Experimental computation of real numbers by Newtonian machines

@article{Beggs2007ExperimentalCO,
  title={Experimental computation of real numbers by Newtonian machines},
  author={Edwin J. Beggs and J. V. Tucker},
  journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  year={2007},
  volume={463},
  pages={1541 - 1561}
}
Following a methodology we have proposed for analysing the nature of experimental computation, we prove that there is a 3-dimensional Newtonian machine which given any point x 2 [0,1] can generate an infinite sequence [pn,qn], for n = 1,2,..., of rational number interval approximations that converges to x as n ! 1. The machine is a system for scattering and collecting particles. The theorem implies that every point x 2 [0,1] is computable by a simple Newtonian kinematic system that is bounded… CONTINUE READING

Figures and Tables from this paper.

Citations

Publications citing this paper.
SHOWING 1-10 OF 26 CITATIONS

Some surprising instabilities in idealized dynamical systems

VIEW 5 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

Five Views of Hypercomputation

VIEW 4 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

Computations with oracles that measure vanishing quantities

  • Mathematical Structures in Computer Science
  • 2017
VIEW 4 EXCERPTS
CITES METHODS

The Computational Roots of Hyper-Causality?

VIEW 2 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

Computational complexity with experiments as oracles

  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2008
VIEW 13 EXCERPTS
CITES METHODS & BACKGROUND

References

Publications referenced by this paper.
SHOWING 1-10 OF 38 REFERENCES

Church's thesis meets the N-body problem

  • Applied Mathematics and Computation
  • 2006
VIEW 1 EXCERPT

The myth of hypercomputation

M. Davis
  • Alan Turing : life and legacy of a great thinker
  • 2004
VIEW 2 EXCERPTS

The myth of hypercomputation. In Alan Turing: life and legacy of a great thinker (ed

M. Davis
  • 2004
VIEW 3 EXCERPTS