[FRIAM] A* and emulatoin

[Steve Smith]

> >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.

<tangent>only if the topic we are studying is infinitely differentiable 
I suppose.    So the implication of every tangent on a tangent is that 
the topic of interest is (yet more) smooth?</tangent>
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