Tuco Benedicto Pacífico Juan María Ramírez (en_ki) wrote,
Tuco Benedicto Pacífico Juan María Ramírez

This Day In History

Few know that, after a chance meeting in Düsseldorf a hundred years ago today, J. R. R. Tolkien enjoyed a long and fruitful private correspondence with the great mathematician David Hilbert. Tolkien, like Lewis Carroll before him, was a lover of mathematical and linguistic games, but was also (in the great English tradition of arrant pedantry up with few may put) intensely devoted to semantic correctness in all things; and so one of his great concerns, as he developed his seminal Silmarilion, was with the technicality of whether the animate trees known as Ents were, in fact, nude. Does bark constitute clothing? Can ambulatory trees truly be covered with something that is, in fact, bark, or is it rather a bark-like skin, which necessarily itself be bare?

Ultimately, of course, Tolkien's constructed languages Entish, Quenya, and Sindarin must be used as the source of semantic distinctions here: it would hardly be appropriate in context to rely upon English-language definitions, after all. Fortunately, Hilbert had introduced Tolkien to the works of Bertrand Russell and Alfred North Whitehead, inspiring him to construct each language with precise logical foundations about which it was possible to prove meaningful theorems, and hope was held out that every statement about the language (e.g., "Enydi ier helda'") could be proven true or false by a formal process which would then be automated.

Further, in Tolkien's lifetime, Kurt Gödel showed that the provability of statements in any formal language of interest to be sharply limited. This work naturally inspired Alan Turing, a passionate lover of Elves and Men alike, to develop his own followup paper in the field now known as computer science, of which he is well known as a founder. Less well-known is Turing's post-war monograph inspired by the Hilbert-Tolkien correspondence, in which he applies a similar diagonalization argument to the languages discussed above and shows the aforementioned question of nudity to be ultimately unresolvable; it is titled

"On decidable languages, with an application to the Entkleidungsproblem".

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