>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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