[FRIAM] A* and emulatoin

[Frank Wimberly]

>does a tangent of a tangent (of a tangent) imply higher and higher
derivatives,
>it seems like it is precisely that?!  but in what dimension?

Given a differential function R -> R  a new function can be constructed
which at each point is the derivative of the original function.

if the original funcion is infinitely differentiable (snooth) its
derivative also is.  Many funcatons such as ax + b yield a constant
function after one derivatie and infinitely many 0 functions after that
where 0 means the function f(x) = 0 for all x.  Other differentiable
functions such as exp(x) or sin(x) simply return similar infinitely
differentiable functions; or themselves.  A function f: R^n -> R^m
gemeralize these ideas.  As for dimensions, read about differentials,
exterior derivatives, 1-forms etc.

That  probably doesn't help much.

Frank
-- 
Frank Wimberly
140 Calle Ojo Feliz
Santa Fe, NM 87505
505 670-9918

Research:  https://www.researchgate.net/profile/Frank_Wimberly2
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