  The development of new statistical and computational methods is increasingly
making it possible to bridge the gap between hard sciences and humanities. In
this study, we propose an approach based on a quantitative evaluation of
attributes of objects in fields of humanities, from which concepts such as
dialectics and opposition are formally defined mathematically. As case studies,
we analyzed the temporal evolution of classical music and philosophy by
obtaining data for 8 features characterizing the corresponding fields for 7
well-known composers and philosophers, which were treated with multivariate
statistics and pattern recognition methods. A bootstrap method was applied to
avoid statistical bias caused by the small sample data set, with which hundreds
of artificial composers and philosophers were generated, influenced by the 7
names originally chosen. Upon defining indices for opposition, skewness and
counter-dialectics, we confirmed the intuitive analysis of historians in that
classical music evolved according to a master-apprentice tradition, while in
philosophy changes were driven by opposition. Though these case studies were
meant only to show the possibility of treating phenomena in humanities
quantitatively, including a quantitative measure of concepts such as dialectics
and opposition the results are encouraging for further application of the
approach presented here to many other areas, since it is entirely generic.
