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Complexity, Relevance and the Emergence of Culture

William Downes


The purpose of this inter-disciplinary study is to propose a theory of culture; what it is, how it arises from the information processing of mind/brains, its noisy turbulence and our consequent collective inability to fully predict, understand and control our thoughts and actions in the unfolding of history. The strategy is to bring together Sperber and Wilson’s (1995) relevance pragmatics and the new science of complexity in order to gain insight into the emergence of collective culture from individual acts of communication. It begins by explaining and illustrating the relevance theory of cognition and communication and Sperber’s (1996) epidemiological approach to culture, while interpreting both these in terms of cultural emergence. It concludes with an exploratory attempt to re-analyze relevance principles quantitatively in terms of the mathematical concept of algorithmic complexity and hence gain a new information theoretic perspective on cultural emergence. This further develops the cognitive pragmatics of culture in Downes (2011).



1. Three basic ideas

Culture innovates, changes and spreads over time within history through millions and millions of mind/brains in many diverse communities in countless acts of communication. To explore this, we need three basic ideas: first, relevance pragmatics and communication; second, cultural concepts; and third, complexity theory.[i]

1.1 Relevance pragmatics

Relevance theory is a cognitive pragmatic theory of communication (Sperber and Wilson 1995; Wilson and Sperber 2004). It is pragmatic because it is that part of linguistics that studies language use in context, and cognitive because it does this within cognitive science, explaining utterance comprehension and communication in terms of mental processing within a modular theory of mind. The fundamental idea, the cognitive principle of relevance, is that all cognitive processing is governed by the search for maximal relevance. Relevance is a matter of degree; stimuli may be more or less relevant to a system depending on its prior assumptions. Degree of relevance is a measure of the positive cognitive effect of an input on this prior state relative to the amount of processing effort required to produce that effect. The maximally relevant stimulus for a system is that which yields the most improved representation of the world and costs the least in processing effort.

One importance of this idea is that it is the degree of relevance of a subset of conceptual representations that allows them to reach cultural levels of distribution within a population. This is fundamental to Sperber’s (1996) concept of culture within the epidemiology of representations. The more relevant a concept is for many minds in more and more diverse contexts, the more widely distributed it is throughout a population. The more widely distributed it is, the more it is cultural. There may be some non-innate, and thus contingent, concepts so relevant to all human minds that they are cultural universals. Conversely, concepts restricted to one or few minds are not cultural concepts.

1.2 Cultural concepts

Most culture consists of the class of non-universal but widely disseminated and epidemiologically successful concepts.These are the basic units of cultural selection and dissemination. So to analyze culture and cultural change is to analyze its truly vast numbers of constantly changing cultural concepts, their deployment in thoughts, attitudes to them and their intricate logical relationships. I need to make a series of further points about concepts, so we can use the idea later. Concepts are the constituents of thoughts and in relevance theory, thoughts which are treated as true or probably true and are therefore used in action and communication are called assumptions. So a cultural assumption is a thought containing cultural concepts widely used in action and communication.

Not all concepts are cultural. Besides cultural concepts and those restricted to individual minds, there are also basic concepts (Downes 2011:12-13 and references therein). These are constituents of the rich underlying Kantian presuppositions of experience – transcendental schema re-interpreted in cognitive psychological terms - as basic as cause, self, and individual objects in space and time. We can add basic categorization, class terms like animacy, basic actions like moving and stopping and the deictic orientations. These are part of the innate mental equipment provided to the mind/brain by evolution, which are crucially adaptive to the selecting environment. They are specific to either given input systems or other modules of mind. Under this heading would come the prototype theory (Rosch et. al. 1976) of basic levels for perceptual classification, putative universal semantic primitives (Jackendoff 1989, 1993; Wierzbicka 1996), semantic roles (Halliday 1994), and the basic structure of formal logic (Allwood et. al.). Also fundamental perhaps are the schemas identified by Johnson (1987) and Lakoff (1987) and from which are developed the cognitive metaphors that provide overall structure for cultural concepts in their cognitive linguistics. By contrast, cultural concepts are historical developments of basic concepts. They derive from the various modules of mind within a population, given perceptual input and communication and they are emergent, new, freely variable and usually inter-modular. They connect modules. In Downes (2011: 19-21), I demonstrate this using the inter-modular cultural concepts SPIRIT TRAVEL and PRICE. (Henceforth, by convention, I will use capitals for concepts, double quotes for words and lower case for objects referred to.)

We mustn’t think of a concept as a thing or a place in the brain. It is simply a term for how information is organized and represented as part of a cognitive theory, like a schema (Rummelhart and Norman, 1985) or a frame (Minsky, 1977). Schemas/frames can be part of a concept (see also Martin, 1994). Sperber and Wilson (1995: 86) consider a concept a conceptual address which assembles information of various types. We can consider a concept as a set of formal functions that connect concepts with each other and with some other functions of the mind like lexical entries, semantic role frames and deductive rules, and in so doing form many and diverse structural and operational relationships between information of different types. A concept organizes the dynamic relationships between types of information and how it is used in processing new input. It is the functionof concepts in processing, mainly in perception and reasoning, which defines them. This will be illustrated below.

There are a number of key types of information organized in a concept (Sperber and Wilson, 1995: 86f.). There is simplified default information about the concept. It can be in different forms. It may be definitional or analytic like a meaning postulate. But it is more usually a stereotype: for perceptual category concepts a prototype; for functional kinds, how they are meant to be used (if X is a CHAIR, it is to SIT in); for names, rigid designation of the intended object. For events, the default may be dynamic and normative as in a script (Schank and Abelson, 1977). Default information is the logical function of a concept because it specifies how the concept figures as input to deductions, including conditional probabilities, in the deductive device.

This differs from a concept’s encyclopaedic information. This is all the myriad factual assumptions about the concept, based on experience or communication and treated as true in processing. The encyclopaedia ties the mind together with respect to its overall processing of empirical data, of facts, because it automatically contains and is therefore connected to the many other concepts to which a given concept is related. This network is contextually accessible for deductive reasoning in a hierarchy ranked according to frequency of use. A concept connects abstract information with information in other mental formats; for example, imagery, and attitudes, norms and hence motivations and drives, experienced as emotions, either basic or culturally constituted by the concept of which they are a part. There is also the lexical function of the concept. This connects the concept to its public face, a word, if it has one. It includes all the linguistic information about the lexical item. Most possible concepts aren’t lexicalized. They have to be expressed periphrastically, with many words.

It is concepts as just defined that are the constituents of culture, and the basis of practices. If one considers the many millions of cultural concepts just expressed in the public lexicons of languages, and how these exponentially combine into single new assumptions and then function in inferences to generate many more assumptions, one can only reflect in awe at human culture. And this is only the concepts for which we have single words. It doesn’t include either non-lexicalized concepts or merely possible concepts and thoughts, true or fictional. Because of the open creative emergence of new concepts combined with recursion in logic, what we can think as a species is infinite, and so is what we can say or do.

As I also said earlier, Sperber (1996; see also Sperber and Hirschfield, 2004) and others such as Richard Dawkins (1976) and Daniel Dennett (1995) whose unit of culture is the meme, consider only those concepts cultural which become widely disseminated. The use of the term “concept” signals that, unlike the term “meme”, which replicates only by imitation, our unit of cultural dissemination is embedded in cognitive psychology and has a more complicated role in perception, action and communication. Therefore pragmatics is a key for explaining culture. As noted above, Sperber (1996) argues that cultural concepts reproduce because they are constituents of assumptions used in the calculation of relevance in many contexts. One reason for this is that they may be counter-intuitive with respect to basic concepts or perceptions, and therefore surprising, very relevant if true. Thus, relevance explains cultural dissemination. However, both memetics and epidemiology are broadly evolutionary models because they are based on the idea that cultural concepts emerge because variations differentially reproduce. While a basic concept is in all minds necessarily, and an individual concept is in one or few minds, a cultural concept, in the environment both of other concepts and the world, successfully reproduces in many minds throughout a population and persists in time because it is adapted to minds and contexts.

Our new idea is to examine this picture of culture from the point of view of complexity theory. For our purposes, the main point is that new structures, i.e. concepts and thoughts, emerge and spread through the natural self-organizing nature of complex systems, which are then selected on a higher emergent level. The principle that cognitive processes are governed by the search for maximal relevance, explains both the self-organization and emergence of cultural concepts within individual minds and then their dissemination throughout populations. It is from the innovations provided by these emergent concepts from sheer conceptual possibility, the “adjacent possible”, as Stuart Kauffman (2008) calls it, that differential reproduction selects new cultural concepts.

1.3 Complexity theory

This is the new inter-disciplinary paradigm in science that models and explains dynamic non-linear systems, those natural systems which change as their energy input varies (Prigogine and Stengers, 1984; for a summary, see Waldrop, 1993). I argue that human information processing, within an individual mind and between the interacting minds of a population through time is such a complex system of systems. John Holland (1995; 1998) calls such systems complex adaptive systems. They have such properties as self-organization, or “order for free” (Kauffman: 1993). This is where the synergistic inter-action of simpler sub-systems automatically produces a more complex higher-level pattern creating a hierarchy of systems. This happens because the parts, each sub-system, has internally modelled their environment and learned in an entirely mechanical way. It adjusts in order to function within a new higher-level whole. Each has adapted to the other parts of the system, which has also adapted to it and co-evolved creating a higher-level whole whose parts are co-ordinated. The resulting higher-level whole is emergent, something new and, although law-governed, largely unpredictable because so complex. Evolution selects from these already emergent patterns through differential reproduction. Darwin’s natural selection applies this in biological reproduction; the mind/brain’s innate modules and basic concepts have this biological, Darwinian basis. By contrast, newly emergent cultural concepts differentially reproduce according to their relevance – that is their adaptation – to others and to the environment in perception, action and communication

Examples of complex adaptive systems are everywhere, evidenced by the law-governed but unpredictable emergence of the new things in nature - from planetary systems to typhoons, from our own bodies to cities and economies and the whirlpools below the rapids in a river. The insect colonies of ants, termites or bees and the flocking behaviour of birds are common examples. Each individual bird is following simple algorithms, but the interaction when each bird does this is the self organized emergence of the higher level pattern, the flock. Conversely, the flock pattern itself feeds back into the action of each individual bird, sustaining the pattern, which behaves unpredictably.

Holland (1995) illustrates emergence with the example of board games. Sets of simple building blocks, governed by a few simple rules, generate, out of all possible states of the board, an on-going flux of emergent patterns with perpetual novelty. A board game with ten possible moves from each configuration, after 2 moves, has had 10X10=100 or 10 ways of playing the game, or states of play. If the game terminates after 10 moves, then there emerges 10(10,000,000,000) possible states of play, after 50 moves 10 (10 followed by 50 zeros) ways of playing. From these possibilities, in a particular game each player selects using a non-random strategy which takes into account, thus co-evolves with or mutually adapts to, the strategy of the other player. The resulting complexity yields unpredictability of outcome and endlessly novel games.

Communication is somewhat different. When two people are communicating, the requirement is that there must be some simple selection principle in order to choose among all the possibilities, the meaning potential, and which allows a single state of play, as it were, to emerge in a co-ordinated, mutually adaptive way between two minds, the speaker and the hearer. This is the problem of pragmatics. The communicative principle of relevance, to be explained below, serves this function (Sperber and Wilson, 1995: 49; Wilson and Sperber, 2004: 612).

2. How relevance in action and communication creates culture

This section will demonstrate how novel cultural concepts emerge unpredictably from the complexity of the interaction of minds, themselves complex, in contexts, also complex. Cultural concepts are generated within and spread between mind/brains much in the way that birds flock. To show how relevance theory helps explain this process, I will use scenarios drawn from Downes (2011: 68-78). The scenarios are set in Prince of Wales Road (henceforth P of W Rd.) in Norwich, England. This busy road runs in a curve roughly west to east for a short distance from the city centre to Thorpe Bridge crossing the River Wensum. On the other side is the Riverside area. There you are immediately confronted on your right with the pedestrian entrance to Norwich Railway Station, invisible from further up the road.

2.1 The complexity of cultural action

In the first scenario, I am walking on the north side of the road near the city centre. Suddenly I notice Peter, who also teaches linguistics at the university. Peter is on the opposite side of the street and walking purposively east down P of W Road towards the bridge. He is carrying bags. It is about 2.00pm.

In the first scenario, Peter does not notice me across the street as the traffic roars by. How does my mind comprehend this scene? First, I recognize Peter, using the appropriate module. I access my concept PETER from long term memory, initially just the default information concerning his identification, but potentially connected to all the encyclopaedic information I have about him based on past experience. I recognize P of W Rd. and do the same for the concept PRINCE OF WALES ROAD, including a schematic spatial mental map of the area. How does the inferencing go? The three most relevant assumptions based on this input are;




Guided by the cognitive principle of relevance, the greatest number of contextual effects for the least effort will be achieved when I construct a context, the most accessible assumptions from my memory based on my past processing, take as premises the above input assumptions, combine them with the newly constructed context, and perform a simple deduction. In Holland’s simulation, an adaptive agent’s chains of simple ‘if-then’ rules are called “classifiers” and they perform the same function in an equally simple way (Holland, 1995; Waldrop, 1983: 182).

For my mind, given this input, the most accessible assumption was,


In terms of a frame or schema, this is a default representation with respect to P of W Rd., accessed if there is no good reason to access anything else. In relevance theory terms, it is the most accessible assumption because in previous successful processing of P of W Rd., it has been most frequently used and has therefore gained inductive strength. In fact, much of the successful use has been my own employment of P of W Rd. to get to the station. Combined with the new input this rule leads to the deduction that Peter ‘probably’ is going to the rail station. It is only probable, because Peter could in principle be going to many other places but, based on past use, the most accessible assumption involves going to the railway station. My conclusion may provide enough new information for the effort, the energy spent. Therefore, it is the maximally relevant new information.

However, by making the further effort of accessing more rules from my encyclopaedia, I can gain even more new information. My mind/brain may be willing to do this.

A simple default rule is,


This would lead to the additional contextual effect that Peter is probably going to travel by train soon. (A deduction employing the BAG input would strengthen this conclusion but would yield only minimal new information for the extra effort.) If my mind/brain is now satisfied, processing stops. The important thing is that there are many other places Peter might be going, or things he might be doing at the station. But consideration of these is ruled out by the cognitive principle of relevance. They cost too much processing effort to derive too little information, so they are irrelevant. The relevance principle, as its name suggests, manages the overwhelming number of possibilities implicit in input from the environment.

What lessons can we learn from this scenario? The first is that the result is accomplished through complexity; that is, the interaction of a number of simpler sub-systems: the visual input systems; the encyclopaedic information in the cultural concepts – PETER, RAIL STATION, PRINCE OF WALES ROAD, TRAVEL, the default schemes, and iterations of the simple deductive device. The second is that a new ad hoc thought has been created: PETER IS PROBABLY GOING TO TRAVEL BY TRAIN SOON. In fact, I have a new, slightly changed cultural concept, PETER. Cultural concepts are active and dynamic. My mind/brain is a complex adaptive system constantly adjusting to its changing environment, organizing itself. If I am wrong too often, I won’t survive. But perhaps the key point of scenario one is that it is not a case of communication, Peter didn’t even see me.

2.2. The complexity of communication

The next scenario illustrates how relevance theory explains intentional communication. The same sub-systems are involved as in the first scenario. But my new cognitive task is to comprehend an exact message that Peter intends to communicate.

Peter sees me and shouts out “Must Run” across P. of W Rd. Apply the quest for maximal relevance to this complex input. It is only relevant if I recognize that Peter intended me to notice it and to try to calculate its relevance. It therefore makes obvious both a higher level communicative intent and a lower level informative intent to convey some specific information. What is this informative intent? According to the communicative principle of relevance, his ostensive stimulus is guaranteed to be optimally relevant, to convey what Peter intended in the most relevant way. That is, the stimulus is guaranteed to be the most relevant way possible to convey what he intends. So I simply need to work out the maximal relevance of his utterance.

The most accessible context is that it is probably mutually manifest to us both that Peter is going to the station. Peter’s new information might simply serve as a confirmation of this assumption. Is that enough? It might be, but I feel not. After all, it doesn’t account for the new semantic content he provides. What else might Peter intend to communicate? I hypothesize that because he said that he MUST move, something objective is OBLIGING him to move, and to do so in a MANNER OF MOTION which is FAST relative to the scale of NORMAL WALKING. Therefore, he must be in a HURRY to go somewhere, and in this context this is most likely to be to catch a specifically scheduled TRAIN at the STATION. I could stop there, but I’m still not satisfied. So, without much further effort, I can infer that he also intends to convey that, if he wasn’t in such a hurry, he would have preferred to stop, cross the street, and chat, as we would normally do if we met on the street. This confirms how much he values our relationship. Interestingly, the expression of this preference, without actually doing it, is enough to do the same social job. This is what I infer from “Must run”. If this new conclusion satisfies me it is optimally relevant, and I stop my mental work. This is probably what Peter intended to communicate. (All other possible interpretations – e.g. he is avoiding me – are excluded because irrelevant. They are not even entertained because not deductively derivable in the most accessible context.)

Two other characteristics of verbal communication are also illustrated by the “Must run” scenario. Peter’s utterance is logically incomplete. The logical form conveyed by the linguistic input must be enriched or logically filled out so that a more fully developed proposition is available from which to draw contextual inferences. The utterence itself is just provides clues. Sperber and Wilson (1995:81) call this process “the development of a logical form” and the inference that does this job, an explicature. The hearer has to supply the subject “Peter” to “Must run”, add the kind of manner of motion that would count as FAST in this situation – fast walking – and the fact that he must run ‘to the station’. Furthermore, the utterance isn’t TRUE. Peter isn’t in fact running. The utterance isn’t meant literally, but is intended merely to imply that he is in a hurry. Peter has aimed for relevance, not truth.

What can we learn from this second scenario? We can now add communication, language and explicature to the complexity of the interaction. We also see that a huge amount of potential information is packed into the input and that it is the principle of communicative relevance that coordinates the two minds in order that the receiver of the message can select from all the possibilities just the information that the sender intended. Communicating minds create the conditions for their own successful co-ordination. The two minds together form a self-organizing system.

This creates something new: the co-ordination of communicating minds is emergent. Communication connects at least two complex systems, the participants’ minds and brains - each of which of course is constantly communicating with many others - and they adapt to each other and co-evolve. From this emerges a new higher level system, both a social system and a cultural system consisting of the concepts that each one has to construct to comprehend the other, according to relevance principles. This is the emergent dynamically self-organizing content of the human species-mind which collectively adapts to its containing natural environment, automatically using only those concepts which pragmatically enable successful action, over the long run (Downes 2011: 163-226).

4. Emergent culture: the concept of CONSULTING.

In the last scenario, Peter stops, crosses the street to talk.

After initial pleasantries, he says “//hiya …// just off to do some consulting // at the Great Ape Trust //”.

Given this input, I need to assume optimal relevance, so I start my inferential work. 

First of all, I need to enrich the logical form by interpreting “just” and “off” and filling in “Great Ape Trust” as the place to which Peter is travelling. I also infer BY TRAIN. So again there is an implicature that my assumption that Peter was going to the station was correct, strengthening my beliefs about P of W Rd. But my real job is to interpret the intonationally focused new information about the concepts CONSULTING and GREAT APE TRUST. I access the latter from the larger conceptual address PRIMATE RESEARCH in my enclycopaedia.

Consider the cultural concept CONSULTING. The input is the gerund –ing nominalization. “Some consulting” needs enrichment to obtain a proposition. I find it most relevant to infer that the Great Ape Trust is consulting Peter and not that Peter is consulting them. I also infer that it is the primate researchers and not the apes themselves or the trust management that are consulting Peter. To me, one of the most contextually relevant aspects of the concept CONSULTING is the entailment that If Y CONSULTS X, then X HAS EXPERTISE OR AUTHORITY THAT Y WANTS. Combining this with the assumption that Peter is a LINGUIST, leads to the new conclusion that Peter has been asked to provide linguistic expertise that is of interest to primate researchers.

There I stop. But there is an enormous amount that I don’t know. I haven’t any idea what specific kind of linguistic expertise Peter has which could be of interest. I don’t know if Peter has set himself up as a CONSULTANT and is being paid. To-day, CONSULTANCY is big business and CONSULTING expertise is often MARKETIZED. Alternatively, of course, he may simply be going to visit a friend at the Trust and is using the word “consultant” loosely.

However, what is of particular interest in this scenario is the rapidly changing cultural concept CONSULTING and the new cultural concept LINGUISTIC CONSULTANT with respect to PRIMATOLOGY. Here we have conceptual innovation by restructuring (Norman and Rummelhart 1978 cited in Martin 1994). The new concept has involved just altering the set of values of the variables EXPERTISE and CLIENT in the CONSULTING schema, which in relevance theory is called “loosening the concept”. (We also find schema induction in which a new schema is created by combining two distinct schemas. This is related to analogical mapping and conceptual blending.)

In the last 30 years consultancy has exploded. The more complex lexicalizations and modifications of CONSULT in English is a sure sign of its widespread relevance, hence cultural significance. There are derivations from the verb consult: consulting, consultation, consultant (who has clients), consultancy and the vast increase in frequency of use. This could be studied empirically through the comparison of directories and websites over time. We have many “consultancy firms” and many “freelance” consultants. Especially revealing are the fixed phrase nominal modifiers that productively trace the diffusion of the concept of professional CONSULTING throughout culture. Beginning with medicine and law, there emerged CONSULTING ENGINEERS and MANAGEMENT CONSULTANTS. Then the term spread to accountancy, marketing, the environment, health, HR, politics, public relations, marketing, crisis management, tourism, tax law, art, literature, waste management, fashion, graphic design, urban planning, transport, IT and even life management. This creates other new concepts, such as LIFE COACH. Without doubt, cultural elaboration has taken place, the concept has disseminated, and become more complex in its contexts, because it has become very relevant to many minds in the course of their practices.

This rapidly developing concept reflects the increasing specialization and the highly technical nature of much professional expertise in the KNOWLEDGE ECONOMY. As specialization rapidly increases, it is far more economical for businesses to HIRE-IN EXPERTISE from a CONSULTANCY. Rather than have the expertise IN-HOUSE it is OUT-SOURCED. Here we have a cluster of new cultural concepts. Because it is so relevant across contexts, the concept CONSULTING has not only reached cultural levels of distribution and become more and more complex as it generates new sub-types within the space of logical possibility. The intense relevance of the concept in many contexts in a marketized knowledge economy accounts for its widespread dissemination. Consulting is an emergent phenomenon, new in the world. But it is only one of many millions of inter-connected concepts in ‘emergent culture’. In principle, the number of possible new cultural concepts is infinite.

5. Relevance as degree of algorithmic complexity

There is a remarkable hierarchy of emergence of complex organization, beginning at the molecular level billions of years ago. Cultural concepts form the highest emergent level, arising out of the coordinated communication of many billions of mind/brains and ever increasing in complexity, depending on the energy input available. As complexity grows in a cultural system its behaviour becomes more and more unpredictable. In economics, one can easily see how maximal relevance in the context of rising prices and easy credit in a specific market, especially one with de-regulation and ‘free market’ values, can lead to a feed-back loop which forms an emergent “bubble”, although these aren’t easily predictable in advance or visible to participants at the time. As more cultural concepts emerge within the interaction of more mind/brains over time, the process of emergence iterates and the number of concepts feeds on itself – like the states of play in a board game – and increases exponentially. 

We can assume that the species is also communicatively more and more technologically inter-connected, both to-day and connected with the culture of the past with new concepts becoming more widely available to more and more minds. Mathematically there must be an exponential growth in the number and inferential connectedness of cultural concepts with a culture (and within a single mind). There will also be a greater potential for schema induction and restructuring of concepts both within cultures and between different cultural lineages. This growth creates huge and increasing problems of information management both on a social and individual level (Gleick 2011:373f.). This is now called “Big Data”– information volume grows by 59% annually. “Analytics” is the name for businesses that hunt for relevant patterns in “unstructured data”, according to Business Technology (published by Lyonsdown, distributed by The Guardian Nov. 2011: 5).

This increasing cultural complexity in a collective is the result of the search for maximal relevance – the cognitive principle of relevance - in communicating individual minds. And this search is a strategy for excluding, for not considering some information that could provide context. In this sense relevance is about reducing complexity, and yet it leads in the collective to increasing cultural complexity. To use notions of complexity to understand how relevance principles have this outcome with respect to information processing, we need another related notion of complexity, algorithmic complexity, within algorithmic information theory as formulated by the mathematicians Gregory Chaitin (1966; Gleick, 2011: 324-333) and Andrei Kolmogorov (Gleick, 2011:333-340). This notion will be defined shortly.

A founding assumption of cognitive science was that whatever else the mind/brain does, it processes information. Information here is purely a quantity, the amount of Shannon information in a message, represented as bits, 0 or 1 in a binary system of patterned possibilities (Shannon and Weaver, 1949; Cherry, 1966). It measures the contrasting amount of surprise inherent in each one of the contrasting possibilities of the system; that is, the probability of that message with respect to the other possible messages. Viewed as Shannon information, information has no semantic content; that is, it has no intentionality, it isn’t ‘about’ anything. It was the contribution of Fred Dretske (1980; 1981) to show how this pure information could actually be intentional because its ‘if, then’ conditional probabilities, were nomic, representing causal patterns. This shows how the parts of a purely physical system can be ‘about’ something and gain a function. He also argued that it is higher-level intentionality within an information processing system like ours that leads to the emergence of cognitive states; the ones we represent conceptually and make public using language.

When Holland (1995) constructed a complex adaptive system in the form of a program that could learn, he wrote his deductive rules, not in symbols with pre-specified semantic content, like BIRD or CONSULTING, but in binary strings of 0s and 1s, the meanings of which would emerge as the strings came to be related to each other and to sensors connecting the system to its world of input. Waldrop (1993: 104)) explains the strategy very clearly:

Like clouds emerging from the physics and chemistry of water vapour, concepts are fuzzy, shifting, dynamic things. They are constantly recombining and changing shape. “The most crucial thing we’ve got to get at in understanding complex adaptive systems is how levels emerge”….. To capture that … emergence in his adaptive agent, Holland decided that his rules and messages would not be written in meaningful symbols. They would be arbitrary strings of binary 1’s and 0’s. A message might be a sequence such as 10010100 …. And a rule, as paraphrased in English, might be something like, “If there is a message on the bulletin board with the pattern 1###0#00, where # stands for ‘don’t care’, then post the message 01110101….” Holland took to calling his rules by a new name, “classifiers”, because of the way their if-then conditions classified different messages according to specific patterns of bits …. In his classifier systems, the meaning of a message would have to emerge from the way it caused one classifier rule to trigger another, or from the fact that some of his bits were written directly by sensors looking at the real world. Concepts and mental models would likewise have to emerge as self-supporting clusters of classifiers, which would presumably organize and reorganize themselves in much the same way as autocatalytic sets.

Within a framework like Holland’s, I propose we can reformulate the degree of relevance of an input to an information processing system in quantitative terms using the binary code of information theory, rather than in terms of the manipulation of symbols which represent semantic concepts.

The algorithmic complexity of any object, such as a message or set of data, equals the size of the shortest program that can generate it; that is, the number of steps required for a Turing machine to derive it. This also measures the amount of information in the message: the more complexity, the more information; the less complexity, the less information. (A Turing machine is an abstract machine that can derive anything computable, anything that can be stated as a fully explicit effective procedure.)

In order to use this idea to gain insights into relevance, the algorithmic complexity of a message needs to be relativized to a particular information processing system in a given informational state when it receives the input, what it already has stored that can form a potential context. In this case, the algorithmic complexity of the message with respect to the system would equal the amount of information in the message available to that system given its prior states. We can now define the relevance of an input message.

The degree of relevance of an input message to a system is the inverse of the algorithmic complexity of that input for the system, which equals the number of processing steps required to derive the input from prior states of the system.

The less the algorithmic complexity of the input, the number of steps required to derive the input, the greater is its relevance to the system. The more the algorithmic complexity of the input - the number of steps required to derive it - the less is its relevance to the system. The maximally relevant stimulus to the system is the least algorithmically complex, requiring the least steps to derive. The least relevant stimulus to the system is the most algorithmically complex, requiring the most steps to derive. The limiting case would be that the input is random from the point of view of the system, connected to no pattern between the new and prior information that could deductively predict it. The opposite of this is the least algorithmically complex, most relevant stimulus, where there is a patterned relationship between the input and the prior information most accessible to the system such that the input can be deduced with the fewest possible steps, which integrate the new information with old information, creatively adapting the old information if needs be. This is the input with the least algorithmic complexity relative to the system and hence with the most relevance to it.

A distinguishing feature of our evolved brains as information processing systems is a ‘stop’ function which turns off processing when the system is contextually satisfied with the amount of new information it has integrated or ‘understood’: the appropriate degree of relevance in each case. This is evolutionarily necessary because the potential algorithmic complexity of the input from any complex environment at any time is so huge that, without such an evolved regulator, the device could never stop. Humans have evolved to handily vary that amount, a matter of degree, according to intrinsic motivational and extrinsic contextual factors, experienced as the phenomenology of understanding something adequately for the purposes at hand.

This re-analysis of degree of relevance gives us, in principle, a quantitative account of relevance. The cognitive principle of relevance is that the mind-brain in all its processing tasks seeks input with the least algorithmic complexity in order to maximize relevance. Stated quantitatively, it is geared to gain new information by the smallest number possible of processing steps from its prior state of information; that is, utilizing its most accessible contexts. It is set to maximize relevance and minimize complexity. Since the amount of complexity equals the amount of information, the reformulated cognitive principle is trying to reduce the amount of information, to ‘rule things out’, as expected. This principle forms a higher level control parameter on the system. This parameter has previously determined the emergence of each prior state of the system, the state of its encyclopaedia and the order of accessibility of assumptions. This in its turn determines contexts for the ever further emergence of cultural concepts. In this way the mind-brain has evolved to deal with complexity of input; that is, to solve the frame problem, to integrate new input with what it already assumes in a way that the former is most relevant to the latter. The mind/brain automatically performs analytics in the management of information.

This also has implications for evolution theory, since a system of this kind effectively raises entropy, using energy to find patterns that contain the systematic information it needs to predict its environment, creates order out of chaos, the order and information which it uses to survive and reproduce. An environment selects the system in a state which best relates to it, for which it has the least algorithmic complexity, predicts it best. This relation to an environment is a presupposition of evolutionary success.

Higher algorithmic complexity is a measure of the degree of randomness of an input viewed as information. Furthermore, the more complex and random is the number, the more information it contains, the more surprising it is. This also correlates with its entropy, its degree of disorder. The less the entropy, the more order or pattern is available, therefore the less information. More entropy is the converse. Thus the three key concepts - entropy, information and complexity - are inter-related. Entering the individual mind-brain, highly complex informational systems with much randomness - lots of surprise - which are information rich, have high entropy and introduce that into the mind/brain. They are disordered in the sense that we can’t get cheap access to their order in terms of work and we experience that as confusion or frustration in calculating relevance. This would be the case with much ‘cultural’ input; for example, applying linguistics to great ape research, understanding works of art or difficult economic or scientific problems. The cognitive principle of relevance construed as seeking minimal complexity is essentially about the mind-brain spending energy discovering what is most non-random about new information in relation to the prior context; that is, its most relevant pattern of relationships, its chains of ‘if, then’ classifier relationships among information messages, genuinely causal relationships between categories. This information’s new intentionality, or what it is about with respect to the system and the world, transforms it into a psychological entity, a concept, like CONSULTING, made manifest in a word “consult”. This transforms Shannon information into organized systems of intentional concepts and public messages in language.

We now have a quantitative account of the evolved design pressure that leads to the emergence of new concepts and their cultural dissemination. The mind-brain spends energy doing this, hence raising its own entropy while lowering that of the information. The state of the mind/brain becomes more ordered. It slows down, becomes more patterned. This is what the mind/brain has evolved to do. It seeks the most patterning in an input relative to its prior states (i.e. the most accessible contexts based on past experience) for the least energy expended. That is, it is designed to reduce the potential complexity of the environment, to seek exactly the amount of information it needs from the environment, given its current state, its abilities and preferences.

As noted above, what makes this possible are the new relationships or patterns discovered with respect to what is already known, expressible as patterns of inference. In a chaotic informational environment, patterning is so obscured by the sheer energy of the system, the information isn’t easily available for use; system isn’t discoverable. However, a somewhat lower energy, complex, nearly chaotic environment has more accessible patterning, contains more potentially useable systematic information. The state of culture described above – the exponentially increasing number of new concepts - is very complex indeed and can be seen to behave with seemingly random fluctuations; in a chaotic way from our mind’s point of view. This is the state described with respect to markets, an emergent cultural form, by Mandelbrot and Hudson (2005). It is only de post facto that individual minds come to better understand emergent bubbles and the deeper patterns causing the unpredictable fluctuations (see the flood of books on the 2008 economic crisis; most recently, Lewis, 2011). Conversely, an environment with low energy and hence reduced complexity and information, would be over-patterned, and although relevance would be much easier to achieve for a system, requiring less effort, the patterns would be repetitive, non-innovative, contain less information.

But, as we saw above, the constant generation of maximally relevant new concepts, which minimize complexity for individual mind-brains, for that very reason exponentially increase the complexity of the overall informational environment within emergent culture, which then requires ever more energy for individuals to reduce its complexity, as well as to represent and disseminate it. That is, it is automatic that the amount of entropy or disorder in cultural systems increases; there are more “adjacent possible” ways to rearrange its concepts while it manifests itself overall in a way that appears to be the same. This further motivates the need for a philosophy of uncertainty (Downes 2011: 259-263).

Both these physical informational processes happen automatically and are independent of will. Our culture, and therefore our actions and practices, are out of our conscious control. This is what is correct about the meme theorists’ claim that we are simply vehicles for our cultural representations. If this lack of control of culture is so, it is politically very important to think about moral norms - what ought to be - in order to inhibit our behaviour even if we can’t control our thoughts. Combine these sheer numbers and the chaotic behaviour of complex systems with the forever semi-understood nature of most cultural assumptions, which following Sperber (1996), I term, “cultural mysteries”, and it is clearly impossible in principle for the species-mind to grasp itself or predict cultural change, or for anyone to have anything but the most limited understanding of their situation (Downes 2011). In a trivial way, this is one factor in the rapid spread of consulting. Another consequence should be the increasing importance of literature and other arts. Poetics shows us how art, like a poem, novel, drama or film, models cultural complexity, with all its uncertainty, and allows us to critically reflect upon it in a de-coupled way with an indeterminate number of relevant interpretations.

I’ll end with the observation that, in the technical Buddhist sense, each of these complex systems of systems is empty. It is totally made of dynamic relationships and only momentarily appears to be a thing: a complex system has no inner essence other than the abstract principles that arise through the lawful interaction of its parts. Our bodies, minds, societies and cultures are like flocking birds or the moving whirlpool in a fast flowing river. That is, the Asian tradition of Buddhism is probably correct in its metaphysics, and not Western empiricism.

[i] Earlier versions of some of this material was presented to the Glendon College Linguistics Club, York University, Toronto, Canada, Oct.20, 2010 and as a plenary lecture at the National Linguistics Conference, National Sun Yat - sen University, Kaohsiung, Taiwan, Sept. 23, 2011. Many thanks to both sets of participants for their comments.

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