Chapter 12. Quaternions and the Belt Trick: Connecting to the Identity

There is an ancient parlor trick, whose popularization in the physics community has long been attributed to Dirac (e.g., see Hart et al. [87] and Misner et al. [126]), that catapults the reality of the quaternion into an everyday context seemingly innocent of such esoteric constructs. We have already met the belt trick in Chapter 2, and now we are ready to follow the details of the quaternion visualization.

The belt trick begins with two people holding opposite ends of an ordinary leather belt. (In one of many variants, sometimes known as the Dirac string trick, two or more strings replace the edges of the belt.) As illustrated in the initial frames of Figures 12.1 and 12.2 ...

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