🚀 go-pugleaf

In article <10258@sun13.scri.fsu.edu>, jac@ds8.scri.fsu.edu (Jim Carr) writes:
>In article <1992Aug9.135659.22013@usenet.ins.cwru.edu> aa751@cleveland.Freenet.Edu (Fran Rosen) writes:
>>
>>I just finished a philosophy class which was quite enlightening.
>>I now have a conception of the difference between Euclidian and
>>non-Euclidian geometry.  What I am curious about is what Calculus
>>and Trigonometry show or at least what their purpose is.  
>
> Mathematics (whether geometry or calculus) does not "show" anything 
> since its purpose is to provide a framework for obtaining reliable 
> answers to well-posed questions within some domain of applicability 
> of that framework.  It spends most of its time on proofs concerning 
> when and how various methods can be used, and inventing more of same. 
> A mathematical method that happens to be useful to describe the physical 
> world is rare and valuable to a physicist, embarrasing to a mathematician. 

  One of the answers that calculus provided in its early days was the
solution to Zeno's Paradox and a validation of the notion of an instantaineous
velocity.  A crude formulation of Zeno's paradox is as fallows.  Consider 
and arrow shot some distance to a wall.  Before the arrow can get to the wall
it must travel one half of the distance in some time period.  Now continue to
the wall but it will have to travel one half of the distance left (1/4 of the 
original distance).  But this process is never ending thus one might conclude
that the arrow will never reach the wall because there is a never ending 
stream of time periods to add up.  This paradox was used a long time ago to
argue that the notion of velocity (distance/time) led to a logical inconsistancy
and there for had to be wrong since we all know the arrow will arrive.
  Calculus defines the notion of continuity which can be used to define 
an instantaineous velocity in such a way that one can avoid these specious
difficulties.

                                                   RANDY