Autocatalytic networks in cognition and the origin of culture
AAutocatalytic networks in cognition and the origin ofculture
Liane Gabora and Mike Steel
Abstract
It has been proposed that cultural evolution was made possible by a cogni-tive transition brought about by onset of the capacity for self-triggered recalland rehearsal. Here we develop a novel idea that models of collectively auto-catalytic networks, developed for understanding the origin and organizationof life, may also help explain the origin of the kind of cognitive structurethat makes cultural evolution possible. In this setting, mental representa-tions (for example, memories, concepts, ideas) play the role of ‘molecules’,and ‘reactions’ involve the evoking of one representation by another throughremindings and associations. In the ‘episodic mind’, representations are socoarse-grained (encode too few properties) that such reactions must be ‘cat-alyzed’ by external stimuli. As cranial capacity increased, representationsbecame more fine-grained (encoded more features), which facilitated recur-sive catalysis and culminated in free-association and streams of thought. Atthis point, the mind could combine representations and adapt them to spe-cific needs and situations, and thereby contribute to cultural evolution. Inthis paper, we propose and study a simple and explicit cognitive model thatgives rise naturally to autocatylatic networks, and thereby provides a possiblemechanism for the transition from a pre-cultural episodic mind to a mimeticmind.
Affiliations: [LG] Department of Psychology, University of British Colombia,Okanagan Campus, Kelowna BC, Canada;[MS] Biomathematics Resarch Centre, University of Canterbury, Christchurch,New Zealand (corresponding author).
Email: [email protected], [email protected]
Keywords: autocatalytic network, conceptual closure, episodic, mimetic, rep-resentational redescription, stream of thought
Preprint submitted to Elsevier today a r X i v : . [ q - b i o . N C ] A ug . Introduction We are surrounded by evidence of a cultural evolution process that iscumulative (new ideas build on old ones), and open-ended (there is no apriori limit on the generation of novelty). By ‘culture’ we refer to extra-somatic adaptations—including behavior and technology—that are sociallyrather than sexually transmitted. In order to contribute in a meaningfuland reliable way to cultural evolution, one must be able to develop and re-fine ideas by thinking them through (i.e., engage in a stream of abstractthought). Since the capacity for a stream of thought is not specific to a par-ticular domain of knowledge or cognitive process, the origins of this capacityare not straightforwardly traced to a particular area or even neural circuitof the brain. We could possess all the relevant neuroscientific data, as wellas the relevant archaeological and anthropological data, yet still not under-stand how the human mind became able to evolve culture. Data alone areinsufficient to explain this; what is needed here is a theory.Once humans could engage in abstract thought, we could combine con-cepts, draw analogies, look at situations from different perspectives, modifyplans according to unforeseen circumstances, and adapt ideas to new con-ditions, tastes, and desires. In other words, abstract thought enabled usto modify mental representations in light of one another, and thereby ‘re-shape’ our web of understandings as a whole. However, to engage in abstractthought requires that these representations be within reach of one another(i.e., they must already be somehow related to one another in our mind).Thus, in attempting to formally model the conditions for the emergence ofcultural evolution, we are faced with the problem of explaining how a com-plex system composed of mutually dependent parts could come into existence.Which came first: the associative links between mental representations (i.e.,the ‘tracks’ that a ‘train of thought’ runs on)? Or did trains of thoughtcement the connections from one rung (i.e., one mental representation) tothe next? We have a ‘chicken and egg problem’. In short, the answer to thequestion of how we arrived at the capacity for a stream of thought is relatedto the question of how we acquired an integrated web of understandings, andhow this came about is not straightforward.Theories of how life began also face a ‘chicken and egg’ problem as tohow a self-replicating structure composed of mutually dependent parts couldcome into existence. The improbability that such a structure could comeabout spontaneously has led to widespread support for the hypothesis that2he earliest forms of life were autocatalytic molecular networks that evolvedin a relatively haphazard manner without an explicit self-assembly code,through a non-Darwinian process involving self-organization and horizontal(lateral) transfer of innovation protocols (Farmer et al., 1986; Gabora, 2006;Kauffman, 1993; New and Pohorille, 2000; Segre, 2000; Vetsigian et al., 2006;W¨achtersh¨auser, 1997). Kauffman (1993) showed that when polymers inter-act, their diversity increases, and so does the probability that some subsetof the total reaches a critical point where there is a catalytic pathway to ev-ery member, a state Kauffman referred to as autocatalytic closure . Althoughthe term ‘closure’ has several different meanings in mathematics, and it issometimes used to mean a condition that bounds or limits the set, Kauffman(following in the footsteps of Erd¨os and R´enyi (1960)) used the term to ex-press the property that the set surpassed a threshold density of connectednessby way of catalysis events. Thus, many closed sets within a system can exist,and they can become larger by combining together or through the introduc-tion of new items. Kauffman showed that autocatalytic sets emerge for awide range of hypothetical chemistries (i.e., different collections of catalyticmolecules).This paper explores the feasibility of adapting a generalized autocatalyticapproach to model the emergence of the kind of cognitive structure necessaryfor complex culture. In other words, we draw upon a body of work developedto model the origin of life to model the transition to the kind of cognitivestructure responsible for the origins of cultural evolution. While this paper isnot the first to broaden the concept of ‘catalysis’ and apply it in a cognitivecontext (see, for example, Gabora (1998, 2013); Cabell and Valsiner (2014)),here we build on these efforts to develop a more formal model that allows foranalysis and predictions.
Although the origin of the kind of chemical structure necessary for biolog-ical evolution, and the origin of the kind of cognitive structure necessary forcultural evolution would appear superficially to be two very different prob-lems, at a formal, algorithmic level they share a common deep structure.They both involves processes in which elements interact, generally referredto as reactions , resulting in element transformation. In the case of the be-ginnings of biological evolution and the origin of life (OOL), the elementsare catalytic molecules. In the case of the beginnings of cultural evolutionand the origin of complex cognition (OOC), the elements participating in3reactions’ are thoughts, memories, concepts, ideas, and chunks of knowledgeencoded in memory which are referred to collectively as mental representa-tions , or MRs. We use the term mental representation in what philosophersrefer to as the ‘weak sense’, in that we do not aim to provide a theory ofconsciousness. In this paper, the term ‘reaction’ will be used to refer to theprocess in which two or more MRs interact and at least one of them changesas a result. Although this paper does not delve into the mechanisms un-derlying this cognitive form of reactivity, we believe it arises due to overlapof receptive fields in distributed, content-addressable representations, as dis-cussed in detail elsewhere (Gabora (2002b, 2010, 2018b); Gabora and Ranjan(2013)). The term ‘reactant’ will be used to refer to the MRs participatingin such a reaction.It is useful to distinguish between externally-driven and internally-drivenreactions. In the OOC case, we use the term learning to refer to the cognitiveprocess of revising a MR on the basis of new external input from the environ-ment. We use the term reflection to refer to a cognitive process of revising aMR on the basis of internal input from the mind. The mapping of the basicelements of OOL scenario to the OOC scenario is summarized in Table 1. Inboth the OOL and the OOC, certain elements, referred to as catalysts , speedup or help certain reactions along. In the OOL these elements are catalyticmolecules, and in the OOC they are catalytic MRs.Component OOL OOCFood set original polymers innate conceptsReactants polymers mental representationsProducts polymers mental representationsReactions ligation and cleavage learning and reflectionCatalysts polymers stimuli and catalytic mental representationsAutocatalytic sets chemical RAFs cognitive RAFsTable 1. Comparison of the basic components of the two evolutionary pro-cesses that we propose are productively understood in terms of autocatalyicmodels. OOL refers to ‘origin of life’ and OOC refers to ‘origin of culture’.Despite these similarities between the OOL and OOC scenarios, there aresome important differences, which present interesting challenges. For exam-ple, in the OOC scenario, externally registered stimuli are held in workingmemory, whereas there is no similar bottleneck in the OOL. Such differences4ose interesting theoretical challenges which are addressed in this paper.
This paper sketches out the beginnings of a formal model of how themind could have developed the kind of integrated structure that enablesself-triggered recall and abstract thought, drawing upon a formal frameworkdeveloped for the formal description of autocatalytic networks. The paperbegins with a bare minimum of background material from psychology, an-thropology, and archaeology concerning the uniqueness of human cognitionand our ability to evolve complex, cumulatively creative culture. Next, weprovide the mathematical definitions of the basic concepts of our model, fol-lowed by the model itself. We then investigate the predictions of this model,in particular the factors that play an important role in the emergence of akind of cognitive structure that is able to participate in cultural evolution,which we propose owes to the fact that is, in a fundamental sense, autocat-alytic. Finally, we conclude with some caveats and limitations, as well asunanswered questions and possibilities for future research.
2. Background from cognitive anthropology: A transition in cog-nitive functioning
We now summarize briefly the archaeological evidence that the origin ofculture did reflect a transition to a different kind of cognitive functioning(see Mithen (1998); Gabora and Smith (2017); Penn et al. (2008); Chomsky(2012); Donald (1991)). There is no consensus as to why
Homo erectus crossed the threshold to the capacity for cumulative cultural evolution, butthe cranial capacity of
Homo erectus was approximately 1,000 cc—about25% larger than that of
Homo habilis (Aiello, 1996). Although simple stone(and some bone and antler) implements can be found in the archaeologicalrecord dating back to as long ago as 3.3 million years ago (Harmand et al.,2015), it is not until over a million years later that
Homo constructed toolsthat were intentionally symmetrical (Lepre et al., 2011) and required multipleproduction steps and varied raw materials (Haidle, 2009). By this time theywere transporting tool stone over greater distances than their predecessors(Moutsou, 2014), and they had acquired the ability to use and control fire(Goren-Inbar et al., 2004), had crossed stretches of open water up to 20km (Gibbons, 1998), ranged as far north as latitude 52 (Parfitt et al., 2010),revisited campsites possibly for seasons at a time, sometimes building shelters5Mania and Mania, 2005), and ranked moderately high among predators(Plummer, 2004). Thus, cumulative cultural evolution is believed to haveoriginated approximately two million years ago, following the appearance of
Homo erectus (Mithen, 1998).It has been proposed that the increase in brain size enabled a transitionto a fundamentally different kind of cognitive architecture (Donald, 1991). Donald (1991) refers to the cognition of
Homo habilis as an episodic mode of cognitive functioning because it was limited to the ‘here and now’ of thepresent moment. He proposed that the enlarged cranial capacity enabledthe hominin mind to undergo a transition to a new mode of cognitive func-tioning made possible by the onset of what he calls a self-triggered recall andrehearsal loop , which we abbreviate STR. STR enabled hominins to voluntar-ily retrieve stored memories independent of environmental cues (sometimesreferred to as ‘autocuing’) and engage in pantomime, re-enactive play, and,importantly, representational redescription, which involves embellishing andrevising thoughts and ideas as they are reflected upon from different per-spectives. Donald referred to this as the mimetic mind because it could actout or ‘mime’ events that occurred in the past or that could occur in the fu-ture, thereby not only temporarily escaping the present but, through mimeor gesture, communicating the escape to others. STR also enabled attentionto be directed away from the external world toward ones’ internal represen-tations, which paved the way for abstract thought. It enabled systematicevaluation and improvement of thoughts and motor acts by adapting themto new situations, resulting in voluntary rehearsal and refinement of skillsand artifacts.Donald’s concept of STR bears some resemblance to the suggestion byHauser et al. (2002) that what distinguishes human cognition from that ofother species is the capacity for recursion (Corballis, 2011), as well as theconcepts of relational reinterpretation by Penn et al. (2008) and of ‘merge’by Chomsky (2012) (for an overview, see (Gabora, 2018a)). What thesetheories have in common is that they focus not on abilities in a particulardomain (such as social or technical abilities) but on a cognitive trait thatcuts across domains. STR enabled not just the redescription and therebyrefinement of previous representations but the sequential chaining of them,and in a way that, through autocuing, could build upon past representations. For related proposals see (Gabora, 1998; Mithen, 1998; Penn et al., 2008).
3. Earlier approaches
We now briefly review the earlier work upon which this paper builds.Inspired by Stuart Kauffman’s (Kauffman, 1986, 1993) models of the emer-gence of the earliest kind of living structure (sometimes called a protocell)through autocatalytic closure of a set of catalytic polymers, Gabora (1998,2000, 2001) proposed that the cognitive analog of the protocell is an indi-vidual’s integrated web of knowledge, beliefs, and so forth, that constitutean internal model of the world, or worldview. In Kauffman’s OOL model,each polymer, composed of up to a maximum of M monomers, is assigned alow a priori probability P of catalyzing each ligation (joining) and cleavage(cutting) reaction. In the cognitive scenario, the analog of the set of poly-mers is the set of MRs (i.e., mental representations in working or long-termmemory). The cognitive analog of M (the maximum polymer length) is themaximum number of properties of a MR, and the analog of P , the proba-bility of catalysis, is the probability that one representation brings about areminding or associative recall of another.It was proposed that, as exposure to similar items or events causes theformation of abstract concepts that connect these instances (for example, itis recognized that experiences of specific rocks are instances of the conceptROCK), a critical ‘percolation threshold’ is eventually reached because thenumber of ways of forging associations amongst items in memory increasesfaster than the number of items in memory. Following Kauffman’s use of theterm ‘autocatalytic closure’ in early biochemistry, the analogous state in cog-nition was referred to as conceptual closure (Gabora, 2000), a term we willuse later in this paper, with a precise definition. In this way, the assemblageof human worldviews changes over time not because some of them replicatein their entirety at the expense of others (for example, by natural selection)but through piecemeal mutual interaction and self-organized transformation.Artifacts, rituals, and other elements of culture reflect the states of the world-views that generate them. Interactions amongst items in memory increasestheir joint complexity, eventually transforming them into a conceptual net-work, which continually revises itself as new inputs are incorporated. This7nables the creative connecting and refining of concepts and ideas necessaryfor the individual to participate in the evolution of cultural novelty.Kauffman found that, the lower the value of P , the greater M has to be(and vice versa) in order for autocatalytic closure to be achieved. In otherwords, there is a transition from a subcritical process to a critical processwhich depends sensitively on these parameters. Similarly, there is a trade-offbetween (the analogues of) these parameters in conceptual closure. In thecognitive scenario, if the probability of associative recall is low, a networkis subcritical: the worldview is expected to be stable but to have difficultyincorporating new information. Conversely, if the probability of associativerecall is high, the network is super-critical: the worldview is expected toincorporate new information readily, but be at risk of destabilization (i.e.,everything seems reminiscent of everything).In the next few sections, we take these ideas in a new direction, andprovide for a more explicit mathematical framework. We stress once againthat in the terms autocatalytic closure and conceptual closure, the word‘closure’ is not a condition that requires the set of items to be bounded orunable to grow larger. Rather it expresses a property that that the set issufficiently connected together by catalysis events. In this way, many closedsets within a system can exist and they can become larger by combiningtogether or by the introduction of new items.
4. Background from Theoretical Work on Autocatalytic Sets
As noted, the role of autocatalytic networks in OOL was introduced byKauffman (1993, 1986) in a pioneering approach to explain how complexbiochemistry might have arisen from primitive chemistry, based on reactionsthat combine polymers. The notion of self-sustaining autocatalytic sets wasdeveloped further (mathematically) as RAF-theory (here, RAF= Reflexively-autocatalytic and F-generated set, reviewed in Hordijk and Steel (2016)).Formally, a catalytic reaction system (CRS) is a tuple Q = ( X, R , C, F )consisting of a set X of molecule types, a set R of reactions, a catalysis set C indicating which molecule types catalyze which reactions, and a subset F of X called the food set. A Reflexively Autocatalytic and F-generated (RAF)set for Q is a non-empty subset R (cid:48) ⊆ R of reactions which is:1. Reflexively Autocatalytic : each reaction r ∈ R (cid:48) is catalyzed by at leastone molecule type that is either a product of R (cid:48) or is present in thefood set F ; and 8. F-generated : all reactants in R (cid:48) can be created from the food set F using a series of reactions only from R (cid:48) itself.In words, a RAF set is a subset of reactions that is both self-sustaining (i.e.,every molecule involved in a reaction can be generated from the food set F bya sequence of reactions within the subset) and collectively autocatalytic (i.e.,every reaction is catalyzed by a molecule generated by the subset or the foodset). Such a set is a basic requirement for all living systems. Kauffman (1993)first demonstrated this in a simple binary polymer model, the emergence ofsuch a RAF occurs when the complexity of the polymers reaches a certainthreshold. This has been further formalized and analyzed (mathematicallyand using simulations) and with applications to real biochemical systems(Hordijk et al. (2010, 2011), Hordijk and Steel (2004, 2012, 2016), Mosseland Steel (2005)). RAF theory has proven useful for identifying how suchtransitions might occur, and at what parameter values.Our approach here is to apply the theory of RAFs in a form that is maxi-mally abstract, and show how this can be used to address the question of howa mind that is more or less a brittle, un-creative stimulus–response machinecould transform into a mind capable of viewing situations from different per-spectives, combining information from seemingly unrelated sources to solveproblems, and adapting responses in contextually appropriate ways. We willstart with this generic form of the model and examine how this might occur.We will see that as we incorporate aspects unique to the OOC scenario, thesituation becomes more complex but the RAF approach can still effectivelymodel it.In short, although results concerning the emergence of RAFs in chemicalnetworks cannot be applied directly to the question of how human cognitionevolved, related mathematical techniques can be, as we show after introduc-ing some further background material and definitions.
5. A simple cognitive model based on reactions and catalysis
At a top level, our highly simplified cognitive model can be viewed as acontinuous-time, stochastic process involving three sets. As mentioned inthe introduction, we use the term mental representation , abbreviated MR, torefer collectively to items in memory (either working memory or long-termmemory), as well as percepts, concepts, thoughts, and ideas, as well as more9omplex mental structures such as schemas. For simplicity, we view a MRto be an ensemble of a collection of hierarchically organized properties . • S t denotes the set of stimuli at time t registered by the senses (i.e.,percepts that arise from sensory experiences). We can take t = 0 to bethe time of conception of the individual. • L t denotes the set of items encoded in long-term memory. This includesthe set I of any innate knowledge with which the individual comes intothe world. • M t denotes the set of items encoded in working memory and/or long-term memory at time t (and so I ⊆ M ). Each element of m in M t isassociated with a set of properties, denoted P ( m ), and we let | m | be thenumber of those properties. Items in long-term memory encode largelystatic ‘invariances’ of the world, while the items in working memoryoften reflect variances from this static model. • ˚ w t denotes the mental representation of a particular instant of expe-rience at time t . We will call ˚ w t the attended item at time t . It iswhatever is in the ‘spotlight’ of attention at time t . • W t denotes items in working memory. It consists of ˚ w t as well as anyother similar or recently-attended items that are still accessible. It isa very small subset of M t , of size in the order of 1 to ∼ . Thus,˚ w t ∈ W t ⊂ M t .There is a straightforward way to define what ‘associated’ means here (inthe definition of M t ), based on a natural partial order on the set of mentalitems. For two mental items m and m (cid:48) let us write m (cid:22) m (cid:48) if the propertiescomprising m are a subset of the properties comprising m (cid:48) . This partial orderallows us to capture the notion of an item m generalizing more particularinstances m , m , . . . , m k if m (cid:22) m i for each i (for example, m has preciselythe properties shared by each of m , . . . , m k ). The items m and m (cid:48) are saidbe members of a concept if (though, not if and only if), on the basis of one ormore shared properties, there exists a representation of an abstract categoryor prototype of which both are instances . For example, if m = a smooth Not to be confused with M from Section 3. m (cid:48) = a rough STONE, then m (cid:48)(cid:48) = STONE is a lower bound(under (cid:22) ) to both of them. More generally, the partial order also allows for associations amongstitems. We will say that m and m (cid:48) are associable if there is some propertythey share, i.e., there exists m (cid:48)(cid:48) with m (cid:48)(cid:48) (cid:22) m and m (cid:48)(cid:48) (cid:22) m (cid:48) . Note thatthe properties associated with a mental representation are not fixed but canbe biased by context or by mode of thought (i.e., convergent/analytic ver-sus divergent/associative) (Veloz et al. (2011); Sowden et al. (2015); Gabora(2018b)). The fact that they share a particular property need never havebeen explicitly noted by the individual. For example, even if an individualhas never consciously noticed that wood and rock share the property ‘hard’,they are nevertheless implicitly associable. We will say that m and m (cid:48) are associated if the fact that they share this property has been explicitly per-ceived and encoded in memory. For example, if an individual noticed thatwood and rock share the property ‘hard’, they would be associated.The reason we stress the distinction between associable and associatedis that explicit recognition of previously unrecognized shared properties iscentral to the creative processes that fuel cultural evolution. For example, onemight consciously recognize that wood and rock share the property ‘hard’.If one had previously carved something durable out of wood, this would be afirst step toward recognizing that a durable object might also be carved outof stone. There are several sources of cognitive structure. One is innate structurein the form of instincts, fixed action patterns, and so forth. A second isstructure on the basis of aspects of the MR perceived at the time of initialencoding, such as on the basis of properties shared by the MR and otherpreviously encoded MRs. A third is structure on the basis of aspects ofthe MR perceived after the time of encoding, such as occurs during mindwandering, contemplation, reflection from different perspectives, or creativethought.As mentioned, the term catalysis refers to one MR evoking another, asin a stream of thought. A MR that was present at time t plays the role of Note that there are other ways that mental representations can be associated witheach other (beyond sharing properties), such as via classical conditioning (for example, ifa bell always goes right before food appears). reactant , whereas a MR that is present at time t + δ is referred to as the product . Catalysis may be precipitated by an ex-ternal stimulus—as when something in the environment triggers a particularthought—or by another MR—as when the shift from one thought to an-other is triggered by looking at it from (one’s internal representation of) theperspective of someone else. A stimulus or MR that precipitates cognitivecatalysis is referred to as a catalyst . We write the ‘reaction’ x → z or x y −→ z ,where x is a reactant and y is a catalyst .In biochemistry, the distinction between reactant and catalyst is thatthe reactant is transformed (and therefore replaced by its product) in thereaction. The catalyst simply enables this to occur, without being itselfused up in the reaction. In cognition, however, both the reactant and thecatalyst may be affected by the reaction. For example, if x is the MR ofa piece of wood, and y is the MR of an event in which the wood is dentedby a falling rock, this may change the individual’s conception of both wood(i.e., it is now dented) and rock (i.e., it is capable of denting wood). Inthe cognitive scenario, the distinction between reactant and catalyst is thefollowing: the reactant is the MR that is generally (though not always) thefocus of attention, whereas the catalyst is a stimulus or another MR thatallows the reactant to give rise to a new MR as the next focus of attention. We posit that the dynamics of an episodic mind can be modeled bythe following three processes. Note that in writing + δ , we allow either acontinuous-time process or a finely-discretized (i.e., nearly continuous time)process. Encoding in memory : An item in W t can be encoded to long-termmemory m in L t + δ . We denote encoding by writing w (cid:59) m . and foran attended item ˚ w , we write ˚ w (cid:59) m . Note that w may or may notremain in W t + δ when encoded to long-term memory. Shift in attention : Attention may shift from one thought or stimulus˚ w in W t to another ˚ w (cid:48) in W t + δ . After attention shifts away from aparticular item ˚ w , it persists for some time in W t , and during this timeit is still readily accessible. Once it is no longer present in workingmemory, it is denoted w (cid:55)→ ∅ . Note, however, that it meanwhile may12ave been encoded in long-term memory. ˚ w (cid:48) may either come fromworking memory (in which case, we denote this shift in attention bywriting ˚ w (cid:55)→ w and w (cid:48) (cid:55)→ ˚ w (cid:48) ) or it may be a new item generated byone of the following processes. Updating by stimuli : Without entering a detailed discussion on thenature of awareness and perception, (in order to keep the focus on theforest rather than the trees), we use the term updating by stimulus torefer to a stimulus-driven change in what is paid attention to, whetherit be social in nature (such as a smile, gesture, or speech), or nonsocial(such as a change in the weather). Note that we are not using theterm ‘learning’ for this purpose because learning could imply that thechange is encoded to long-term memory; what we are referring to hereis any attended stimulus change, no matter how trivial, whether or notit is ever consolidated to long-term memory.We say that the subject of attention, ˚ w , shifts to ˚ w (cid:48) ∈ W t + δ , due tocatalysis by a stimulus s in S t ; in other words:˚ w s −→ ˚ w (cid:48) and ˚ w (cid:55)→ w. A concrete example of updating by stimuli is given in the lower part ofFig. 1.Sometimes the new content of working memory is not an external stim-ulus s ∈ S t , but a mental representation m ∈ M t that was evoked bythe stimulus because they are associated. This association may eitherhave been hardwired or learned. For now, we will not concern ourselveswith exactly how the stimulus affects the content of working memory,or the role of long-term memory (as well as goals, attitudes, motives,and so forth) on this process; what we focus on is the fact that thecontent of working memory has changed. Note that, in a society ofinteracting individuals, the expression, through speech or action, of anitem m ∈ M t in one individual’s mind can be regarded as a stimulus s for another individual, thereby provide a social learning ‘reaction’ inthat individual. 13 .3. Modeling the mimetic mind So far we have considered cognitive processes that occur in the episodicmind, which carries out appropriate responses to stimuli, but these responsesare fixed. We now consider an additional process that is a distinguishingfeature of the mimetic mind, which as mentioned earlier was physically largerthan the episodic mind, and which Donald (1991) posited was capable of self-triggered recall and rehearsal.
Cognitive updating : In the process of reflecting upon , or thinkingabout an attended item ˚ w ∈ W t , we think about it in a new way orconsider it appears from a different context or from another person’sperspective, which we denote as m ∈ M t . We say that ˚ w ∈ W t iscatalyzed by an item m ∈ M t . This ‘reaction’ updates the subject ofthought, which is now denoted ˚ w (cid:48) ∈ W t + δ . We will refer to a single stepsuch as this type of reflection process as cognitive updating and denoteit by writing: ˚ w m −→ ˚ w (cid:48) , and ˚ w (cid:55)→ w. As an example, suppose you are thinking about a dog (this is ˚ w ) andyou wonder what your mother would think of it (thus, m is yourmother’s perspective, which plays the role of catalyst). Then ˚ w (cid:48) isa new opinion of the dog that incorporates your mother’s perspective.This example involves representational re-description , i.e., the modifi-cation or redescription of a MR of a dog.Abstract thought can also involve the chaining , or sequencing, of multi-ple MRs—such as representations for simple, single-step actions—intoa more complex MR that involves multiple steps. It occasionally re-sults in concept combination : the merger of two concepts into a morecomplex concept.Another example of representational re-description is illustrated by thetop dashed arrow in Fig. 1. Again, in order not to lose sight of the forest forthe trees, we omit details of how causal relationships arise in cognition, anactive area of research in psychology and artificial intelligence largely carriedout using Bayesian statistical models (Goodman et al., 2011; Tenenbaumet al., 2011). 14 ood is sappy Burning well
Sappy wood burns well Wood is not sappy
Burning poorly
Low-sap wood burns poorly Sap helps the wood to burn well
Figure 1: The lower two reactions (green circles) correspond to ‘updating by stimulus’ (i.e.,˚ w s −→ ˚ w (cid:48) where, for example, ˚ w = (wood is sappy), s = (burning well), and ˚ w (cid:48) =(sappywood burns well)). This kind of reaction is possible in either an episodic or mimetic mind.However, in the representational re-description reaction at the top of the figure (bluecircle), a MR undergoes change in the absence of a stimulus; it is instead catalyzed byanother MR. Representational re-description is the outcome of self-triggered recall, whichis believed to be a distinguishing feature of a mimetic mind (Donald, 1991). Note that the key difference between this process and updating due tostimulus is the nature of the catalyst: here it is internal—i.e., an item in M t —rather than external—i.e., a stimulus in S t . In order to revise one’sunderstanding of something, it was no longer necessary for something tohappen in the physical world; this new understanding could arise due to‘putting 2 and 2 together’, or making more integrated use of thoughts andideas encoded in memory.Notice also that there are various ways to model the fraction of men-tal representations that are close enough to the current subject of thoughtto generate a retrieval or reminding event. Under a binomial distribution,very few items are highly similar to any given item m , a great many are ofintermediate similarity to m , and very few are extremely different from m .This distribution widens as we allow for abstract categories, of which specific15nstances are members (Gabora, 1998).
6. Dynamics of cognition under the model A Cognitive Catalytic Process (CCP) is a sequence of attended items C = ˚ w t (1) , ˚ w t (2) , . . . , ˚ w t ( k ) , (where ˚ w t ( i ) ∈ W t ( i ) , and where the t ( i ) values are increasing) with the prop-erty that each item ˚ w t ( i ) after the first is generated from an earlier one by acognitive updating reaction. In words, a CCP is a stream of thoughts, eachof which builds on an earlier one, via its connection to (catalysis by) an itemin long-term or working memory. Newly generated MRs may subsequentlybe encoded in long-term memory and thus are available to catalyze furthercognitive catalytic processes. We note that CCPs take shape in conjunctionwith drives and goals (though the details of how this works is beyond thescope of the current paper). Fig. 2 provides a simple schematic example toillustrate the distinction between processes where CCPs are absent (i) andwhere they are present (ii).We suggest that by providing a mechanism whereby ideas can be com-bined, developed, enhanced, integrated with existing knowledge, and madeavailable for further such processes, the emergences of CCPs can allow thedevelopment of a mimetic mind from a simpler episodic mind, regarded asa key step in the origin of cultural evolution. The encoding of MRs aris-ing from CCPs in long-term memory can then leads to a more integratedcognitive network (‘conceptual closure’) which we describe in Section 7.1.We now describe some generic features of the dynamics of CCPs andtheir emergence in the transition from an episodic to a mimetic mind. Wefocus on the impact of two parameters: the richness of MRs (i.e., the detailwith which items in memory are encoded) parameterized by the maximumnumber N of properties of MRs, and their reactivity (i.e., the extent to whichfeatures in a mental item trigger associations with other items), denoted P .Here N and P can be viewed as the analogues of the maximum polymerlength M and the catalyzation probability P (respectively) in Kauffman’sOOL model from Section 3. We will also describe how CCPs correspondto the autocatalytic network concepts of RAFs and CAFs that have beendeveloped in origin-of-life research (Section 7).We begin by noting that whether or not a given MR in M t catalyzes agiven cognitive updating reaction depends on numerous factors, such as how16 (cid:48)(cid:48) s (cid:48)(cid:48)(cid:48) ss (cid:48) time t L t W t S t (i) time t L t W t S t (ii) sm Figure 2: In this figure, the attended item in W t is shown in solid green lines, with otheritems in W t as thin orange lines; × denotes that the item is no longer present in workingmemory. (i) Item updating due to stimulus (the four reactions, with catalysis indicated bydotted arrows) together with encoding (an item from W t is cemented in L t ) is denoted bywiggly arrows). These do not allow for a cognitive catalytic processes (CCP) to form. (ii)The additional ability of items in M t to catalyze cognitive updating from L t (the lowerdotted arrow) and from within W t (the two uppermost dotted arrows). This leads to theformation of a CCP of size four. The disconnect in the solid green path near the top is aninstance of a shift in attention to an item in working memory. closely associated the items are in terms of shared properties, what stimuliare present, and what other MRs are active in working memory. The rateat which an item m ∈ M t catalyzes an attended item ˚ w in W t will be higherthe more properties the two items share.Rather than trying to model the impact of increasing N directly on theemergence of CCPs, we consider the simpler case of increasing the averagerate λ at which items in W t and L t catalyze cognitive updating reactions (therates within these two classes may differ, so λ should be viewed as a scalingfactor for both rates). Note that λ is an function of both P and N .We are particularly interested in understanding how the formation andpersistence of CCPs depends on this catalysis rate λ and a possible transitionthat occurs when this catalysis rate increases, which could provide a feasibleexplanation for the transition from an episodic to a mimetic mind. The fol-lowing broad predictions, which can be easily derived in overly-simplifiedmodels (using techniques familiar from branching processes and random17raph theory), are generic properties that would be expected to hold in morespecialized models.1. When λ is below a critical value, the dynamics of ˚ w t , W t , and M t areessentially determined by the external stimuli S t . This situation ischaracteristic of an episodic mind. If CCPs form at all, they do notpersist, and therefore have negligible impact on the structure of thewhole. Thus, items in memory remain essentially disconnected; theyare activated in response to particular stimuli or situations, and evokeappropriate responses, but do not transform into an architecture thatis continually revising its own structure by way of streams of thought.2. As λ increases towards a critical threshold, CCPs begin to form, andtheir size increases. This threshold depends on a sensitive interplaybetween P and L t , such that when long-term memory is denser, lowervalues of P suffice.3. The emergence of CCPs causes M t to grow at a faster rate than it wouldotherwise by generating a stream of thought that need not be relatedto current stimuli. Such streams of thought may be encoded in M t thereby providing a richer array of catalysts in L t for future cognitiveupdating reactions (and thereby CCPs) and so generating a positivefeedback process. This situation is characteristic of the mimetic mind.
7. Cognitive RAFs: The mind as an autocatalytic network
The model that we have described can be viewed as an instance of anautocatalytic set in an abstract reactive network, as described in Section4, in which the transition from episodic to mimetic mind corresponds tothe emergence of an RAF set. To describe this more formally, consider themyriad of ways that M t could develop from M (at conception) to its stateat some particular time t . More precisely, for a fixed time t >
0, consider thefollowing catalytic reaction system Q = ( X, R , C, F ), where: • F = F t = (cid:0)(cid:83) t (cid:48) ≤ t S t (cid:48) (cid:1) ∪ M (this is what the external environmentprovides (stimuli); • X = (cid:0)(cid:83) t (cid:48) ≤ t M t (cid:48) (cid:1) ∪ F t (this is the set of all mental representations thathave been present in the mind from conception up to some time t ,together with F t ). 18 R is the set of all the updating reactions that can potentially take placefrom conception up to time t ; • C is all the catalysis assignments that are potentially possible. R and C are not prescribed in advance. Because C includes remindings andassociations on the basis of, not just a single shared property, but also onthe basis of multiple shared properties, MRs can develop in a potentiallyunlimited number of directions through interactions with other MRs. Never-theless, it makes perfect mathematical sense to talk about R and C as sets.The justification of the following result is provided in the Appendix, in whichwe assume that t is large enough that updating reactions have commenced,and that the rate at which stimuli occur is bounded. Proposition 1. Q contains a RAF that increases in size with t (namelythe set of updating reactions that actually do occur between time 0 and t ).Moreover, while λ is below a critical threshold, CCPs in this RAF are shortand few in number, but when λ exceeds this threshold, CCPs become morefrequent, persistent and complex. We will refer to the particular RAF described in Proposition 1 as the cognitiveRAF . It has, in fact, the stronger property of being a CAF, as defined inMossel and Steel (2005). The significance of a transition from linear to super-linear growth in Proposition 1 is in providing a mechanism for generatingdensely linked connections in the mimetic mind. This is described in moredetail in the next section.This formal connection between the RAF structure of (i) our simple modelof the mind and (ii) a model that has been used to understand the transitionto self-sustaining autocatalytic life in biochemistry, may be helpful in subse-quent work. This is because efficient (polynomial-time) algorithms exist fordetecting RAFs (and CAFs) in catalytic reaction systems in general, and forstudying their organisation and structure. (For further details, see Hordijkand Steel (2016) and the references therein).
Our simple model provides a mechanism by which items involved in thecognitive RAF (reactants, products, and catalysts) and in the sequences(streams of thought) that form CCPs present in this cognitive RAF cangive rise (via the encoding process) to increasingly interlinked associations19etween mental representations in long-term memory. Formally, we say thata set C of items in L t (i.e., long-term memory) is a conceptually closed set if, for any two items m i , m j in C , there is a possible sequence of cognitiveupdating reactions that (if activated) can relate m i to m j , and such that eachreaction in that sequence has a catalyst that is also an item in C . In thisdefinition, saying that the sequence of reactions relates m i to m j means thatfor each reaction in the sequence, the reactant and product are associated(here ‘associated’ is as defined in the paragraphs before Section 5.1).As N increases in the transition from episodic mind to mimetic mind, L t begins to increase more rapidly (via Proposition 1) and P becomes tunedto match N such that reminding events are neither too frequent, such thatthe network is super-critical (an ‘everything reminds you of everything’ sit-uation), nor too infrequent, such that the network is subcritical (a ‘nothingreminds you of anything’ situation), as discussed in Section 3. Thus, concep-tually closed sets of increasing size and complexity can form.
8. Conclusions
We suggest that it was not a change to any particular brain area thatenabled the threshold to cumulative cultural evolution to be crossed, buta change to how the brain functions as a whole, and this change can bearticulated using a mathematical model.It has been proposed that cultural evolution was made possible by a cog-nitive transition brought about by onset of the capacity for self-triggeredrecall and rehearsal. However, self-triggered recall requires that conceptsand ideas be accessible to one another (i.e., that they collectively constitutean integrated structure). We suggest that, much as models of self-sustaining,autocatalytic networks have been useful for understanding how the the originof life, and thus biological evolution, could have come about, they are alsouseful for understanding how the the origin of the kind of cognitive structurethat makes cultural evolution possible could have come about. Mental repre-sentations (such as memories, concepts, and schemas) play the role of ‘reac-tants’ and ‘catalysts’, and relationships amongst them (such as associations,remindings, and causal relationships) are the ‘reactions’. In the pre-cultural‘episodic’ mind, such reactions are catalyzed only by external stimuli. Ascranial capacity increases, representations become richer (more features orproperties are encoded), and thus reactions become more plentiful, leadingto streams of thought. Streams of thought cause the reaction network to20ecome even denser. Eventually, it becomes almost inevitable that a per-colation threshold is surpassed, and collectively the representations form anintegrated autocatalytic set. At this point, the mind can combine represen-tations and adapt them to specific needs and situations, and thereby becomea contributor to culture. We posit that an interacting population of suchminds is capable of cumulatively creative cultural evolution.Our model provides a means of differentiating between the episodic mindof
Homo habilis , the mimetic mind of
Homo erectus , and the mind of ayoung child. The proposed similarities and differences amongst them aresummarized in Table 2.
Variable Variable Homo Homo Young(Symbol) (In Words) habilis erectus Child N MR richness Low High High X Set of existing MRs Large Large Small P Reactivity Fixed Tuned to N Tuned to Nλ Catalysis rate Small Larger Small W t Working memory Small Larger Small L t Long-term memory Small Much larger Small M t Memory ( W t and/or L t ) Small Much larger Small CCP s Streams of thought Absent Present Absent C Conceptual Closure Absent Present AbsentTable 2. Summary comparison of the episodic mind of
Homo habilis , themimetic mind of
Homo erectus , and the mind of a young child.We suggest that in the mind of a developing child, MRs are sufficientlyrich, and the catalysis rate is sufficiently high, but memory is not yet packeddensely with enough MRs for CCPs to occur. As more MRs are encoded inlong-term memory, the effective rate of cognitive updating increases as itemsget encoded into long-term memory (the more items there, the more likelyone is to catalyze a cognitive updating reaction). This, in turn, increasesworking memory, which also eventually increases the rate of cognitive up-dating reactions from within working memory. In short, while the OOC is This is supported by findings that measures of performance on tests of working memoryincrease continuously between early childhood and adolescence (Gathercole et al., (2004). N and corresponding fine-tuning of P , in thedevelopmental transition of a young child to a contributing member of cul-ture, N and P are sufficiently high but X is not sufficiently dense for theformation of CCPs.While our model is individual-based, it also allows for societal interactionsand development. More precisely, if we have a collection of minds (society),then an item m ∈ M t in one individual can (through speech, gesture, or ac-tion) be regarded as a stimulus s for another individual, and thereby providean ‘updating by stimuli’ reaction in that individual. Thus the collection ofminds (together with other stimuli from the environment) provides a higher-level network structure.There are several caveats and limitations to this work. Firstly, we havenot dealt with the problems that have arisen in psychology and artificialintelligence in trying to deal with mental representations, reasoning and in-ference, creativity, and language understanding. These challenges are notthe subject of this paper. Nevertheless, we believe that by introducing anarchitecture conducive to self-organized emergent cognitive complexity, theproposed framework has the potential to facilitate such efforts.Also, in this paper we have not provided a mechanism that accounts forawareness, though one of us has proposed such a mechanism elsewhere (Gab-ora (2002a)). Nor have we provided a mechanism for subconscious processingwithin working memory, although one of us has published on this extensivelyelsewhere (Gabora (2002b, 2010, 2018b); Gabora and Ranjan (2013)). In asubsequent paper, we will aim to show how implicit processing fit into thismodel.Indeed, the model proposed here is quite general and schematic. Tomake it precise enough to allow a detailed mathematical analysis requiresspecifying a large number of assumptions and parameter choices, estimatedfrom empirical studies. Since the goal of the present paper is merely to showthat, for a range of reasonable values, the kind of cognitive reorganizationthat we propose made cultural evolution possible is likely to occur, and leadsto testable predictions. Rather than exploring any particular choice here—atopic that we wish to pursue in future work—our approach is to considergeneric properties of the simple and general model described.Other fruitful arenas for future research would be to more fully explorehow transitions in the network structure map onto cognitive developmentalstages, or how different ways of achieving a closure structure map onto per-sonality differences. We might speculatively suggest that the fact that there22re different ways of satisfying the criterion (for example, very high reactivitywith a medium number of episodes, versus a very high number of episodesand medium reactivity) could form the basis of fascinating personality test.A person with high reactivity might be likely to understand things in termsof analogies and metaphors and make decisions in a context-dependent way,whereas a person with a high number of episodes would be more likely tounderstand things in terms of their large repertoire of cultural teachings andmake decisions according to how its been done in the past as opposed totaking context-specific factors into account.We conclude by suggesting that the common mathematical approach oftwo superficially different evolution processes (the origin of life and the originof culture) depends on a certain kind of deep abstract structure, which hasalso recently been identified in other fields, such a ecology (Gatti et al., 2017)and economics (Hordijk, 2013). This may prove useful for studying emergentprocesses in other fields.
9. Acknowledgments
We thank an anonymous reviewer for a number of helpful comments andsuggestions. This work was supported by a grant (62R06523) from the Nat-ural Sciences and Engineering Research Council of Canada.
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0. Appendix: Justification of Proposition 1
Let R t be the set of actual updating reactions that occur in W t up totime t (as noted, we assume that t is large enough so this set is nonempty),and let r , r , . . . , r k be a list of the sequence of these reactions in the orderthey occur. The reactant of each reaction r i in R t is either an element of M (which is a subset of F ) or another attended item that is the productof an earlier reaction r j (where j < i ) in the sequence (this holds even inthe presence of attention shifts). Moreover, each reaction in R t is catalysedeither by an stimulus (which is an element of F ) or by the product of anearlier reaction r j (where j < i ) in the sequence. Thus, R t satisfies therequired properties to be a CAF (constructively autocatalytic F-generatedset) as defined in Mossel and Steel (2005), and so is a RAF.For the second part of Proposition 1, if λ is sufficiently small then therate of cognitive updating reactions will be less than the rate µ at whichitems in working memory become no longer present in this set. By standard(birth-death process) arguments, it follows that a sequence of consecutivecognitive updating reactions (as in Fig. 2(ii)) will eventually die out, andas λ declines further the frequency of such sequences of length greater than1 tends to zero. However, as, λ grows beyond the rate at which cognitiveupdating reactions exceeds µµ