Modeling a Cognitive Transition at the Origin of Cultural Evolution using Autocatalytic Networks
RRunning Head:COGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS
Modeling a Cognitive Transition at the Origin of CulturalEvolution using Autocatalytic Networks
Liane Gabora
Department of Psychology, University of British Columbia
Mike Steel
Biomathematics Research Centre, University of CanterburyThis is a pre-publication draft. There may be minor differences from the version acceptedfor publication in Cognitive Science.Corresponding Author:Liane GaboraDepartment of Psychology, University of British ColumbiaOkanagan Campus, Kelowna BC, CanadaEmail: [email protected]
LG acknowledges funding from Grant 62R06523 from the Natural Sciences and Engineering ResearchCouncil of Canada. We thank Russell Gray for drawing our attention to the paper by Stout et al. thatinspired this one. We thank Claes Andersson and anonymous reviewers for comments, and thank ConnerGibbs for assistance with the manuscript. a r X i v : . [ phy s i c s . s o c - ph ] J u l OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 2
Abstract
Autocatalytic networks have been used to model the emergence of self-organizingstructure capable of sustaining life and undergoing biological evolution. Here, we modelthe emergence of cognitive structure capable of undergoing cultural evolution. Mentalrepresentations of knowledge and experiences play the role of catalytic molecules, andinteractions amongst them (e.g., the forging of new associations) play the role of reactions,and result in representational redescription. The approach tags mental representationswith their source, i.e., whether they were acquired through social learning, individuallearning (of pre-existing information), or creative thought (resulting in the generation of new information). This makes it possible to model how cognitive structure emerges, andto trace lineages of cumulative culture step by step. We develop a formal representation ofthe cultural transition from Oldowan to Acheulean tool technology using ReflexivelyAutocatalytifc and Food set generated (RAF) networks. Unlike more primitive Oldowanstone tools, the Acheulean hand axe required not only the capacity to envision and bringinto being something that did not yet exist, but hierarchically structured thought andaction, and the generation of new mental representations: the concepts EDGING,THINNING, SHAPING, and a meta-concept, HAND AXE. We show how this constituteda key transition towards the emergence of semantic networks that were self-organizing,self-sustaining, and autocatalytic, and discuss how such networks replicated through socialinteraction. The model provides a promising approach to unraveling one of the greatestanthropological mysteries: that of why development of the Acheulean hand axe wasfollowed by over a million years of cultural stasis.
Keywords:
Achuelean hand axe, autocatalytic network, cognitive transition, culturalevolution, origin of culture, Reflexively Autocatalytic Food set generated network (RAF),representational redescription, semantic networkOGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 3
The question of how biological evolution arose—i.e., the origin of life (OOL)problem—is one of the biggest unsolved questions of science. Since cultural change iswidely viewed as a second evolutionary process, the question of how cultural evolutionarose—i.e., the origin of culture (OOC) problem—presents another unsolved problem. By culture , we mean extrasomatic adaptations, including behavior and artifacts, that aresocially rather than genetically transmitted. Although cultural transmission —in whichone individual acquires elements of culture from another—is observed in many species,cultural evolution is much rarer (and perhaps, unique to our species). By evolution , wemean change that is cumulative (later innovations build on earlier ones), adaptive newinnovations that yield some benefit for their bearers tend to predominate), and open-ended(the space of possible innovations is not finite, since each innovation can give rise tospin-offs). The literature on cultural evolution, including mathematical and computationalmodels, is vast, flourishing, and interdisciplinary (Bentley, Hahn, & Shennan, 2004; Boyd& Richerson, 1988; Cavalli-Sforza & Feldman, 1981; Enquist, Ghirlanda, & Eriksson, 2011;Gabora, 2013; Holden & Mace, 2003; Mesoudi & Laland, 2006; Powell, Shennan, &Thomas, 2009) with increasing recognition paid to the cognitive processes and abilities(e.g., problem solving, analogy, and so forth) underlying the generation of cultural novelty(Fogarty, Creanza, & Feldman, 2018; Gabora, 2019; Henley & Kardas, 2020; Heyes, 2018;Overmann & Coolidge, 2019). However, although cognitive science has made considerableprogress in understanding how such processes are carried out, little effort has beendevoted to the question of how hominids acquired the capacity for an integratedconceptual framework that guides how and when these processes are applied.This paper addresses what kind of structure minds must possess to be capable ofcumulative, open-ended cultural evolution, and how hominid minds acquired this kind ofstructure. We propose a network-based model that tags mental representations with their The term ‘cultural evolution’ is occasionally used in a less restricted sense to refer to novelty generationand transmission without the requirement of cumulative, adaptive, open-ended change, e.g., (Whiten, 2019).
OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 4source, i.e., whether they were acquired through individual learning, social learning, orcreative reflection. This makes it possible to model how a semantic network emerges, andto trace cumulative change in cultural lineages step by step. The approach isdemonstrated using a formal representation of one of the earliest and most well-studiedtransitions in human cultural history: the transition from Oldowan to Acheulean tooltechnology approximately 1.76 million years ago (mya).Although evolutionary theory is widely applied to culture, natural selection cannotshed light on the origins of an evolutionary process (as Darwin himself noted); it can onlyexplain how, once self-sustaining, self-reproducing entities have come into existence, theyevolve. However, although natural selection does not address the ‘origins’ question,another theory, the theory of autocatalytic networks, does. This theory grew out ofstudies of the statistical properties of random graphs consisting of nodes randomlyconnected by edges (Erdös & Rényi, 1960). As the ratio of edges to nodes increases, thesize of the largest cluster increases, and the probability of a phase transition resulting in asingle giant connected cluster also increases. The recognition that connected graphsexhibit phase transitions led to their application to efforts to develop a formal model ofthe OOL, namely, of how abiogenic catalytic molecules crossed the threshold to the kindof collectively self-sustaining, self-replicating, evolving structure we call ‘alive’ (Kauffman,1993, 1986). In the application of graph theory to the OOL, nodes represent catalyticmolecules, and edges represent reactions. It is exceedingly improbable that any catalyticmolecule present in the primordial soup of Earth’s early atmosphere catalyzed its ownformation. However, reactions generate new molecules that catalyze new reactions, and asthe variety of molecules increases, the variety of reactions increases faster. As the ratio ofreactions to molecules increases, the probability increases that they will undergo a phasetransition. When, for each molecule, there is a catalytic pathway to its formation, theyare said to be collectively autocatalytic , and the process by which this state is achieved has Research on epigenetics and the origin of life has shown that natural selection is but one (albeit impor-tant) component of evolution (Gabora, 2006; Kauffman, 1993; Koonin, 2009; Segre, 2000; Vetsigian, Woese,& Goldenfeld, 2006; Woese, 2002).
OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 5been referred to as autocatalytic closure (Kauffman, 1993). The molecules thereby becomea self-sustaining, self-replicating structure (i.e., a living protocell (Hordijk & Steel, 2015)).Thus, the theory of autocatalytic networks has provided a promising avenue for modelingthe OOL and thereby understanding how biological evolution began (Xavier, Hordijk,Kauffman, M., & Martin, 2020).Autocatalytic networks have been developed mathematically in the theory ofReflexively Autocatalytic and Food set generated (RAF) networks (Hordijk & Steel, 2016;Steel, Hordijk, & Xavier, 2019). The term reflexively is used here in its mathematicalsense, meaning that every element is related to the whole. The term food set refers to thereactants that are initially present, as opposed to those that are the products of catalyticreactions. It has been demonstrated (both in theory and in simulation studies) that RAFscan evolve (through selection and drift acting on possible subRAFs of the maxRAF)(Hordijk & Steel, 2016; Vasas, Fernando, Santos, Kauffman, & Szathmáry, 2012).It has been proposed that autocatalytic networks hold the key to understanding theorigins of any evolutionary process, including the OOC (Gabora, 1998, 2000, 2013; Gabora& Aerts, 2009; Gabora & Steel, 2017). This kind of evolution has been referred to asSelf-Other Reorganization (SOR) because it interleaves internal self-organization withexternal interactions with other self-organizing networks (Gabora, 2019). In application tothe OOC, the products and reactants are not catalytic molecules but mentalrepresentations (MRs) of experiences, ideas, and chunks of knowledge, as well as morecomplex mental structures such as schemas and scripts (Tables 1 and 2).MRs are composed of one or more concepts: mental constructs such as ISLAND orBEAUTY that enable us to interpret new situations in terms of similar previous ones.The rationale for treating MRs as catalysts comes from the literature on conceptcombination, which provides extensive evidence that when concepts act as contexts for For related approaches, see (Andersson & Törnberg, 2019; Cabell & Valsiner, 2013; Muthukrishna,Doebeli, Chudek, & Henrich, 2018). Although we use the term ‘mental representation,’ our model is consistent with the view (commonamongst ecological psychologists and in the situated cognition and quantum cognition communities) thatwhat we call mental representations do not ‘represent,’ but rather, act as contextually elicited bridgesbetween mind and world.
OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 6other concepts, their meanings change in ways that are often nontrivial and that defyclassical logic (Aerts, Broekaert, Gabora, & Sozzo, 2016; Aerts, Gabora, & Sozzo, 2013;Hampton, 1988; Osherson & Smith, 1981). The extent to which one MR modifies themeaning of another is referred to here as its reactivity . A MR’s reactivity varies in acontext-sensitive manner. For example, in a study of the influence of context and mode ofthought on the perceived meanings of concepts (as measured by property applicabilitiesand exemplar typicalities), the concept PYLON was rated low as an exemplar of HAT,but in the context FUNNY (as in ‘worn to be funny’) it was rated high as an exemplar ofHAT (Veloz, Gabora, Eyjolfson, & Aerts, 2011). Thus, the degree to which PYLONqualified as an instance of a HAT changed dramatically depending on the context. Thecontext FUNNY had an even greater effect on the rating of MEDICINE HAT (as in thename of the Canadian town) as an instance of HAT. We say that the reactivity was highhere because the context exerted a dramatic influence on the perceived meaning. Eachinteraction between two or more MRs alters (however slightly) the network of associationstrengths in memory (Brockmeier, 2010; McClelland, 2011). Eventually, for each MR,there is an associative pathway to its formation, i.e., any given concept can be explainedusing other concepts, and new ideas can be reframed in terms of existing ones.Table 1
Application of graph theoretic concepts to the origin of life (OOL) and origin of culture(OOC).
Graph Theory Origin of Life (OOL) Origin of Culture (OOC) node catalytic molecule mental representation (MR)edge reaction pathway associationcluster molecules connected via reactions MRs connected via associationsconnected graph autocatalytic closure (Kauffman, 1986, 1993) conceptual closure (Gabora, 1998)In previous work, we used the RAF framework to model an initial transition towardOGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 7Table 2 Abbreviated terms used throughout this paper.
Abbreviation Meaning
OOL Origin of LifeOOC Origin of CultureMR Mental RepresentationsMR simple Mental RepresentationcMR complex Mental RepresentationRR Representational RedescriptionRAF Reflexively Autocatalytic and Food set generated (F-generated)CCP Cognitive Catalytic Processthe kind of cognitive organization capable of evolving culture (Gabora & Steel, 2017). Ourmodel followed up on the proposal that the increased complexity of
Homo erectus culturecompared with other species such as
Homo habilis reflected the onset of representationalredescription (RR), in which the contents of working memory were recursively restructuredby drawing upon similar or related ideas (Corballis, 2011; Donald, 1991; Gabora & Smith,2018; Hauser, Chomsky, & Fitch, 2002; Penn, Holyoak, & Povinelli, 2008). We showedhow the capacity for RR would have enabled the forging of associations between MRs,thereby constituting a key step toward an essentially ‘autocatalytic’ structure (Gabora &Steel, 2017). The present paper elaborates on the approach, showing how RR enabled theemergence of hierarchically structured concepts, making it possible to shift between levelsof abstraction as needed to carry out tasks composed of multiple subgoals.To address how the mind as a whole acquired autocatalytic structure, the modelpresented here is, by necessity, abstract. This paper does not distinguish betweensemantic memory (memory of words, concepts, propositions, and world knowledge) andepisodic memory (personal experiences); indeed, we are sympathetic to the view thatOGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 8these are not as distinct as once thought (Kwantes, 2005). Nor does it address how MRsare obtained (i.e., whether through Hebbian learning versus probabilistic inference).Although MRs are represented simply as points in an N –dimensional space (where N isthe number of distinguishable differences, i.e., ways in which MRs could differ), our modelis consistent with models that use convolution (Jones & Mewhort, 2007), random indexing(Kanerva, 2009), or other methods of representing MRs. We assume that associationsform between MRs but we do not address whether these associations are due to similarityor co-occurrence, and whether they are learned through Bayesian inference (Griffiths,Steyvers, & Tenenbaum, 2007) or other means. We view associations as probabilistic; thuswhen we say that a new association has been forged between two concepts we mean aspike in the probability of one MR evoking another, which we refer to here as the‘catalysis’ of one MR by the other. We view context as anything that influences theinstantiation of a MR in working memory (for example, the properties it possesses, or theexemplars it instantiates). Context in our model can be either external (e.g., an object orperson) or internal (e.g., other MRs). Although our approach is influenced by how contextis modeled in quantum approaches to concepts (Aerts et al., 2013, 2016), it is notcommitted to any formal approach to modeling context. We now summarize the key concepts of RAF theory. A catalytic reaction system (CRS) is a tuple Q = ( X, R , C, F ) consisting of a set X of molecule types, a set R ofreactions, a catalysis set C indicating which molecule types catalyze which reactions, anda subset F of X called the food set. A Reflexively Autocatalytic and F-generated set—i.e.,a RAF—is a non-empty subset R ⊆ R of reactions that satisfies the following twoproperties:1. Reflexively autocatalytic : each reaction r ∈ R is catalyzed by at least one moleculetype that is either produced by R or is present in the food set F ; andOGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 92. F-generated : all reactants in R can be generated from the food set F by using aseries of reactions only from R itself.A set of reactions that forms a RAF is simultaneously self-sustaining (by the F -generated condition) and (collectively) autocatalytic (by the RA condition) becauseeach of its reactions is catalyzed by a molecule associated with the RAF. A CRS need nothave a RAF, but when it does there is a unique maximal one. Moreover, a CRS, maycontain many possible RAFs, and it is this feature that allows RAFs to evolve (asdescribed in Section 6 of (Hordijk & Steel, 2016); see also (Vasas et al., 2012)).In the OOL context, a RAF emerges in systems of polymers (molecules consisting ofrepeated units called monomers) when the complexity of these polymers (as measured bymaximum length) reaches a certain threshold (Kauffman, 1993; Mossel & Steel, 2005).The phase transition from no RAF to a RAF incorporating most or all of the moleculesdepends on (1) the probability of any one polymer catalyzing the reaction by which agiven other polymer was formed, and (2) the maximum length (number of monomers) ofpolymers in the system. This transition has been formalized and analyzed(mathematically, and using simulations), and applied to real biochemical systems(Hordijk, Hein, & Steel, 2010; Hordijk, Kauffman, & Steel, 2011; Hordijk & Steel, 2004,2016; Mossel & Steel, 2005) and ecologies (Cazzolla Gatti, Fath, Hordijk, Kauffman, &Ulanowicz, 2018). RAF theory has proven useful for identifying how phase transitionsmight occur, and at what parameter values.In this application of RAFs to the OOC, we first summarize the archaeologicalevidence for a cognitive transition approximately 1.7 mya, limiting the discussion toaspects that either were not addressed elsewhere (Gabora & Steel, 2017) or that areessential in order to follow the arguments presented here. We then discuss cognitivemechanisms underlying the invention of the Acheulean hand axe, and present the RAFmodel of this. We conclude with a discussion of the implications of this new approach andideas for further developments.OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 10 The large cranial capacity of
Homo erectus (approximately 1000 cc, 25% larger thanthat of
Homo habilis (Aiello, 1996)) is believed to have played a role in a culturaltransition to significantly more complex tools, as epitomized by the Acheulean hand axe1.76 mya, shown in Fig. 1 (Edwards, 2001). Like its predecessor the Oldowan stone flake,the Acheulean hand axe was a multi-use implement, but whereas the former simplyrequires repeated percussive action, the latter is notoriously difficult to make (Pargeter,Khreisheh, & Stout, 2019; Stout, Toth, Schick, & Chaminade, 2008). It requires a skilled,multi-step process involving multiple different hierarchically organized actions, as shownin Fig. 2. The Acheulean hand axe is the most tangible evidence of a cognition transitioncharacterized by a suite of related abilities. This transition is thought to have involved theonset of autocuing : the capacity to voluntarily retrieve a specific memory item in theabsence of environmental cues (Donald, 1991). Encephalization likely played a role in theonset of autocuing by enabling memories to be encoded in sufficient detail to evoke oneanother based on relevant (i.e., situation-specific) similarities (Gabora & Smith, 2018).Autocuing paved the way for mental time travel : the capacity to escape the immediatepresent by remembering past episodes or imagining events taking place at other locations,or in the future (Corballis, 2011). Autocuing and mental time travel enabled individualsto engage in imaginative thought, and to reflect upon and update (i.e., elaborate, modify,restructure, and/or perform mental operations upon) the contents of working memory,drawing upon relevant knowledge or experience, as needed. This kind of recoding ofinformation has been referred to as representational redescription (RR) (Karmiloff-Smith,1992). In this paper, the term RR refers to any internally-generated modification to aMR’s network of associations, whether it be the result of a sudden flash of insight, or anew perspective on, or application for, an old idea. The capacity for autocuing, mental Detailed comparison of the making of Oldowan (
Homo habilis ) versus Acheulean (
Homo erectus ) tools,including the brain regions involved, can be found in (Stout et al., 2008).
OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 11
Figure 1 . Change in Early Stone Age technology and cranial capacity. From (Stout, 2008).OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 12time travel, and RR culminated in a suite of related abilities that include the rehearsaland refinement of skills and the miming of past or possible future events (Corballis, 2011;Donald, 1991).The recursive application of RR, such that the output of one redescription serves asthe input to the next, we refer to as abstract thought . It may be accompanied bybehavioral action that modifies the environment, and thereby tracks or externallymanifests this internal process. It is hypothesized that such MRs consisted of not justsensory representations of raw materials and the tools of which they are made, but also oftheir affordances with respect to the body, i.e., their capacity to be altered, used, ormanipulated. (See (Overmann & Coolidge, 2019) for further discussion of the content ofprimitive toolmakers’ MRs).Summarizing an argument developed in detail elsewhere (including discussions ofthe relationship of RR to the concept of ‘merge’ (Gabora & Smith, 2018), and to thepsychological literature on concept combination (Gabora & Aerts, 2009; Gabora & Kitto,2013; Gabora & Steel, 2017), we propose that RR was made possible because the larger
Homo erectus brain enabled a finer-grained associative memory such that episodic andsemantic knowledge could be encoded in greater detail, as illustrated in Fig. 3. This meantthat, once an individual had lived lived long enough to accumulate a sufficiently richrepository of experience, there was more overlap in his or her distributed representations.This in turn meant that there were more routes by which these MRs could evoke oneanother, and more ways for the individual to generate novel cultural contributions.RR enabled
Homo erectus to combine MRs and chain them into streams of thoughtor sequences of action, and mime past or possible future event sequences to others (sinceit is generally believed that complex language was not yet established). Although the evolution of language is stubbornly resistant to empirical inquiry (Hauser et al., 2014;Perreault & Mathew, 2012), it is thought that language as we know it, with syntax and grammar, camesubstantially after the Oldowan to Achuelian transition modeled here (Klein, 2009; Lieberman, 2007; Mithen,2006), most likely preceded by ‘protolanguage’ (Bickerton, 2007), and the use of gesture and mime (Corballis,2011, 2013; Donald, 1991). In this way, the content of experience could become detached from the immediatesensory perceptions of the ‘here and now’ (in what has been called ‘mental time travel’ (Corballis, 2011)).Since RR forges new associations between MRs, the onset of the capacity for RR could, through spreading
OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 13
Figure 2 . Left: initial (top), intermediate (middle), and final (bottom) stages in the makingof an Acheulean hand axe. Right: Physical processes required to bring the tool from initialto intermediate stage (top), and from the intermediate to the final stage (bottom). From(Stout, 2008).OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 14
Figure 3 . Schematic illustration of the proposed changes set into motion through theevolution of finer grained memory, culminating in an individual’s capacity to become acreative contributor to cultural evolution. Note that, for this sequence of events to unfold ina given individual, not only must that individual’s representations be sufficiently distributed(due to the biologically evolved changes depicted on the upper left) but they must also besufficiently plentiful (due to the developmental changes depicted on the upper right).OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 15
We now delve more deeply into the cognitive mechanisms underlying onset of thecapacity for Acheulean toolmaking, arguably the earliest significant transition in thearchaeological record. We cannot know exactly how the first Oldowan tool was invented,and there are different scenarios by which it could have come about. One scenario is thatthe inventor of this tool imagined the impact of percussive action on a stone, andcreatively redescribed the transformation of a stone into a tool. In this scenario, the newconcept TOOL was not imported from the external world; rather, using RR, thetoolmaker generated a mental image of something that did not currently exist. Thehominin developed a complex MR (cMR) composed of the simple MRs (sMRs) STONE,TOOL, and PERCUSSIVE ACTION. This cMR can be understood as: in the context ofthe catalyst percussive action , STONE may become a TOOL.However, there are other scenarios by which this cMR could have come about,through individual learning.
Individual learning refers to learning from the environmentby nonsocial means through direct perception. Note that in much of the cultural evolutionliterature, abstract thought and creativity, if mentioned at all, are equated with individuallearning, which is thought to mean ‘learning for oneself’ (e.g., (Henrich & Boyd, 2002;Mesoudi & Laland, 2006; Rogers, 1988). However, individual learning is distinctlydifferent from abstract thought. In individual learning (obtaining pre-existing informationfrom the environment through non-social means), the information does not change formjust because the individual now knows it. Going into a forest and learning for oneself todistinguish different kinds of insects is an example of individual learning. In contrast, in activation, affect other MRs, thereby facilitating categorization, generalization, and property induction. RRfacilitated the formation of abstract concepts, including complex and sometimes spontaneously-generated ad hoc concepts (Barsalou, 1983). Abstraction may be facilitated by dimensional reduction, ensuring thatconcepts contain no more detail than necessary. The MR of an object could be redescribed as affordingdifferent actions and uses, so as to alternate between different subgoals, as needed, to reach an ultimategoal. Note that unlike purely social hypotheses regarding this transition, RR would facilitate not just theability to make tools but the ability to demonstrate the process step-by-step to others; thus it could beput to use in social settings as well as technical tasks. The fact that PET imaging studies indicate thattoolmaking and language share overlapping neural circuity (Stout et al., 2008) suggests that RR may havecontributed to the evolution of language. We note that the model proposed in this paper does not rely on aprecise timeline for language origins.
OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 16abstract thought (reiterative processing of internally sourced mental contents), the information is in flux (Barsalou, 2005), and when this incremental honing process resultsin the generation of new and useful or pleasing ideas, behavior, or artifacts, it is said to becreative (Basadur, 1995; Chan & Schunn, 2015; Feinstein, 2006; Gabora, 2017).Since in individual learning, the information retains the form in which it wasoriginally perceived, it does not involve RR. For example, upon seeing boulders fall from acliff and splinter a stone flake below into something that could be used as a tool, a hominidcould have then imitated the percussive action of the falling boulders to create the firstintentionally manufactured tool. The distinction between individual learning and RR isnot black and white; it is possible that a certain amount of redescription was required torealize that one could intentionally mimic the action of the boulder on the rock. However,applying Occam’s razor, we will model the simple possibility that the initial idea for thecMR of using percussion to make a stone tool emerged through imitation of some kind ofaccidental breakage of a stone flake, and RR was not required. Note that even in thissimple scenario, the toolmaking process was far from trivial; it required careful deliberateaction (Toth & Schick, 2009, 2018). In any case, this not only resulted in a new concept(e.g., PERCUSSION) but also modified the affordances (in the sense of (Gibson, 1997)) ofSTONE (i.e., stone was now something that could be fractured through percussive action).Although there may have been some degree of convergent evolution, Oldowantechnology was transmitted through social learning processes such as imitation or guidedinstruction, from one generation to the next, and Acheulean technology built on thispre-existing technology, as indicated in Fig. 4. To make an Acheulean hand axe required(1) skillful coordination of perception and motor skills involving recursive modification ofan action according to the outcome of the previous action, and (2) shifting betweenhierarchically organized (short-term) sub-goals at different spatiotemporal scales toachieve the desired (long-term) outcome (Stout et al., 2008; Inizan, Reduron-Ballinger,Roche, & Tixier, 1999). The toolmaker had to bear in mind not just the current anddesired final states of the tool but also the multiple procedural actions—edging, thinning,OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 17
Figure 4 . Hierarchical organization of tasks in Acheulean toolmaking. From Stout, 2008.and shaping—required to achieve the final state. Since these actions were not yetobservable in the environment, the concepts EDGING, THINNING, and SHAPING hadto be generated from scratch.Given the cumulative increase in the sophistication of the Acheulean hand axe overtime (see Fig. ?? ), it appears not to have been the handiwork of one individual, but ratherinvented collectively, with the intentional scaffolding of each new improvement (e.g.,edging, thinning, and shaping), potentially separated by generations. Note that not onlydo EDGING, THINNING, and SHAPING constitute new MRs but, collectively, theyconstitute a cMR, that of how to make an Acheulean hand axe. Moreover, each newconcept further modified the perceived affordances of STONE (i.e., stone was no longerjust something that could be fractured with percussive action, but something that couldalso be edged). Although (as mentioned previously) it is generally believed that complexlanguage was not yet possible, social learning processes involving demonstration and/orimitation of the finished product would have enabled spatiotemporal diffusion of theseOGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 18‘partial solutions.’ We now introduce the mathematical framework and terminology that will be usedto model the invention of the Oldowan and Acheulean tool technologies.
All mental representations (MRs) in a given individual i are denoted X i , and aparticular MR x i in X i is denoted by writing x ∈ X i . As in an OOL RAF, we have a foodset ; for individual i , denoted F i . In the OOC context, F i encompasses MRs for individual i that are either innate, or that result from direct experience in the world, includingnatural, artificial, and social stimuli. F i includes everything in the long-term memory ofindividual i that was not the direct result of individual i engaging in RR. This includesinformation obtained through social learning from someone else who may have obtained itby way of RR. For example, if individual i learns from individual j how to edge a blankflake through percussive action, this is an instance of social learning, and the conceptEDGING is therefore a member of F i . F i also includes existing information obtained by i through individual learning(which, as stated earlier, involves learning from the environment by nonsocial means), solong as this information retains the form in which it was originally perceived (and doesnot undergo redescription or restructuring through abstract thought). The crucialdistinction between food set and non-food set items is not whether another person wasinvolved, nor whether the MR was originally obtained through abstract thought (by someone ), but whether the abstract thought process originated in the mind of theindividual i in question. Thus, F i has two components:1. S i denotes the set of MRs arising through direct stimulus experience that have beenencoded in individual i ’s memory. It includes MRs obtained through social learning Non-verbal transmission of stone-tool technologies and its relationship to language evolution is discussedfurther in (Morgan et al., 2015; Ohnumma, Aoki, & Akazawa, 1997).
OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 19from the communication of an MR x j by another individual j , denoted S i [ x j ], andMRs obtained through individual learning, denoted S i [ l ], as well as contents ofmemory arising through direct perception that do not involve learning, denoted S i [ p ].2. I i denotes any innate knowledge with which individual i is born.A particular catalytic event (i.e., a single instance of RR) in a stream of abstractthought in individual i is referred to as a reaction, and denoted r ∈ R i . A stream ofabstract thought, involving the generation of representations that go beyond what hasbeen directly observed, is modeled as a sequence of catalytic events. Following (Gabora &Steel, 2017), we refer to this as a cognitive catalytic process (CCP). The set of reactionsthat can be catalyzed by a given MR x in individual i is denoted C i [ x ]. The entire set ofMRs either undergoing or resulting from r is written A or B , respectively, and a memberof the set of MRs undergoing or resulting from reaction r is denoted a ∈ A or b ∈ B .The term food set derived , denoted ¬ F i , refers to mental contents that are not partof F i , i.e., the products of any reactions derived from F i and encoded in individual i ’smemory. Its contents come about through mental operations by the individual in question on the food set; in other words, food set derived items are the direct product of RR. Thus, ¬ F i includes everything in long-term memory that was the result of one’s own CCPs. Itmay include a MR in which social learning played a role, so long as the most recentmodification to this MR was a catalytic event ( i.e., it involved RR). ¬ F i consists of allthe products b ∈ B of all reactions r ∈ R i .The set of all possible reactions in individual i is denoted R i . The mental contentsof the mind, including all MRs and all RR events is denoted X i ⊕ R i . This includes F i and ¬ F i . Recall that the set of all MRs in individual i , including both the food set andelements derived from that food set, is denoted X i . R i and C i are not prescribed inadvance; because C i includes remindings and associations on the basis of one or more This distinction between food set and food set derived may not be so black and white but for simplicitywe avoid that subtlety for now.
OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 20shared property, different CCPs can occur through interactions amongst MRs.Nevertheless, it makes perfect mathematical sense to talk about R i and C i as sets. Table 3summarizes the terminology and correspondences between the OOL and the OOC.Table 3 Terminology and correspondences between the Origin of Life (OOL) and the Origin of Cul-ture (OOC).
Term Origin of Life (OOL) Origin of Culture (OOC) X i all molecule types in protocell i all mental representations (MRs) in individual ix ∈ X i a molecule in X i a MR in X i F i food set for protocell i innate or directly experienced MRs by ir ∈ R i a particular reaction in i a particular representational redescription (RR) in iC i [ x ] reactions catalyzed by x in i RR events ‘catalyzed’ by x in i ( x, r ) ∈ C x catalyzes r x ‘catalyzes’ redescription of ra ∈ A member of set of reactants in r member of set of MRs undergoing rb ∈ B member of set of products of r member of set of MRs resulting from r ¬ F i non food set for i ; (i.e., all B of R i ) MRs resulting from R i ; (i.e., all B of R i )Our model includes elements of cognition that have no obvious parallel in the OOL.We denoted the subject of attention at time t as ˚ w t . It may be an external stimulus, or aMR retrieved from memory. Any other contents of X i ⊕ R i that are accessible to workingmemory, such as close associates of ˚ w t , or recently attended MRs, were denoted W t , with W t constituting a very small subset of X i ⊕ R i . In the present paper, the focus is not onthese OOC-specific components of the model in order to tackle the question of hownon-food set derived MRs (i.e., a non-empty ¬ F ) came about, because these non-food setderived MRs are essential to the emergence of a semantic network that is self-organizingand autocatalytic.Now that the mathematical framework has been introduced, let us compare theOGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 21 Figure 5 . Left: Sources of simple and complex mental representations (sMRs and cMRs)and symbols used here to depict them. Right: cMRs and the sMRs of which they arecomposed, involved in the invention of the Oldowan tool (top row) and the Acheulean handaxe (lower rows). For each tool, only one scenario discussed in the text is portrayed here.Each instance of social learning (Column 4) must be preceded by a relevant instance ofindividual learning (Column 2) or representational redescription (RR) / abstract thought(Column 3).cognitive processes involved in the invention of Oldowan versus Acheulean tools from theperspective of RAFs using an autocatalytic framework. This is illustrated in Fig. 5 andFig. 6.
We begin by modeling the invention of an Oldowan tool by individual learning andimitation of the possible effect of percussive action on stone, arising through observationof accidental breakage (as discussed above). The invention involves noticing thatpercussive action increases the capacity of a rock to be used as a tool. It involves theformation of an association between the concepts ROCK and TOOL, and results in a cMROGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 22
Figure 6 . Left: Key showing the depiction of complex MRs arising through individuallearning, social learning, representational redescription (RR) or abstract thought, or a com-inbation of these. Right: Schematic representation of possible events culminating in theinvention of Oldowan (top) and Acheulean (bottom) tools. Top right: Individual i obtainsan understanding of percussion through individual learning by watching falling rocks splin-ter the stone below. Individual i imitates the action of the falling rock on a piece of stone,thereby creating a tool. Individual j obtains the toolmaking technique from individual i through social learning. Bottom right: Individuals i and j both acquire the concept ofPERCUSSION through social learning from their parents, but only in i does it undergocatalysis to generate the concept of EDGING, which i shares with j through social learn-ing. Similarly, j invents the concept THINNING and shares it with i , and i invents theconcept SHAPING and shares it with j . At this point, they both possess the entire skillset to make an Acheulean hand axe. Note that although for simplicity this sequence isportrayed here with only two individuals, in reality the multiple stages in the invention ofthis tool likely involved numerous individuals spanning generations. As in Fig. 5, only oneof the scenarios discussed in the text is portrayed here.OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 23that relates stone, percussive action, and tool.Note that the inventor’s thought process involves recursion, in the sense that theoutput of a previous percussive action serves as the input to the decision of whether tocontinue, and recursive processing continues until the task is complete. However, since nonon food set MRs are derived, there is no ‘internally catalyzed reaction’ as we are definingit. Therefore, from a RAF perspective, the mind of an early hominid that relied onOldowan technology can be described as one for which all mental contents are members ofthe food set of innate or directly experienced MRs. Thus, the set of non food set MRs isempty. In terms of the formalism we are using, Q = ( X, F ); in other words, we need notconsider R and C .For individual k ( k = i, j ), let P k be the complex MR that combines the sMRsSTONE, PERCUSSION, and TOOL. Thus, in the Oldowan setting illustrated in Fig. 6,the generation of a tool through either individual learning (in i ) or social learning (in j )amounts to adding P k to the food set of individual k . Formally, we can write this as: F i F i ∪ { P i } , where P i ∈ S i ( l ) , and F j F j ∪ { P j } , where P j ∈ S j ( P i ) . Thus, the first cMR results from individual learning, whereas the second arises from sociallearning by individual j of the concept P i from individual i .Note that although the sMRs STONE, PERCUSSION, and TOOL are connected byassociations, these associations were not obtained through abstract thought, but throughobservations of cause and effect in the external world. Since invention of the Oldowan toolrequired only one cMR (the CMR of how to make an Oldowan tool), there would havebeen no back-and-forth social exchange of partial solutions involved in its invention, andthere are no higher-level cMRs.OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 24 Acheulean tools were the culmination of several (perhaps spatiotemporallyseparated) steps that intertwined individual learning, social learning, and creativethinking, as illustrated in Fig. 6. To model the cultural transition from Oldowan toAcheulean technology, we begin with social transmission of the cMR for the process ofmaking an Oldowan tool. In the mind of each individual that acquired this cMR throughsocial learning, the food set was enlarged, as described above. Social transmission of thiscMR continued for generations before it was elaborated.Elaboration entailed three insights into new ways of processing the basic Oldwowantool to make it more useful. These insights are represented as ‘catalysis events’ becausethey resulted in the generation of something new: a new MR. Each catalysis event cameabout through a CCP and resulted in a new non food set item. Catalyzed reactionstransform an element of F k into an element of ¬ F k . For an individual k (where k = i, j ),we write a k b k −→ c k to denote the reaction that transforms one MR ( a k ) to a resulting MR c k (in ¬ F k ) by catalyst b k .The first catalysis event was provoked by the context: need to sharpen periphery .This context was internally represented as a thought, or MR. It caused modification of the reactant , PERCUSSION, to generate a product : the new concept EDGING. SinceEDGING is connected through association to ROCK, this event expands the affordances ofROCK (i.e., it is now perceived as something that can be edged). Affordances are a kindof association and, as such, they increase the connectivity of the conceptual network. Werepresent this by a catalyzed reaction (and the associated individual learning) as follows: P i p i −→ E i , F i F i ∪ { E i } , (1)where p i is the catalyst MR need to sharpen periphery , and E i ∈ S ( l ) is the resulting cMR.The specifics of the situation that inspired the invention—what we are modeling asthe context that ‘catalyzed’ this event—need not be socially transmitted. Thus, what wasOGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 25invented is not necessarily identical to what is socially transmitted. It is the newaffordance of ROCK and its association with the new concept of EDGING that aresocially transmitted. We represent this transmission event as follows: F j F j ∪ { E j } , E j ∈ S j ( E i ) . (2)In the second catalysis event, the context was need to thin the center . The reactantEDGING was modified to generate another product, the new concept of THINNING. Thiscan be represented as follows: E j t j −→ T j , F j F j ∪ { T j } , (3)where t i is the catalyst MR ‘need to thin centre’ and T j ∈ S j ( l ) is the resulting cMR.Similarly, in the context, need to create symmetrical shape , the reactant—the conceptTHINNING—was modified to generate another product, the concept of SHAPING. Theformal description of these two catalytic processes is analogous to that of the formation ofthe EDGING cMR.To summarize, the cultural evolution of Acheulean technology depicted in Fig. 6 isdescribed formally in the following sequence of six processes, where steps (i) to (iii)correspond to equations (1) to (3) above. Again, although for simplicity we consider onlytwo individuals, the steps described as catalyzed reaction were likely contributed byindividuals separated across generations. Catalyzed reactions take place in steps (i), (iii)and (v). For example, in step (v), the catalyst is the MR of ‘need symmetrical shape’,denoted s i . S i and S j are the resulting complex MRs in individuals i and j , respectively.OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 26(i) [RR leading to E by i ] P i p i −→ E i , F i F i ∪ { E i } ;(ii) [social learning of E from i by j ] F j F j ∪ { E j } , E j ∈ S j ( E i );(iii) [RR leading to T by j ] E j t j −→ T j , F j F j ∪ { T j } ;(iv) [social learning of T from j by i ] F i F i ∪ { T i } , T i ∈ S i ( T j );(v) [RR leading to S by i ] T i s i −→ S i , F i F i ∪ { S i } ;(vi) [social learning of S from i by j ] F j F j ∪ { S j } , S j ∈ S j ( S i ) . The formation of abstract concepts such as SHAPING was essential for theemergence of more extensive autocatalytic structure because abstract concepts tend tobecome more densely connected through associations than superficial concepts. Asextreme examples, the concepts DEPTH and OPPOSITE are relevant to almost everyknowledge domain. The concepts that arose in the invention of the hand axe may be lesswidely applicable than concepts such as OPPOSITE, but they could potentially beapplied to other domains (such as food preparation). Abstract concepts create newaffordances for existing concepts (e.g., the concept SHAPING could have createaffordances for ANIMAL SKIN that enabled it to be turned into clothing). This thenfurther increased the density of associations.The Acheulean hand axe required not just the invention of the three cMRsassociated with each phase of the toolmaking process, but also recursive RR on them so asto generate an even more complex MR: the representation of the entire process of makinga hand axe. If we denote this complex meta-RR (capturing the entire process of making ahand axe) in individual i by H i , then we can describe the generation of H i by the(catalysed) reaction: E i + T i + S i c i −→ H i , (4)where the catalyst c i is the realization by individual i that combining E , S , and T willOGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 27 E i E j T j T i H i H j S i S j t j s i p i c i c j catalyzing MR in individual *MR for reactions in individual *reaction pathwayRR (reaction)catalysis c ⇤ , p ⇤ , s ⇤ , t ⇤ P ⇤ , E ⇤ , S ⇤ , T ⇤ , H ⇤ P i social learning Figure 7 . Part of the RAF structure involved in the invention of the Acheulean hand axe.Again, although for simplicity we have only individuals i and j , these steps were likelyspread out spatiotemporally. The figure depicts the processes labeled (i)–(vi) in the text, aswell as the process of combining the three steps EDGING, THINNING, and SHAPING, intothe final mental representation in each of the two individuals of how to make an Acheuleanhand axe, Hi and Hj .lead to the desired tool. The recognition (on the part of both individual i and individual j ) that the entire series of steps can be clumped together as ‘how to make an effectivetool’ constitutes yet another catalyzed reaction, as indicated in Fig. 7.The invention of the Acheulean hand axe corresponds to the emergence of RAF setsof MRs that are close associates, and accessible to one another. In particular, RR enablesthe content of working memory to be updated through abstract thought or reflectiondrawing on content from long-term memory, with or without an environmental stimulus Although successful completion of a task may result in neural signals that reinforce the eliciting behavior,that happens after the action has taken place; it is not the catalyst. The catalyst acts before the action hastaken place. It is the thought that prompts the action to take place. Creative insights (i.e., those that make significant contributions to culture) often arise subconsciously;
OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 28acting as a reminder or cue. We describe this more formally as follows, following (Gabora& Steel, 2017).We denote each MR in a RR reflection process as m ∈ M t . We say that ˚ w ∈ W t iscatalyzed by an item m ∈ M t . This ‘reaction’ updates the subject of thought, which isnow denoted ˚ w ∈ W t + δ . A single step RR (referred to in (Gabora & Steel, 2017) as cognitive updating ) is denoted: ˚ w m −→ ˚ w , and ˚ w w. A sequence of recursive RR events, which, as mentioned above, is referred to as aCCP, is described as: C = ˚ w t (1) , ˚ w t (2) , . . . , ˚ w t ( k ) , (where ˚ w t ( i ) ∈ W t ( i ) and where t ( i ) values are increasing), such that each MR ˚ w t ( i ) is thereactant catalyzed by an environmental stimulus or MR from memory to generate a newMR, the product of that reaction.Thus, the CCP that connected EDGING, THINNING, and SHAPING resulted in ameta-cMR composed of three hierarchically structured cMRs, which were themselvescomposed of simple MRs. This constituted an important step toward a self-organizing,autocatalytic structure, not just because the CCPs forged associations between items inmemory but because (as discussed above) the abstract concepts EDGING, THINNING,and SHAPING could potentially be applied to other domains, creating still moreassociations. We now ask: does the Acheulean mind as described above contain a genuine RAF?To answer this question, we must consider the mean rate at which RR reactions are takingplace, denoted λ , and whether or not this exceeds a certain threshold. We can describe i.e., they arise from just beyond the confines of working memory (Bowers, Farvolden, & Mermigis, 1995). OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 29this more precisely as follows (from (Gabora & Steel, 2017), where a proof is provided). Proposition 1. Q contains a RAF that increases in size with time t (namely the set ofRR reactions that actually occur between time 0 and t ). Moreover, while λ is below acritical threshold, CCPs in this RAF are short and few in number, but when λ exceeds thisthreshold, CCPs become more frequent, persistent and complex. The RAF described in Proposition 1 has the additional feature of being a‘constructively autocatalytic F-generated set’, as defined in (Mossel & Steel, 2005). Such aRAF has the property of being self-organising, and able to self-replicate and evolve (albeitin an inefficient manner, without a self-assembly code). In the current cultural context, werefer to such a RAF as a persistent cognitive RAF, or simply, a cognitive RAF . In ourcultural context, λ is expected to vary positively with the complexity of the existingnetwork structure (more ways to reflect on something new) and negatively with the degreeto which one’s internal model already appears to faithfully capture the content of one’senvironment (nothing left to think through).Returning to the question with which we began this section, although the mind ofthe Acheulean toolmaker did not achieve a cognitive RAF, it achieved what could becalled a transient RAF because it contains the cognitive equivalent of catalyzed reactions(as discussed above), and it appears, for an instant, like a RAF. A transient RAF is notself-organizing, and therefore it cannot generate open-ended cultural novelty. However,compared to the mind of the Oldowan toolmaker, in which (as far as we know from thearchaeological evidence) there were no catalyzed reactions, it marks the crossing of asignificant hurdle toward the achievement of genuine, persistent RAF structure.The next question is: once hominids were capable of recursive, hierarchicallystructured thought and creative problem solving, why was the invention of the Acheuleanhand axe followed by approximately one million years of cultural stasis (Tattersall, 1998)?This is an open and much-pondered question in the archaeological literature, and the It is assumed that t is sufficiently large that RR reactions have commenced, and that the rate at whichnew environmental stimuli appear is bounded. OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 30autocatalytic approach to culture developed here suggests a tentative answer. Specifically,our model suggests that this was because λ (the mean rate at which RR reactions occur)did not rise above a critical threshold to generate self-sustained cognitive reorganization,meaning that any CCPs that arose were short and few in number. Although in the mind of the Acheulean toolmaker the RAF was only transient, anddid not self-organize and evolve in an open-ended manner, it yielded an ongoingdynamical process nonetheless, by way of its influence on other individuals. As mentionedearlier, based on current thinking, the above model assumes that although early hominidsthat did not yet possess complex language, the results of creative thought—modelled hereas CCPs—could extend beyond a single individual through social learning and pedagogy(Tehrani & Riede, 2008). This means that a social group can be described as ahigher-level transient RAF that follows the same processes as described earlier.We model this as follows. Given a social group G composed of individuals i , j , ...,the collection M of all MRs in the social group is the disjoint union of the MRs in eachindividual mind. The union is disjoint because m i and m j refer to MRs in differentindividuals ( i and j ). When the MRs m i and m j in two individuals concern the samefeature of the world, we say that m i and m j are homologous , denoted by writing m i ∼ m j .If individual j provides the context that triggers a RR event or creative insight in anotherindividual i , the process of cognitive change extends across two individuals. Moreprecisely, if a reaction ˚ w i s −→ ˚ w i in individual i is catalyzed by a MR s ∈ S ( w j ) then wecan (formally) regard this as the catalyzed reaction˚ w i w j −→ ˚ w i . (5)Note that the MRs involved in this reaction as reactant and product are in the mindof one individual ( i ), whereas the catalyst is in the mind of another ( j ). Therefore, weobtain an equivalence ( ≡ ) between social learning and a cognitive reaction (involving aOGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 31catalyst in a different mind). This leads to the notion of a RAF that consists of reactionsand CCPs within and between the items in the collective minds of the social group. Sociallearning processes enable a MR (such as the procedure used to produce a hand axe) tobecome established as homologous MRs across individuals, and spread amongst groupmembers in G , as illustrated in Fig. 7. Thus, the transient RAF replicates acrossindividuals of a social group. The size of the resulting CCPs in the group as a whole isinfluenced by two parameters. The first is the structure of the digraph (directed graph) D with vertex set G and an arc from i to j if individual i is able to communicate concepts toindividual j . Note that D depends on time; for example, new groups of individuals formand split over time.The connectedness of D could vary from a single individual with arcs to and fromall others (a political leader, celebrity, or ‘guru’), to a network in which each individualhas an arc to every other individual. A second parameter, denoted ρ , scales the rate atwhich catalysis events of the type described in Reaction (5) above occur when ( j, i ) is anarc of D . Thus, when ρ = 0, it is never the case that one individual provides the contextthat triggers RR in another. In reality, the rate of catalysis for the arc ( j, i ) may dependmore finely on i and j , so ρ is treated as an overall scaling factor. The response of CCPsin the social group to increasing ρ (presumably related to the emergence of increasinglysophisticated communication) is summarized in the following result (an analogue ofProposition 1 but at the level of the social group). Recall that any digraph has a uniquecomposition into strongly connected components. The following result follows from asimple percolation argument on directed graphs (see Appendix). Proposition 2.
For small values of ρ , most CCPs occur within individuals, andhomologous items tend to occur only between closely linked individuals (in D ). As ρ increases, CCPs grow in size and involve longer chains of catalyzation events, leading tohomologous items spreading throughout each strongly connected component of D . OGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 32
To understand how cultural evolution got started, we must ask what kind ofsemantic structure would be capable of initiating and sustaining open-ended culturalchange, and examine how such structure came about in the minds of our ancestors.Building on earlier work (Gabora, 1998; Gabora & Steel, 2017; Gabora, Leijnen, Veloz, &Lipo, 2011; Veloz, Tempkin, & Gabora, 2012), this paper examines early
Homo cognitionthrough a particular lens: the emergence of semantic structure that is self-organizing,self-reproducing, and autocatalytic. Of course, minds are part of living organisms, whichhave these properties, but we are interested in the emergence of a second-order level ofself-organizing structure that pertains not to cellular or organismal processes but to thewebs of associations by which hominids weave together an understanding of their world.We suspect that these properties were as important to cultural evolution as they were tobiological evolution. Since autocatalytic networks possess these properties and have beenuseful in modeling the origin of life, we used an autocatalytic RAF framework to modelwhat is arguably the earliest significant transition in the archaeological record: thetransition from Oldowan to Acheulean tool technology.We hope that future research will build on this direction by comparing the culturalRAF approach developed here with other standard semantic network approaches (Beaty,Benedek, Silvia, & Schacter, 2016; Baronchelli, Ferrer-i-Cancho, Pastor-Satorras, Chater,& Christiansen, 2013). Although these standard semantic networks suffice for modelingsemantic structure in individuals, we believe that the RAF approach will turn out to besuperior for modeling lineages of cumulative cultural change, because it distinguishessemantic structure arising through social or individual learning (modeled as food setitems) from semantic structure derived from this pre-existing material (modeled as nonfood set items generated through abstract thought processes that play the role ofcatalyzed reactions). This makes it feasible to model how cognitive structure emerges, andto trace lineages of cumulative cultural change step by step. It also frames this projectwithin the overarching scientific enterprise of understanding how evolutionary processesOGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 33(be they biological or cultural) begin, and unfold over time. Data for comparing culturalRAFs against other semantic networks could come not just from existing archaeologicaldata sets and analyses of social learning and pedagogy in stone toolmaking (Tehrani &Riede, 2008), but from neuroscience, building on neuroscientific studies of brain activationduring toolmaking by modern-day novice and expert Oldowan and Acheulean toolmakers(Stout et al., 2008). We note that there now exist established methods for developingsemantic networks using neuroscientific data (Betzel & Bassett, 2017; Karuza,Thompson-Schill, & Bassett, 2016; Medaglia, Lynall, & Bassett, 2015). To our knowledgethese methods have not yet been used in the study of cultural lineages but we see noreason why they couldn’t be.The model as it stands has limitations; it is highly simplified, and we do notprecisely know the context in which the cognitive events modelled here took place. Futureversions could incorporate a more sophisticated representation of interactions amongstMRs (Aerts et al., 2016, 2013) and a dynamic representation of context (Howard &Kahana, 2002; Veloz et al., 2011). There is also more work to be done on the implicationsof cognitive RAF theory for the evolution of cooperation (see (Voorhees, Read, & Gabora,2020)), and the evolutionary pressures shaping cognitive RAFs (a promising effort in thisdirection is (Andersson & Törnberg, 2019)).Since there are multiple ways that a given set of MRs can be networked togetherinto a viable cognitive RAF, this model may also provide a new approach tounderstanding the origins of psychological differences at the individual (Sackett, Lievens,Van Iddekinge, & Kuncel, 2017) and cultural (Sng, Neuberg, Varnum, & Kenrick, 2018)levels. The question arises as to how the inventors of new concepts (such as EDGING)differed from their less creative kin may be due to individual differences in two parametersof our model: (1) reactivity (the extent to which the meaning of a MR is perceived to bealtered in an interaction—or ‘reaction’—with another MR), and (2) λ (the rate at whichreactions occur). For example, what is referred to as cognitive rigidity may be a matter oflow λ , resulting in a semantic network that is subcritical , whereas creative thinking mayOGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 34be a matter of high λ , resulting in a semantic network that is supracritical . Which of thesetwo regimes a particular individual falls into may also depend on variables associated withthe ‘food set’ MRs, including the degree of detail in which these MRs were encoded, andtheir diversity. For example, the food set MRs will be more diverse for individuals thathave experienced different climates, environments, or cultures.Although the invention of the Acheulean hand axe modeled here resulted in genuinealbeit transient autocatalytic structure, as mentioned earlier, archaeological evidencesuggests that over a million years passed before the emergence of a persistent cognitiveRAF. In another paper (in progress), we propose that rapid cultural change in theMiddle-Upper Paleolithic between 100,000 and 50,000 years ago required the ability to,not just recursively redescribe the contents of thought, but reflect on ideas from widelyvarying perspectives, at different levels of abstraction, and that this in turn required thecapacity to tailor the reactivity of thought to the current situation. This resulted in asecond cognitive transition culminating in the crossing of a percolation threshold yieldinga self-organizing autocatalytic semantic network that extended across different knowledgedomains, and routinely integrated new information by reframing it in terms of currentunderstandings. The proposal is consistent with there being a genetic basis to cognitivemodernity (Corballis, 2004), except that onset of the capacity for variable reactivity wouldhave underwritten, not just complex language, but also other cultural innovations of thisperiod, such as the ability to adapt tools to widely differing task-specific uses, andgenerate art that served utilitarian, decorative, and possibly religious purposes. Thus, themodel developed here can be extended beyond the Oldowan-Acheulean transition andapplied to other periods of cultural change such as the Middle-Upper Paleolithic, andpotentially also, the explosion of cultural novelty we are witnessing currently.There are formal models of many aspects of human cognition, such as learning,memory, planning, and concept combination, but little in the way of formal models of howthey came to function together as an integrated whole, and how such wholes affect oneanother over the course of human history. The structure of a modern human mind servesOGNITIVE TRANSITION CULTURE AUTOCATALYTIC NETWORKS 35as a scaffold for the interpretation of both external and internally generated MRs, whichperpetually reinforce and revise that structure. It generates a unique stream of thoughtand experience, which expresses itself through its contribution—through a smile, a turn ofphrase, or a world-changing innovation—to cultural evolution. 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If we treat the transfer of CCPs between individuals (underthe process described by Expression (5)) as a stationary Markov process on the directedgraph D = ( V, A ), the probability P that no such events occur in the time interval [0 , T ] isgiven by: P = Y v ∈ V [exp( − cρT )] o ( v ) = exp( − cρT | A | ) , (6)where o ( v ) is the out-degree of v , and c > P v ∈ V o ( v ) = | A | ). Itfollows from Eqn. (6) that P converges to 1 as ρ → v lies in a strongly connected component C of D and let d denote the smallest integer for which, for every vertex w in C , there is a directedpath from v to w of length at most d ( d is well-defined, since v and w lie in the samestrongly connected component of D ). Then, for any other individual w in C , theprobability that at least one CCP percolates from v to w in the time interval [0 , T ] (eitherdirectly or via a chain of other individuals in C ) is at least: (cid:18) − exp (cid:18) − c ρ Td (cid:19)(cid:19) d , (7)and this quantity clearly converges to 1 as ρ grows (here, c > v = v , v , v , . . . , v k is any path in C of length k ≤ d , then the probability that agiven CCP percolates from v i to v i +1 (where 0 ≤ i < k ) in the time interval[ iT /d, ( i + 1) T /d ] (which has duration
T /d ) is 1 − exp( − c ρT /d ). Thus, by the Markovproperty, the probability of a percolation along this path of length kk