Transferring ways of thinking and mathematizing: The statistical approach between physics and biology

I pose the epistemological question of what makes the transfer of statistical approaches across disciplines, specifically between physics and biology, legitimate and fruitful despite intrinsic differences in their objects of study - a problem that resurfaces in contemporary interdisciplinary research relying on machine learning for statistical model building. I address it through the historical reconstruction of pivotal steps in the development of statistical thinking in the 19th century, where the appeal to the mathematical formalism of the Gaussian distribution acted as the visible trace of the diffusion of statistical approaches from astronomy to biological and social sciences. My analysis positions the wide-reaching, nowadays accepted applicability of statistics as something historically acquired through gradual conceptual and technical elaboration. It expounds the forms of re-sanctioning that accompanied and enabled the cross-domain transfer of the statistical approach, articulating them in terms of re-interpretation of the mathematical descriptions involved, re-formulation of the underlying assumptions, and re-conceptualization of their theoretical status and foundations from theory-related abstractions to approximations. The latter culminated in a shift of attitude that led to perceiving, as is standard nowadays, statistical mathematical descriptions as convenient tools for quantitative analysis, further legitimating and accelerating their interdisciplinary transfer. This work aims to familiarize historians and philosophers of science, as well as physicists, mathematicians and biologists with an interest in the history of their discipline, with these key episodes, and to dissect the epistemological assumptions and implications, as well as the interpretive frameworks, at stake in the application of a statistical approach across disciplines.