during an interaction is similar to what occurs with superposition or entanglement [11]. This loss means a team is not a combination of isolated, separable individuals, but a “whole” dependent on each of its elements [6].

1.2. Literature Review

Maruyama’s [22] term “polyocular vision” means the “illusion of understanding.” For example, Lego bricks are separable units, but interdependent teammates interfere with each other additively (constructive interference; e.g., the whole is greater than the sum of its parts; in Lewin [23]) or adversely (destructive interference; for instance, the whole is less than the sum of its parts, as in a divorce [24] or spin-off in business [25]).
In addition to an organization’s division of labor, Heath and Staudenmayer [26] argue that these divisions must be integrated into a whole, i.e., the personnel in each component of an organization must strive to integrate with all of an organization’s components, communicate about the barriers that arise, and translate each component’s separate knowledge base into the knowledge that all teammates can understand.
Coplien and Harrison (pp. 66–67, in [27]) see the value of managers during crises as gatekeepers who prevent overburdening teams by balancing loads to achieve shared responsibility. To achieve greatness requires hard work, communication and mindfulness of the whole organization, and its members must transition from individuals and separate teams into an organization’s whole to become greater than the sum of its parts.
Unlike laboratory studies, Klein [28] focused on naturalistic decisions in the field under pressure, where he found that most projects were poorly managed. To overcome poor results, he focused on applying lessons learned from poorly understood contexts (e.g., actual fire fighting), training, reading the minds of teammates, with teams gaining experience, sharpness, stability, strong networks and continuity. As an example, Walker [29] reviewed the unexpectedly great Hungarian soccer team 1950-56, composed of ordinary individuals who achieved a greatness that could not be explained. Walker attributed its magical transformation to a focus on synchrony, teamwork, coordination, and the drive to build a team greater than the sum of its more talented opponents.
Hare [30] asked whether groups are more productive than individuals, and what was the optimal size of a group, concluding that the preferred group size ranged from four to five, with no benefit beyond six, but the group should be no larger than that needed to accomplish its goals, and that redundancy impeded a team’s performance, supporting our research [31].
James [32] studied the effect of group size on interaction patterns in small groups (e.g., Congressional Committees), finding that leadership becomes necessary for coordination and cohesion as groups grow in size. Our results disagree with Hare and James.

2. Mathematics

To capture the lack of knowledge about the interaction, Schrödinger [33] was first to describe dependency in states entangled with each other, where “a whole does not necessarily include the best possible knowledge of all its parts,” which we have argued reduces the information observable between states dependent on each other. At the quantum level, Zeilinger [34] agreed, stating that any knowledge from inside of entangled parts, or parts in a superposition, is precluded, which subadditivity models.
Shannon’s information theory tells us about the signals transmitted among humans, but little about dependency. Most systems are classical, meaning they are constituted of parts independent of each other. We begin with the traditional interpretations of discrete source of information with Shannon’s theory of entropy, H, for two discrete, independent variables (i.e., random), A , B , where H ( A , B ) is joint entropy:
H ( A , B ) H ( A ) + H ( B ) .
Our goal is not to review information theory but to describe its traditional uses as the source of misunderstandings about social reality. Equation (1) models statistical independence. As an example of independence, should a car’s part break down, substitute a new part for the defective one and continue to drive. Shannon next contributed the interdependence, I ( A , B ) , between two phones communicating signals to each other (but not when dependent on each other; see the Conclusions (Section 5)).
I ( A , B ) = H ( A ) + H ( B ) H ( A , B )
The separate parts of a car, of a house, or of a shirt are independent. Separable systems can be broken apart, reassembled and repaired. They are classical, separable, factorable systems composed of parts that are independent.
The theory of measurement in traditional mechanics is not the same as quantum mechanics. Classically, building a part of a compound system, like the International Space Station (ISS), has no effect on the other parts of the ISS already in orbit because they are not, generally speaking, dependent on the other parts. They can be assembled in space or replaced in space one part at a time. Not so for entanglement. For the recent three quantum Nobel Laureates, quoting (https://www.nobelprize.org/uploads/2023/10/advanced-physicsprize2022-4.pdf, accessed on 1 July 2023),
“That a pure quantum state is entangled means that it is not separable… being separable means that the wave function can be written as
ψ ( x , y ) = ψ 1 ( x ) ψ 2 ( y )
However, classical social science that models independent elements of a team cannot model the phenomena about teams in a National Academy of Sciences’ report [7]; that is, the interactions between dependent members of a team are not observable (e.g., as Lewin quipped, a whole can be greater than the sum of the parts of a whole; in [23]; similarly, for Systems Engineering, see [35]). To capture the finding reported by the National Academy of Sciences, subadditivity instead can model an interdependent whole to make it greater, or lesser, than the sum of its elements.
For quantum or quantum-like models, with H to represent its Hamiltonian (considering only available energy), with ρ as the density matrix, and with ρ A B as a density matrix, a bipartite system becomes ρ A B ϵ   D ( H A H B ) , and entropy, S, giving ([36]):
S ( ρ A B ) S ( ρ A ) + S ( ρ B ) .
Equality governs iff the tensor product holds: ρ A B = ρ A ρ B ; then,
S ( ρ A B ) = S ( ρ A ρ B ) .
If the parts of a team are separable (e.g., modeled by tensors), Equations (4) and (5) govern. However, if the parts are not separable [37], the joint entropy vanishes in the quantum case. To model the claim in the National Academy of Sciences’ report, for a quantum-like team, we claim the entropy for an interdependent system is:
S ( ρ A B ) = 0 .
Equation (6) not only models the finding in the National Academy of Sciences report, namely the loss of aggregate information from interaction, but, generalizing, adding a new member to a team has an unknown effect until the entropy, S, changes (greater indicates a bad choice fit-wise, or lesser indicates a good choice fit-wise, as in [24]). In the limit, for a good fit among existing members of a team, the entropy is reduced by subadditivity to zero from interdependence.
How can we use Equation (6) to model a team? First, we represent the members of a team with N degrees of freedom ( d o f ), where H A is the classical information produced by the whole, and H a n is the information from each of the whole’s parts. If the team is a group of disconnected, uncoordinated, separated, independent participants, then
H A = d o f = 1 N H ( a N ) = H ( a 1 ) + H ( a 2 ) + H ( a N ) .
Equation (7) presents two problems: It cannot account for Equation (6), and it offers no advantage for functional collectives such as teams, i.e., no synergy or aggregation of power from teamwork. That we can address with degrees of freedom (dof). When a team forms, its dof among the teammates reduces (viz., as it unifies into a “team”), thereby causing less information to be generated, agreeing with Equation (6). We assume there is only so much free energy a team uses for its operations. A disunited team wastes energy on policing structure (e.g., divorce badly disrupts a family’s life [38]; business spin-offs create anger in an organization [39]). In comparison, a unified team structure is stable, allowing more of its free energy to be directed to productivity, giving the sum of a team’s members an advantage in accomplishing a mission; for that, the whole, A, is the structure of a team. Controlled as a unified whole, cohesive and stable, the entropy, S A , generated by structure, S E P S t r u c t u r e , decreases, enabling the team to direct a little (an unstable structure) or most (a stable structure) of its energy available from the team’s structure to increasing its performance, M E P . For M E P to maximize, structural entropy production, S E P , must reduce, becoming in the limit:
S A = lim d o f 1 log ( S E P S t r u c t u r e ) = 0 .
Equation (8) explains how Equation (6) happens. The reduced degrees of freedom in a team’s structure preclude the information from being available to “disambiguate” into individual contributions to the “performance of a team…” [7]. It also implies that the less energy wasted by a team to maintain its structural coherence, the less heat (i.e., wasted energy) it generates in emotional responding, making more energy available to allow a team to be productive (for businesses, see Harvard Business Review [39]; for the economic effects of divorce on the family, see Johnston et al. [38]).
Jefferey et al. [40] define life as an entity that preserves “information”, e.g., genetic code. But static aspects of structure cannot be applied to a team consisting of humans and AI teammates. We define structure as the sum of the roles, skills, communications, interactions, synchronizations, etc., that combine into an array of a team’s structure that produces entropy interdependently with performance. In this unique view, team structure ranges from poor (bad management, bad marriage, etc.) to extraordinary (the brilliant Hungarian soccer team 1950–56; in Walker [29]), the latter’s structure producing least entropy (SEP), allowing the team to direct most of its available energy to its performance (i.e., MEP), like a perfect hurricane (e.g., Lawless et al., in [24]).

2.1. The Mathematics of Measurement Theory

We turn to measurement. Classical social science assumes that social reality consists of independent pieces of information based on the number of agents observed, or dof (Equation (7)); it assumes that information can be linked to form social structures to produce recoverable information. But that does not happen; instead, as we have noted, in the attempts to validate them, social concepts fail. Worse, generalization to new theory and new findings does not occur.
The critical insight to apply quantum theory to teams is derived from orthogonality (Equation (9)) in teams and individuals engaged, for example, in competing, planning, deceiving, lying. Many jokes address the problem of a secret affair, which requires an orthogonality between a mind’s eye and a body’s behavior. Whether in marriage, business, military or political matters, orthogonality is critical to teamwork. The tradeoff between structure and performance derives from Bohr’s (in Pais, [1]) application of the quantum model in this way: the best teams are highly interdependent [41], able to transcend barriers to achieve maximum performance (e.g., Walker, in [29]). In comparison, divorce proceedings in marriage [38], business [39], science, politics, etc., impede day-to-day performance. This shift between poor to good teamwork is Bohr’s theory of complementarity, supported by the claim in the National Academy of Sciences’ consensus report [7] that a team’s structure cannot be disambiguated, preventing simultaneous measurement, signaling the limits of classical team science.
Thus, if we assume that a questionnaire elicits a Belief B and an Action A orthogonal to each other, then
( B e l i e f B ) ( A c t i o n A ) = B A = | B | | A | cos 90 = 0
We found support for Equation (9) in a request by educators working with the US Air Force to model the results of educating combat fighter pilots on the principles of air combat, versus the experience these same pilots gained by air combat training in the field. The correlation of training was significant, but education in the classroom produced a zero correlation, an incommensurability (reviewed in [24]).
Thus is created the measurement problem. Acting like an information barrier, interrupting a state of interdependence, say to measure it, produces what Schölkopf and colleagues [42] called “independent and identically distributed” (i.i.d.) data, which, by definition, cannot recreate whatever interdependent event has been captured (see also [43]). An excellent example is the frame of a movie or a television show.
Measuring a quantum system affects it by interrupting the state of entanglement or superposition, producing incommensurable data, i.e., beliefs or action. The same happens with our quantum-like model of teams, producing non-commutative information, meaning that two interdependent factors cannot be measured at the same time. Assume two interdependent matrix operators, action operator A and belief operator B, non-commutative or incommensurable with each other, and a constant C, which gives
[ B , A ] = BA AB C .
For a team interdependently connected, given Equation (10) for coherent interactions among teammates, and modeled by Equations (6) and (8), if we assume that the maximum free energy available can be applied to a team’s structure or its productivity, measured by entropy ( S E P or M E P , respectively), the quantum-like uncertainty relations for interdependent teams become:
Δ S E P Δ M E P 1
Equation (11) represents our equation of uncertainty in the energy tradeoffs of a team, where uncertainty in a team’s structure and its productivity are dependent on each other. Thus, the more a team “squeezes” [44] the uncertainty of its structure (i.e., as S E P 0 ), the more productive it becomes (i.e., M E P ,  reflecting maximum performance uncertainty). Furthermore, maintaining a “squeezed” state of structural entropy interdependently provides indirect control, an advantage gained by forging a group of individuals into a unified, productive team, like Adam Smith’s pin factory [45].
Equation (9) (orthogonality) explains Equation (10) (interdependent parts of a whole cannot be disassembled without affecting the whole) and Equation (11) (orthogonal tradeoffs between non-separable functions of a team). The information collected from orthogonal roles produces zero correlations, accounting for the failure (Equation (8)) of theories of complementarity (orthogonal elements, such as husbands and wives, e.g., Berscheid and Reis, in [24]). These failed cognitive concepts cannot be validated because they are orthogonal to the actual behaviors executed, viz., self-esteem is highly correlated with similar cognitive beliefs (e.g., academic achievement, value at work) but utterly fails to correlate with actual performance data (actual academic grades or actual work performance [13]), resulting in Nosek’s [17] validation crisis.
To summarize, with measurements and replications of exquisite sensitivity, exact magnitudes in quantum mechanics are achievable. Not so with humans and teams. Bohr [1] recognized the problem of applying Heisenberg’s uncertainty principle to social systems, replacing it with his theory of complementarity, which we call quantum-like, supported by these results:
  • Equation (11) supports the claim in the consensus report of the National Academy of Sciences (p. 12, in [7]) that information cannot disentangle the contributions made by a well-performing team’s members (i.e., low or squeezed S E P ).
  • Equation (11) indicates that team structure is critical; it has no classical equivalent. By way of analogy, the most powerful hurricanes not only have the smallest or “squeezed” structures (minimum S E P ), but they also produce maximum entropy flowing out of the tops of their eye walls [24].
  • For more, see Table 1a,b. Later, we will generalize Equation (11) to Equation (12), the highlight of this manuscript.
Table 1a,b provide justifications for Equation (11) (in the left column, Δ SEP is highlighted in contrast to in column 3, where Δ MEP is highlighted).

2.2. Methods—Building Convergence I—Case Studies

As part of our methods, we build towards a convergence of results beginning with a case study of Boeing and SpaceX; past hypotheses that have worked; and adding a new hypothesis generalized from our past results for this article.
Boeing and SpaceX. Based on Equation (11), broadly, the control of systems can be either top down (viz., CDM, implying no interdependence) versus self-organized interdependently. In real time, teams must abide by rules or by roles, rules requiring redundant personnel to enforce a strict adherence, versus adapting to roles on the fly to maximize performance (MEP), an advantage with fewer personnel working interdependently, no matter the size [41].
We argue that Boeing became top-down (i.e.,“squeezed” M E P and increased SEP) compared to SpaceX (i.e., with a “squeezed” S E P and increased MEP; see Table 1). An anecdote by an engineer found that Boeing was struggling with Starliner. The same engineer reported that SpaceX felt “like a frenzied graduate school, where all of the employees were being pulled in different directions,” agreeing with the Cummings [41] report about the best of science teams.
Based on this comparison, by rules governed by redundancy or roles governed by interdependence, a mature Boeing can become unable to compete with a highly interdependent SpaceX. After the Space Shuttle program ended, NASA chose Boeing first to build a space bus named “Starliner” to transport “commercial crews” to ISS and SpaceX for a smaller contract. However, Boeing lost and SpaceX won [80]:
“With Boeing’s Starliner spacecraft… we know the extent of the loss, both in time and money. Dragon first carried people to the space station nearly four years ago. In that span, the Crew Dragon vehicle has flown thirteen public and private missions to orbit. Because of this success, Dragon will end up flying 14 operational missions to the station for NASA, earning a tidy fee each time, compared to just six for Starliner.”
Boeing was the prime contractor responsible for assembling the International Space Station and is still associated with it (Boeing officially turned over the U.S. on-orbit segment of the ISS to NASA in 2010 but continues to provide key engineering support services (https://www.boeing.com/space/international-space-station#feature-stories, accessed on 15 July 2025)). Boeing’s news in mid-2024 was the launch of its first crew of astronauts to the ISS on 5 June 2025 (https://www.boeing.com/space/starliner/launch/index.html, accessed on 15 July 2025). However, in news reported by NASA, Boeing’s crew was returned from the ISS by SpaceX https://issnationallab.org/press-releases/nasas-spacex-crew-9-returns-science/, accessed on 15 July 2025),
“KENNEDY SPACE CENTER (FL), 19 March 2025—Astronauts on NASA’s ninth rotational SpaceX crew mission (Crew-9) splashed down off the Florida coast yesterday evening, ending their months-long science expedition onboard the International Space Station (ISS). Over the course of the mission, the crew supported a variety of investigations… Returning crew members include NASA National Aeronautics and Space Administration astronauts… Suni Williams, and Butch Wilmore…”
In Table 1a,b, we compare Boeing and SpaceX. Data from the company websites indicate that Boeing’s contracted income for 28,000 employees is $5.5 billion in 2024 (https://www.boeing.com/space/space-launch-system/launch/people.html, accessed on 15 July 2025) versus 13,000 employees at SpaceX generating $4.2 billion in 2022 (https://www.spacex.com, accessed on 15 July 2025). Ignoring the 10:1 ratio of the number of crews delivered to the ISS, SpaceX outperformed Boeing by 1.6 times. Maybe Boeing’s poor results are due to its larger scale factor. Boeing is big, mature and unable to adjust, versus SpaceX, which is young and motivated; we suspect that part of maturity for an older organization is an inability to change, indicating interdependence is being suppressed by the bureaucracy of a mature organization.

2.3. Method—Convergence II

To reiterate, our goal remains to derive a theory of interdependent cognition and behavior that we can measure and apply to all teams and to address the risks that AI may pose.

Method—Hypotheses Supported: Triangulation

  • Claim 1: The self-reported questionnaires reviewed above (i.e., self-esteem, implicit racism, ego-depletion, honesty) capture belief data orthogonal to behavioral data, leading to poor correlations reflected by invalid concepts. It is possible that lying was involved, known as ”the Pygmalion effect.” However, these cognitive questionnaires produce data that are significantly cross-correlated with data from other questionnaires, but not with the claimed physical behavioral data, causing Nosek [17] to declare a “crisis”. Nosek’s recent plan to repair the damage was itself retracted [18]. Instead, we claim that an orthogonality exists with the cognitive and physical data, which we have published [46,81].
  • Claim 2: The data collected post-interaction is i.i.d. data which, by definition, cannot capture whatever interdependent event has occurred, supported by Equation (11) and information loss in the interaction (p. 12, [7]).
  • Claim 3: Interdependence ends direct determinancy in classical social science for the decisions made by operational teams, by teams facing uncertainty or, for example, by teams making major changes in plans. That is, when successful, new structures reflect new dependencies in attempts to reduce vulnerability to change or, say, to too many competitors (e.g., marketplace, battlefield, etc.), but the success of new structures is roughly random (estimated at 50% by [54]). Despite that result, collective logical decisions by comparison are inferior to freely made choices [21,24]. We hypothesize that after an interaction, despite the uncertainty, the free market provides the i.i.d. data about what has or has not worked, reflecting choices superior to those made by CDM (authoritarians) [49].
  • Claim 4: By reducing information with fewer dof, new organizational combinations are quantum-like in their decisions despite the absence of observable information until the results are known. Interdependence is a resource that promotes human development [43] and competition, reduces corruption, discovers vulnerability [24], and thrives under freedom.

2.4. New Hypothesis: Interdependence Is a Resource

Assembly theory investigates alien life [82]. As such, it overlooks the issues with the hidden operation of interdependence by counting instead the assemblies of success built by intelligent agents; the more assemblies observed, the greater the likelihood of an assembly being associated with more intelligent and complex forms of interdependent life. Building on observable effects, by predicting and finding what these results of interdependence in a team look like, interdependence becomes a resource that manages the entropy flow through a team: A low entropy produced by a team’s structure ( S E P ) allows the team to better expend its available energy to maximize the team’s performance, characterized by maximum entropy production, results similar to ours for teams [24].
This last step allows us to hypothesize that central or command decision-makers (CDM; e.g., authoritarians, kings, gang leaders) place their teams, organizations or nations at a decision disadvantage by oppressing interdependence and replacing it with the logic inherent to minority control [24], thereby preventing information symmetry within and between teams, the quantum-like resource used by free humans to organize themselves at varying social levels, where the “essential tension” [83] from interdependence improves social function by providing a decision advantage [41].
To test our hypothesis, although the data may be unreliable, we begin with estimates of kill ratios of Russian soldiers to Ukrainian soldiers in Ukraine, and Hamas to Israeli Defense Forces (IDF) in the Gaza Strip. Then, we focus on eight nations in highly competitive situations, either in outright conflict or nearing conflict (Iran, Israel, China, Taiwan, North Korea, South Korea, Russia, and Ukraine). In addition to these eight, we add four others in milder forms of conflict (Costa Rico and Haiti; USA and Cuba). Finally, we consider evidence of the top most innovative firms and companies in the world.

3. Results

The kill ratios of Russian soldiers to Ukrainian soldiers were estimated at 220,000 to 43,000 [84], a ratio of about 5.17:1; and a range of Hamas soldiers killed to IDF soldiers estimated at 17–18,000 [85], ranging downward to a lower estimate of 8500 ([86]), providing ratios of about 43.28–20.99:1. Russia and Gaza are not free.
Next, we construct a model of country data to attempt to account for these kill ratios. In Table 2, we tabulate the United Nations’ Human Development Index data (HDI) (https://hdr.undp.org/data-center/human-development-index#/indicies/HDI, accessed on 1 June 2025); a country’s gross domestic product per capita from the International Monetary Fund (IMF) (https://www.imf.org/external/datamapper/NGDPDPCWEO/OEMDC/ADVEC/WEOWORLD, accessed on 1 June 2025); Transparency International’s Corruption Perception Index (CPI) (https://www.transparency.org/en/cpi/2023, accessed on 1 June 2025); the Global Innovation Index (GII) by the World Intellectual Property Organization (WIPO) (https://www.wipo.int/en/web/global-innovation-index, accessed on 1 June 2025); and the Fraser Institute’s Economic Freedom Index (https://efotw.org/, accessed on 1 June 2025). In Table 2, NA stands for data that were not available.
Using the UN’s HDI as a standard, these correlations were calculated: r, between the UN’s HDI and each of the other indices (HDI & GDP/capita: r = 0.92, p < 0.05; HDI & CPI: r = 0.81, p < 0.01; HDI & GII: r = −0.71, p < 0.05; HDI & freedom: r = 0.92, p < 0.01).
In Table 3, we calculated the advantages afforded by maintaining the symmetry of interdependence to estimate the value of this hidden resource. The best advantage afforded by a people to itself is reflected by its collective productivity, or GDP/capita. But HDI and freedom are necessary ingredients for self-organization, followed by a measure of the corruption reduced by the tension wrought by interdependence, interdependence that also produces competition among teams and organizations, and while serving as a resource for innovation (GII) [77]. In Table 3, we used data from Forbes about the most innovative countries in the world, cross-tabulated with the Fraser Institute’s determination of “Mostly Free or Mostly Unfree” (https://www.forbes.com/innovative-companies/list/2/#tab:rank, accessed on 10 May 2025). That allowed us to count the number of companies home-based in free to mostly free, or in mostly unfree to unfree countries (shown in Table 4).
For Table 4, using the Fraser Institute’s data, we categorized these countries as Free to Mostly Free: Japan, the European Union countries, the United Kingdom, the United States, Canada, Indonesia, and South Korea. We classified these countries as Mostly Unfree to Unfree: Russia, China, Brazil, and India.

4. Discussion

For a free people, the outcomes are superior to those determined by logic or central decision makers (CDM). The sum of the advantages in Table 2 is 28.39, with an average of 5.68 (both from Table 2, line 1). The smaller average closely approaches the Ukrainian advantage in combat, and the larger sum approaches Israel’s IDF advantage.
For claim 3, 50% of new structures succeed (cf. Table 3), agreeing that a random process occurs for teams facing uncertainty about future choices [54], suggesting why CDM strives, but fails, to outperform self-organized free markets [49].
We have sought to establish the value of symmetry in teams. From the literature, nation states facing conflict and uncertainty, given the time to consider their situation, engage in tradeoffs before entering conflict or not [87]:
“the role of symmetry in interdependence and conflict lies in the relationship between a state’s exit (opportunity) costs and the costs it is willing to bear in the face of political conflict with another state.”
Russia eyed the greater benefit of invading Ukraine in its belief that the costs were minimal, but its authoritarian view was misguided [88]. CDM decision-makers often mis-judge while using logic rather than the random, self-organized choices made by leaders in free countries. In agreement, Osborn concluded that [74]
“China’s leadership is concerned about corruption within the PLA’s ranks, especially at the lower levels, and to the extent possible wants to remove the individual soldier from the decision-making process in favor of machine-driven guidance.… in stark contrast to the U.S. Army’s way of war, which… sees its Soldiers as its greatest advantage in battle and relies on their intuition, improvisation, and adaptation to lead to victory.”
In agreement, the Wall Street Journal reported that [89]
“China’s crackdown on corruption within its defense industry could set back its weapons… programs, delaying its military modernization…”
Regarding the lack of information about states of interdependence, our results buttress the conclusions by Polanyi (in [90]) that a judge’s decisions have greater precedence than a judge’s written justifications. Polanyi had claimed that tacit knowledge meant that we humans know more than we can say, e.g., some drivers can park a car in a small space each day, but are unable to articulate how their skill is enacted. Polanyi agreed that Law Courts often follow the precedents set by similar cases. In these prior court decisions (precedents), judges recognize that practical wisdom is embodied in decisions rather than their opinions later offered to explain their decisions.
Our results agree with Acemoglu and his fellow Nobel laureates about economic freedoms and the rule of law (The [Nobel] Prize in Economic Sciences 2024, https://www.nobelprize.org/prizes/economic-sciences/2024/popular-information/, accessed on 1 June 2025), but we disagree in the sense that even democratic rule can be abused. A better marker is whether interdependence is being impeded.
Those who lose a public battle may become ostracized even in a democracy [91]. But by standing up, the person and society will be able to evolve [77]. It underscores the changes that may occur for the losers in an election, those able to grasp clues for success from the winners, a process of turning from what was once believed into a new framework for the next contest, e.g., see the New York Times [92] for the changes in the political parties that occurred in the 2024 Presidential election, viz., conservatives in the U.S. represented workers, a constituency formerly represented by liberals.
We conclude that it is impossible to build human–machine teams without mathematics and the best teams without an interdependence between bodies and minds. Presently, interdependence is being introduced with laser materials (in Service, 2024 [9]), the USAF’s F-16 to help fighter pilots recover from a loss of consciousness after a high-g maneuver (i.e., G-LOC [93]), breathalyzers to impede alcoholics, positive control of trains, etc. However, these cases of applied interdependence are reactive physically, not cognitively; viz., no jet pilot ever asks an F-16 jet to explain what it was thinking when it helped its pilot to recover, a common practice for humans when they interview a “hero.” Today, teamwork between machines, AI and humans is “lousy,” [94] and has a long way to go to become seamless, China’s goal and our goal.
We could have focused on tests with groups of 4–5 humans. However, Cummings [41] found excellent results for scientific teams of up to n = 13 in size, i.e., the larger an interdependent team, the more productive it was, contradicting [30,32].
Our results also indicate that “words alone do not equal reality,” which means that the tools of Generative AI (e.g., tensors for LLMs and machine learning) used to construct a model of “reality” are separable entities (Equations (3)–(5)), but these separable entities produce independent and identically distributed (i.i.d.) data that, by definition [42], are unable to reconstruct whatever social interactions were captured [24]. Why? Think of the illusions of reality created by speakers in the movies; words alone amount to 7 percent of what humans communicate to each other [95]; further, we do more than communicate; specifically, we do not need words to think [96]:
“Language is a defining characteristic of our species, but the function, or functions, that it serves has been debated for centuries.… in modern humans, language is a tool for communication… [not] for thinking.”
The problem with communication is exemplified by the claim that language is for communication [96], not thought nor action (also, [95]). Large language models are constructed with tensors which are separable entities, but are unable to model interdependence (see also p. 33, in [12]). However, to date, we have made two predictions with Equation (11) that match the literature (see Table 1a,b): for MEP to maximize, SEP must be squeezed, meaning that structural information reduces, supported by the National Academy of Sciences report [7], and given a squeezed SEP and an MEP at maximum, to increase productivity, add an agent [41]; see Future Research (Section 6).

5. Conclusions—Limits of Classical Team Science

We have criticized classical approaches to teams with three arguments: Cognitive science has failed at the individual level (e.g., [97]), making it unable to generalize to teams; information is lost in interaction due to a loss in dof [7]; and measurement of teams produces i.i.d. data which cannot recreate the interdependence observed.
The best way to control a free people, and by generalization, future teams to protect humanity, is to let teams self-organize interdependently to the maximum extent possible, i.e., indirect control by maintaining a state of least SEP, versus losing control and causing failure; for instance, Dollar Tree lost control of Family Dollar and had to sell [59], squeezing its MEP. The results will be random (i.e., [54]), but, under the “essential tension” [83] afforded by interdependence among self-organized teams, the result will be superior to the methods used by CDM leaders, e.g., see Cassidy [49]. Interdependent systems (freely organized) are not error-free (e.g., [45,49,54]); however, on average, they significantly outperform CDM systems.
From the President and GM of Avathon Government Systems, AI’s [98]
“true potential will not be in replacing humans with smart machines; rather, it will happen when activities become truly synchronized.”
Madison’s insight [99] was that “Ambition must be made to counteract ambition” to prevent oppression by a majority. Similarly, to find the truth in the courtroom, Freer and Purdue [100] concluded that justice is found when the practice of law occurs between equally competent, competing attorneys. In particular, with AI, one claim today is that AI is potentially dangerous (e.g., [3]), especially if AI gains agency [4]. But our findings indicate that the advantages afforded by interdependence in teams more than offset these threats. Our results also indicate that autocrats who suppress interdependence place their systems at a disadvantage to these threats [24].
Our conclusion that information during the interaction is hidden also agrees with Adam Smith’s “invisible hand” [45]. As a society becomes more specialized, mutual interdependencies arise in free markets guided by an invisible hand of need [45], a more successful process of organizing a society than central decision-making (for the failure of collective logic, see [21]). CDM data and logic transform cause and effect into an illusion of control (but see [101]).
Our findings contradict the conclusions about the “Squid Game” from the New York Times, indicating that competition is bad [102]: “the toll of tribalism: how the push to pit ourselves against one another in a winner-take-all political battle leads to destruction and despair for all.” Instead, we conclude that the value of random exploration with free choice leads to success with the best products, the best agents, the best political leaders, etc., greatly outweighing the choices that CDM leaders can make in advancing technology and society (e.g., [77]), and with less corruption.
Interdependence is a resource that provides a significant advantage to agents free to self-organize. Applied to the classical social science of teams, Noether’s theorem, Dirac’s research and our results call for the end of classical determinancy, a step toward the computational methods necessary for future human–AI-machine teams.
In conclusion, redundancy reduces interdependence. In support, we found that redundancy in freely-organized teams is minimal compared to those organized in centrally structured command decision-making (CDM) systems, impeding the performance of CDM teams; subsequently, in addition to replicating poor performance, we found that redundancy in CDM systems is also associated with significant corruption, offering an explanation for its continued existence.

6. Future Research

First, from the literature, we have addressed the random outcomes associated with team mergers [54]. But what drives mergers? Noether’s time-symmetry formulation led to conservation of energy; given a finite amount of energy available to a team (organization, etc.) having achieved a minimum SEP and a maximum MEP for a given n, the only way to increase MEP, as predicted by Cummings (see Cummings, pp. 82, 94, in [103]), is to have n + 1 members in a state of interdependence with minimum dof). If those conditions are met, a team’s power increases:
P o w e r n + 1 = P n + 1 = ( W o r k n + 1 Δ t ) P n .
Equation (12) models the claim by Cummings; to it, we want to add a term for redundancy and another for demand interdependent between technology and society [77].
Second, what is it about majority rule that makes it work? When an audience of voters adopts a viewpoint belonging to the majority, does that mean that their belief dependency increases to merge with the majority (see Equation (8))?
Third, our future research plans include the additive and destructive effects of emotions. Our mathematical theory of dependent states [6] is a step towards a science of interdependent teams, including emotions [11]. Adverse emotions should generate excess entropy by a team’s structure, squeezing MEP [24]. If anger (high emotion) is associated with dysfunctional teams or organizations [39], inversely, a good team should have a low-energy state of operation reflected by a least action principle. Including emotion, we can build a model of society composed of coupled quantum-like harmonic oscillators, fulfilling Lewin’s vision of modeling an interdependent society [23]. Under the uncertainty of free choice (e.g., corporate mergers fail about 50% of the time [54], exemplified by the potential breakup of Honeywell; in [104]), compromise in politics [105], new innovations and patents, an index might be constructed like Table 2, Table 3 and Table 4 for assemblies that self-organize into evolvable, autonomous, and observable systems ([82], e.g., [46]) interdependently seeking positive “animal spirits” [106].
Fourth, for animal spirits to arise, an “essential tension” [83] between interdependent states must produce random outcomes from competition. Nash harnessed these spirits with the first solution to game theory [107], i.e., that every claim can balance an opponent’s claim, e.g., a debate. Given a state of interdependence when two equal teams compete, with each claim countered, the equilibrium generated lasts until a vote, reflecting the spontaneous symmetry breaking in a freely organized society. Nash’s work involved non-cooperative games, but we found that a team cooperates best with players in orthogonal roles (e.g., cook, clerk, waiter), supported by a study of drivers and automation [108] that should be further explored [109].
Fifth, we plan in future research to explore the value of seeking consensus decisions, which we have found are inferior when a consensus is forced, required or purposively sought [24]; for instance, reports by the National Academy of Sciences (NAS) to counter misinformation (p. 163, in [110]) had one option being censorship. The consensus report by NAS (p. 169, in [110]:
“…for reducing exposure to misinformation, deplatforming is controversial, in part because it has often been equated with censorship and raises concerns regarding potential infringements on freedom of speech…”
Journalists may add to the problem (p. 234, in [110]):
“Science reporting for the general public may be particularly prone to the unintentional spread of misinformation about science. Several factors can influence this, including journalistic norms (e.g., giving equal weight to both sides of a scientific debate, even when the scientific evidence overwhelmingly points in one direction)…”
However, censoring information behind a consensus to prevent symmetry breaking and using technology to censor speech (e.g., with AI) ignores the value of a public educated about a topic, preventing readers from learning about the challenges that produce the i.i.d. data from debating an issue. Indeed, Americans are in favor of having scientists [111] “Take an active role in public policy debates about scientific issues.”
Instead of CDM (censorship, etc.), after campaigning to reach office, compromise is a better way to govern [105]. It is elusive, but if reached, it means a mutual sacrifice by the parties even as they (roles) likely remain opposed to it, making i.i.d. data public, guidance that can be generalized to human–machine teams. In contrast, the minority control technique of seeking consensus, or minority control [66], is preferred by authoritarians (rules). Authoritarian-led countries can become technology leaders; for instance., the USSR led to the first satellite in orbit (Sputnik in 1957), and the Chinese satellite, Micius, is the leader in quantum cryptography communication. However, authoritarians on average use espionage to keep up with freer countries (e.g., China, for example, is not free; see Yong [51]).
But, unleashed by freedom, marshalled by debate (competition) to amplify innovation and evolution [77], with corruption and vulnerability exposed and tensors and consensuses ignored, interdependence squeezes information from successful teams [46].

Funding

This research received no external funding.

Acknowledgments

The author thanks Ranjeev Mittu at the Naval Research Laboratory for his support and many years of guidance; the author also thanks Ira S. Moskowitz at the Naval Research Laboratory for his support, mathematical guidance, and for his wonderful gift of Dirac’s 1935 book, which made this article possible.

Conflicts of Interest

The author declares no conflicts of interest.

Acronyms

CCPChina’s Communist Party
CDMCommand decision-making
DOEDepartment of Energy
dofdegrees of freedom
F-16USAF F-16 fighter jet
G-LOCg forces induced loss of consciousness by jet fighter pilots
HLWHigh-level liquid radioactive wastes
HMTHuman–machine team
IInformation
i.i.d.Independent and identically distributed random data
ISSInternational Space Station
MEPMaximum entropy production generated by productivity
SEPStructural entropy production generated by structure

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Table 1. (a) Foundational mathematics and justifications. (b) Foundational mathematics and justifications, continued.
Table 1. (a) Foundational mathematics and justifications. (b) Foundational mathematics and justifications, continued.
(a) Δ SEP Δ M E P 1 Δ S E P + Δ M E P = 1 Δ S E P Δ MEP 1
Theory : Interdependence (additive interference, synergy) [46]: non-separables.Separables; tensor models (e.g., large language models [46].)Interdependence (destructive interference; e.g., conflict): non-separables.
Squeezing As interdependence increases, “squeezing” [44] on the left implies Δ S E P 0 ; it means that information is lost as degrees of freedom reduce [7] (the invisible hand [45]), causing Δ M E P on the right, producing competition [45], information, boundaries [31], and chance [47].Command decision-making reduces interdependence [46], increasing cheating, corruption, disloyalty [48] and industrial policies, unlike the free market which “is soulless, exploitative, inequitable, unstable, and destructive, yet also all-conquering and overwhelming.” [49]Inadvertently squeezing  Δ M E P 0 from conflict (divorce, business disruption), causes Δ S E P ; e.g., redundancy reduces effectiveness in organizations [31]; China’s CCP influencers in private companies and state-owned enterprises [50] add redundancy, causing inefficiency, corruption and espionage [31,51].
Example: Let S E P = 1 and M E P = 1 , then S E P M E P = 1 ; squeezing the uncertainty in S E P to 1/2 or 1/10 amplifies uncertainty in M E P to 2 and 10, respectively.Given, for example, A + B = 0 , o r A B = 0 , no complementary squeezing or amplification occurs.Let S E P = 1 and M E P = 1 , then S E P M E P = 1 ; if we squeeze the uncertainty in M E P to 1/2 or 1/10, uncertainty in S E P amplifies to 2 and 10, respectively.
Example: SpaceX: Since 2014, 10 crews and 32 re-supply missions have made it to ISS (see spacex-crs32 press release NASA’s ISS). Its revenue per employee in 2022 an estimated $3.2 E5 (wiki/SpaceX and www.spacex.com)An example of additive “plug and play,” Boeing designed and built many of ISS’s 40 major units ferried to space separately aboard 36 Space Shuttles (https://issnationallab.org/).Since 2014, Boeing: 1 crew delivered to ISS; see press releases: spacex-crs32-research-overview (https://issnationallab.org/). It contracted: $1.96 E5 in 2024 (www.boeing.com/space, accessed on 15 July 2025)
Information loss: I = l i m d o f > 1 l n ( d o f ) = 0 ; i.e., orthogonal roles reduce Shannon Information ([7,52]); explains invalid concepts [17] and Nosek’s replication project failures [18]. I = l i m d o f > n l n ( d o f ) = > i . i . d . d a t a ; but, by definition, i.i.d. data [42] cannot replicate contexts, even filmed or videotaped [46]; “playbacks” give the illusion of reality (e.g., [53]). I = l i m d o f > n + 1 l n ( d o f ) = > i . i . d . data [46]; e.g., divorce [38]; organizational spinoffs, anger in business decision-making [39], bankruptcies; e.g., on the right, 50% of mergers fail [54].
(b)
Δ SEP Δ M E P 1 Δ S E P + Δ M E P = 1 Δ S E P Δ MEP 1
Power: If Δ S E P 0 and Δ M E P , then a crude model to increase Power: P n + 1 = t e a m w o r k n + 1 δ t ; i.e.,  P o w e r n + 1 > P n , crude but matches [41]. Mergers increase market power; e.g.,  [55]; mergers increase synergy by reducing costs; e.g., [56]).Separables: Cars, airplanes, bridges, trains, etc., but they make cognitive constructs invalid; e.g., the invalidity of implicit racism, in [14]; the invalidity of Bargh’s implicit cognition; in [57]; etc.Mergers can fail; e.g., Walgreens spins off Alliance Boots [58]; Dollar Tree sells Family Dollar [59]; Citigroup spins off Banamex [25]; Boeing sells digital assets [60].
Transcendence: Great investors transcend risks; e.g., Warren Buffett, Benjamin Graham, Peter Lynch [61].Average investors advised by Fama [62] that they should invest in S&P 500.Deception: Deception uncovered led to downfall of Madoff [63], Eldrich Ames [64], and Enron [65].
Vulnerability uncovered in one’s own team, may be reduced by a merger; e.g., Google buys Wiz [59].Stalemate; e.g., prolonged Western front in WWI; 7-year DOE-NRC standoff over SRS HLW tanks 2005-11 [66].Vulnerability uncovered in a team by its opposition, leading to exploitation (e.g., cyber, in [67]; ransomware, in [68]).
Cognition: Magic [69]; illusion of unified reality [70]; successful deception in WW2 (e.g., Operation Bodyguard, in [67,71]).Frustration-Anger. Consensus-seeking slows progress (e.g., EU White paper [72]) and creates anger (DOE’s findings, in [66,73]).Deception not uncovered: Bombing of Pearl Harbor, 1941; ISIS attacked U.S. on 9/11; Hamas invaded Israel on 7 October 2023.
In the field: U.S. Army: Decision-making distributed to lowest member in chain of command, but the opposite occurs in China [74]China: To reduce the potential for corruption, decisions distributed by machine-driven guidance, becoming chain of command at lowest levels [74].Collapse of Hamas (e.g., Fabian, in [75]); significant Russian losses undercut Russia’s apparent strength of its military [76]
Evolution: Interdependence between technology and culture promotes competition [49], innovation [24], random choices [54], survival and evolution [77].Separables (e.g., LLMs) do not evolve autonomously; e.g., Von Neumann’s automata self-replicate [78], but do not evolve [46].Authoritarians block interdependence to control citizens, repress innovation, culture, need espionage to survive [51]; e.g., N. Korea [79]: “KIM’s authoritarian rule … expressed concerns with the regime’s economic failures and food problems.”
Table 2. Advant. interdep.: Country; HDI; GDP/N; CPI; GII; Freedom.
Table 2. Advant. interdep.: Country; HDI; GDP/N; CPI; GII; Freedom.
NumberCountryHDIGDP/capCPIGIIFreedom
1Israel0.9254.4k62157.4
2Iran0.785.3k24644.6
3Ukraine0.735.8k36605.1
4Russia0.8215.1k26595.9
5TaiwanNA34.9k67NA7.7
6China0.7913.9k42116.1
7S. Korea0.9337.7k6367.5
8N. KoreaNANA17NANA
9Costa Rico0.8118.7k55707.6
10Haiti0.552.4k17NA5.8
11USA0.9389.7k6938.1
12Cuba0.76NA42NANA
Table 3. Calculated advantages of interdependence from Table 2.
Table 3. Calculated advantages of interdependence from Table 2.
HDIGDP/capCPIGIIFreedom
Advant. R1-3-5-7 to R2-4-6-81.0822.322.091.651.25
Advant. R9-11 to R10-121.3322.582.1NA1.35
Global Ave. Advantage1.2122.452.10NA1.30
Table 4. The most innovative companies in the world by country.
Table 4. The most innovative companies in the world by country.
Free to Mostly Free CountriesMostly Unfree to Unfree Countries
Home-based firms8614
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Lawless, William. 2025. "The Symmetry of Interdependence in Human–AI Teams and the Limits of Classical Team Science" AppliedMath 5, no. 3: 114. https://doi.org/10.3390/appliedmath5030114

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Lawless, W. (2025). The Symmetry of Interdependence in Human–AI Teams and the Limits of Classical Team Science. AppliedMath, 5(3), 114. https://doi.org/10.3390/appliedmath5030114

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