9. Limitations

Why then have these contributions never been recognized? Why is Leonardo regularly dismissed as a chaotic amateur? It is mainly because hardly anyone reads the notebooks. Artists feel that they can limit themselves to his paintings. Scientists believe that they need not read them because they assume that unpublished works had no effect. The few individuals who have nonetheless read the notebooks have usually taken the surface chaos at face value. Three notable exceptions have been Venturi, Solmi and Keele mentioned at the outset.^[372] Their work inspired the present study.

It is easy, however, to overemphasize this structure and method, and necessary to note very important limitations on various fronts. Some are practical. Had paper not been so scarce, had Leonardo had more space on which to write his work, he would not have needed to be so cramped in his writings, sometimes writing in the margins, sometimes having to skip a few, or even a great number of pages, to find the next empty space to pursue his idea. Some limitations are more subtle. He may have a mechanical view of the universe, but the microcosm-macrocosm analogy lingers. His mechanical anthropomorphism leads him to consider mechanical birds, but not airplanes. Some are problems of classification. A modern reader who finds a page (e.g. A1^v) with discussions of images hitting the eye, sounds hitting the ear and hammers hitting the ground may assume this is pure chaos. In Leonardo's mind it is not: for him all three are instances of percussion. Some limitations are technical: Leonardo sets out to make lenses in order to make the moon appear large. But he could not hope to see what Galileo did a century later with better equipment. Some are procedural. While praising the mathematical sciences, Leonardo views mathematics mainly in terms of geometry. He does not treat geometry and arithmetic together in the systematic way that begins in the 1580's. He has effectively no algebra. He has no conception of trigonometry, let alone calculus.

Unlike his mediaeval prodecessors who were frequently concerned with learning and keeping secrets to themselves, Leonardo wants to communicate his ideas. He teaches, noting "If you do not teach you will only be excellent."^[373] He writes with a view to being read, and also wants to be published in order to be more widely read. If the limitations of printing at the time made infeasible the publication of his many illustrations, his new visual demonstrations, this was not his fault. He lived in a time when war and politics repeatedly forced him to move. So the chaos of his notes is partly the chaos of his times. And for all these reasons he is Leonardo and not Galileo, Newton, Helmholtz or Einstein. To acknowledge these limitations does not threaten his unique place in the history of early modern science. He was one of those giants on the shoulders of whom later scientists stood, whose greatness lay in focussing attention on four fundamental principles, which introduced to the myriad impressions of nature herself a new sense of structure and method.