The most reasonable model for our faster-than-exponential growth in long-term IT trends is that of a phase transition.
At a second-order phase transition, the heat capacity becomes discontinuous.
L. Witthauer and M. Diertele present a number of excellent computations in graphical form in their paper The Phase Transition of the 2D-Ising Model.
There is another interesting article by B. Derrida & D. Stauffer in Europhysics Letters, Phase Transitions in Two-Dimensional Kauffman Cellular Automata.
The divergent increase in heat capacity is similar in form to the greater-thean-exponential increase in IT measurables, as discussed in my previous post, Going Beyond Moore’s Law and identified in Super-exponential long-term trends in IT.
In one of my earlier posts, starting a modeling series on phase transitions from metastable states (using the Ising model with nearest-neighbor interactions and simple entropy), I identified a key challenge in identifying what it was that we were attempting to model. That is, What is x?. When we identify what it is that we are trying to model, we can figure out the appropriate equations.
Now, we have the same problem – but in reverse! We have an equation – actually, an entire modeling system (the Ising spin-glass model works well) – that gives us the desired heat capacity graphs. What we have to figure out now is: What is it exactly that is being represented if we choose the “phase transition analogy” for interpreting our faster-than-exponential growth in IT (and in other realms of human experience)?
That will be the subject of a near-term posting.
(Another good heat capacity graph is viewable at: http://physics.tamuk.edu/~suson/html/3333/Degenerate_files/image108.jpg)