Simple mathematical structures such as numbers or elementary geometry are directly tied to physical observations. Wigner pondered the existence of similar one-to-one correspondences between more advanced mathematical concepts, such as algebras, and the actual world. The compilation of such a list of “maps" is in itself a formidable research project en route to finding limits of the interplay between mathematics and physics. In this essay we will study the weighing problem, an example given in the 1930s to illustrate the idea of “complex experiments", and construct step by step the underlying group Z2xZ2 and its representations. The concepts involved are advanced enough to highlight a non-trivial link between mathematics and physics without losing the idea midway through the formalism.
Sascha Agne