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As I understand it, String theory requires 6 other dimensions compactified so small we can't measure them directly. But the way they compactify determines the physical constants of the universe such as the mass of the electron and the strength of gravity and the EM field, etc. Yet there is a plethora of ways in which the extra dimensions could compactify, and we don't know how to uniquely determine which one fits our observations. OK. My question is can we work back-wards from the constants and determine which way the Calabi-Yau must be compactified?