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Topos Institute - Towards a Research Program on Compositional World-Modeling

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In this post, we lay out a vision and challenge for using category theory to build tools for understanding systems at a global scope. In scientific applications (biology, ecology, epidemiology, chemistry, physics, economics, etc.) and related engineering domains, full modeling of a complex system frequently involves the following considerations: Multi-disciplinarity. Problems may show up in a certain domain that cannot be solved with the customary mathematical tools and software frameworks of that domain, and the mathematical, scientific, technical, and cultural assumptions of another scientific domain may be illegible from the perspective of the original domain. For instance, modeling hydraulic systems often involves both rigid body physics and fluid physics. Openness. One is not always lucky enough that one part of the world can be fully isolated from the rest. Rather, systems tend to have interfaces or boundaries, on which (and beyond which) one’s model does not make endogenous pred

Towards a Research Program on Compositional World-Modeling – Topos Institute 1 The problem In scientific applications (biology, ecology, epidemiology, chemistry, physics, economics, etc.) and related engineering domains, full modeling of a complex system frequently involves the following considerations: Multi-disciplinarity . Problems may show up in a certain domain that cannot be solved with the customary mathematical tools and software frameworks of that domain, and the mathematical, scientific, technical, and cultural assumptions of another scientific domain may be illegible from the perspe

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