Travail, force vive et fatigue dans l'oeuvre de Daniel Bernoulli: vers l'optimisation du fait biologique (1738-1753) / Work, vis viva and tiredness in Daniel Bernoulli's works: towards the optimization of the biological fact (1738-1753)

TL;DR

This paper explores Daniel Bernoulli's evolving concepts of work, vis viva, and fatigue between 1738 and 1753, highlighting their implications for understanding biological optimization and the distinction between organic and mechanical energy.

Contribution

It clarifies Bernoulli's changing views on work and vis viva, and how these relate to biological fatigue and the distinction between natural and artificial energy.

Findings

Bernoulli distinguished vis viva from potentia absoluta and work.

Work can be converted into vis viva, especially intra-organically.

The concept of tiredness relates to the expenditure of animal spirits and vis viva.

Abstract

The concept of mechanical work is inherited from the concepts of potentia absoluta and men's work, both implemented in the Section IX of Daniel Bernoulli's Hydrodynamica in 1738. Nonetheless, Bernoulli did not confuse those two entities: he defined a link from gender to species between the former, general, and the latter, organic. Besides, Bernoulli clearly distinguished vis viva and potentia absoluta (or work). Their mutual conversions are rarely explicitly mentionned in this book, except once, in the Section X of his work, from vis viva to work, and subordinated to the mediation of a machine, in a driving forces substitution problem. His attitude significantly evolved in a text in 1753, in which work and vis viva were unambiguously connected, while the concept of potentia absoluta was reduced to the one of men's work, and the expression itself was abandoned. It was then accepted that work can be converted into vis viva, but the opposite is true in only one case, the intra-organic one. The concept of tiredness, seen as an expenditure of animal spirits conceived themselves as little tensed springs liberating vis viva, allowed direct conversion, even never quantified and listed simply as a model, from vis viva to work. Thus, work may have ultimately appeared as a transitional state between two kinds of vis viva, which the first is non-quantifiable. At the same time, natural elements were discredited from any hint of profitable production. Only men and animals were able to work in the strict sense of the word. Nature did not work by itself, according to Bernoulli. Despite his will to bring together rational mechanics and common mechanics, one perceived in the work of Bernoulli the subsistence of a rarely crossed disjunction between practical and theoretical fields.