@article {Beggs1541,
author = {Beggs, E.J and Tucker, J.V},
title = {Experimental computation of real numbers by Newtonian machines},
volume = {463},
number = {2082},
pages = {1541--1561},
year = {2007},
doi = {10.1098/rspa.2007.1835},
publisher = {The Royal Society},
abstract = {Following a methodology we have proposed for analysing the nature of experimental computation, we prove that there is a three-dimensional Newtonian machine which given any point x∈[0, 1] can generate an infinite sequence [pn, qn], for n=1, 2, {\textellipsis}, of rational number interval approximations, that converges to x as n{\textrightarrow}$\infty$. The machine is a system for scattering and collecting particles. The theorem implies that every point x∈[0, 1] is computable by a simple Newtonian kinematic system that is bounded in space and mass and for which the calculation of the nth approximation of x takes place in O(n) time with O(n) energy. We describe variants of the scatter machine which explain why our machine is non-deterministic.},
issn = {1364-5021},
URL = {http://rspa.royalsocietypublishing.org/content/463/2082/1541},
eprint = {http://rspa.royalsocietypublishing.org/content/463/2082/1541.full.pdf},
journal = {Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences}
}