A Copernican Revolution in the Lagoon: When Galilean Mathematician Benedetto Castelli Tried to Solve the Hydrogeological Problems of Venice

The work On the Measurement of Running Water (Della misura dell’acque correnti, 1629) by Galileo’s pupil, Benedetto Castelli has been considered one of the foundational works of modern hydrodynamics. It offered geometrical demonstrations aimed to make the measurement of running waters possible through the isolation of few variables: the section of a waterway and its velocity. From this viewpoint, Castelli’s work represented another ‘Galilean’ attempt at mathematization. However, he was not able to convince the Venetian authorities that his method was apt to solve the main problems related to the conservation of the geoenvironmental equilibrium of the lagoon. The Venetian authorities saw the diversion of rivers outside the lagoon as a measure to mitigate the infilling of sediment. By contrast, Castelli argued that it was precisely rivers’ diversion that produced a lowering of the lagoon water level, because it drove away a great quantity of water, which he accurately calculated. His computational approach was dismissive of the comprehensive knowledge and complex methods that Venetian water experts had developed towards a systemic understanding of the hydrogeology and the environment of the lagoon. They took into account manifold factors as varied as the riverine flows, sea tides, the relative positions of the Sun and the Moon, winds, and even the effects of anthropic interventions. Castelli’s reductionist approach, bolstered by his mathematical modeling of running water, was received with skepticism, even rage, thus rejected, in spite of the prestige of his connection with Galileo. We reconstruct this controversy to dwell into the tension between mathematical abstraction and its claims to prescribe solutions to problems of the physical world, sparked off by Castelli’s claim that his mathematical treatment of running waters could solve all of the most urgent problems linked to the management of the Lagoon of Venice. From an epistemological viewpoint, we ask, to what extent it brought about a conflict between physico-mathematical abstraction (which resulted from the isolation of particular variables to yield a set of quantifiable data) against ‘geological’ concreteness (a form of comprehensive knowledge aimed to cope with systemic complexity).