Modeling Quasi-Quantum Social Processes

David L. Sallach
University of Chicago
Argonne National Laboratory

Abstract

Since their development in the early part of the twentieth century, quantum models have proven to be productive in a variety of domains.  After revolutionizing microphysics (Baumann 2005), quantum formalisms have made significant contributions in the areas of chemistry (Szabo & Ostlund 1996), computer science (Deutsch 1985; Nielsen & Chuang 2000), information theory (Deutsch & Hayden 2000; Green 2000; Nielsen & Chuang 2000) and information retrieval (Gabora & Aerts 2002; Van Rijsbergen 2004).  Exploratory work is being conducted in areas such as biology (McFadden 2000), neurology (Hameroff & Penrose 1996; Hagan, Hameroff, & Tuszynski 2002), game theory (Arfi 2005; Chen, Hogg & Huberman 2007) and the social sciences (Arfi 2005; Wendt 2006).  The focus of the present discussion is the potential applicability of quantum models in the realm of theoretical sociology.

Within the social sciences, several quantum concepts appear to be directly applicable, especially superposition (of intentionality) and (social) entanglement (cf., Arfi 2005).  A second point is that social theory can benefit from insights from quantum cosmology (Bell 1981; Gell-Mann & Hartle 1990; Deutsch 2005).  Like cosmology, the social sciences are unable to explore quantum effects at the micro-experimental level.  Rather, they must investigate macro quantum effects that can be analyzed in terms of symmetries and transformations (Gilligan & Roos 2008).  As cosmologists have identified the 'quasi-classical' domain as emergent from a thoroughly quantum universe, social scientists may posit and explore a quasi-quantum (QQ) social domain.  Finally, the emerging focus upon consistent quantum histories (Omnes 1999; Griffiths 2002) appears to provide a useful structural and analytical counterpart to social histories of various types.

Cross-fertilization of the physical, mathematical and social sciences can occur in one of four ways:  analogy, reduction, formality and convergence.  The first is suggestive but lacks rigor.  The second has been scientifically productive, but becomes less tractable as complexity grows.  The third, which focuses upon the cross-domain applicability of generic mechanisms, lacks a substantial basis, including an explanation of why a specific set of formalisms should be so broadly applicable.  The final approach, drawn from transdisciplines like general systems and complexity theory, searches for forms of macrointeraction.  While we may speculate on which approach is likely to be more productive, it is more likely that they form one scientific project, each able to strengthen and supplement the other.

The link between the first and third (analogy and formality) may be of greatest interest for a QQ social domain.  More specifically, if analogical components are mapped to the quantum formalism, it will give expression to the former and substance to the latter.  Of course, such a translation is unlikely to be simple and obvious, but it provides a process through which applicable concepts can be applied and aligned.  Consider, for example, the potential mapping summarized in Table 1:

({{Structure, Quantum, Social, Shared Characteristics}, {Unit, Quantum, Lifeform, Discrete form}, {Force, Energy, Emotion, Source of dynamics}, {Superposition, Physical, Intentional, Possibilistic}, {Entanglement, Cross/scale quantum effects, Diversity of forms, Coevolution through interaction}, {Diffusion, Experimental histories, Social and cultural histories, Chains of divergence and convergence}, {Perspective, Basis, Orientation, Focal interest}})

Table 1.  A Structure Mapping from the Quantum to the Social Domain

The present paper will explore details of how this structure mapping can provide the foundation for a QQ social theory.  This can then be further extended using the consistent history framework (Omnes 1999; Griffiths 2002).

This cross-domain intellectual fertilization would be more difficult to accomplish without powerful tools like Mathematica to define and reframe the underlying mathematics, and visualize the results.  Linear algebraic functions such as Transpose[], ConjugateTranspose[] and KroneckerProduct[] allow quantum concepts to be applied to a new domain in a straight-forward way.  Ultimately, all such theoretical innovations will be assessed in terms of their ability to bring deeper insight to the social domain.

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