Human societies can be represented as collectively intelligent phenomenological structures where the recurrent incidence of mutually coherent Behavioral patterns yields observable socio-economic outcomes. The ‘phenomenological’ adjective means that, whilst the society is composed of individuals, it is structured by and into their recurrent, patterned behaviour. Mutual coherence of Behavioral patterns means that social coordination happens through Behavioral coupling between individuals, tacitly or explicitly.
Formally, a human society can be studied as a complex structure {SR, PSR, LCSR, O}, where SR, PSR, LCSR and O are component sets which represent, respectively: m social roles SR = {sr1, sr2, …, srm} available to individuals and occurring with corresponding probabilities PSR = {p(sr1), p(sr2), …, p(srm)}, which, in turn, happen with mutual lateral coherences (i.e. manifestations of lateral coupling) LCSR = {lc(sr1), lc(sr2), …, lc(srm)}, and are correlated with the achievement of k social outcomes O = {o1, o2, …, ok}.
The structure {SR, PSR, LCSR, O} is collectively intelligent to the extent that learns, i.e. modifies its component subsets SR, PSR, LCSR, and O, by experimenting with many alternative versions of itself. Experimentation is sequential, i.e. each such alternative version of the structure {SR, PSR, LCSR, O} occurs in a different moment t in time. Therefore, the process of collectively intelligent learning happens as a chain of states {SR(t), PSR(t), LCSR(t),O(t)}.
Consistently with the Interface Theory of Perception (Hoffman et al. 2015 op. cit., Fields et al. 2018 op. cit.), as well as the theory of Black Swans (Taleb 2007 op. cit.; Taleb & Blyth 2011 op. cit.), it is assumed that collective learning with respect to exogenous stressors can happen only if the structure absorbs those stressors into endogenous mechanisms of adaptation. Unacknowledged stressors, which remain purely exogenous, without being coupled with exogenous adaptation in the structure, are irrelevant.
Absorption of external stressors means their transformation into endogenous constraints, which are expressed, in the first place, as regards collective outcomes. Any given instance {SR(t), PSR(t), LCSR(t),O(t)} of the structure {SR, PSR, LCSR, O} pitches its real local outcomes O(t) against their expected local state E[O(t)]. It is to stress that expected outcomes are essentially local, i.e. they are instrumental to absorbing external stressors. There are no grounds to assume something like a general state of expectation E(O) in the structure {SR, PSR, LCSR, O}.
With the above-stated assumptions, the sequence of states from instance {SR(t0), PSR(t0), LCSR(t0),O(t0)} to {SR(t), PSR(t), LCSR(t),O(t)} can be studied as a Markov chain of states, which transform into each other through a σ-algebra. The current state {SR(t), PSR(t), LCSR(t),O(t)} and its expected outcomes E[O(t)] contain all the information from past learning, and therefore the local error in adaptation, i.e. e(t) = {E[O(t)] – O(t)}*dO(t) - where dO(t) stands for the local derivative (local first moment) of O(t) - conveys all the information from past learning. Error e(t) in adaptation is factorised into a residual difference and a first moment, as it is assumed that any current state instance {SR(t), PSR(t), LCSR(t), O(t)} is essentially dynamic, i.e. on the move towards a subsequent state {SR(t+1), PSR(t+1), LCSR(t+1), O(t+1)} in the Markov chain. The use of Markov chains in this model is largely consistent with the author’s understanding of the Interface Theory of Perception (Hoffman et al. 2015, Fields et al. 2018).
Theoretically, it is possible to assume e(t) = 0, with either E[O(t)] = O(t) or dO(t) = 0, yet such a perfect standstill is rather a very special state than normal step in collective learning. A society experiencing e(t) = 0 does not learn anything new: all constraints are met, and no external stressors impose new constraints. The expected state of the structure {SR, PSR, LCSR, O} is E[O(t)] ≠ O(t) and dO(t) ≠ 0, and therefore {SR(t), PSR(t), LCSR(t),O(t)} = {SR(t-1) + e(t-1), PSR(t-1) + e(t-1), LCSR(t-1) + e(t-1), O(t-1) + e(t-1)} and E[O(t)] = E[O(t-1)] + e(t-1). Collective learning is essentially incremental, and not revolutionary. Each consecutive state {SR(t), PSR(t), LCSR(t),O(t)} is a one-mutation neighbor of the immediately preceding state {SR(t-1), PSR(t-1), LCSR(t-1),O(t-1)} rather than its structural modification. Hence, we are talking about arithmetical addition rather than multiplication or division.
Constraints produced by the structure {SR, PSR, LCSR, O} in response to external stressors take two forms: recurrent and incidental. The former impact individual decisions to endorse a given social role, i.e. those decisions take into account the past state of the structure {SR, PSR, LCSR, O} and randomly distributed, current exogenous information X(t). That random exogenous parcel of information affects all the people susceptible to endorse the given social role sri which, in turn, means arithmetical multiplication rather than addition, i.e. PSR(t) = X(t)*[PSR(t-1) + e(t-1)].
Incidental exogenous stressors, thus events in the type of Black Swans, consist in short-term, violently disturbing events, likely to put some social roles extinct or, conversely, trigger into existence new social roles. Extinction of a social role means that its probability becomes null: P(sri) = 0. The birth of a new social role, on the other hand, means that some pre-existing skillsets gain social recognition from the distant social environment of people possessing them, and therefore turn into professions, crafts, business models etc.
Mathematically, it means that the set SR of social roles entails two subsets: active and dormant. Active social roles display p(sri;t) > 0, and, under the impact of a local, Black-Swan type event, they can turn p(sri;t) = 0. Dormant social roles are at p(sri;t) = 0 for now, and can turn into display p(sri;t) > 0 in the presence of a Black Swan.
In the presence of active recurrent stress upon the structure {SR, PSR, LCSR, O}, thus if we assume X(t) > 0, I can present a succinct mathematical example of Black-Swan-type exogenous disturbance, with just two social roles, sr1 and sr2. Before the disturbance, sr1 is active and sr2 is dormant. In other words, P(sr1; t -1)*X(t-1) > 0 whilst P(sr2; t -1)*X(t-1) = 0 . With the component of learning by incremental error in a Markov chain of states, it means [P(sr1; t - 2) + e(t-2)]*X(t-1) > 0 and [P(sr2; t -1) + e(t-2)]*X(t-1) = 0, which logically equates to P(sr1; t - 2) > - e(t-2) and P(sr2; t -1) = - e(t – 2). After the disturbance, the situation changes dialectically, namely P(sr1; t -1)*X(t-1) = 0 and P(sr2; t -1)*X(t-1) > 0, implying that P(sr1; t - 2) = - e(t-2) and P(sr2; t -1) > - e(t – 2).
The above development leads to the issue of negative probabilities. With the assumptions stated above, in the local state {SR(t), PSR(t), LCSR(t),O(t)} it is possible that some p(sri) < 0, i.e. E[O(t-1)] > O(t-1), with dO(t-1) > 0. It is an otherwise frequent situation when the actual outcomes are below expectations, and yet display a positive gradient of change. The case of p(sri) < 0 is, technically, an impossible state. Can collective intelligence of a human society go into those impossible states? Quantum physics supply a possible interpretation in that respect. If the probability of an event is conditional on another probability, and this is precisely the case with the here-presented model, negative probability corresponds to an essentially intermediary state, i.e. a state impossible to hold or impossible to be verified directly (Feynman 1987; Curtright & Zachos 2001). That formal interpretation in quantum physics somehow mirrors the distinction between economic equilibrium, and the lack thereof, in the theory of economic cycles (Schumpeter 1939). In that perspective, states marked by p(sri) < 0 are the necessary spin and push in the long-term learning of the collectively intelligent social structure.
Economic sciences supply interesting stylized facts with respect to equilibriums. There are some fundamental proportions in societies, such as the average time worked per person per year, or the average consumption of energy per person per year, which we collectively adjust ourselves around without even noticing much of it, and yet there are visible trends of change in those proportions. Adjustment of size, would it be demographics or the gross real output, is a bit harder, in the sense that it entails occasional bumps and requires collective effort (e.g. proper economic policies). Adjustment in markets is probably the hardest and the bumpiest, whence the common observation that prices and their gradient of change are the beating pulse of the economic system and can become volatile under new external stressors. Hence, a working hypothesis is being formulated for the empirical application of the above-presented model: ‘Under the sudden, Black-Swan-type impact of external stressors, human societies can develop one of the three possible paths of collectively intelligent learning: a) structural, cyclical adjustment without visible social change b) adjustment of size with visible social change and c) long-term destabilization’.