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The most baffling aspect of our physical world to me is the handedness which is imposed on most living beings! No explanation for it at all, and how it came about even larger mystery.
Handedness appears in Maxwell's Equations (cross product) which is even more exciting to note.
Let V be a finite-dimensional vector product algebra, then d=Sum (e_i.e_i) e_i some orthonormal basis of V satisfies d(d-1)(d-3)(d-7)=0
For Real d, then spaces supporting such vector products are limited to dimensions 0,1,3 and 7.