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KEYWORDS: autocatalysis, cognitive origins, cultural origins, evolution, memory model, memetics, mimetic culture, representational redescription, worldview

ABSTRACT: This paper presents a model of the cognitive mechanisms underlying the transition from episodic to mimetic (or memetic) culture with the arrival of Homo erectus, which Donald claims paved the way for the unique features of human culture. The model draws on Kauffman's theory of how an information-evolving system emerges through the formation of an autocatalytic network. Though originally formulated to explain the origin of life, this theory also provides a plausible account of how discrete episodic memories become woven into an interconnected conceptual web, or worldview, capable of generating an internally-driven (rather than perceptually-driven) stream of thought.

1. The subject of cultural origins is generally approached from an archeological perspective. For example, by dating artifacts such as tools we learn approximately when humans acquired the ability to make and use those tools. This paper takes a more cognitive approach. It outlines a theory of the psychological mechanisms underlying the major cognitive transition that, Donald [1991, 1993a, 1993b] proposes, made possible the trademark ingenuity and complexity of human culture.
2. The theory proposed here was inspired by an idea originally put forward to explain the origin of life. The origin of life and the origin of culture might appear at first glance to be very different problems. However at a high level of analysis they amount to the same thing: the bootstrapping of a system by which information patterns self-replicate, and the selective proliferation of some variants of these self-replicating patterns over others. The theory is thus consistent with the perspective of culture as a form of evolution [Dawkins 1975; Gabora 1995, 1997]. In keeping with this evolutionary framework, we use the term meme to refer to a unit of cultural information as it is represented in the brain. Thus meme refers to anything from an idea for a recipe to a memory of one's uncle to an attitude of racial prejudice. Memes that have been implemented as actions or vocalizations or objects are referred to as artifacts.
3. The paper opens with a discussion of the origin-of-life paradox and an analogous paradox one encounters when investigating the psychological prerequisites for the origin of culture. Next we will frame the ideas we have been developing in the context of a mathematical model of memory. We will then see how autocatalysis yields a potential solution to the both paradoxes. Finally we will discuss psychological implications, and the role of autocatalysis in any sort of evolutionary process.

4. In Origins of the Modern Mind, Donald [1991] argues convincingly that the capacity for abstract thought is the bottleneck of cultural evolution, and that it came about during the transition from episodic to mimetic culture with the arrival of Homo erectus approximately 1.5 million years ago. The episodic mind, so called because it can store perceptions of specific episodes [Olton 1984], is widely associated with primates. It is capable of social attribution, insight, and deception, and is sensitive to the significance of environmental events. However, it has great difficulty accessing memories independent of environmental cues. It can learn symbols but can't invent them or experiment with them, and doesn't improve skills through self-cued rehearsal.
5. In contrast, the mimetic mind has, built upon its episodic foundations, a "multimodal modeling system with a self-triggered rehearsal loop". In other words, it can retrieve and recursively operate on memories independent of environmental cues, a process referred to by Karmiloff-Smith [1992] as representational redecription. By redescribing an episode in terms of what is already known, it gets rooted into the network of understandings that comprise the worldview, and the worldview is perpetually renewed as new memes are assimilated. A mimetic individual is able to rehearse and refine skills, and therefore exhibits enhanced behavioral flexibility, and more precise control over intentional communication. The upshot is cultural novelty. "Mime, play, games, toolmaking, and reproductive memory," Donald claims, "are thus manifestations of the same superordinate mimetic controller." The appearance of sophisticated stone tools, long-distance hunting strategies, and migration out of Africa, as well as the rapid increase in brain size at this time [Bickerton 1990; Corballis 1991; Lieberman 1991], are cited as evidence for the transition from episodic to mimetic culture.
6. Donald claims "it is not clear that the mimetic controller must be localized in any single anatomical structure, although it must have functional unity", and that it "would have required a fundamental change in the way the brain operates." Mimetic ability seems to encompass a broad panoply of skills associated with several distinct regions of the brain. Since miming accounts for only a small part of what the mimetic mind can do, and since mimetic skill seems to boil down to the capacity to evolve memes, we will use the term memetic instead of mimetic.
7. Donald's proposal is invaluable in that spurs us to consider the cognitive basis of culture, but it leaves us hanging as to what sort of functional reorganization could turn an episodic mind into a memetic one capable of implementing the abstract thought processes that culminate in cultural novelty. In particular, it leaves us with a nontrivial problem of origins. In the absence of streams of representational redescription, how is structure built into a set of memes so that it becomes an interconnected worldview? And in the absence of a structured worldview-a memory that incorporates the network of relationships between stored items-how does one meme evoke another which evokes another, et cetera, in a stream of thought?
8. We will clarify the situation with a concrete example. We know that culture is hosted by brains, so we are safe in saying that it originated in the brain of some ancestor who we will refer to as Groga. Somehow Groga's brain became an instrument for the variation, selection, and replication/transmission of memes. What happened to get the ball rolling, to enable the process of memetic evolution to take hold?
9. When Groga had her first experience there were no previously-stored episodes to be reminded of; just external and internal stimuli (such as hunger). As episodes accumulated in her memory, occasionally it happened that an instant of experience was similar enough to some stored episode that a retrieval process occurred, and she was reminded of that past episode. But since her memory consisted only of stored episodes, no abstractions, this was the only kind of influence memory could have on her stream of thought. She could not chain memories together to refine a concept or perspective; her awareness was still dominated by the stimuli of the present moment. At some point in her life, however, she managed to initiate an autonomous stream of thought, and keep it going long enough to generate something novel. But if you need an interconnected worldview to generate a stream of associations, and streams of associations are necessary to connect discrete episodic memories into a worldview, how could one have come into existence without the other?
10. We will put the aside question of cultural origins for now, and turn to the problem of biological origins. The paradox of the origin of life can be stated simply: if living things come into existence when other living things give birth to them, how did the first living thing arise That is, how did something complex enough to reproduce itself come to be? In biology, self-replication is orchestrated through an intricate network of interactions between DNA, RNA, and proteins. DNA is the genetic code; it contains instructions for how to construct various proteins. Proteins, in turn, both catalyze reactions that orchestrate the decoding of DNA by RNA, and are used to construction a body to house and protect all this self-replication machinery. Once again, we have a chicken-and-the-egg problem. If proteins are made by decoding DNA, and DNA requires the catalytic action of proteins to be decoded, which came first? How could a system composed of complex, mutually dependent parts come into existence?
11. The most straightforward explanation is that life originated in a prebiotic soup where, with enough time, the right molecules collided into one another at the same time and reacted in exactly the right ways to create the DNA-RNA-protein amalgam that is the crux of life as we know it. Proponents argue that the improbability of this happening does not invalidate the theory because it only had to happen once; as soon as there was one self-replicating molecule, the rest could be copied from this template.
12. Miller [1955] increased the plausibility of this hypothesis by showing that amino acids, from which proteins are made, form spontaneously when a reducing mixture of oxygen, hydrogen, carbon, nitrogen, water, and ammonia is subjected to high energy. These molecules were all likely to have been present on the primitive earth, and energy could have come in the form of electric discharges from thunderstorms, ultraviolet light, or high temperatures generated by volcanoes. Other experiments have shown that the molecular constituents of DNA and RNA, as well as the fatty acids from which membranes are constructed, can be formed the same way. Unfortunately, however, the complexity of the DNA-RNA-protein structure is so great, and in the earth's early atmosphere the concentrations of the necessary molecules were so dilute, that the probability of life originating this way is infinitesimally low. Hoyle and Wickramasinghe (1981) likened it to the probability that a tornado sweeping through a junkyard would spontaneously assemble a Boeing 747.
13. The less complex something is, the more feasible its spontaneous generation. The discovery of ribozymes-RNA molecules that, like proteins, are capable of catalyzing chemical reactions-brought hope that first living molecule had been found. With ribozymes you wouldn't need DNA or proteins to establish a self-replicating lineage; these RNA molecules would do the job of all three. Unfortunately, self-replication of RNA is in practice fraught with difficulties. They tend to fold back on themselves creating an inert, tangled mess [Joyce, 1987]. Furthermore, the probability of a ribozyme assembling spontaneously from its components is remote [Orgel 1987], and even if it managed to come into existence, in the absence of certain error-detecting proteins found in all modern-day organisms, its self-replication capacity would inevitably break down in the face of accumulated error over successive generations [Eigen and Schuster, 1979]. Thus it is far from obvious how the stream of autonomous self-replicating systems that eventually evolved into you and I and all other living things on this planet got started.
14. The parallels between the two paradoxes we have looked at--the origin of culture and the origin of life--are intriguing. In both cases we have a self-replicating system composed of complex, mutually interdependent parts, and since it is not obvious how either part could have arisen without the other, there is a problem determining how the system came to exist. In both cases, one of the two components is a storehouse of encoded information about a self in the context of an environment. In biology, DNA encodes instructions for the construction of a body that is likely to survive in an environment like that its ancestors survived. In culture, an internal model of world encodes information about the self, the environment, and the relationships between them. In both cases, decoding a segment of this information storehouse generates another class of information unit that coordinates how the storehouse itself gets decoded. Decoding DNA generates proteins that, in turn, orchestrate the decoding of DNA. Retrieving a memory or concept from the worldview and bringing it into awareness generates an instant of experience, a meme, which in turn determines which are the relevant portion(s) of the worldview to be retrieved in the next iteration.
15. In biological evolution, transmission and replication go hand-in-hand; genetic information gets replicated and is transmitted to offspring. But that isn't necessarily the only way of getting the job done. In memetic evolution, the most straightforward means of meme replication is through processes such as teaching or imitation, but there is a second form of replication that takes place within an individual. In the mind of someone engaged in a stream of thought, each meme is a statistically similar variant of the one that preceded and prompted it. It is in this sense that they self-replicate without necessarily being transmitted to another host. (For simplicity, from here on we will refer to inter-individual meme replication/transmission as transmission, and intra-individual meme replication as replication.)
16. It could be argued that the correlation between consecutive memes is so low that this hardly deserves to be called a form of self-replication. One certainly wouldn't even want consecutive memes to be identical! Surely Eigen and Schuster's error catastrophe argument applies here; that is, the copying fidelity of this process is so low that errors would quickly accumulate and in no time the lineage would die. But this argument doesn't apply. The only reason it is a problem for biological evolution is that copying error tends to impair the capacity to self-replicate. So long as offspring are as good as their parents at reproducing themselves, and live long enough to do so, it doesn't matter how much error is introduced from one generation to the next. It is only when a generation of offspring dies without having reproduced that is there a problem. In the biological world, once something is dead it can not spring forth life.
17. But in memetic evolution this isn't necessarily the case. To show why this is so, say that half-way through the train of consecutive memes in Einstein's brain that culminated in the theory of relativity, a tiger burst in through the window. Sure, the correlation between the relativity meme of one instant and the tiger-perception-meme of the next instant would be almost zero. This momentous memetic lineage would come to a screeching halt. But would it be lost forever? No. Sooner or later, once the tiger situation was taken care of, the relativity stream of thought would inevitably resume itself. Memory (and external artifacts) function as a sort of memetic sperm bank, allowing a defunct ancestral line to be brought back to life and resume self-replication. The upshot is that in culture you can get away with a much higher error rate than in biology. Though highly inaccurate, this second form of meme replication is of enormous consequence. Without it there would be no coherence to abstract thought, no thread of continuity linking one meme to the next. Abstract though, unlike episodic thought, can not rely on the continuity of the external world to lend a thread of continuity to conscious experience.
18. Cultural evolution has not only an internal form of replication, but internal forms of selection and variation as well. The process of representational redescription mentioned earlier can itself be redescribed as the selective generation of variant replicants. Since consecutive memes aren't exact replicas, each meme is a variation of the one that preceded it. Selection comes in the form of drives, needs, and the associative organization of memory, which constrain how, in a train of thought, one meme draws upon previously-stored memes to evoke the next. The memory-driven generation of a stream of correlated memes can thus be viewed as a coevolutionary relationship between replication, variation, and selection. Thus, embedded in the outer, inter-individual sheath of memetic evolution we find a second intra-individual sheath, where the processes of replication, variation, and selection are not spatiotemporally separated but intimately intertwined. Together they weave a stream of abstract thought, one meme fluidly transmuting into the next.

19. To proceed further it is useful to clarify the intuitive concepts we have been developing with a mathematical model of the mechanics underlying the storage and retrieval of memories, specifically one capable of addressing how new memes get invented, and how they are progressively refined through recursive representational redescription. The sparse distributed memory (SDM) model not only provides us with this, but is highly compatible with the architecture of common neural components and circuits in the brain [Kanerva 1988].
20. Vital to this theory is the notion of the focus-that part of the mind in which sensation and stored memory interact to produce a stream of experience. The states of the neurons that comprise the focus determine the content and experiential (phenomenal) qualities of an instant of awareness. We can now think of a meme as a pattern of information that is or has been encoded in an individual's focus. It can be subjectively experienced as a sensation, idea, attitude, emotion, or combination of these, and it can direct implementation by the motor apparatus.
21. Kanerva draws an analogy between the focus and a combined address-datum register in a computer; both contain data and serve as a pointer to memory, and can read from and write to memory. An instant of experience is encoded in the focus by a very high-dimensional vector of difference relations, or bits, that represent the presence or absence of some feature. It may seem simplistic to encode a meme as a vector of bits. However perception has to bottom out somewhere, so we encode all aspects of the meme down to the minimum level of granularity the senses are capable of detecting. The mathematics generalizes such that it can also handle continuous variables. The Hamming distance between two memes is the number of bits that differ. (So the Hamming distance between 11111 and 11001 is two.) Each meme has an address that specifies where that meme is stored.
22. If L is the number of possible features in a meme, the number of possible memes is 2L. Assuming L is large, the size of this space is enormous, so the memory is sparse in that it stores only a small fraction of all possible memes. For example, to construct a SDM with L=1,000, then there are 21,000 possible addresses. A workable number of them, say 1,000,000, are chosen at random to be actual storage locations. The number of memes at Hamming distance k away from any given meme is equal to the binomial coefficient of L and k, which is well approximated by a Gaussian or normal curve. Thus, if meme X is 111...1 and its antipode is 000...0, and we consider meme X and its antipode to be the poles of the hypersphere, then approximately 68% of the other memes lie within one standard deviation (sqrt[L]) of the equator region between these two extremes (FIGURE 1). As we move through Hamming space away from the equator toward either Meme X or its antipode, the probability of encountering a meme falls off sharply by the proportion sqrt[L]/L. In our example, the median distance from one location to another is 424 bits, and 99.8% of stored memes lie between 451 and 549 bits of any given location.

23. A computer reads from memory by simply looking at the address in the address register and retrieving the item at the location specified by that address. The sparseness of the SDM prohibits this kind of one-to-one correspondence, but it has two tricks up its sleeve for getting around this problem.
24. First, it feigns content addressability, as follows. The particular pattern of 1s and 0s that constitutes a meme causes some of the synapses leading out from the focus to be excited and others inhibited. The locations where memes get stored are memory neurons, and the address of a neuron amounts to the pattern of excitatory and inhibitory synapses from focus to memory that make that neuron fire. Activation of a memory neuron causes the meme to get written into it. Thus there is a systematic relationship between the memes? information content and the locations they activate.
25. Second, since the probability that the ideal address for storing a meme corresponds to an actual location in memory is vanishingly small, storage of the meme is distributed across those locations whose addresses lie within a sphere (or more accurately, hypersphere) of possible addresses surrounding the ideal address (FIGURE 2). The radius (in Hamming metric) of this sphere is determined by the neuron activation threshold. Each location participates in the storage of many memes. In this example we assume that 10,000 memes have been stored in memory. Each meme is stored in 1,000 (of the 1,000,000 possible) locations, so there are approximately 10 memes per location. The storage process works by updating each of the L counters in each location; to store a 1 the counter is incremented by 1, and to store a 0 it is decremented by 1. These nearly one million operations occur in parallel.

26. If after a meme, say meme X, is stored, the individual's attention is directed toward external stimuli, then nothing is retrieved from memory. But to the extent that memory contributes to the next instant of awareness, the storage of X activates retrieval of not only X itself but also all other memes stored in the same locations as where X was stored. The next meme to be encoded in the focus, X', is found by determining the best match; that is, by averaging the contributions of all retrieved memes feature-by-feature. Whereas the 1,000 retrieved copies of X (and memes similar to X) reinforce one another, the roughly 10,000 other retrieved memes are statistically likely to cancel one another out, so that X' ends up being similar to X. Though X' is a reconstructed blend of many memes, it can still be said to have been retrieved from memory. X' can now be used to address the memory, and this process can be reiterated until it converges on meme Y that satisfies a current need. The closer Y is to X, the faster the convergence. In our example, assuming r = 425, if X and Y are more than 200 bits apart then Y is unlikely to be retrieved, but if they are 170 bits apart, Y will be retrieved in about four iterations. Working memory can now be viewed as the memes that lie within some Hamming distance of the meme in the focus such that they are retrievable within some number of iterations.
27. Keeler [1988] showed that SDM is a superset of Hopfield-type and connectionist models of autoassociative or heteroassociative memory. In SDM, associations between memes are not explicitly represented as connection strengths but as proximity in multidimensional space. However in the end they amount to the same thing. The smaller the Hamming distance between two memes, the higher the probability that they will be retrieved simultaneously and blended together in the focus. What allows them to be retrieved simultaneously, however, is that they are either stored in the same neurons, or in neurons with nearby addresses, which in turn reflects the neurons' connectivity. Thus factors that affect the storage of a meme will also affect retrieval of that meme; the two processes are connected.
28. There are two changes we need to make to Kanerva's model before we can put it to use. We redefine L to be the maximum length of a meme. Memes of any length up to L are allowed. The number of possible memory items is now:

This enables the memory to store abstractions, to categorize. For example, if the meme piano is represented as 111010, and harp is represented as 111101, the musical instrument meme can be represented as 111*** where * means either 1 or 0, or more simply as 111, since the last three features have an equal probability of being 0 or 1; musical instrument carries no information about them. Categorization projects the original information space, which had n relevant dimensions, onto a new space that has fewer than n dimensions (for example, here the attribute music-making object, represented using the first three bits, is all that is relevant). That is, it enables logical operations on previously-stored memes-in this case an OR gate-which could be realized in the brain via adjustment of connection strengths.

29. Since N has increased, given the same number of storage locations as before, the memory should now be even sparser. However the change we made actually makes the memory potentially denser. A visual metaphor can help explain why (FIGURE 3). If you picture the mind as a set of concentric spheres like an onion, and memes as points on these spheres, an episodic mind is one in which only the outermost sphere stores memes. In order for a meme, say meme A, to evoke a reminding of meme B, they have to be very similar at a superficial level. In a memetic mind, on the other hand, the onion layers are traversed by wormholes that put related concepts within working memory reach of one another. Musical instrument is a more general concept than piano or harp, and is therefore stored in a deeper layer of the onion. If Harry can not play the piano for us tonight, an episodic mind is not going to think of inviting Lois to play her harp. Piano and harp are just too far apart in Hamming space for one to evoke the other. But a memetic mind can easily get from piano to musical instrument and from there to harp. The need a pianist meme selectively generates a stream of redescriptions or variant replicants of itself each within k bits of its predecessor; need a pianist evokes need a musician which evokes need Lois the harp player.

FIGURE 3. An explanatory metaphor for the role of abstractions in retrieval. Black dots represent memes, pale circles around them represent radius k hypersphere of memes that are immediately retrievable from central black dot meme. Memes lie within an onion-like structure such that deeper, more abstract memes lie at deeper onion layers. Piano and harp are too far apart in Hamming distance for one to evoke the other directly. A memory that has abstracted the meme musical instrument from episodes of piano and harp is capable of thinking to invite the harp player when the pianist is ill.

30. Next we add habituation to the model. When consecutive instants are almost identical, no reminding process occurs. Thus if in instant A the sensory input is 111...1, and in instant B the sensory input is also 111...1, instant C is not going to consist of the experience of being reminded of instant A. B only produces retrieval of A when they are far apart in time.
31. We now have a framework from which we can think more concretely about intra-individual meme self-replication. The pattern of information that constitutes a meme determines which of the synapses leading out from the focus are excited and which are inhibited-it determines how activation flows through the memory network-which in turn determines the neurons where the meme is stored and from which the next meme is retrieved. Thus, embedded in the neural environment that supports their informational integrity, memes act as implicit pointers to other memory locations. These pointers prompt the dynamic reconstruction of the next meme to be subjectively experienced, which is a variant of (statistically similar to) the one that prompted it. It is in that sense that they self-replicate with variation.
32. The content addressable nature of the memory ensures that the composition of a meme in the focus, say X', is largely determined by the compositions of the memes in locations activated by its predecessor, meme X. The relationship between X, the memes it activates, and X', may be superficial, or it may reflect a deep or metaphorical similarity. This relationship need not even be a semantic one. In wordplay, for example, meme X' bears a syntactic relationship to X rather than, or in addition to, a semantic one. In the recollection of a sequence, meme X is used as the address to write Y, Y as the address to write Z, and so on. Thus the association-based retrieval and reminding process constrains how stored memories and abstractions are retrieved to shed light on present experience. This form of selection affects episodic thought on a periodic basis, but in a stream of representational redescription it operates recursively, in conjunction with meme replication and variation to progressively refine and connect elements of the worldview.
33. Equipped with a model of how memes evoke one another in a stream of abstract thought, and of how this process constitutes an inner sheath of meme evolution, we are in a position to reframe our central question. We want to know how a mind comes to assume a self-sustained stream of thought that progressively shapes and is shaped by, a worldview. Abstract thinking requires that for each meme that enters the focus there exist in memory at least one other meme less than k bits away. However, representational redescription is the process that puts related memes within working memory reach of one another; it is what recognizes abstract similarities and restructures the memory to take them into account. How do you get the wormholes without the worms?

34. Let us resume our unraveling of the origin of life paradox. We left off with the discovery of ribozymes, RNA molecules that (like proteins) can catalyze chemical reactions, and the unsuccessful attempt to get them to self-replicate. Despite the myriad difficulties encountered in this enterprise, the idea behind it-that life originated in a simple self-replicating system that eventually evolved into the complex DNA-RNA-protein complex we know and love-was a good one. After all, once you have some sort of self-replicating structure in place, anything whatsoever that accomplishes this basic feat, natural selection can enter the picture and help things along.
35. Kauffman (1991) suggested that knowing as much as we do about what life is like now may actually get in the way of determining how it began. Accordingly he decided to focus on how to get from square zero-no life at all-to square one-any kind of primitive self-replicating system-and leave the problem of getting from square one to DNA-based life, to natural selection, which is unsurpassed in its ability to bring about adaptive change. Given the conditions present in the early earth at the time life began, how might some sort of self-replicating system have arisen? The answer he came up with is that life may have begun not with a single molecule capable of replicating itself, but with a set of collectively self-replicating molecules. That is, none of the molecules could replicate itself, but each molecule could induce the replication of some other molecule in the set, and likewise, its own replication was induced by some other member of the set. This kind of dual role as both ingredient (or stimulant) and product of different chemical reactions is not uncommon for polymers such as protein and RNA molecules.
36. Polymer molecules induce each other's replication by acting as catalysts. Catalysts speed up chemical reactions that would otherwise occur very slowly. A collectively autocatalytic system is a set of molecules which, as a group, catalyze their own replication. Thus if A catalyzes the conversion of X to B, and B catalyzes the conversion of Y to A, then A + B comprise an autocatalytic set (FIGURE 4). In an environment rich in X and Y, A + B can self-replicate. A set of polymers wherein each molecule's formation is catalyzed by some other molecule in the set is said to exhibit catalytic closure.

FIGURE 4. An autocatalytic set: A catalyses the formation of B, and B catalyses the formation of A. A dark line represents a catalyzed reaction. A pale line represents action of catalyst on reaction.

37. It is of course highly unlikely that two polymers A and B that just happened to bump into one another would happen to catalyze each other. This is, however, more likely than the existence of a single polymer catalyzing its own replication. And in fact when polymers interact their diversity increases, and so does the probability that some subset of the total will reach a critical point where there is a catalytic pathway to every string in the subset. To show that this is true we must show that the number of reactions by which they can interconvert increases faster than their total number. Given polymers made up of, say, two different kinds of monomers, of up to a maximum length of L monomers each, then N, the number of possible polymers is 2L+1 as per equation 6.1. Thus as L increases-which it obviously does, since two of the longest polymers can always join to form a longer one-the number of polymers increases exponentially. Now we need to show that the number of reactions between them increases even faster. We will be conservative and consider only cleavage (e.g. 110 -> 1 + 10) and ligation (e.g. 1 + 10 -> 110) reactions on oriented polymers (such as protein and RNA fragments). Note that cleavage, like categorization, creates a product of lower dimensionality than the reactants, while ligation, like inventions that arise through the combination of different ideas, creates a product of higher dimensionality.
38. The number of possible reactions is the product of the number of polymers of a certain length times the number of bonds, summed across all possible lengths:

Dividing equation 6.1 by equation 6.2, we find that as L increases, the ratio of reactions to polymers increases by a factor of L-2. This means that if each reaction has some probability of getting carried out, the system eventually undergoes a transition to a state where there is a catalytic pathway to each polymer present. The probability of this happening shifts abruptly from highly unlikely to highly likely as R/N increases. This kind of sharp phase transition is a statistical property of random graphs and related systems such as this one. Random graphs consist of dots, or nodes, connected to each other by lines or edges. As the ratio of edges to nodes increases, the probability that any one node is part of a chain of connected nodes increases, and chains of connected nodes become longer. When this ratio reaches approximately 0.5, almost all these short segments become cross-connected to form one giant cluster (FIGURE 5). The larger the number of nodes, the steeper the vertical portion of the resulting sigmoidal curve. The relationship between nodes and edges is similar to the relationship between polymers and catalyzed reactions. The larger our value for N, the more abruptly the system becomes capable of autocatalysis.

FIGURE 5. When the ratio of edges to nodes reaches approximately 0.5, short segments of connected nodes join to form a large cluster that encompasses the vast majority of nodes.

39. Of course, even if catalytic closure is theoretically possible, we are still a long way from knowing for certain that it is the correct explanation for the origin of life. How likely is it that an autocatalytic set would have emerged given the particular concentrations of chemicals and atmospheric conditions present at the time life began? In particular, some subset of the R theoretically possible reactions may be physically impossible; how can we be sure that every step in the synthesis of each member of an autocatalytic set will actually get catalyzed?
40. Kauffman's response is: if we can show that for a wide range of hypothetical chemistries-i.e. different collections of catalytic molecules-that autocatalytic sets emerge, then the particular details of the chemistry that produced life do not matter so long as it falls within that range. We begin by noting that much as several different keys can sometimes open the same door, each reaction can be catalyzed not by a single catalyst but by a hypersphere of catalytic molecules, with varying degrees of efficiency. So we assign each polymer a (very low) a priori random probability P of catalyzing each reaction. We then show that for any value of P there exists some value of L for which the probability of catalytic closure > 0.999. Kauffman claims that the necessary values for L and P are highly plausible given the conditions of early earth. I will not delve into the evidence for this here, since for our purposes we are more interested in whether autocatalysis is a computationally feasible mechanism for bootstrapping an evolutionary process, rather than whether it is the correct explanation for the origin of life. It is interesting to note, however, that experimental evidence for this theory using real chemistries [Lee et al. 1996, 1997; Severin et al, 1997], and computer simulations [Farmer, Kauffman, and Packard 1986] have been unequivocally supportive. Farmer et al. showed that in an artificial soup of information strings capable of cleavage and ligation reactions, autocatalytic sets do indeed arise for a wide range of values of L and P. FIGURE 6 shows an example of one of the simplest autocatalytic sets it produced. The original set of polymers from which an autocatalytic set emerges is referred to as the food set. In this case it consists of: 0, 00, 1, and 11. As it happens, the autocatalytic set that eventually emerges contains all members of the original food set. This needn't necessarily be the case. We discussed earlier how the correlation between consecutive memes in a stream of thought can be viewed a form of intra-individual self-replication. Here we see something similar going on: there is also a correlation between successively-formed memes in a sequence of reactions. For example, the molecule at the top, 00100111, is highly correlated to the leftmost of the two memes from which it was formed, 001001.

FIGURE 6. A typical example of a small autocatalytic set. Reactions are represented by dark lines connecting ligated polymer to its cleavage products. Red (or pale) lines indicate catalysis. Darkened ovals represent food set.

41. Now the question is: given that an autocatalytic set did emerge, how would it evolve? The answer is fairly straightforward. Since each molecule is getting duplicated somewhere in the set, eventually multiple copies of all molecules exist. If the space they occupied were a membrane-bound structure such as a coascervate or bilipid membrane vesicle, this abundance of molecules would exert pressure on its walls which might well cause it to pinch off and divide into two twins, each containing at least one copy of each molecule. This common process is referred to as budding. In an even simpler self-replication scenario, the molecules are floating a pool that overflows into a lower pool when it rains, bringing self-replicating molecules with it.
42. Either way, replication is far from perfect-an offspring is unlikely to be identical to its parent. Different chance encounters of molecules, or differences in their relative concentrations, or the arrival of new food molecules, could all result in different catalysts catalyzing a given reaction, which in turn alters the set of reactions to be catalyzed. So there is plenty of room for heritable variation. Error catastrophe is unlikely because, as mentioned earlier, initially each reaction can be catalyzed not by a single catalyst but by a hypersphere of potential catalysts, so an error in one reaction would not have much effect on the set at large.
43. Selective pressure is provided by the affordances and limitations of the environment. For example, say an autocatalytic set of RNA-like polymers arose. Some of its offspring might have a tendency to attach small molecules such as amino acids (the building blocks from which proteins are made) to their surfaces. Some of these attachments inhibit replication, and are selected against, while others favor it, and are selected for. We now have the beginnings of the kind of genotype-phenotype distinction seen in present-day life. That is, we have our first indication of a division of labor between the part of the organism concerned with replication (in this case the RNA) and the part that interacts with the environment (the proteins).
44. The autocatalysis origin of life theory circumvents the chicken-and-the-egg problem by positing that the same collective entity is both code and decoder. This entity doesn't look like a code in the traditional sense, because it is a code not by design but by default. The code is embodied in the physical structures of the molecules themselves; their shapes and charges endow them with propensities to react with or mutually decode one another such that they manifest external structure, in this case a copy of its collective "self"?. Since autocatalytic sets appear to be a predictable, emergent outcome in any sufficiently complex set of polymers, the theory lends support to the notion that life is an expected outcome rather than a lucky long-shot.

45. Following Donald's lead, we have argued that the most likely bottleneck in cultural evolution is the establishment of a network of inter-related memes, a worldview, that progressively shapes and is shaped by a stream of self-triggered thought. We want to determine how such a complex entity could come to be. Drawing from the origin of life scenario presented above, we will posit that meme evolution begins with the emergence of a collective autocatalytic entity that acts as both code and decoder. Let us examine how this might work.
46. In the origin-of-life case we asked: what was actually lying around on the primitive earth with the potential to form some sort of primitive self-replicating system? The most promising candidate was catalytic polymers, the molecular constituents of either protein or RNA. Here we ask an analogous question: what sort of information unit does the episodic mind have at its disposal? It has memes, specifically memories of episodes. Episodic memories then constitute the food set of our system.
47. Next we ask: what happens to the food set to turn it into a self-replicating system? In the origin-of-life case, food set molecules catalyze reactions on each other that increase their joint complexity, eventually transforming themselves into a set for which there exists a catalytic pathway to the formation of each member molecule. We propose that an analogous process takes place to turn an episodic mind into a memetic one. That is, food set memes activate redescriptions of each other that increase their joint complexity, eventually transforming themselves into a set for which there exists a retrieval pathway to the formation of each member meme. Much as polymer A brings polymer B into existence by catalyzing its formation, meme A brings meme B into conscious awareness by activating a retrieval or reconstruction process. Here we come to an interesting difference between the origin of life case and the origin of culture. Since short, simple molecules are more abundant and readily-formed than long, complex ones, it makes sense to expect that the origin-of-life food set members were the shortest and simplest members of the autocatalytic set that eventually formed. Accordingly, in simulations of this process the direction of novelty generation is outward, joining less complex molecules to form more complex ones through logical AND operations (see FIGURE 5). In contrast, the memetic food set molecules are relatively complex, consisting of all the features of a particular episode. In order for them to form an interconnected web, their interactions would tend to move in the opposite direction, starting with relatively complex memes and forming simpler but more abstract ones through logical OR operations. The net effect of the two is the same, however: a network emerges and joint complexity increases.
48. The process of categorization through OR operations created new lower-dimension memes, which made the space denser, and increased susceptibility to the autocatalytic state. On the other hand, creating new memes by combining previously-stored memes through logical AND operations could interfere with the establishment of a sustained stream of thought by increasing the dimensionality of the space, and thereby decreasing density. If indeed cross-category blending disrupts conceptual networking, one might expect it to be less evident in young children than in older children, and this expectation is born out experimentally [Karmiloff-Smith 1990].
49. How might Groga's mind have differed from that of her ancestors such that she was able to perform OR operations on episodic memes to create a new kind of memes-abstractions? Recall that in the SDM, meme X activates all stored memes within a hypersphere of radius k bits, and meme X' is determined by averaging the contributions of each retrieved meme bit-by-bit. If the memory is episodic, the activation threshold is so high that the only memes to fall within k bits of the currently-experienced meme are ones that are very similar to it. Therefore reminding events are rare, and when they do occur, the retrieved memory is very superficially similar to the current one. Without abstractions there are no shortcuts or wormholes connecting episodes that are related in any less-than-obvious way.
50. Let us consider what would happen if Groga's activation threshold were lower than average, say k = 10 rather than 5, as is typical of her tribe. (So any stored meme that differs from the current meme by ten or fewer bits gets retrieved.) When X goes fishing in memory for meme X', sooner or later this large hypersphere is bound to catch a stored meme that is not superficially similar to X. For example, perhaps Groga watched foxes every day, so there were lots of fox memories stored in her brain, all containing a sequence of ten 0's followed by a five bit long variable sequence. She happens to look off in the distance and see a grazing buffalo, which gets represented in her focus as 000000011101010. The buffalo meme will be referred to as meme X. All of the fox memories lie within ten bits of meme X, so they are therefore evoked in the construction of meme X' (as is meme X itself). Since all the components from which X' is made begin with a string of seven positions, there is no question that X' also begins with a string of seven zeros. These positions might code for features such as has eyes, eats, et cetera. The following set of three 1s in the fox memes are canceled out by the 0s in the buffalo memes, so in X' they are represented as *s. These positions might code for features such as has wings. The last five bits constituting the variable region are also statistically likely to cancel one another out. These code for other aspects of the experience, such as, say, the color of the sky that day. So X' turns out to be the meme 0000000********, the generic concept animal, which then gets stored in memory in the next iteration. This evocation of the animal meme by the buffalo episode isn't much of a stream of thought, and it doesn't bring her much closer to an interconnected conceptual web, but it is an important milestone. This is the first time she derived a new meme from other memes, her first creative act.
51. Other categories form in analogous fashion. Since memories are stored and retrieved on the basis of similarity, these categorization acts are inherently biased to find similarities between stored memes, and to reclassify or redescribe them so as to make these similarities more explicit. Now we come to the crux of this paper. As Groga accumulates both episodic and abstract memes, the statistical probability that a current meme is similar enough to some previously-stored meme to activate retrieval of it increases. Therefore, reminding acts of the sort that lead to an act of categorization increase in frequency, and eventually become streams of remindings. These streams of remindings get progressively longer. Eventually the memory becomes so densely packed that any meme that comes to occupy the focus is bound to be close enough in Hamming distance to some previously-stored meme(s) to activate a variant of itself. There is a potential pathway of associations from any one meme to the others; the memes form an autocatalytic set. This marks a phase transition to a state where, just as with the origin of life, the sequential activation of self-similar patterns is self-propelled. Memes are organized and reorganized until what was once just a collection of isolated memories becomes a highly-structured network of concepts, instances, and relationships-a worldview. Groga's focus is now more than just a spot for coordinating stimuli with action; it is a forum for the variation-producing operations that emerge naturally through the dynamics of iterative retrieval.
52. Now that we have an autocatalytic network of memes, how does it evolve In the origin-of-life scenario, new polymer molecules accumulate one by one until there are at least two copies of each, and their shell divides through budding to create a second replicant. In the culture scenario, Groga shares ideas, stories, and experiences with her children and tribe members, spreading her worldview meme by meme. Categories she had to invent on her own through the process of abstraction are presented to her children and experienced by them much as any other episode. They are handed a shortcut to the category; they don't have to engage in abstraction to obtain it.
53. Recall how the probability of autocatalysis in Kauffman's simulation could be increased by raising either the probability of catalysis or the number of polymers (since number varied with maximum length). Something similar can happen here. Eventually, once enough of Groga's abstractions have been assimilated, her tribe members? memories become so densely packed that even if their activation thresholds are higher than Groga's, a version of Groga's worldview snaps into place in their minds. Each version resides in a different body and encounters different experiences. These different selective pressures sculpt each copy of Groga's original worldview into a unique internal model of the world. Small differences are amplified through positive feedback, transforming the space of viable worldview niches. TABLE 1 presents a summary of how the components of the proposed theory of cultural autocatalysis map onto their biological counterparts.

V. Biological Evolution of the Inner Sheath of Culture

54. The ability to reach and maintain this autocatalytic state depends not only on meme density but also on the neuron activation threshold. If the threshold is too high (the hypersphere of potentially activated memes is too small) then even very similar memes can not evoke one another, so a stream of remindings, if it happens at all, is likely to die out before it produces something creative. The focus is virtually always impacted with external stimuli or internal drives such as hunger, and memory is pretty much reserved for recalling how some goal was accomplished in the past. This kind of mind corresponds to what Donald refers to as episodic.
55. On the other hand, if the threshold is too low (the hypersphere too large), then any meme will evoke a multitude of others not necessarily meaningfully related to it. The system is catalytic but not autocatalytic. Successive patterns in the focus have little resemblance to one another, and thinking may be so muddled that survival tasks are not accomplished. Thus, the penalty for overshooting and ending up with too low a threshold is great. The free-association of a schizophrenic [see Weisberg 1986] seems to correspond to what one might expect of a system like this.
56. For memory to produce a steady stream of meaningfully-related yet potentially creative remindings, the threshold must fall within a narrow intermediate range. This is consistent with Langton's [1992] finding that the information-carrying capacity of a system is maximized when its interconnectedness falls within a narrow regime between order and chaos. The situation may actually turn out to be more complicated. Sustaining a creative train of thought may involve not only keeping the activation threshold within a narrowly-prescribed range but dynamically tuning it in response to the situation at hand. This is particularly likely if the memory is not uniformly dense (i.e. clusters of highly-correlated memes) or if different kinds or stages of thought require different degrees of conceptual blending. For example, finding unusual associations may depend on the preconscious ability to temporarily increase hypersphere radius, and then decrease it again to refine or sharpen the idea.
57. What factors would have produced sufficient evolutionary pressure to risk tinkering with the activation threshold until it achieved the requisite delicate balance to sustain the autocatalytic state? An episodic mind is rather dull-it can not engage in witty word-play, or invent a new game-but it is pretty good at surviving. Lowering the threshold presents perilous risks, and since in an evolutionary line there is individual variation, even once the ideal threshold is found, the lower the average activation threshold, the higher the fraction of individuals for which it is so low they might not survive. One such factor may have been environmental upheaval such as an earthquake, flood, or temperature change. The episodic mind is particularly disadvantaged when faced with an unpredictable environment, where old ways of doing things may suddenly no longer work, and new strategies must be invented. Other factors may have been the advent of upper limb freedom afforded by two-legged locomotion, and the descent of the larynx which enabled human vocalization. Each of these changes increased the complexity of what could be expressed; brilliant memes are of little use unless the neuromusculature yields sufficient degrees of freedom such that the implementation of them does them justice.

58. We have seen that the components of an evolutionary process do take place in the mind of an isolated individual. The mind generates new memes, and the variation-generating process inherently involves internal self-replication, in the sense that statistical similarity is preserved across sequentially retrieved memes in a train of thought. Moreover, the mind not only selects which memes to implement, but which aspects of the environment to assimilate into its meme stream, and the associative organization of memory selectively constrains the generation of variant replicants every step of the way as an idea is refined.
59. Although intra-individual meme replication is sufficient for evolving memes, the culture of a single individual would be extremely impoverished compared to that of a society of interacting individuals. This is because the number of memes increases exponentially as a function of the number of interacting memetic-level individuals. As a simple example, a single memetic individual who invents ten memes is stuck with just those ten memes. A society of ten interacting individuals, only one of whom has reached the memetic stage and can invent ten memes, is not any better off; there are still only ten memes. In a society of ten non-interacting individuals, each of whom invents ten memes but doesn't share them, each individual still has only ten memes. But in a society where each of the ten interacting individuals invents ten memes and shares them, each individual ends up with one hundred memes. The bottom line is: although a single individual is capable of evolving memes, cultural evolution as we know it, with its explosive array of meaningful gestures, languages, and artifacts, depends on both intra-individual and inter-individual meme replication.
60. Returning briefly to the origin-of-life puzzle, recall that traditional attempts to explain how something as complex as a self-replicating entity could arise spontaneously entail the synchronization of a large number of vastly-improbable events. Proponents of such explanations argue that the improbability of the mechanisms they propose does not invalidate them, because they only had to happen once; as soon as there was one self-replicating molecule, the rest could be copied from this template. However, Kauffman's theory that life arose through the self-organization of a set of autocatalytic polymers suggests that life might not be a fortunate chain of accidents but rather an expected event.
61. Whether this theory provides a more accurate account of how life originated on this planet is hard to say. But if we are interested in the more general question of how information evolves, we now have another data point, another kind of evolutionary process to figure into the picture-cultural evolution. Culture, like biological life, is a workable system for evolving information through variation, selection and transmission/replication. The relationship between these three phases, however, is not as straightforward as it is in biological evolution. There are two layers of replication, one embedded in the other, and to actualize the inner layer of replication, every member of the culture must establish their own unique autonomous stream of sequentially activated self-similar patterns, their own personal worldview. Consistent with Kauffman's assertion that the bootstrapping of an evolutionary process is not an inherently improbable event, the it only had to happen once argument does not hold water here because the cultural analog to the origin of life takes place in the brain of every young child. Autocatalysis may well be the key to the origin of not only biological evolution, but any information-evolving process.

62. Cultural evolution presents a puzzle analogous to the origin of life: the origin of an internal model of the world that both generates and is generated by streams of self-sustained, internally-driven thought. In this paper we looked at a plausible scenario for how cultural evolution, like biological evolution, could have originated in a phase transition to a self-organized web of catalytic relations between patterns. The scenario outlined here is nascent. Nevertheless, I know of no other serious attempt to provide a functional account of how memetic evolution got started. Whether or not the scenario outlined here turns out to be correct in its details, my hope is that it draws attention to the problem of cultural origins, suggests what a solution might look like, and provides a concrete example of how we gain a new perspective on cognition by viewing it as an architecture that has been sculpted to support a second evolutionary process, that of culture.

I would like to thank David Chalmers, Harold Edwards, Norman Johnson, and William Macready for helpful comments.

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