Sunday, July 29, 2012

7. Geometry and finesse

The 17th century mathematician and philosopher Blaise Pascal made a distinction (in his Pensées) between the ‘spirit of geometry’ and the ‘spirit of finesse’. Geometry (mathematics) is hard, in the first approach, because there, as Pascal formulates it, in the twist of abstraction one must turn one’s head away from the world before us in all its complexity and variability. But then it becomes easy because in rigorous deduction one can march straight to clear and indubitable conclusions. Finesse, by contrast, is easy, at first, because one can hold one’s gaze on the world as it lies before to us. But then it becomes difficult to argue without error while maintaining full complexity and variability. According to Pascal both have their value but they cannot be mixed, like water and oil. We must shuttle to and fro between them. There often is division of labour: some are better in the one and others in the other. We find it in the difference between exact science and humanities. The English author C.P. Snow talked about ‘the two cultures’. 

Pascal himself was at home in both: he was a mathematical genius but also a philosopher. While philosophy was usually conducted with finesse, Spinoza tried, in his Ethics, to arrest it in the spirit of geometry, with his use of axioms and deduction of theorems ‘in geometrical fashion’. The spirit of geometry is connected to the bent towards immutable, universal ideas. It is Platonic, while the finesse is more Aristotelian. The distinction is related to the distinction that Aristotle made between certain, provable and deductive knowledge (episteme) and practical wisdom or prudence (phronesis). The second concerns ethics and human conduct, and cannot be caught in the regimentation of rigorous deduction and universal laws.

While geometry and finesse cannot be mixed, they can be combined, in the return, again and again, from the abstract and general to the concrete and the individual. Finesse need not be obscure. In the finesse of philosophy one can try to select each word judiciously and exactly and fit it into the right place. And if I had the opportunity of finding a new math that does justice to finesse I would not hesitate a minute and grab it. But it would not be math as we know it. 

History, law and the humanities generally require finesse and dodge geometry. Aristotle recognized that one cannot in all fields demand the same degree of precision, and one should in every case that arises take into account the matter and purpose at hand, and the degree of precision that fits the conditions. Economists have become hooked on geometry and have in large numbers become blind to finesse, removing themselves from practical wisdom. Bankers, by contrast, had the finesse to circumvent the economic order.