Empty space and calculus

Remember the proof that Pi is a convergent series?  We divided up the pie in successively smaller slices, and showed the curvature ratio converged uniformly.    The slices use up empty space more efficiently each time make them smaller.  Calculus describes a symbolic grammar, all of the magic transcendentals are reservations of empty space. The imaginary number means, I will be along in turn, save some empty space. Phi keeps the empty space minimal.  All of these are algorithms, the the premise of calculus is: 
There exists convergent algorithms. such that....   
Hence all the Taylor series can be assumed to converge sufficiently, we  insert symbols to enforce that, symbolically.

But:

There is no empty space in nature folks.  But natures tries its best to follow the good Calculus, it is simply stuck using finite, local transactions to estimate the transcendentals.