Thomas Hardy and then Simon Armitage wrote their ‘Convergences of the Twain’ addressing loss. Hardy wrote about the sinking of the Titanic, Armitage about the 9/11. Both are reported not too empathetic (I do not have any intention to seek the Armitage). The deuce need not be that of a mess as for contemporary linguistics.
Convergence, like many other terms, has been used not in an absolutely consistent fashion in language and other sciences. Uniformity is not my postulate – there is always the context. Words always may mean more than one thing.
Within the sociologic perspective, convergence may refer to a symbolic convergence theory – Rene Girard would call it the scapegoat syndrome. As regards Girard’s concept on the origins of language, the ‘Quest for Fire’ might be a bit more perceptive. I do not mean the parental advisory parts of the movie, language acquisition definitely not having anything in common with some psychologist theories on the purpose in life.
Psychology would recognize convergence in the so-called ‘crowd psychology’. The convergence theory would try to resolve between the singular and the plural to my linguist perspective. The endeavor could not be fail safe. The ‘Space Odyssey‘ begins with a crowd of hominids and ends with a single individual. As not fail safe as the odyssey was, a little girl saying that mommy was gone TO shopping would be insightful about another convergence – that to apply naturally in a natural language.
The singular versus plural dispute may never come to a resolve and could be redundant. Whether this is the individual to influence a group or the group to influence an individual, the fact is that humans need to learn their languages. You need another human to acquire language. On the other hand, the convergence as in human language processing, would be strictly individual. Your language faculty has to be able to work on its own, or you cannot say a word.
As for the ‘singular versus plural’, the phonological and logical filters as well as forms of minimalism are interesting concepts. Yet, you could never abandon the x-bar completely. You need the intermediate between the single and multiple lexical items. Please feel welcome to compare ‘Is it me, or am I a primitive‘.