Language Graphs are Orderless
Human language is pretty simple at its core. It can be visualized a graph, as in a graph theory graph, that shows relationships between various ideas. For example, 'He eats bread' shows that the relationship between bread and he is such that the former is eaten by the latter. As pointed out by many, these relationships are quite similar to functions in programming, where a function applies some transformation to its inputs and returns this as an output. We could render the first example with the pseudocode 'eat(he, bread)', which can be thought of as returning (bringing your attention to) the mental model of this relationship.
How do we know whether he is eating the bread or the bread is eating him, though? In English, it's mostly indicated by word order, although pronouns do change to indicate the object (he -> him). This is not true of all languages though. In highly inflected languages, like Sanskrit, subjects and objects are differentiated by case endings. Subjects are usually suffixed with -h and objects (accusative case) are usually suffixed with -m. Rather than saying 'He eats bread', we're able to say 'He-h eats bread-m' or 'Bread-m eats he-h' or 'He-h bread-m eats'. The word order is no longer relevant.
The problem with this approach, and most natural language's approaches to quantifying semantic relationships, is that it leaves much room for ambiguity, inefficiency, and difficult structure parsing. For example, with a word order approach, I might say something like 'He eats bread and the lion eats him' or 'The lion eats him, who eats the bread'. In the first sentence, there's just inefficiency and the separation with an 'and' may break the meaning we're going for. In the second sentence, the issue comes back to word order. If I said 'The lion, who eats the bread, eats him.' the meaning would change because English dependents refer back to the primary clause mostly based on proximity.
In an inflectional language, the problem persists. In this pseudo-Sanskrit we're using, I'd say 'Lion-h he-m eats he-h bread-m eats' and it's back to word order. If I switch he-m and bread-m, the meaning changes. So the question I pose is, since the graph relationships in your head are orderless, can we build a truly orderless language—that is, identical in speech as in mental representation?
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