Counterfactual Imaginative Culture as Evidence Hallucination in Support of Entropy Reduction

1. Introduction

Human beings are unique in their exposure to counterfactual realities. That is, to representations of objects and states of affairs that are acknowledged not to exist, which cannot be proven to exist, or which exist only by way of social convention [1,2]. These include religion, literature, art, popular culture, mythology, ideology, and other forms of symbolic or material fabulation that, to greater or lesser degrees, innovate on or compete with what is known to be the case. Moreover, this is not a minor phenomenon: One estimate suggests that the average Briton spends 6% of their waking life immersed in counterfactual realities [3], and this figure is likely to generalize cross-culturally. The question that emerges is why this should be the case. Unlike practical culture, for which there is an obvious payoff [4,5], counterfactual cultural elaborations are—at least on the surface—wasteful of cognitive resources like attention and memory, and are often complicit in reproducing illusory folk beliefs about the nature of reality and where humans feature in it [6,7]. How do we explain this puzzle?

This study accounts for the existence of counterfactual cultural elaboration as a form of evidence hallucination, where explanatory models of the world are made to be `true’ by flooding the perceptual environment with evidence that their predictions are correct. The core claim is that the incentive to do this comes from the desire to reduce anxiety. As a concomitant of chronic stress that is actuated by unpredictability in the environment anxiety is future pointing: not knowing what will happen next feels unpleasant. From this, it follows that anxiety avoidance will take the form of uncertainty reduction––typically, by constructing predictive models of the environment. Necessarily, if these models are to bring about anxiety reduction then their predictions must be accurate. In scientific modes of inquiry this is secured by hypothesis testing against independent data. But the human capacity for counterfactual thinking offers a more efficient shortcut: If I can saturate the environment with low-cost, perceptually salient simulations of evidence, then I gain the benefits of anxiety reduction without the extra work of hypothesis testing. Thus, counterfactual cultural elaboration can be explained as the attempt to reduce anxiety by performing `cheap’ work on the environment that makes it conform with model predictions. Given that hallucinated evidence is typically not veridical, the ultimate failure of most predictive models means there is a persistent stimulus to produce either new evidence or new cultural and cognitive models—and hence the generative nature of counterfactual fabulation.

This hypothesis draws on several lines of theoretical and empirical inquiry. Firstly, foundational work in thermodynamics and information theory demonstrates the convertibility between information and work [8,9], which gives an in-principle viability to the idea that there can be trade-offs between model construction and environmental manipulation. In particular, the Landauer limit gives the minimum possible amount of energy required to erase one bit of information, where E is the energy, $k_B$ is the Boltzmann constant, and T is the temperature of the system in Kelvins [Equation  (1)].

$$E\ge k_{B}Tln2$$

(1)

Because every model of the world is a representation that involves a deletion of some aspect of the world that is noisy with respect to the model, the principle here is that simplification requires work. Physical intuition for this idea is typically provided by thought experiments like Maxwell’s demon [10]. Specifically, the eponymous demon uses their omniscient knowledge of the velocities and positions of gas molecules in a box to open and close a partition between the two halves of the box. By selectively letting only high velocity particles into one partition, the demon creates an energy gradient and thereby converts information into work. But one can just as easily come from the other direction and see that work that compresses physical particles of any specific type into a smaller volume increases the predictability of a system, and thus work can also be converted into information. Whilst these abstract considerations may seem a far remove from cultural processes that operate at orders of magnitude above the Landauer limit, they have already been used speculatively to formulate potential solutions to the Fermi paradox by predicting the behaviour of more technologically advanced civilizations (the `aestivation’ hypothesis [11]). From the more mundane perspective of the present study, their value lies in showing that cultural modeling and environmental manipulation are linked by deep thermodynamic principles that do not require an especially rich account of human cognition.

The account of cognition that is required is provided by active inference models that identify surprise minimization as the principle guiding the interactions of an agent with its environment [12,13,14,15,16]. That is, the agent acts so as to not find itself in sensory states that lie outside the expected values of the sensory states that evolution has encoded into its cognitive and somatic architecture. For instance, the fact that I have lungs rather than gills means that I will act so as to not to surprise my respiratory system by spending long periods of of time underwater. In general, this is done by generating on-the-fly predictions about the sensory data I should be receiving and gauging these against the sensory data that I am receiving. Where these diverge, I act so as to decrease this divergence, which has an upper bound in the negative log probability of my sensory state. This approach is evolutionarily useful because it reduces the computationally intractable task of modeling the entire environment to the estimation of those environmental states that are relevant to the agent. Once again, the value of active inference approaches here lies in their cognitively `thin’ nature, which allows them to be applied to natural and cultural phenomena, ranging from collective behaviours in animals [17] to narrative cognition in humans [18,19].

Anxiety enters the picture by way of `dark room’ objections to active inference models [20]. Specifically, if the object is to act so as to minimize surprise, then the easiest solution is to seek out environments that are highly predictable (the dark room). As this does not capture the totality of any agent’s behavior, there is clearly a need for prediction to be guided by a flexible cognitive orientation that conditions predictions on what is known about specific environments and calibrates actions accordingly. The literature converges on anxiety—in both its clinical and non-clinical manifestations—as a cross-species, negatively valenced aversive response to uncertainty in the environment in this way [21,22,23]. Usefully, this can be connected with the active inference and thermodynamic frameworks described above by way of Shannon entropy, H(hereafter, just entropy) [24,25,26] [Equation  (2)]

$$H\left(X\right)=-\sum _{i=1}^{n}P\left(x_i\right)logP\left(x_i\right)$$

(2)

To the extent that entropy represents the expected value of surprise across all the states $x_i$ of a system, increases in anxiety should track increases in entropy. Equivalently, any predictive model will reduce anxiety by reducing surprise. Qualitative appreciations of cultural models have long recognised the link between certainty-offering rituals and aesthetic practices and anxiety reduction [27,28]; more recent work by the present author and others has explicitly formalized this in terms of cultural models as entropy reduction devices that serve to minimize anxiety [19,29,30,31].

Putting all of these considerations together, what emerges is an account of counterfactual cultural production that sees it as a form of low-cost work that reduces anxiety by flooding the environment with simulated evidence for a predictive cultural or cognitive model. While it is obviously impractical to test this hypothesis against the entire cultural record, the present study trials it against two representative examples: a religious model of the world, as articulated in the Gospels of the King James Version Bible; and secular representations of collective identity in the form of national flags. As these test cases span linguistic and visual modes of representation, the cultural salience of the examples is complemented by a more robust test of the hypothesis.

1.1. Methods

Testing this hypothesis requires an encoding of language that allows for all of the relevant variables to be quantified. The Lancaster sensorimotor norms for English provide one efficient way to do this for sensory states [36]. By providing human sourced scores for how strongly each of 39,707 lemmas is associated with 11 sensorimotor dimensions (the five senses plus interoception and the motor effectors of head, arm/hand, leg/foot, torso, and mouth/throat), the Lancaster norms capture the embodiment profile for most common English words. Significantly, the norms show that even abstract concepts have a stable sensorimotor profile across individuals [Figure 1].

No less significantly, the norms allow for English to be partitioned into equivalence classes of words that have a similar sensorimotor profiles. This is important because it creates a probability distribution across the equivalence classes that allows entropy to be calculated. That is, if there are N equivalence classes and religious language uses words from each class with a different probability than English as a whole, it becomes possible to measure the entropy difference between religious language and background English with respect to their sensorimotor impact. In effect, this amounts to vocabulary reduction, where lemmas are mapped into a small number of superordinate `words’ that are defined by their somatic impact rather than their meaning, allowing that the two will be related. (Food related lemmas, for example, are likely to map into the same category.) On the one hand, this makes for a more succinct formal model; on the other, that fact that religious behavior is as much a matter of corporeal experience as cognitive suggests the procedure is especially appropriate to the phenomenon of interest. [37,38,39,40]. Here, the reduction was done by performing a median split on the score of all 39,707 lemmas on the six sensory modalities (the motor modalities being incidental to the hypothesis under test). This generates $2^6=64$ possible sensory states into which words can be mapped [Table 1]; an interactive plot showing a 3D projection of all 39,707 lemmas grouped by the 64 sensory states can be accessed here.

The religious model chosen was that articulated in the four Gospels of the 1611 first edition of the King James Bible (KJV). Though any religious text should show the same result, the KJV was chosen for its significance as a book “designed to control the language of salvation and to occupy the linguistic high ground in such a way as to allow its rivals [...] less verbal space, less legitimacy, less power” [41]—in other words, for its representativeness as an evangelical document. The text was prepared by tokenizing, lemmatizing, and removing the stopwords from the four Gospels using a custom function built in the spaCy natural language processing library for python [42]. This meant breaking the text into words, reducing morphological variation in words to a root form (`ran’, `running’, `runs’ → `run’), and stripping out words with no semantic content like prepositions, conjunctions and articles. The result was a Bible vocabulary of 2,398 meaningful lemmas. Intersecting this with the sensorimotor lemmas gave 1,960 words for which data was available; all 64 sensory states were represented in these words. (It should be acknowledged that sensorimotor norms were scored by speakers of modern English, so their application to the KJV is necessarily anachronistic. Nevertheless, the semantic accessibility of the KJV to modern readers suggests that the less fine-grained sensorimotor profiles should also have descriptive validity.)

1.2. Results

The first prediction of $H_1$ is that the entropy of religious language will be lower than English as whole, measured relative to the distribution of words across sensory states. That is, religious language, compared to English as a whole, will over-sample words from from some sensory states and under-sample from others, thereby making the over-sampled states more perceptually salient. This was tested by creating two probability distribution defined by normalizing the number words in each sensory state relative to the total vocabulary size for the KJV and English as a whole respectively. As predicted, the entropy of the KJV Gospels (5.274 bits) was lower than the entropy of English as a whole (5.415 bits)—a difference of -2.673%. (Entropy was calculated as per Eqn  2 using the SciPy python library [43].) This value is about what one would expect for a text that is designed to normatively regulate everyday life: too large a simplification invites falsification of hallucinated evidence by experience, and small entropy difference like 2.673% ensures that the KJV is complex enough to represent most human sensory states, but simple enough to make them more predictable. The wider implications of this difference for predicting the frequency of religious behaviours will developed further in the discussion below.

The second and third predictions of $H_1$ relate to positively valenced and transcendentally oriented language. That is, the language of the KJV Gospels should, relative to background English, select words from the 64 sensory categories that engender pleasant sensory states [44] and index values that point to a supra-mundane reality [40]. Both variables can be calculated using the valence-arousal-dominance norms published in Warriner at al [45] and the semantic size norms in the Glasgow norms of Scott et al [46]. Valence is a straightforward measure of positive sentiment; semantic size is slightly more complicated and concerns how `large’ a word is felt to be. For concrete words, this tracks physical size: CATHEDRAL has a larger semantic size than CHAPEL. In the case of abstract words, the tracking is guided by psychological or cultural salience: VOTE has a larger semantic size than CHOOSE. Given this, semantic size provides a useful proxy for the `transcendental’ freighting of a word. As the two data sources use different scales for rating words, valence and semantic size variation were rescaled between 0 and 1.

Both predictions were evaluated by scoring lemmas from the KJV and background English for both valence and semantic size across each of the 64 sensory states [Figure 2]. These scores provided DVs for separate two-way ANOVAs that took source (KJV Gospels vs background English) and sensory category as the IVs. Tests were conducted using the pingouin statistics library for python [47]. For valence, there was a statistically significant difference in the predicted direction with respect to sensory state ($F(63,30120)=19.83$, $p<.001$, ${\eta }^2=0.039$), as there was also for source ($F(1,30120)=258.67$, $p<.001$, ${\eta }^2=0.009$). Similarly, differences for semantic size were in the predicted direction for sensory state ($F(63,30120)=99.72$, $p<.001$, ${\eta }^2=0.173$) and source ($F(1,30120)=139.123$, $p<.001$, ${\eta }^2=0.005$). As expected from the entropy results, there were no significant interaction effects for source and sensory state in either model: i.e., there was a substantial overlap across all sensory categories between the vocabulary of the Gospel writers/translators and background English. This is likely because a complete decoupling of the two vocabularies would make the KJV inapplicable to everyday life, and hence negatively impact on the `plausibility’ of the hallucinated evidence.

These results support the claims of $H_1$ with respect to the likely cognitive and perceptual effects of hallucinated evidence generated by a textually articulated religious model. That is, that the KJV selectively over-samples words with a high transcendental freighting and that are associated with positively valenced sensory states, and its vocabulary encodes a world model that is lower in entropy than that implicit in background English.

1.3. Methods

Flag data were acquired by downloading a comprehensive dataset of 254 national flag bitmaps from the Flags of the World website. As these are normalized for size and resolution, they ensured that all image metrics would be standardized. Entropy and contrast scores were extracted for all flags using the mahotas image processing library for python [56]. This provided the two dependent variables.

As exogenous and endogenous anxiety cannot be measured directly, proxies were used for both. In the case of exogenous anxiety, the proxy used was the number of land borders a country has. It is an established result that the frequency of conflict scales with the number of borders a country shares, so from this it is reasonable to infer that exogenous anxiety will be more pronounced in countries with more borders [57,58,59]. (It is certainly the case, for example, that proximity to porous and contested borders in general engenders higher levels of of anxiety [60,61].) Border counts were obtained using the pycountry library for python by counting the number of neighbors each country had [62]. A proxy for endogenous anxiety was obtained by using the internal fractionalization data published in Alesina et al [63], which provides indexes of ethnic, religious, and linguistic division for 185 countries. Each index is calculated by estimating the probability that two randomly selected individuals will belong to a different ethnic, religious, or linguistic group. Here, a mean was taken across all three indexes to capture the aggregate level of internal division for each country. (This, in addition to missing border data for some countries, reduced the number of usable flags to 181.)

1.4. Results

Two linear regressions were performed with contrast and entropy as DVs and mean internal social division and number of borders as IVs. As expected, number of borders predicted a decrease in the contrast of flags ($DF=180,\beta =-4.524,t=-2.067,p=.04,r^2=0.023$). Also as expected, mean internal division positively predicted the entropy of flags ($DF=180,\beta =0.435,t=2.402,p=.017,r^2=0.031$) [Figure 3]. There was no statistically significant effect of number of borders on entropy, or of mean internal division on contrast. These results were consistent with the claim that flags can be thought of hallucinated evidence that serves to reduce collective anxiety, and that increases in exogeneous and endgoenous have anxiety have predicable effects on the visual features of flags.

The prediction that contrast would anchor entropy variation in the low contrast position was tested by zero-centering the entropy and contrast scores relative to the midpoint of each range and performing a ${\chi }^2$ test of goodness of fit on observations by quadrant. The results showed there to be a statistically significant effect of quadrant on frequency of flags ($DF=(3,253),{\chi }^2=216.866,p<.001,\mathrm{Cramer}\text{’}\mathrm{s}\mathrm{V}=0.533$). 96% of observations were below the midpoint for contrast, confirming the prediction that contrast would anchor entropy variation in the low contrast position, with there being no observations at all in the least optimal high-contrast, low-entropy quadrant [Figure 4]. Assuming that the optimal flag is the flag that offers highest entropy for lowest contrast and the least optimal is the flag offering lowest entropy and highest contract, taking the absolute value of the product of entropy and contrast for each flag in the relevant quadrants allowed these to be identified. On this assumption, the flags of Benin and Saint Pierre and Miquelon respectively emerged as the most and least optimal for purposes of anxiety reduction [Figure 5].