Sir

The Science in Culture article “Leonardo lifts off” (Nature 421, 792; 2003) provided a critique of the myth that Leonardo da Vinci was “a man ahead of his time”, by suggesting that his plans for a successful flying machine design depended more on luck than his knowledge of fluid dynamics. In particular, it was stated that Leonardo “did not pay attention to the fact that air, unlike water, is compressible, and had not considered such a possibility”.

I believe that a number of writings by Leonardo indicate the contrary. On a page now in the Codice Atlantico (at the Ambrosiana Library in Milan), Leonardo wrote: “Water is incompressible. ... The opposite is the case for air, which when forced into vases with small openings, containing some water, ... drives away the water with such fury (furore) that it will be sprayed a great distance away, till that air that remains in the vase recover its initial density” (the translation from the Italian original is mine).

In the same collection there are notes made by Leonardo about the compression of air below birds' wings during flight.

I do not think, however, that the correctness of observations such as these makes Leonardo any closer to contemporary science. Leonardo, unlike Galileo and Newton, did not rely on abstract mathematical models, capable of producing quantitative predictions, which could then be confirmed by experiment. His own studies in fluid dynamics show this very clearly. They were firmly rooted in extremely penetrating visual observation, as witnessed by his drawings of water streams (see figure), but they totally lacked the mathematical approach of Bernoulli's Hydrodynamica (1738).

In Leonardo's water studies, the separation between art and science itself becomes a fluid boundary. His Study of Flowing Water, made in about 1509–1511, is a masterly representation of water flow carried out with supreme keenness of observation and attention to detail, powerfully conveying the sense of movement of the fluid. Nature here is not yet understood in terms of abstract concepts and mathematical models; rather, its phenomena (and movement in particular) are directly grasped by the mind through the eye, in a manner which is closer to our experience of aesthetic contemplation than to the approach of modern science.