## Church's thesis meets the N-body problem (1999)

Citations: | 22 - 0 self |

### BibTeX

@MISC{Smith99church'sthesis,

author = {Warren D. Smith},

title = {Church's thesis meets the N-body problem},

year = {1999}

}

### Years of Citing Articles

### OpenURL

### Abstract

THIS IS A REVISION-IN-PROGRESS! NOT QUITE FINAL YET! "Church's thesis" is at the foundation of computer science. It is pointed out that with any particular set of physical laws, Church's thesis need not merely be postulated, in fact it may be decidable. Trying to do so is valuable. In Newton's laws of physics with point masses, we outline a proof that Church's thesis is false. But with certain more realistic laws of motion, incorporating some relativistic effects, the Extended Church's thesis is true. Along the way we prove a useful theorem: a wide class of ordinary differential equations may be integrated with "polynomial slowdown. " Warning: we cannot give careful definitions and caveats in this abstract, and interpreting our results is difficult. Keywords --- Newtonian N-body problem, Church's thesis, computability, numerical methods for ordinary differential equations. Contents 1 Background 1 2 Introduction. Our results and their interpretation. 2 2.1 First way to interpret the...