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Lexical Analysis, Minimal Pairs, Headspace and the Justification for Liberal Education

I was reading the dragon book just now  (for work; for fun; work is fun!); in the chapter on lexical analysis they mention minimal-distance error correction as a possibility, mainly theoretical, for lexical error recovery.  That is, when you encounter a lexical error, find the path of the least number of insertions, deletions, transpositions or changes of characters that lead to a valid lexing, and proceed as if you’d encountered that.

This is a terrible idea, because it’s expensive and it can introduce horrific errors.  In practice,  nobody does it.  In their lexers.

But what if we do it in our brains?

So this got me thinking about human natural language “lexing”, such as it is, and how the brain interprets sound into phonemes, lexemes, and eventually meaning.  We have a pretty good ability to recover from a bad lex if we hear something that doesn’t resolve to a lexeme, and the ability to “search” the nearby phonetic/lexical space if the sounds we heard don’t resolve to a meaningful parse.

Trivial example: if a Southerner asks me for “a /pin/ to write something down with” I understand that they are saying “pen”.

So then I was thinking about minimal pairs, or groups of minimal-distance lexemes, such as “grin”/”grid”/”grit”.  These are mutually minimal pairs phonetically, with the /n/ /d/ and /t/ all dental or alveolar with substantial stop chracter.  They’re even all nouns.

What struck me, though, is that they don’t feel much like a minimal set.  I think that’s because they’re not very similar in denotation or connotation.  Which is to say, that the space in which I’m distinguishing them, mentally, is not merely the space of the phonetic differences between /n/ /d/ and /t/ but also the whole space of my internal lexicon, my experiences and memory including the sensations indexed under “grid” which are rather different from those near “grit”.  I guess what I’m really trying to say is that my experience of my internal lexicon is something like the OED’s list of citations, except that the citations are drawn from texts I personally have read and my own experiences.

I certainly have had the experience, while learning languages, of encountering what seems to me like a minimal pair, asking a native speaker about it, and getting a laugh because, I would argue, that person’s experience of the two words has a  large distance between them.

And that is what brings me to liberal education; the idea that in order to be well-rounded each person should read widely and get some experience of foreign, even hostile ideas.  What if the primary value of a liberal education is that it expands your lexicon — not just directly, in that more entries are added, but also by increasing the differentiation of nearby entries by increasing the distance between them?  This could work either by expanding the actual space (Ha – he said reading makes you big-headed) or it might increase the subjective experience of lexical distance by, effectively, fiddling with the metric that you use to measure the space.

Either way, I think it’s a good thing; it’s a literal expansion of the mind, and it’s one form of growth as a person that has no obvious downside.

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