Language in Numbers

Everything can be expressed in numbers, said Alan Turing and Kurt Gödel when they were thinking up methods to come to mathematical statements and proofs – about mathematical statements and proofs. Turing sought a systematic approach to tackle Hilbert’s Entscheidungsproblem, while Gödel used his eponymous numbering system to prove his own incompleteness theorems. Which happened to constitute a negative proof to the same Eintscheidungsproblem. You can go back one post if you are interested in the particulars.

In that previous post, I have already attributed the ascent of the universal automata – computers – to this approach. Now I will show how this same approach enabled the mathematical treatment of language, giving birth to the processing of human languages on computers.

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Universal Understanding, Universal Machine

Roughly six weeks ago, I went to see The Imitation Game – I caught one of the last English-language screenings in my city. Opinions might vary about this movie, but Alan Turing’s attitude, as shown in the film, reflected the mindset of a true programmer. True programmers, when they face a specific problem, tend to go one abstraction level up, and create a solution not just for the problem at hand, but for an entire class of similar problems. In fact, this is the very attitude that gave us language technology.

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