Jokes as Solutions of Simultaneous Aequations
Considering that jokes are prae-eminently matters of ambiguity involving mistaken identity (which in non-joking personal contexts could realistically involve embarrassment; the laughter occasioned is a sort of derision directed toward the embarrassed parties, which thus-interested parties may include one’s self in the case of self-demeaning jokes); this may be understood as entailing the definition of "simultaneous aequations". For, at any point (or line, or surface) whereat the aequations share a solution in common (by overlapping thereat), such point may be regarded as a place of ambiguity as to which of the identity-defining aequations is being pursued. This would apply to essentially all jokes, and could be taken as a mathematical-type of definition of jokery generally.
The ambiguity must, furthermore, be forced into a process of mistaking an identity, before the standard definition of jokery can be fully applied. This process could entail a praesumption that the aequations involved (described in terms of variables) are more actual than are any particular numerics; so that a quaestionality as to which particular aequation is implied by the ambiguous (simultaneous-aequations) solution can be compelled to arise. This actuality is an existential one; the actual (as a sort of universal) being treatable as having a more real existence than its particulars (numerics).
[Existential quaestions are by their very nature comical, as they tend to involve shiftable category-hierarchies as to expounding which sort of entity which is involved is deemed "more" real (and thus a source of the existence of some other entity) : because of the shiftable nature of such attributions (of "greater" or "lesser" degrees of reality), cases of mistaken identity (as to relative degree of reality) can easily arise (especially in the social contexts – of social ranking – which can be analogues of metaphysical hierarchies of reality).]
It is the co-ercing a consideration of existential ranking (which in mathematics in defined in terms of the "givens" of a theorem) that is necessitated for a full definition of jokery to be imparted a mathematical description.