The effect of memorability, population density and mobility on the diffusion of cultural practices

PhD Anders Lisdorf

AbstractOn the basis of our knowledge human cognition we created an agent based model of transmission of memes. These memes represent units of cultural transmission, such as cultural practices or ideas. With this model we simulated the process of adoption in a population of such a cultural practices based on its memorability. We tested how two different types of meme, one with high memorability and one with low memorability disseminated under varying circumstances. The circumstances that were varied were the population density and the mobility of the agents in the population. This showed that cultural practices that are difficult to remember can not be widely disseminated in a population, but they spread with the same rate as easy to remember practices in densely populated settings. Further it was found that mobility increased diffusion rate in a sparsely populated setting but did not increase it in densely populated settings. In some cases it even worked against it.

Introduction

The last couple of decades several attempts have been made to understand human culture based on insights from the cognitive sciences (Shore 1996, D'Anrade and Strauss 1992, Donald, 1993, Sperber 1996). Still much work needs to be done to understand how the individual properties of human cognition generalize to produce cultural artifacts. The cognitive science of religion has produced several attempts to try to explain religion as a culturally widespread phenomenon by recourse to basic human cognitive functions. The basic hypothesis holds that content that is easily handled by this cognitive system is easy to remember and therefore easy to transmit (Sperber & Hirschfeld 2004, Boyer 2001).

Some of the most successful accounts of the dissemination of religion have postulated that memory of the the religious content, be it ritual or dogma, plays a key role in the diffusion of religion (Boyer 2001; Whitehouse 2004). For ease of reference and without subscribing to any particular theoretical school I will call this religious content memes. I take meme in the original sense that Richard Dawkins, who coined the term, had in mind: A unit of cultural information, such as a cultural practice or idea, that is transmitted verbally or by repeated action from one mind to another. It is this sense Dawkins originally described the meme as “a unit of cultural transmission” (Dawkins 1976: 192). One thing universally true about memes is that they need to be remembered to be transmitted. The life-span of a meme is determined by how long it can be remembered by a human mind.

With regard to religious ideas, research in the cognitive science of religion has converged to show that minimally counterintuitive ideas are better remembered than intuitive ideas (Barrett & Nyhoff 2001, Boyer & Ramble 2001). Maximally counterintuitive ideas are worse remembered than intuitive ideas (Gonze et al 2005). Some religion is of the first type other of the second type.With regard to rituals it has been argued that emotionally stimulating rituals are better remembered than non stimulating. There is evidence that certain types of rituals are better remembered than others (Whitehouse, Richert & Stewart 2005)

All these claims regarding the dissemination of ideas are made on the basis of controlled experiments in a lab and generalized assumptions about how these individual properties would work at population level. While the epidemiological approach has been generally advertised (e.g. Sperber 1996), little research has systematically investigated whether these assumptions hold true empirically.

It is, however, not straight forward to generalize from individual properties to a global pattern. One successful technique to understand how such patterns emerge from interactions between agents is agent based modeling.1 This has been used in such diverse areas as, ecology, biology, traffic, supply chain management etc. If we want to understand the pattern of dissemination of religious memes across a population a good way to start is to apply an agent based model.

I will model two types of religious memes: easy and hard to remember. Those that are easy to remember reflect minimally counterintuitive “folk religion”. Those that are hard to remember reflect maximally counterintuitive “dogmatic” religions like christianity and buddhism. The difference in memory degradation reflects data from an experimental setting.2

Since the epidemiological framework is the most advertised it would be a good idea to look to epidemiology to start. In epidemiology some of the primary parameters in understanding the diffusion pattern of an infectious disease in a population is population density and mobility. Therefore we will see how these two types of memes can spread relative to these two parameters.

Operationalization

The model is constructed in the application Netlogo designed by Uri Wilensky.3 It consists of a population of agents. The “world” is of a fixed size, but without borders. When the model is initialized agents are randomly distributed to patches in the world. This place is their home. One of the agents have the meme from the beginning and is able to transmit it.

At every click of time agents can move randomly to a patch in any direction. The mobility parameter of the model limits how far from the agents' home it can go. At every click the gents forget, that is, accuracy of the meme degrades with a percentage. When the meme is below 50 percent, the agent will not be able to transmit it any longer.

When an agent is next to another they will exchange information. If agent A has the meme in memory with greater than 50 percent accuracy it will boost agent B's memory with the accuracy it has itself, (but B's accuracy can not exceed 100%) and vice versa. 4

The “easy meme” reflecting easily transmitted content was operationalized as being forgotten 10 times slower than the “difficult meme”.The low population density condition had 4 times less density (50 agents) than the high population density condition (200 agents). The low mobility condition had a 5 times smaller distance for the agents to move away from their homes than the high mobility. Every combination of these conditions were set to run until a fixed time. This was repeated 20 times. The timeframe is fixed (to 500 clicks), so all runs were of the same length and the world was similarly of the same size in all runs. The agents did not have a life cycle.

Results

The results of the simulations can be seen in figure 1. The graphs show the number of agents

1 Agent based modeling also allows us to evade the assumption typical in previous work on transmission of culture: that “ ..any two individuals have the same probability of contact” (Cavalli-Sforza and Feldman 1981: 47). In real populations the location of an agent naturally constrains the probability of contact.

2 In Gonze et al 2005 maximally counterintuitive items were remembered about 10 times worse than minimally counterintuitive items.

3 The model was originally developed by Istvan Czachesz, but adapted to the present purposes.4 The model is similar to a simple epidemiological model of an infectious disease which is transmitted from an infected to a susceptible individual. The difference from typical infectious diseases like the flu is that there is no incubation period, and there is no immunity subsequent to the disappearance of the disease. You can get infected again any number of times.

in the population “carrying” meme with an accuracy higher than 50% in all the different combinations of the three variables: population density, mobility and memorability of the meme.

Population density

Low High

Low mobility High mobility Low mobility High mobility

High memorability

1 2 3 4

Low memorability

5 6 7 8

We may note that:

1. Diffusion in low population density is invariably slower than in higher population densities. In the time it takes to disseminate the meme to 100 % of the population in high population densities, in low population densities the meme has only reached between 20% and 50% of the population.

2. Mobility has no, or limited effect in a high population density (conditions 3, 4, 7, 8). It even seems to work against diffusion in some cases. In condition 8 where the meme had low memorability some runs had the meme become extinct. The reason for this is that this meme depends on frequent communications between carriers. Increased mobility lowers the probability of encountering a carrier of the meme in the beginning stages of the diffusion process where more different agents will be met.

3. Mobility does significantly increase the rate of diffusion for memorable memes in low population densities (condition 1 vs 2). This is even though the average number of communications per day is the same.

4. Memes with low memorability can only survive in high population densities. They die out in low population densities.

5. Variation between runs is higher in low population densities (1, 2) than in high population densities (3, 4).

6. Low memorability (7, 8) resembles the dissemination pattern than high memorability in high population densities (3, 4), but is more linear and slightly slower in.

Conclusion

These results, while only tentative, suggest some more general conclusions that should be possible to detect empirically. In the following in I will give try to apply them to some empirical observations.

Cultural practices that are hard to remember can only prosper in urban settings. Urban settings naturally afford high population density. A good illustration of this is the rise of christianity. Christianity is and was a low memorability cultural practice 5 and although it had its origin in a palestinian rural context it grew only in the largest urban centers (Stark 1996). It was of course the case for most religions in the Roman empire that they were present in the cities. Therefore it is illuminating to compare christianity to one of its high memorability contemporaries which has sometimes been named as a competitor: Mithraism. 6 While mithraism was present in the big cities of most of the empire, it was just as widespread in the most desolate rural areas (Clauss 1993).

But there are also other ways of orchestrating a high population density. For religions, we see this in the establishment of centers of theological excellence such as monasteries. Before christianity, monasteries as a full fledged institution did not exist. It is striking that also buddhism, another religion that has a large memory load, also developed monasteries. For the sciences, universities and campuses have a similar stabilizing effect. Science is hard to remember and frequent repetition and rehearsal is necessary to disseminate the cultural practice of science. Thus we see the earliest examples of science develop around centers of excellence in Greece and China (Lloyd 1990).

Cultural practices that are easy to remember are diffused with largely the same rate as those that are hard to remember in urban contexts. 7 This may seem surprising, but this model does not take in to consideration the learning curve. Usually things that are hard to remember also take longer to learn. If the learning curve was taken in to consideration the difference may have been larger.

Perhaps a more startling observation is that mobility has little effect on the rate of diffusion in urban contexts. In some cases it can even be detrimental to the diffusion of a low memorability meme. This suggests that globalization and the increased mobility of people does not significantly increase the rate of diffusion of new ideas in and of itself. This may be surprising since most theories of globalization stipulate that the increased connection between people does do that.

Conversely mobility has a great effect in low population densities. This is against what would be expected. In both cases the frequency of interaction between agents is the same. From the cognitive point of view this was stipulated to be the determining factor behind the diffusion of a meme, but apparently a non-cognitive factor such as the mobility of the agent has an effect in conjunction with population density for the diffusion of a meme at the population level.

Discussion

5 Christianity is based on maximally counterintuitive ideas such as the trinity (god being one and three, Jesus being both god and man and his father and died for the sins of others). These ideas are as mentioned earlier difficult to remember. Furthermore there are many things to remember accurately in christianity, such as laws, hymns, prayers, stories etc. All in all christianity places heavy burdens on the memory of its carriers. 6 Mithraism was based on images and astral lore that was already widely known in the Roman world (Beck 2006). Apart from this probably some phrases of a few lines were to be memorized. Furthermore the religion was staged with imagistic ritual (Martin 2004) which has been demonstrated to increase memorability (Whitehouse 2004). All in all Mithraism did not place in heavy burden on the memory of its carriers.7 This goes against the prediction of Harvey Whitehouse's theory of modes of religiosity. He stipulates that doctrinal

practices that are heavy on the memory are transmitted faster than the imagistic practices that are very memorable. I have elsewhere demonstrated that imagistic practices have a similar quick rate of spread in the Roman world (Lisdorf forthcoming), which fits the predictions made the model here.

On the basis of our knowledge human cognition we have created an agent based model of transmission of memes. These memes represent units of cultural transmission, such as cultural practices or ideas. The only aspect of this meme we decided to test is the memorability. In the model we tested how two different types of meme, one with high memorability and one with low memorability disseminated under varying circumstances. The circumstances that were varied were the population density and the mobility of the agents in the population. This produced some illuminating results that we tried to generalize, so that comparison with empirical examples was possible.

A general methodological caveat is that the model presented here is based on very limiting generalizations, which naturally restricts its predictive power. However we have been able to test more rigidly some assumptions that have here to fore been unwarranted or untested in the cognition culture studies so far. In the evolutionary study of culture, it has been more common to use modeling, but these models have been mathematical models known from population biology (Boyd & Richerson 1986, Feldman & Cavalli-Sforza 1976). While they are rigid, they do not incorporate the randomness that agent based modeling does.We have found that cultural practices that are hard to remember can only prosper in urban contexts and do not spread significantly slower than easy ones. Mobility does not significantly increase the diffusion rate in Urban contexts, while it does do so in rural contexts. We have seen that these generalizations made on the basis of the model does have a suggestive empirical basis.

Appendix

Pseudo code

To communicate

if other-agent not nobody [; if there is one there

if random-float 100 < receptiveness [ ; take receptiveness into account

if [meme] of other-agent > 5 [ ; only active followers spread the message

set meme to meme + [meme] of other-agent ; get the message

if meme > 10 [ set meme 10 ]; meme does not exceed 100 percent. ]

] end

To forget

At every click [ set meme meme * ( ( 100 - forgetting-rate ) / 100 )]; everyone forgets at a predetermined rateend

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