Duality in Descartes: Esprit Geometrique and Vortex Theory

NOTICE

• DO NOT TRUST THE FOLLOWING

Summary

• Rene Descartes' natural philosophy had two incompatible views of nature in it: "esprit geometrique" (as named by Blaise Pascal), or geometric methodology, and the vortex theory. Two views should have appeared in separate books if there were no political problem with exposition of Heliocenterism
• Isaac Newton took the former, although Gottfried Leibniz took the latter
• Vortex would be naturally derived from a view regarding Keplerian system as a part of a whole system of various perturbations, rather than two-body system (so Newton's success was due to his cutoff of higher degree corrections)
• Pascal, as fluid mechanician, was probably aware of the limit of efficiency of geometric, or exact, method, but his alternative "esprit finesse" (spirit of sensibility) is unclear: In [DELETED:his rarely-known book On the Spirit of Geometry and on the Art of Persuasion, he admitted the limited efficiency of Cartesian view, and suggested use of somewhat obscure art of persuasion, and] his conclusive aphorisms in Pansee, he was turned into a thorough critic to Cartesian way, and looks even almost abandoned any model building
• His awareness to the limit of Cartesian view is still hypothetical, lacking evidences that Pascal had found Cartesian view is only appliciable to isolated fluid with no vortex
• With a broadest interpretation far beyond its proper limit, we might say that Pascal's view is well consistent to such methods that simultaneously use several granularities ("finesse") of approximation, as actually done in computer simulation of multi-scale physics
• Also with too much analogy, we surmise that Descartes himself was not troubled with the apparent incompatibility between his method and the vortex theory: we still can think, as John von Neumann did, any effective model to be a projection to finite-dimensional space from infinite-dimensional nature and all we can do is, in principle, [ADDED:multi-]linear approximation

TODO

• Show evidences of Pascal's fluid-mechanical thought on non-equilibrium systems
• [ADDED:Pascal's treaties on esprit geometrique deserve thorough analysis, the other essay by him on the art of persuasion looks like a sort of logical positivism]