# Maximally dissecting lexicon according to meaning (heuristically)

I'm trying to find a set of N English terms that maximally express the 'space of meaning' that all words are encapsulated within. I don't know the correct nomenclature to describe what I'm looking for so I'll try my best to articulate with an example.

I have two novels. One is upbeat, spritely, happy and fun. The other is sombre, violent, turbulent and upsetting. How could I build a lexicon of maximally different terms such that these two books would occupy two obviously distinct clusters within the lexicon?

I would look to discover or implement f such that

So f(2) may produce:

``````Good
``````

And f(50) may include:

``````Light
Dark
Good
Close
Far
Thought
Speech
Hot
Cold
...
``````

f(Infinity) would include all words.

Another way to describe what I'm looking for: If meaning could be expressed as an N-dimensional space, then I'd like for my function to return a set of terms that are evenly distributed within that space. I believe this is virtually impossible, but I'm wondering if a heuristic algorithm exists that could approximate it.

Apologies for the ambiguity of this question.

• I'm not sure that this is realisable even in principle, because of polysemy. Are you familiar with Roget's Thesaurus? Dec 19 '18 at 19:14
• @ColinFine That's a good point. If limited to words with singular meanings, do you think this would then be possible? Given the example of two quite different novels, there's no real need for the lexicon space to be exhaustive, it would only have to be sufficiently populated to allow two distinct clusters to emerge. Dec 20 '18 at 8:56
• I'm not convinced there are that many words with only one meaning ;-) It seems to me that you are effectively trying to define a measure on the space of Words, the measure being some sort of semantic relatedness. I'm dubious that that is possible, partly because I'm not convinced that the measure so defined would be well-defned in any mathematical sense. For example, I think the distance between two particular words may be vastly different depending on which other words occur close to them. I suppose if your heuristic is by some algorithm run on a particular text or corpus ... /1 Dec 20 '18 at 16:43
• 2/ then your algorithm will give you your partition, but I'm dubious that you will get much agreement between the partitions derived from different texts or corpora. Dec 20 '18 at 16:44