The problem with the da Vinci quote is it refers to art in the older sense, a knowledge that lets one build something. One makes shoes by the shoemaker’s art. By science he had in mind theoretical statements such as the kind one finds in geometrical theorems, and of the definitional kind one gets in principles, for instance, concerning the the law of a country.
Crude, but hopefully not utterly misleading, précis (with barest skeleton of info): The Reformation led to the opening of academies with non-religious painting. The British came up with the notion of the Fine Arts, Beaux-Arts in France. The current Chinese word for art dates from the Vienna World Exposition of 1876, before that each of the things one calls art were not bundled together by the Chinese, as měishù. The breakdown of the academies opened the age of art for its own sake, personal art. (Remember, that in many places, such as India even after intense British contact in the 18th and 19th centuries, most art went unsigned, and no attention was payed to the maker as a person of distinction or talent.)
I would say. 1.Art today concerns biography, personality, the human being as inner being and not as the objective neuronal knowledge of brain systems. 2.Science the possibility of collecting effects, relative to space and time, which could at anytime, and forever, be deployed; but often without essential connection to human affairs.
This is a very profound question. I believe one must start by making a distinction between the arts and Art. Insofar as all handicraft, professions, shoemaker, lawyer, chemist (apothecary), were, in former times, regarded as arts, art meant, making something according to a knowledge, according to an art. Today, however, art largely refers to the idea of the artist, the special individual with artistic powers. In a certain sense, the human is totally explored by the figure of this artist, who is supposed to be utterly free. For example, one says, the artist should not be constrained by politics or--most especially--by financial considerations. Art in the older sense, was the art commissioned by patrons. Art in the current sense, is art as the artist going to the limit of their art, and then, also being paid (as though it were something disgusting and beyond art. Or, as it were, what is the same, increasingly these days, with total cynicism and open exploitation of the elite HNWI.)
The artist, Art, aims at total annihilation of the human being, as the normal specimen. Art becomes a name for freedom, and not for what the sciences deal with, necessities of nature. But this freedom, can by its more harsh critics, be named the destruction of the human being, insanity, inhumanness, the biography of the “other”, the alien being, the future.
On the other hand, when the sciences, become Science, it means we are dealing with that ability to harness all the necessary power of empirical nature. Everything that can be done and kept as a knowledge, as what can be at any time deployed, and repeated. The periodic table of elements, the knowledge of how to combine vast numbers of chemicals and what result that would bring. The knowledge of building all manner of helpful tools, of medical techniques, of warmachines, of destructive gases. What this Science shares with the current art is the emphasis on the absence of moral rectitude. On both sides man shatters his will against the openness of all possibility as never before. Since any limitation, on the basis of moral consideration, that some discovery, stem cells, would threaten the possibility of advancement, is felt somehow as Christian, as backward, as unacceptable to the unconstrained search.
