The Experiment

We set out to confirm that the Ising model can adequately represent phenomena that occur in language evolution.

The methods of physics' formal inquiry usually require a specific approach that goes beyond heuristics. Data is gathered in a systematic way. Running an Ising model simulation requires us to set state parameters to a certain value, let the system relax into its likeliest state under these set conditions and wait for it to settle. Once this is done, sample constituents, that are considered representative of the entire system, are chosen for formal assessment. The state space of these constituents is mapped out so a formal expression can be stated that describes the state path of these constituents. Figure 6.8 illustrates the state space of a typical Ising model that simulates a first-order phase transition.

  

Figure 6.8: State space of a two dimentional Ising model with a first-order phase transition. The light represents the solid portion while the dark represents the liquid portion The dashed lines illustrates the critical point and the critical temperature at which a first-order phase transition takes place.The region outside of the interface is a space of incoherence where spin activity is so high that it is in disordered state.

This graph illustrates a clear boundary between the two phases. The area beyond the the interface is an area of incoherence where spins have so much energy that they are in constant disordered states. In language, this may be akin to a room full of people talking and the noise level is such that no vocables are distinguishable.

Because we are modeling language and not H₂€0 behavior, we take a more heuristic approach. In the modeling of the phase of H₂€0 the values of state parameters refer quite literally to physical states. The mathematical temperature variable of an Ising model is representative of a similar measure used in the observations of real systems. For example; in the simulation of state changes of H₂€0, it is relevant that changes occur around T_c€ = 0C. In our simulation, it is not. It only matters that at some critical point there is a state change. It also matters that we can simulate that change as a first-order phase transition. In our case, the mathematical measure of the activity variable does not find a counterpart (that we know of) in the real system of language. Moreover, the use of such a formally well understood model relieves us from solving it. At this point in our research our focus is in the observation of the simulation and assess the relevance of the model to language.