Rodrick Wallace1
(1)
New York State Psychiatric Institute, New York, NY, USA
Summary
The stabilization of human cognition via feedback from embedding social and cultural contexts is a dynamic process deeply intertwined with it, constituting, in a sense, the riverbanks directing the flow of a stream of generalized consciousness at different scales: cultural norms and social interaction are synergistic with individual and group cognition and their disorders. A canonical failure mode in atomistic cultures is found to be a “ground state” collapse well-represented by atomistic models of economic interaction that are increasingly characterized as divorced from reality by heterodox economists. That is, high rates of psychopathic and antisocial personality disorder and obsessive-compulsive disorder emerge as culture-bound syndromes particular to Western or Westernizing societies, or to those undergoing social disintegration.
Culture is as much a part of human biology as the enamel on our teeth.
– Robert Boyd.
3.1 Introduction
Cognition and its regulation, we will argue, must be viewed as an interacting gestalt, involving not just an atomized individual, but the individual in a rich context that includes embedding social and cultural norms and path-dependent historical trajectory. There can be no cognition without regulation, just as there can be no heartbeat without the control of blood pressure, and no multicellularity without control of rogue cell cancers. Cognitive streams must be contained within regulatory riverbanks.
We implicitly extend the criticisms of Bennett and Hacker (2003) who examined the mereological fallacy of a decontextualization that attributes to “the brain” what is the province of the whole individual. Here, we argue that the “whole individual” incorporates embedding environmental and regulatory settings that, for humans, must include cultural heritage and social interaction.
More specifically, earlier work in this direction (Wallace 2014a,b) explored how information and control theories could be used to examine the stability of cognitive biological processes, in the sense of Maturana and Varela (1980). The failure of such processes is often expressed by the onset of behavioral pathologies and the chronic diseases of aging. Glazebrook and Wallace (2014) apply somewhat similar methods to autism spectrum disorders. Here, we look at certain characteristic mental dysfunctions more specifically in their social and cultural contexts, focusing on observational studies that contrast Western and East Asian populations.
The criteria for antisocial personality disorder (ASPD) in the Diagnostic and Statistical Manual of Mental Disorders (DSM III-R 1987, pp. 344–346)—a standard US medical nosology—lists a set of chronic disruptive, irresponsible, and antisocial behaviors, including lack of remorse and empathy, and similar matters. See Hare et al. (1991) for discussion. Kessler et al. (1994) found, for the USA, a prevalence of about 3.5% of ASPD. Subsequent studies a decade later found similar prevalence (Grant et al. 2004; Compton et al. 2005). By some contrast, Hwu et al. (1989), using DSM III instruments translated into Chinese, found in Taiwan, prevalences of 0.03, 0.07, and 0.14%, respectively, in a large study of village, small town, and Taipei settings. While the “free air of the city” perhaps attracts or enables those with behavioral patterns similar to ASPD, all rates are markedly lower than in the USA.
Similarly, Weissman et al. (1994) used DSM III criteria to quantify obsessive-compulsive disorder (OCD) across a number of international settings. While the lifetime rates for Western societies were found to be approximately 2.3%, in Taiwan, the observed rate was 0.7%. As they put the matter,
…[T]he lifetime…and…annual prevalence rates (cases per 100) of obsessive compulsive disorder in seven international communities were remarkably consistent (with the exception of Taiwan)…The prevalence rates for Taiwan were substantially lower than all of the other sites, paralleling Taiwan’s low published rates for all psychiatric disorders.
South Korea, in the aftermath of attempts at deculturation carried out during the Japanese occupation between 1910 and 1945, followed by the Korean War, was found to suffer an OCD rate of 1.9% in the study, still lower than the USA at 2.3%.
These observations suggest the necessity of some meditation on the differences between East Asian and Western modes of thinking. Such examination is badly needed: the cultural psychologist Heine (2001) argues that the extreme nature of American individualism suggests that a psychology based on the late twentieth century American research not only stands the risk of developing models that are particular to that culture, but also of developing an understanding of the self that is peculiar in the context of the world’s cultures.
In particular, Western atomistic thinking, which pervades a spectrum of disciplines ranging from economics and evolutionary theory to psychology and psychiatry, has deep cultural roots (Wallace 2015, Chap. 1).
Nisbett et al. (2001), following in a long line of research (Markus and Kitayama 1991; Heine 2001), review an extensive literature on empirical studies of basic cognitive differences between individuals raised in East Asian and Western cultural heritages, which they characterize, respectively, as “holistic” and “analytic.” They argue:
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Nisbett et al. (2001) conclude that tools of thought embody a culture’s intellectual history, that tools have theories built into them, and that users accept these theories, albeit unknowingly, when they use these tools.
Masuda and Nisbett (2006) find that research on perception and cognition suggests that whereas East Asians view the world holistically, attending to the entire field and relations among objects, Westerners view the world analytically, focusing on the attributes of salient objects. Compared to Americans, East Asians were more sensitive to contextual changes than to focal object changes. These results suggest that there can be cultural variation in what may seem to be basic perceptual processes.
Similarly, Nisbett and Miyamoto (2005) argue that fundamental perceptual processes are influenced by culture. These findings establish a dynamic relationship between the cultural context and perceptual processes. They suggest that perception can no longer be regarded as consisting of processes that are universal across all people at all times.
Wallace (2007) explores analogous dynamics involving inattentional blindness and culture.
A canonical example of how tools of thought embody a culture’s intellectual history can be found in mainstream Western economic theory.
3.2 Western Atomistic Economics
The inadequacy of conventional Western economic theorizing has become painfully obvious since the 2008 debacle. Lawson (2010) and Wallace (2015, Chap. 1) provide details and historical context . Important for our purposes is the central point of Lawson’s critique of atomistic mathematical models in economics—including, but not limited to, game theory. He identifies a basic mismatch between the sorts of mathematical methods economists employ and the nature of the social, including economic, phenomena that economists seek to illuminate. Their approach usually involves maximization of a simple “utility function” over a distribution of possible strategies. Most fundamentally, economists’ methods can be seen to be restricted to closed systems where such maximization can be carried out using standard mathematical techniques. To date, such closures have been found to occur only very rarely in the social realm and we have good reason to suppose they will remain uncommon. In addition, as many heterodox economic theories emphasize, real human dynamics are almost never restricted to atomistic interactions (Lawson 2010; Wallace 2015).
Here, however—and contrarily—we will argue that the symptom spectra of certain psychopathologies may actually characterize such a closed system, one in which the individual (or group) is inherently, or becomes under dynamics of social disintegration, divorced from social or cultural embedding, and engages in a strongly self-referential cognitive dynamic that is most pronounced among atomistic, culturally Western, populations. Different “economic” models may then apply to different characteristic patterns of cognitive dysfunction.
Some development is required.
Cohen (1987) describes control and game theory as follows:
[H]euristically…the major problem of control theory is to find the maximum of some performance criterion (or criteria), given a set of constraints. …When the objective function is single valued…then one is dealing with optimal control theory. When more than one objective is involved, and the objectives are generally incompatible, then one is dealing with game theory.
The prisoners’ dilemma, a classic game theory paradox and a singular example of Lawson’s criticisms, is worth special comment. Two prisoners, who engaged jointly in a major crime, have been taken in custody for a relatively minor offense, and are confronted separately and individually by a district attorney. If neither confesses to the major crime, both will serve a short sentence for the minor crime. If both confess, each will receive a longer sentence. If one confesses, and the other does not, the “defector” will be released and the other will serve a very long sentence in prison. Von Neumann game theory predicts—the Nash equilibrium for a one-time game implies—that each will betray the other (Watson 2013).
Field (2014), with a relentless and scathing deconstruction, describes the application of game theory to Cold War nuclear strategy in these terms:
In the Prisoner’s Dilemma played once, for example, the Nash prediction is unambiguous: no cooperation. Defection is the strictly dominant strategy. Experiment…however, provides abundant evidence of positive rates of cooperation. Similar “anomalies” are found in voluntary contribution to public goods games (which are multi person Prisoner’s Dilemmas), where one sees positive contribution levels, in the trust game, where one sees positive transfers in both directions, and in many other instances.
Game theory has faced similar predictive failures in its treatment of behavior in the real world. As John von Neumann argued [and, parenthetically, strongly advocated]…its canonical behavioral assumptions predicted devastating conflict between nuclear adversaries…This has not happened…
Field asserts quite forcefully that, because of the disjunction between human behavior and the self-regarding assumptions often used in formal game theory, the latter offers little guidance, normatively or predictively, in thinking about behavior or strategy in a world of potential conflict.
Again, and by contrast, we argue that the behaviorally depauperate dynamics of formal game theory and other closed system mainstream atomistic economic models may actually provide useful characterizations of several Western culture-bound syndromes defined by symptom clusters, including obsessive-compulsive disorder (OCD) and psychopathic and antisocial personality disorders. The latter appear to represent two ends in a spectrum of “natural” and “socially induced” pathology that may generalize to group phenomena in the context of cultural and social collapse.
While the use of game theory to examine psychopathy is far from original (Mokros et al. 2008; Amsel 2007), our route to a more comprehensive formalism is novel. We find game theory and analogous “economic” behaviors can represent forms of relatively simplistic behavioral “ground states” that follow from the developmentally punctuated collapse of essential regulatory systems, both internal and contextual. Ours is, however, most centrally, a “cultural” perspective consistent with the work of Arthur Kleinman and others (Kleinman 1991).
Below, we pursue a minimal line of formal argument for a dauntingly complicated set of nested dynamical structures. Although expressed in only four equations, the embedding mathematical tools are far from elementary.
We begin with an information theory formulation of cognition.
3.3 Cognition as an Information Source
Natural cognitive systems operate at all scales and levels of organization of biological process (Wallace 2012, 2014a). The failure of low level biological cognition in humans is often expressed through early onset of the intractable chronic diseases of senescence (Wallace and Wallace 2010, 2013). Failure of high-order cognition in humans has been the subject of intensive scientific study for over 200 years, with little if any consensus: medical professionals realize that psychological illnesses occur, but they disagree profoundly about their cause and pathology (Johnson-Laird et al. 2006).
This may be something an understatement.
Atmanspacher (2006) argues that theories of high-level cognition are at a point like that of physics 400 years ago, with the basic entities and the relations between them yet to be determined. Further complications arise via the overwhelming influence of culture on both mental process and its dysfunction (e.g., Heine 2001; Kleinman and Cohen 1997).
The stabilization and regulation of high-order cognition for individuals and groups may thus be as complex as such cognition itself.
Some simplification, however, is possible. Cognition can be described in terms of a sophisticated real-time feedback between interior and exterior, necessarily constrained, as Dretske (1994) has noted, by certain asymptotic limit theorems of probability:
Unless there is a statistically reliable channel of communication between [a source and a receiver]…no signal can carry semantic information…[thus] the channel over which the [semantic] signal arrives [must satisfy] the appropriate statistical constraints of information theory.
The first step in our analysis is a recapitulation of an approach to cognition using the asymptotic limit theorems of information theory (Wallace 2000, 2005a,b, 2007, 2012, 2014a,b).
Atlan and Cohen (1998) argue that the essence of cognition involves comparison of a perceived signal with an internal, learned or inherited picture of the world, and then choice of one response from a much larger repertoire of possible responses. That is, cognitive pattern recognition-and-response proceeds by an algorithmic combination of an incoming external sensory signal with an internal ongoing activity—incorporating the internalized picture of the world—and triggering an appropriate action based on a decision that the pattern of sensory activity requires a response.
Incoming sensory input is thus mixed in an unspecified but systematic manner with internal ongoing activity to create a path of combined signals x = (a 0, a1, …, a n , …). Each a k thus represents some functional composition of the internal and the external. An application of this perspective to a standard neural network is given in Wallace (2005a, p. 34).
This path is fed into a similarly unspecified decision function, h, generating an output h(x) that is an element of one of two disjoint sets B0 and B1 of possible system responses. Let
Assume a graded response, supposing that if
the pattern is not recognized, and if
the pattern is recognized, and some action bj , k + 1 ≤ j ≤ m takes place.
Interest focuses on paths x triggering pattern recognition-and-response: given a fixed initial state a0, examine all possible subsequent paths x beginning with a0 and leading to the event h(x) ∈ B 1. Thus h(a0, …, a j ) ∈ B 0 for all 0 ≤ j < m, but h(a0, …, a m ) ∈ B 1.
For each positive integer n, take N(n) as the number of high probability paths of length n that begin with some particular a0 and lead to the condition h(x) ∈ B 1. Call such paths “meaningful,” assuming that N(n) will be considerably less than the number of all possible paths of length n leading from a0 to the condition h(x) ∈ B 1.
The essence of the Shannon–McMillan Theorem that we will invoke below is that the set of low probability paths has, in fact, vanishingly low probability. We will return to this.
Identification of the “alphabet” of the states aj , B k may depend on the proper system coarse-graining in the sense of symbolic dynamics (Beck and Schlogl 1995). That is, the larger pattern of behavioral dynamics is projected down onto a simpler, but characteristic, “alphabet” whose combinations and permutations form patterns of “words” and “statements” in a kind of behavioral language “spoken” by the system of interest.
Combining algorithm—i.e., the exact form of the function h—and the details of grammar and syntax are all unspecified in this model. The assumption permitting inference on necessary conditions constrained by the asymptotic limit theorems of information theory is that the finite limit
![$$\displaystyle{ H \equiv \lim _{n\rightarrow \infty }\frac{\log [N(n)]} {n} }$$](computational-psychiatry.files/image142.png)
(3.1)
both exists and is independent of the path x. Again, N(n) is the number of high probability paths of length n, with low probability paths forming a set of vanishingly small probability.
Call such a pattern recognition-and-response cognitive process ergodic. Not all cognitive processes are likely to be ergodic, implying that H, if it indeed exists at all, is path dependent, although extension to nearly ergodic processes, in a certain sense, seems possible (Wallace 2005a, pp. 31–32).
Invoking the Shannon–McMillan Theorem (Cover and Thomas 2006; Khinchin 1957), we define an adiabatically, piecewise stationary, ergodic information source X associated with stochastic variates Xjhaving joint and conditional probabilities P(a0, …, a n ) and P(an | a 0, …, an−1) such that appropriate joint and conditional Shannon uncertainties satisfy the classic relations
![$$\displaystyle\begin{array}{rcl} H[\mathbf{X}]& =& \lim _{n\rightarrow \infty }\frac{\log [N(n)]} {n} \\ & =& \lim _{n\rightarrow \infty }H(X_{n}\vert X_{0},\ldots,X_{n-1}) \\ & =& \lim _{n\rightarrow \infty }\frac{H(X_{0},\ldots,X_{n})} {n} {}\end{array}$$](computational-psychiatry.files/image143.png)
(3.2)
This information source is defined as dual to the underlying ergodic cognitive process, in the mathematical sense of Wallace (2005a, 2007, 2012).
Again, following Khinchin (1957), the real value of this theorem is that it shows how paths can be divided into just two sets. The first, of high probability, is consistent with inherent patterns of “grammar” and “syntax” (in a large sense) that characterize the information source. The second set, of vanishingly small probability, violates those rules.
“Adiabatic” means that, when the information source is properly parameterized, within continuous “pieces,” changes in parameter values take place slowly enough so that the information source remains as close to stationary and ergodic as needed to make the fundamental limit theorems work. “Stationary” means that probabilities do not change in time, and “ergodic” that cross-sectional means converge to long-time averages. Between pieces it is necessary to invoke phase change formalism, a “biological” renormalization that generalizes Wilson’s (1971) approach to physical phase transition (Wallace 2005a).
Shannon uncertainties H(…) are cross-sectional law-of-large-numbers sums of the form − ∑k P k log[P k ], where the Pk constitute a probability distribution (Cover and Thomas 2006).
For cognitive systems, an equivalence class algebra can be constructed by choosing different origin points a0, and defining the equivalence of two states am , a n by the existence of high probability meaningful paths connecting them to the same origin point. Disjoint partition by equivalence class, analogous to orbit equivalence classes for a dynamical system, defines the vertices of a network of cognitive dual languages that interact to actually constitute the system of interest. Each vertex then represents a different information source dual to a cognitive process. This is not a representation of a network of interacting physical systems as such, in the sense of network systems biology (Arrell and Terzic 2010). It is an abstract set of languages dual to the set of cognitive processes of interest, that may become linked into higher order structures.
Topology, however, has long been an object of algebraic study, the so-called algebraic topology , via the fundamental underlying symmetries of geometric spaces. Rotations, mirror transformations, simple (“affine”) displacements, and the like uniquely characterize topological spaces, and the networks inherent to cognitive phenomena having dual information sources also have complex underlying symmetries: characterization via equivalence classes defines a groupoid, an extension of the idea of a symmetry group, as summarized by Brown (1987) and Weinstein (1996). Linkages across this set of languages occur via the groupoid generalization of Landau’s spontaneous symmetry breaking arguments that will be used below (Landau and Lifshitz 2007; Pettini 2007). See the Mathematical Appendix for a brief summary of basic material on groupoids.
Recognize, however, that we are not constrained in this approach to the Atlan–Cohen model of cognition that, through the comparison with an internal picture of the world, invokes representation. The essential inference is that a broad class of cognitive phenomena—with and without representation—can be associated with a dual information source. That is, cognition inevitably involves choice, choice reduces uncertainty, and reduction of uncertainty implies the existence of an information source whose dynamics are constrained by the asymptotic limit theorems of information theory.
3.4 Environment as an Information Source
Multifactorial cognitive and behavioral systems interact with, affect, and are affected by embedding environments—including culture and social relations—that “remember” interaction by various mechanisms. It is possible to reexpress environmental dynamics in terms of a grammar and syntax that represent the output of an information source—another generalized language.
Some simple examples:
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Suppose it possible to coarse-grain the (continuously represented) generalized “ecosystem” at time t, in the sense of symbolic dynamics (e.g., Beck and Schlogl 1995) according to some appropriate finite (or at least countable) partition of the phase space in which each division Aj represent a particular range of numbers of each possible fundamental actor in the generalized ecosystem, along with associated larger system parameters. Of central interest is the set of longitudinal paths—system statements, in a sense—of the form x(n) = A 0, A1, …, A n defined in terms of some natural time unit of the system. Thus ncorresponds to an again appropriate characteristic time unit T, so that t = T, 2T, …, nT.
Let N(n) be the number of possible paths of length n that are consistent with the underlying grammar and syntax of the appropriately coarse-grained embedding ecosystem, in a large sense. As above, the fundamental assumptions are that—for this chosen coarse-graining—N(n), the number of possible grammatical paths, is much smaller than the total number of paths possible, and that, in the limit of (relatively) large n, H = lim n → ∞ log[N(n)]∕n both exists and is independent of path.
These considerations represent a parallel with parametric statistics. Systems for which the simplifying assumptions are not true will require specialized approaches.
Nonetheless, not all possible ecosystem coarse-grainings—divisions of a continuous system into a finite alphabet-like structure—are likely to work, and different such divisions, even when appropriate, might well lead to different descriptive quasi-languages for the ecosystem of interest. Thus, empirical identification of relevant coarse-grainings for which this theory will work may represent a difficult scientific problem.
Given an appropriately chosen coarse-graining, define joint and conditional probabilities for different ecosystem paths, having the form P(A0, A 1, …, An ), P(A n | A0, …, A n−1), such that appropriate joint and conditional Shannon uncertainties can be defined on them that satisfy Eq. (3.2).
Taking the definitions of Shannon uncertainties as above, and arguing backwards from the latter two parts of Eq. (3.2), it is indeed possible to recover the first, and divide the set of all possible ecosystem temporal paths into two subsets, one very small, containing the grammatically correct, and hence highly probable paths, that we will call “meaningful,” and a much larger set of vanishingly low probability.
Learned culture (and its associated patterns of social interaction) contextually constrain possible behaviors, spoken language, body postures, and many other phenotypes. That is, different cultures impose different probability structures on essential matters of living and of the life course trajectory. Even sleep is widely discordant across cultural boundaries. Birth, marriage, death, social conflict, economic exchange, and so on are all strongly patterned by culture, in the context of historical trajectory and social segmentation. Some discussion of these matters in the context of mental disorder can be found in Kleinman and Good (1985), Desjarlais et al. (1995), and the references therein. Boyd and Richerson (2005) provide a more comprehensive introduction.
More generally, as Durham (1991) argues, genes and culture are two distinct but interacting systems of heritage in human populations. Information of both kinds has potential or actual influence over behaviors, creating a real and unambiguous symmetry between genes and phenotypes on the one hand, and culture and phenotypes on the other. Genes and culture are best represented as two parallel tracks of hereditary influence on phenotypes, acting, of course, on markedly different timescales. Human species’ identity rests, in no small part, on its unique evolved capabilities for social mediation and cultural transmission, creating, again, high and low probability sets of real-time behavioral sequences.
3.5 Interacting Information Sources
Given a set of information sources that are linked to solve a problem, in the sense of Wilson and Golonka (2013), the “no free lunch” theorem (English 1996; Wolpert and MacReady 1995, 1997) extends a network-based theory (e.g., Arrell and Terzic 2010). Wolpert and Macready show there exists no generally superior computational function optimizer. That is, there is no “free lunch” in the sense that an optimizer pays for superior performance on some functions with inferior performance on others. Gains and losses balance precisely, and all optimizers have identical average performance. In sum, an optimizer has to pay for its superiority on one subset of functions with inferiority on the complementary subset.
This result is known using another description. Shannon (1959) recognized a powerful symmetry between the properties of an information source with a distortion measure and those of a channel. This symmetry is enhanced if we consider channels in which there is a cost associated with the different letters. Solving this problem corresponds to finding a source that is right for the channel and the desired cost. Evaluating the Rate Distortion Function for a source corresponds to finding a channel that is just right for the source and allowed distortion level.
Yet another approach to the same result is through the “Tuning Theorem” of the Mathematical Appendix, which inverts the Shannon Coding Theorem by noting that, formally, one can view the channel as “transmitted” by the signal. Then another kind of “channel capacity” can be defined in terms of the channel probability distribution that maximizes information transmission assuming a fixed message probability distribution.
From the no free lunch argument, Shannon’s insight, or the “tuning theorem,” it becomes clear that different challenges facing any cognitive system, distributed collection of them, or interacting set of other information sources, that constitute an organism or automaton, must be met by different arrangements of cooperating modules represented as information sources.
It is possible to make a very abstract picture of this phenomenon based on the network of linkages between the information sources dual to the individual “unconscious” cognitive modules (UCM), and those of related information sources with which they interact. That is, a shifting, task-mapped, network of information sources is continually reexpressed: given two distinct problems classes confronting the organism or automaton, there must be two different wirings of the information sources, including those dual to the available UCM, with the network graph edges measured by the amount of information crosstalk between sets of nodes representing the different sources.
Thus “embodied” systems, in the sense of Wilson and Golonka (2013), involve interaction between very general sets of information sources assembled into a “task-specific device” in the sense of Bingham (1988) that is necessarily highly tunable. This mechanism represents a broad evolutionary generalization of the “shifting spotlight” characterizing the global neuronal workspace model of consciousness described in Chap. 1.
3.6 Crosstalk Topologies
A mutual information measure of the inevitable crosstalk between information channels—a kind of energy leakage—is not inherently fixed, but can continuously vary in magnitude. This suggests a parameterized renormalization: the modular network structure linked by crosstalk has a topology depending on the degree of interaction of interest.
Define an interaction parameter ω, a real positive number, and look at geometric structures in the network of interacting cognitive and other information sources defined in terms of linkages set to zero if mutual information is less than, and “renormalized” to unity if greater than, ω. A given ω will define a topologically dependent regime of “giant components” of network elements linked by mutual information greater than or equal to it. See Sect. 1.5 above for details. The emergence of the giant component is well known for random networks.
Now invert the argument: a given topology for the giant component will, in turn, define some critical value, ωC , so that network elements interacting by mutual information less than that value will be unable to participate, i.e., will be locked out and not be consciously or otherwise perceived. Thus ω is a tunable, syntactically dependent, detection limit that depends critically on the instantaneous topology of the giant component of linked information sources defining the analog to a global broadcast of consciousness.
That topology is the basic tunable syntactic filter across the underlying modular structure, and variation in ω is the only one aspect of more general topological properties that can be described in terms of index theorems , where far more general analytic constraints can become closely linked to the topological structure and dynamics of underlying networks, and, in fact, can stand in place of them (Atiyah and Singer 1963; Hazewinkel 2002). See Sect. 1.6above for details.
3.7 Punctuated Critical Phenomena
A homology between the information source uncertainty dual to a cognitive process and the free energy density of a physical system arises, in part, from the formal similarity between their definitions in the asymptotic limit. Information source uncertainty can be defined as in the first part of Eq. (3.2). This is quite analogous to the free energy density of a physical system in terms of the thermodynamic limit of infinite volume (Wilson 1971; Wallace 2005a, 2012). Feynman (2000) provides a series of physical examples, based on Bennett’s (1988) work, where this homology is an identity, at least for very simple systems. Bennett argues, in terms of idealized irreducibly elementary computing machines, that the information contained in a message can be viewed as the work saved by not needing to recompute what has been transmitted.
It is possible to model a cognitive system interacting with an embedding environment using an extension of the language-of-cognition approach above. Recall that cognitive processes can be formally associated with information sources, and how a formal equivalence class algebra can be constructed for a complicated cognitive system by choosing different origin points in a particular abstract “space” and defining the equivalence of two states by the existence of a high probability meaningful path connecting each of them to some defined origin point within that space.
Recall that disjoint partition by equivalence class is analogous to orbit equivalence relations for dynamical systems, and defines the vertices of a network of cognitive dual languages available to the system: each vertex represents a different information source dual to a cognitive process. The structure creates a large groupoid, with each orbit corresponding to a transitive groupoid whose disjoint union is the full groupoid, and each subgroupoid associated with its own dual information source. Larger groupoids will, in general, have “richer” dual information sources than smaller.
We can now begin to examine the relation between system cognition and the feedback of information from the rapidly changing real-time (as opposed to a slow-time cultural or other) environment, having source uncertainty 
.
With each subgroupoid Gi of the (large) cognitive groupoid we can associate a joint information source uncertainty 
, where X is the dual information source of the cognitive phenomenon of interest, and Y that of the embedding human context—largely defined in terms of culture, embedding social structure, and path-dependent historical trajectory. Y is seen as having much slower dynamics that the immediate “environmental” system defining .
Real-time dynamic responses of a cognitive system can now be represented by high probability paths connecting “initial” multivariate states to “final” configurations, across a great variety of beginning and end points. This creates a similar variety of groupoid classifications and associated dual cognitive processes in which the equivalence of two states is defined by linkages to the same beginning and end states. Thus, we will show, it becomes possible to construct a “groupoid free energy” driven by the quality of rapidly changing, real-time information coming from the embedding ecosystem, represented by the information rate , taken as a temperature analog.
For humans in particular, is a driver for the underlying cognitive processes of interest, here the tunable, shifting, global broadcasts of consciousness as embedded in culture and social relations. The argument-by-abduction from physical theory is, then, that constitutes a kind of thermal bath for the processes of culturally channeled cognition. Thus we can, in analogy with the standard approach from statistical physics (Pettini 2007; Landau and Lifshitz 2007), construct a Morse Function by writing a pseudoprobability for the jointly defined information sources 
having source uncertainty 
as
![$$\displaystyle{ P[H_{G_{i}}] = \frac{\exp [-H_{G_{i}}/\kappa \mathcal{H})]} {\sum _{j}\exp [-H_{G_{j}}/\kappa \mathcal{H}]} }$$](computational-psychiatry.files/image148.png)
(3.3)
where κ is an appropriate dimensionless constant characteristic of the particular system and its linkages to embedding control signals. The sum is over all possible subgroupiods of the largest available symmetry groupoid. Again, compound sources, formed by the (tunable, shifting) union of underlying transitive groupoids, being more complex, will have higher free-energy-density equivalents than those of the base transitive groupoids.
Landau’s and Pettini’s insights regarding phase transitions in physical systems were that certain critical phenomena take place in the context of a significant alteration in symmetry, with one phase being far more symmetric than the other (Landau and Lifshitz 2007; Pettini 2007). A symmetry is lost in the transition—spontaneous symmetry breaking. The greatest possible set of symmetries in a physical system is that of the Hamiltonian describing its energy states. Usually states accessible at lower temperatures will lack the symmetries available at higher temperatures, so that the lower temperature phase is less symmetric: The randomization of higher temperatures ensures that higher symmetry/energy states will then be accessible to the system. The shift between symmetries is highly punctuated in the temperature index.
A possible Morse Function for invocation of Pettini’s topological hypothesis or Landau’s spontaneous symmetry breaking is then a “groupoid free energy” F defined by
![$$\displaystyle{ \exp [-F/\kappa \mathcal{H}] \equiv \sum _{j}\exp [-H_{G_{j}}/\kappa \mathcal{H}] }$$](computational-psychiatry.files/image149.png)
(3.4)
Then, using the free energy-analog F, we apply Landau’s spontaneous symmetry breaking arguments, and Pettini’s topological hypothesis, to the groupoid associated with the set of dual information sources.
Many other Morse Functions might be constructed here, for example, based on representations of the cognitive groupoid(s). The resulting qualitative pictures would be similar. See the Mathematical Appendix for a summary of results from Morse Theory.
The essential point is that decline in the richness of real-time social and cultural environmental feedback , or in the ability of that feedback to influence response, as indexed by κ, can lead to punctuated decline in the complexity of cognitive process within the entity of interest, according to this model.
This permits a Landau-analog phase transition analysis in which the quality of incoming information from the embedding ecosystem—feedback—serves to raise or lower the possible richness of an organism’s cognitive response to patterns of challenge. If 
is relatively large—a rich and varied real-time environment, as perceived by the organism—then there are many possible cognitive responses. If, however, noise or simple constraint limit the magnitude of 
, then behavior collapses in a highly punctuated manner to a kind of ground state in which only limited responses are possible, represented by a pathologically simplified cognitive groupoid structure.
3.8 Discussion and Conclusions
We have used a Morse-theoretic extension of results from information theory to explore the dynamics of cognition and its inherently necessary regulation that involves synergistic interpenetration among nested sets of actors, represented here as information sources. These may include dual sources to internal cognitive modules, environmental information, language, culture, social network, socioeconomic affordances and limitations, and so on.
Two factors determine the possible range of real-time cognitive response in the model. These are the magnitude of the environmental feedback control signal and the inherent structural richness of the underlying cognitive groupoid. If that richness is lacking—if the available topologies of internal ω-driven connections is limited—then even very high levels of 
may not be adequate to activate appropriate behavioral responses to important regulatory feedback signals. Glazebrook and Wallace (2014), in fact, examine autism spectrum disorders from this viewpoint.
Here, we are particularly interested in a “ground state collapse” in which cultural and social restraints fail to stabilize individual (and perhaps group) behaviors. A key observation, we contend, is the marked difference in observed prevalence of obsessive-compulsive disorder and antisocial personality disorder(s) among “East Asian” Taiwanese and “Western” populations.
Using the theoretical framework above, psychopathic behaviors would be viewed as intrinsic to culturally modulated brain development, represented by failures in the topological ω-mechanisms. Acquired antisocial personality disorder would then stem from imposed psychosocial stresses during the life course, weakening in the phase transition model.
The resulting ground state pathologies seem described by surprisingly uncomplicated behaviors arising from simplistic self-interest calculations that apparently follow something much like von Neumann’s game theory model of a Cold War preemptive thermonuclear exchange, or the calculations of a mainstream economist who analyzes criminal behavior (Becker 1968; Wallace and Fullilove 2014). Amsel’s (2007) work indicates that OCD behaviors may involve analogous, but more subtle, regulatory collapse leading again to simplistic closed-system “cost” analysis. High rates of such pathologies are to be viewed, taking Kleinman’s (1991) perspective, as culture-bound syndromes peculiar to, or at least significantly enhanced in, atomistic Western or Westernizing societies, or, in the case of Korea, communities exposed to severe colonial depredation and war.
The underlying cultural dynamics have been the subject of much past commentary. Maxim Gorky (1972), in his classic City of the Yellow Devil describing New York City, writes:
The youth leaning against the lamppost shakes his head from time to time. His hungry teeth are tightly clenched. I believe I understand what he is thinking of, what he wants…to possess enormous hands of frightful strength and wings on his back, that is what he wants, I believe. So that, soaring 1 day over the city, he may reach down with hands like steel levers and reduce the whole to a heap of rubbish and ashes, mixing bricks and pearls, gold and the flesh of slaves, glass and millionaires, dirt, idiots, temples, the dirt-poisoned trees, and these foolish multi-storeyed skyscrapers, everything, the whole city into one heap, into a dough compounded of dirt and the blood of people—into a loathsome chaos. This frightful wish is as natural in this youth’s brain as a sore on the body of a sick man. Where there is much work for slaves, there can be no place for free, creative thought, and only the ideas of destruction, the poisonous flowers of vengeance, the turbulent protest of the brute beast can flourish. This is understandable—if you warp a man’s soul you must not expect mercy from him.
The French-trained psychiatrist Frantz Fanon (1966), describing the impact of Western colonialism , characterized the underlying mechanism as follows:
The colonized man will first manifest this aggressiveness which has been deposited in his bones against his own people. This is the period when the niggers beat each other up, and the police and magistrates do not know which way to turn when faced with the astonishing waves of crime…
Effective untangling of such developmental knots will require more than interventions at the individual level. Necessary as they may be, they are never sufficient.
In closing, it could be conjectured that the perspective expressed in the chapter title, “Western atomism and its culture-bound syndromes,” might generalize across cultures, perhaps in the direction of “East Asian collectivism and its culture-bound syndromes,” a matter for further study.
Acknowledgements
The author thanks Dr. D.N. Wallace for fruitful discussions and two reviewers for comments useful in revision.
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