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This paper introduces a powerful new tool for topological redescription, theISE Methodology. These tools allow us to remove and replace a theory'stopological underpinnings just as easily as we can switch between differentcoordinate systems. Aspirationally, these novel topological redescriptiontechniques can be used to provide new support for a roughly Kantian view ofspace and time; Rather than corresponding to any fundamental substances orrelations, we can see the spacetime manifolds which appear in our theories asmerely being an aspect of how we represent the world. This view of spacetimetopology parallels the dynamic-first view of geometry as well as a Humean viewof laws; The spacetime manifolds which feature in our best theories reflectnothing metaphysically substantial in the world beyond them it being oneparticularly nice way (among others) of codifying the dynamical behavior ofmatter.  A parallel publication (namely, Grimmer (2023)) will explicitly characterizethe power and scope of the topological redescription techniques offered to usby the ISE Methodology. The modest goal of this paper is simply to introducethe ISE Methodology by applying it to two example theories. Firstly, tofamiliarize ourselves with these techniques, I will show how they can be usedto redescribe a spacetime theory via a Fourier transform. Secondly, I will showhow the exact same techniques can be used to redescribe a lattice theory (i.e.,a theory set on a discrete spacetime, M=RxZ) as existing on a continuousspacetime manifold,M=RxR.

Introducing the ISE Methodology: A Powerful New Tool for Topological Redescription