Playing Detective: Hamlet and the n-dimensional Hyperplane

Digging up details and quirks starting from a quote by Borges.




That one question gives life meaning. How, who, where, when, all lend solidity to our world, but the intangible web of causality tickles our imagination like nothing else. Asking why means staring into a chasm of chaos and glimpsing sense—the intellectual equivalent of climbing into the jaws of a shark, looking around, and coming out with a souvenir. It’s exhilarating.

Why is also the reason everyone likes playing detective occasionally.

Me included.

Today, I’m investigating The Book of Imaginary Beings by Jorge Luis Borges (co-written with Margarita Guerrero), an encyclopedic account of a most eccentric menagerie. It contains familiar names such as Centaur and Cerberus, Norns and Nymphs, Salamander and Satyrs, amongst a whole plethora of unfamiliar ones. The starting point of my investigation is the opening of the Preface to the 1967 Edition.

The title of this book would justify the inclusion of Prince Hamlet, of the point, of the line, of the surface, of n-dimensional hyperplanes and hyper volumes, of all generic terms, and perhaps of each one of us and of the godhead. In brief, the sum of all things—the universe.
(Translation by Norman Thomas di Giovanni in collaboration with Borges)

My question: Why did Borges chose to include in his book Harpies, but not Hamlet, Fauna of Mirrors but not the symmetries of surface friezes, Animals in the Form of Spheres but not the n-sphere …? I suppose that including all generic terms, each of us, and the godhead, would require an infinite book like the The Book of Sand, Borges invented in his eponymous story published in 1975—over a decade after the Quote. In fact, given the Quote, The Book of Sand could be said to begin with an almost familiar sentence:

Lines consist of an infinite number of points; planes an infinite number of lines; volumes an infinite number of planes, hypervolumes an infinite number of volumes…

A gander at Borges’s original work reveals he had other ways of addressing mathematical issues, so perhaps we can assume he simply left that for “later”.

Which leaves the question of why not Hamlet.

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