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I vaguely recall from my academic studies that a professor mentioned that the syntax of sentence could be seen as error-correction-code in signal processing.

In other words, from a pragmatic view - syntax is used as a convention to correct mistakes of the listener in a noisy environment.

This idea is fascinating, but I cannot find a reference for it.

Could you please point me in the right direction ?

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    I can't give you a specific reference for that idea. But, tangentially, if you're interesting in exploring the origins and functions of syntax, I cannot recommend enough that you check out the work of Simon Kirby. He builds computer simulations of speakers without preprogrammed syntax and watches syntax spontaneously develop on its own, it's fantastic stuff. Not the answer you're looking for, but relevant to the broader search for the origins of syntax. Here's an interesting oneː lel.ed.ac.uk/~simon/papers/…
    – Khove
    Apr 23 at 18:29

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