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Presumptive Eruv and the Percolation Transition

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[Abstract In this paper I show that, under certain circumstances, it is reasonable to assume the existence of a physical boundary that will constitute a kosher, physical eruv around a Jewish community (presumptive eruv) without having to explicitly construct, or even identify the eruv route. The basis for this contention lies in an important physical phenomenon called the “percolation transition.” The central idea is associated with the problem of finding a long connected path that traverses a given area if the elements of the path (short elements that are co-joined to make up the long connected path) occur randomly with some fixed probability. If the probability of finding these short elements is very small then there will almost never be a long traversing path. But if the probability of finding the short elements is somewhat higher (but still not extremely large), studies of the percolation transition show that one will almost always be able to find a long traversing path. The short elements here are the walls, fences, embankments, wires, etc. that can constitute portions of the eruv, and the traversing path is the eruv itself. This paper presents the central idea of the percolation transition, exhibits its application to eruv, and briefly discusses some of the practical and halachic issues presumptive eruv raises., Abstract In this paper I show that, under certain circumstances, it is reasonable to assume the existence of a physical boundary that will constitute a kosher, physical eruv around a Jewish community (presumptive eruv) without having to explicitly construct, or even identify the eruv route. The basis for this contention lies in an important physical phenomenon called the “percolation transition.” The central idea is associated with the problem of finding a long connected path that traverses a given area if the elements of the path (short elements that are co-joined to make up the long connected path) occur randomly with some fixed probability. If the probability of finding these short elements is very small then there will almost never be a long traversing path. But if the probability of finding the short elements is somewhat higher (but still not extremely large), studies of the percolation transition show that one will almost always be able to find a long traversing path. The short elements here are the walls, fences, embankments, wires, etc. that can constitute portions of the eruv, and the traversing path is the eruv itself. This paper presents the central idea of the percolation transition, exhibits its application to eruv, and briefly discusses some of the practical and halachic issues presumptive eruv raises.]

10.1163/187180011X604346
/content/journals/10.1163/187180011x604346
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/content/journals/10.1163/187180011x604346
2011-01-01
2016-08-26

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