J. R. Minot

P. S. Dodds, T. Alshaabi, M. I. Fudolig et al.

We define `ousiometrics' to be the study of essential meaning in whatever context that meaningful signals are communicated, and `telegnomics' as the study of remotely sensed knowledge. From work emerging through the middle of the 20th century, the essence of meaning has become generally accepted as being well captured by the three orthogonal dimensions of evaluation, potency, and activation (EPA). By re-examining first types and then tokens for the English language, and through the use of automatically annotated histograms -- `ousiograms' -- we find here that: 1. The essence of meaning conveyed by words is instead best described by a compass-like power-danger (PD) framework, and 2. Analysis of a disparate collection of large-scale English language corpora -- literature, news, Wikipedia, talk radio, and social media -- shows that natural language exhibits a systematic bias toward safe, low danger words -- a reinterpretation of the Pollyanna principle's positivity bias for written expression. To help justify our choice of dimension names and to help address the problems with representing observed ousiometric dimensions by bipolar adjective pairs, we introduce and explore `synousionyms' and `antousionyms' -- ousiometric counterparts of synonyms and antonyms. We further show that the PD framework revises the circumplex model of affect as a more general model of state of mind. Finally, we use our findings to construct and test a prototype `ousiometer', a telegnomic instrument that measures ousiometric time series for temporal corpora. We contend that our power-danger ousiometric framework provides a complement for entropy-based measurements, and may be of value for the study of a wide variety of communication across biological and artificial life.

P. S. Dodds, J. R. Minot, M. V. Arnold et al.

Real-world complex systems often comprise many distinct types of elements as well as many more types of networked interactions between elements. When the relative abundances of types can be measured well, we often observe heavy-tailed categorical distributions for type frequencies. For the comparison of type frequency distributions of two systems or a system with itself at different time points in time -- a facet of allotaxonometry -- a great range of probability divergences are available. Here, we introduce and explore `probability-turbulence divergence', a tunable, straightforward, and interpretable instrument for comparing normalizable categorical frequency distributions. We model probability-turbulence divergence (PTD) after rank-turbulence divergence (RTD). While probability-turbulence divergence is more limited in application than rank-turbulence divergence, it is more sensitive to changes in type frequency. We build allotaxonographs to display probability turbulence, incorporating a way to visually accommodate zero probabilities for `exclusive types' which are types that appear in only one system. We explore comparisons of example distributions taken from literature, social media, and ecology. We show how probability-turbulence divergence either explicitly or functionally generalizes many existing kinds of distances and measures, including, as special cases, $L^{(p)}$ norms, the Sørensen-Dice coefficient (the $F_{1}$ statistic), and the Hellinger distance. We discuss similarities with the generalized entropies of R{é}nyi and Tsallis, and the diversity indices (or Hill numbers) from ecology. We close with thoughts on open problems concerning the optimization of the tuning of rank- and probability-turbulence divergence.