[ExI] Calculus Without Derivatives

Dan danust2012 at gmail.com
Wed Oct 15 20:00:30 UTC 2014

> On Wednesday, October 15, 2014 5:33 AM, Anders Sandberg <anders at aleph.se> wrote:
> Michael Roberts<mike at 7f.com> , 15/10/2014 2:43 AM:
>> While on the subject of mathematical works, I found this one to be 
>> very interesting: 
>> http://mitpress.mit.edu/books/functional-differential-geometry
> Cool. Jack Wisdom's stability analysis of Pluto was what convinced me
> that maybe there is something to symplectic methods and other
> "hightech" calculations

I like to think all this knowledge eventually has some payoff. It's just a matter of being imaginative and determined enough to figure out how.

> rather than just brute forcing it with a high
> order Runge-Kutta method.

Ah, the memories. The horrible memories of diff eq. :)

> The book is pretty neat in that it mixes
> scheme with differential geometry; it feels somewhat exotic and yet
> familiar.

Ever more to play around with here. Don't things usually progress from new discoveries and methods that are clunky/unnatural to ones that seem less intuitive at first, but easier and, in the end, more natural/intuitive? Maybe I'm overgeneralizing. There's also a difference between what's taught to undergrads at one time versus later because, I think, "newer" ideas just take time to work their way from the bleeding edge to the textbook. At least, this is my impression, FWIW.


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