Spatial Dynamics of Culture Spreading in the Presence of Cultural Strongholds

This applet visualises a model of spatial distribution of replicating information where new information outbeats old. Detailed information as well as instructions on how to use the applet is given below the applet window. In order to run the applet you need to have Java Runtime Environment installed

Philosphy

Introduction - It is generally understood in historical linguistics that geolinguistic diffusion, the process by which linguistic features spread geographically from one dialect or language to another, plays a central role in the evolution of languages. Origins of linguistic changes are plentiful where societal changes and movements are of pivotal importance. The dynamics and causes of linguistic change provide therefore important clues to the historical developments of, as well as interplay between, societies and civilisations. It has long been observed that linguistic features, just like innovations, spread out ward from an originating centre. Spatial patterns are, however, rather ambiguous. Some cases bear evidence of a hierarchal diffusion process where e.g. dialect changes propagate in a cascade-like manner from larger to smaller cities. Other cases show a more isotropic geographic distribution where linguistic features spread as a wave front among adjacent speech communities. A unifying theme is, however, that recent changes are found close to the source.

A model of replicating information - We are interested the dynamics of culture spreading around strong culture centres. As a proxy for the spreading of cultural traits we use the spreading of words and put forward a model concerning the spatial dynamics of competing wave fronts where the key feature is that new words are more prone to be adopted than old. This view contrasts most models dealing with information spreading, whether it concerns innovations, opinions or linguistic traits, where two different pieces of information are treated on an equal footing.

Our model is defined on a two dimensional lattice on which words, after being coined in the culture centre, spread. In order to capture the ongoing adoption and subsequent communication of new words originating with a given frequency fword, at each time step a word is replicated and passed on to a neighbouring randomly chosen lattice site. If it is sent to a lattice site inhabited by an older version, the new one is adopted. But, if it is transmitted to a place where an even newer variant exists, the older word is ignored; new concepts always overrules old. The model gives rise to wave-like patterns moving radially outwards from the culture centre(s) on the lattice.

Our model of information spreading bears resemblance to other growth models in biology and physics. The average propagation of a new word into the background of an old is similar to a discrete version the wave front described by Fisherssss equation for bacterial growth. Our model also incorporates stochastic properties of growing interfaces of new information that mimic Eden surface growth in which unoccupied perimeter sites of a growing cluster are filled randomly with probabilities proportional to the number of occupied nearest neighbours.

Spreading of swearwords in Japan - As a case study we consider the geographic distribution of words over Japan. Carful analysis of linguistic maps has unveiled that words are in many cases arranged in concentric ring-like patterns with Kyoto, Japan's ancient capital, as focal point. This was first realised by Kunio Yanagita, a famous japanese folklorist, who studied the distribution of the word for snail. He also found that old variants were used in the southern and northern parts of the country but not in the middle. This lead him to formulate the "periphery propagation theory of dialects" (Hougen Shuken-ron) in which he visualised waves of new words emerging in Kyoto which spread radially outwards.

The most beautiful example of Yanagitasss theory is the distribution of swearwords. Japan is not known as a country where people swear to each other very often, but if you are cursed by someone with baka (dumb), you are probably having trouble with someone from Tokyo. If you instead hear aho (idiot), he or she is most likely from the Kyoto-Osaka area. The result of a comprehensive survey of the different variants of aho-baka} in the figure below; The concentric patterns centred around Kyoto are unmistakable. Aho and baka are indicated by dashed lines and Tokyo is a part of the circular area where baka, not aho, is being used. Baka used to exist in Kyoto too but has been overtaken by the newer aho. Other noticeable features are that the area of the word patches grow with increasing distance from Kyoto and that only a fraction of the words are simultaneously found both on to the north and south of Kyoto

Snapshots of a Java simulation showing the spatial dynamics of word spreading over the japanese mainland where each colour represent a different word. Blue and red circles show two examples where the same word form is found symmetrically on either side of Kyoto. The graph in the upper left corner shows the mean distance between two adjacent fronts (averaged over many runs) as a function of distance from Kyoto. The orange broken circle belongs to a word which only is present at Kyoto's north east side. The probability that a surviving word coexists on both sides decay with distance away from Kyoto in a way shown in the inset. We choose to investigate the behaviour when the spatial resolution (width of lattice site) was set to 15 and 30 km, respectively.

Statistical mechanics of replicating information - Our model has intersting dynamics which is better illustrated on a rectangular lattice rather than the Japanese mainland. Placing a line source at the base, our simulations demonstrate (see figure below) that the spacing between two word fronts increase as z0.5, for large distances z away from the source. This is true in both one and two dimensions, and the crossover to the asymptotic behaviour is set by the frequency of new words and system width. In one dimension our model maps exactly onto the limiting behaviour of the reaction-diffusion problem A+B → A, for which the density decays with time t as ρ(t)∼t-0.5: relating z to the constant average speed of the surface vsurf via z=vsurf t, gives &rho(z)∼z-0.5. The mapping is admissible also in two dimensions when the motion of one interface can be represented by a single coordinate (when correlations extends over the whole boundary).

Tutorial

The Java applet illustrates the spatial dyanimcs of replicating information. There are three main modes of visualisation controlled by the buttons located in the 'Display mode' panel. One can also increase the spatial resolution by clicking on the "Big lattice" button The function of the "Display mode" buttons are the following:

- Word landscape. By clicking on the 'Word landscape' button, you see the spreading of each individual word after being coined in the culture centre (black circle). Each word is given its own colour. At the perimiter sites of a word cluster, the word is transmitted to the neighbouring sites which will adopt the colour of the cluster if they were inhabited by an older word (see more details in the 'Philosophy' section in the right coloumn). The location of the source can be changed by first cklicking on the 'Move source' button in the 'Action button' panel, clicking on the source that you want to move, and simply drag it to the desired location on the lattice. There is also a possibility to add new sources by clicking on the "Add source" button and then clicking where on the lattice you would like to place it. Shortcuts, or communication highways, can also be added using the "Add shortcut" button. Click anywhere in the landscape and while holding the mouse button pressed, drag to a desired enpoint.

- Age landscape. During onging spreading of information each lattice site is marked with an age which can be visualised as an age landscape. Colouring towards dark brown indicate old age which eventually fade a way into the white background. This is the "Dali" colour map and symbolises the decay of the value of information as time progresses. The palette is inspired from Salvador Dali's famous painting The persistence of memory. The painting shows a dream where time has no significance; events occur simultaneously without any abovious causality. This contrasts our idea that recent information is more valuable than old. Colours in the "Munch" palette is taken from Evard Munch's The scream .

- River landscape. As information propagates each lattice point is marked with two pieces of information: the age of the most recent information that reached that point and from which neighbouring lattice site it came. By clicking the 'River landscape' button the latter is explored. The arrows form a navigable information landscape which can be used to, for instance, locate the time walker source from any given point in the lattice. If releasing trackers that follow the arrows in the landscape and keep count of the number of trackers that go through every lattice point on their way to the source, which is analogous to river depth, an information river landscape is built up. White to blue colouring shallow to deep riverer. The dark brown line shows the main river from the chosen lattice point indicated by the red circle, to the source. This point can be changed by clicking on 'Change' to the right of "Main river".