Modeling Trends in Long-Term IT as a Phase Transition

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.

The heat capacity image is provided courtesy of a wikipedia site on heat capacity transition(s).

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)

Going Beyond Moore's Law

Super-Exponential Long-Term Trends in Information Technology

Interesting read for the day:
Super-exponential long-term trends in Information Technology by B. Nagy, J.D. kFarmer, J.E. Trancik, & J.P. Gonzales, shows that which Kurzeil suggested in his earlier work on "technology singularities" is true: We are experiencing faster-than-exponential growth within the information technology area.

Nagy et al. are careful to point out that their work indicates a "mathematical singularity," not to be confused with the more broadly-sweeping notion of a "technological singularity" discussed by Ray Kurzweil and others.

Kurzweil's now-famous book, The Singularity is Near: When Humans Transcent Biology, was first released as a precis on his website in approximately 2000. His interesting and detailed graphs, from which he deduced that we were going "beyond exponential growth," had data points up through approximately 2000. In contrast, Nagy et al. are able to produce data points typically through 2005.



The notion of "singularity" is both interesting and important now. Sandberg (2009) has published an interesting and readable paper, An overview of models of technological singularity".