Global and local

Mathematical Intelligencer 36 (4) (2014)
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Abstract

The global/local contrast is ubiquitous in mathematics. This paper explains it with straightforward examples. It is possible to build a circular staircase that is rising at any point (locally) but impossible to build one that rises at all points and comes back to where it started (a global restriction). Differential equations describe the local structure of a process; their solution describes the global structure that results. The interplay between global and local structure is one of the great themes of mathematics, but rarely discussed explicitly.

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James Franklin
University of New South Wales

Citations of this work

Discrete and continuous: a fundamental dichotomy in mathematics.James Franklin - 2017 - Journal of Humanistic Mathematics 7 (2):355-378.
Emergentism as an option in the philosophy of religion: between materialist atheism and pantheism.James Franklin - 2019 - Suri: Journal of the Philosophical Association of the Philippines 7 (2):1-22.

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