Revisiting the ergative marker in Inuktitut.
The ergative case, at least in Inuit languages, serves two main functions: to denote the subject (in transitive constructs) and possessor. I mentioned that 'possessor' function earlier, but now I want to talk a bit about the 'subject' aspect.
'the seal I caught is huge'
-the subject is not 'I' (ie, the pronominal ending - [-tara]) but the noun root 'nattiq'. The root may also be a verb:
'(the place) I enter is small'
but, again, the subject is not 'I' but the (transitive) verb root 'isiq'. It's as if the actor - 'I' - takes secondary function while the root (whether verb or noun) takes the primary slot.
'give me the thing you are holding'
or (in high abstraction):
hold+you+it give+you+(to) me
'you' (subject form for both first and second phrases), again, serve a secondary purpose while the root (the thing held) is the subject.
In mathematical terms, the pronominals are constants (ie, do not change) while the roots are variables (ie, change according to the situation or circumstances). But, as in mathematics, the structure is extremely rigid - meaning that, in ergative cases, the (primary) pronominal of the main (and second?) clause is always in a subject form (and no other). To carry the math analogy further: to non-Inuit speakers, the equations may not necessarily make much sense but the geometry and relational aspects of the phrasing will (consider the relational aspects of 'you'; 'it'; and 'me' above in their abstract and colloquial phrases - 'you' subject; 'it', 'me' object forms).
'I', 'you', 'me' - in highly simplistic terms - normally function as subjects/objects proper, but in the ergative cases of Inuit Languages they denote a requirement of an adjunct phrase to complete them (transitivity). The pronominal values of the ergative cases are embedded in the larger phrase structures and they denote that the phrasing is necessarily transitive.
In Subject-Verb-Object languages, word/phrase order is important but in a polysynthetic language, such as Inuktitut, the case is important. I could just as easily have re-organized the phrases above and the meaning would not have changed one iota. To some layperson, Inuktitut - in this respect - would appear to have "no grammar" (not an SVO structure in any case), but Inuktitut has a deeper structural integrity that obey and exhibit all mathematical/technical rules of language. Figuring out what these 'rules' are is a worthy subject of serious study.