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It's interesting comparing Arnold's very anti-abstract approach to Gromov's (another great Russian mathematician from the same era and now a professor at the IH
by potbelly83 10y ago
It's interesting comparing Arnold's very anti-abstract approach to Gromov's (another great Russian mathematician from the same era and now a professor at the IHES). Gromov in his later writings take a very categorical approach in his work. For example in the following paper he attempts to define entropy from a very abstract view point
http://www.ihes.fr/~gromov/PDF/structre-serch-entropy-july5-2012.pdf http://www.ihes.fr/~gromov/PDF/structre-serch-entropy-july5-...
- 4ad 10y agoGromov's approach is not abstract, it's extremely concrete. It uses abstractions for a very precise treatment, and it's probably not the best text for an introduction to entropy, but it's essentially a very concrete treatment. It analyses very concrete observations using abstract methods in order to construct an abstract definition. It doesn't simply spew out abstract definition. Everything is motivated by concrete facts. I would not say it's against Arnold's method at all, if anything, it uses the same concrete to abstract treatment. It is, however, not the best way to learn about entropy, but it's a good way to formalise it once you have become familiar with it. It's poor for undergraduate level material, but it's good as graduate level material.