Dr. Bertlmann's Socks in the Quaternionic World of Ambidextral Reality

In this pedagogical paper, John S. Bell's amusing example of Dr. Bertlmann's socks is reconsidered, first within a toy model of a two-dimensional one-sided world of a non-orientable M\"obius strip, and then within a real world of three-dimensional quaternionic sphere, S^3, which results from an addition of a single point to R^3 at infinity. In the quaternionic world, which happens to be the spatial part of a solution of Einstein's field equations of general relativity, the singlet correlations between a pair of entangled fermions can be understood as classically as those between Dr. Bertlmann's colorful socks.
Comment: 18 pages, 7 figures; An appendix is added proving the equivalence of the conservation of spin angular momentum and the twists in the Hopf bundle of S^3; minor improvements