In my previous two blogs I discussed what sociophysics is and why advanced methods from physics can be applied to social systems, and gave a few examples of sociophysics' applications to social systems. In this blog I will discuss the important differences between statistics and sociophysics in terms of methods, concepts, causality, and forecasting.
Methods. Typically, condensed-matter physics formulates a set of original properties of individual objects (e.g., particles) of a given type and considers a mechanism of the system development in time. Statistics usually postulates hypothesis directly and states the fact of some distribution and consequences of it (like those done in the Bayesian sense), but does not touch the origination issues.
Concepts. Sociophysics actively uses such concepts as equilibrium, dissipation, diffusion, chaos, catastrophes, fractals, phase transitions, criticality phenomena, percolation, and others that have universal value, but that are mainly neglected in statistical models of the same processes. It makes the physical approach much closer to the theory of complex systems, which all social systems undoubtedly are. For example, sudden jumps in a public opinion, which lead to weird election results, sometimes cannot be explained by traditional statistical models, but can be by a physical one.
Causality. The two sciences, sociophysics and statistics, have different views on the problem of causality. The statistical theory of causality is still in its inception — and thousands of routine statistical models do not use this concept at all. Physics, on the contrary, deals with causal situations: model assumptions are transparent and correct models are considered causal by design. Of course, physics also periodically experiences problems with conflicting causal models, but it allows to design an experiment to make a correct causal selection. In statistics the situation is less clear, simply because all causal models have deep conceptual drawbacks.
Prediction (forecasting) can naturally be done in both physics and statistics, if some conditions of the past hold true in the future. However, there is a big difference. In statistics, forecast accuracy usually does not depend on the model quality, but rather on the stability of the observations on which the forecast was based, as well as on the researcher's luck. For example, a good dynamic regression model can make decent forecasts without being causal. In physics, forecast accuracy usually depends on the model quality, i.e., on how the model captures the most relevant leading factors of the phenomenon. In physics it is also possible for an incorrect model to be a good forecaster (the famous example is that the geocentric model worked very well in astronomy before Copernicus), but eventually forecasting errors are accumulated, inconsistency with other models becomes clear, and a new, better model is built. Statistics does not have such luxury: forecasting errors may or may not be the indicators of the model's quality, because too many other factors can always be put forward to explain why the model did not work well. In that sense, statistical models are always non-falsifiable: one does not have criteria to conclude what exactly happened (the model is wrong or “circumstances" are changed).
Stability. Physics is intended to find stable laws, not to be oriented around particular data sets. This is opposed to statistics, which has actually never claimed that obtained regularities are “eternal" because even a few extra data points, or a slight change in a model setting, can often turn the statistical conclusions upside down.
As stated before, sociophysics can definitely provide significant enhancements to business analytics in addition to traditional statistics. This is my third blog in a series on sociophysics. I plan to write more blogs on different aspects of sociophysics in the future.