Around six years ago, I embarked on a project to discover the true essence of the information elements. It seemed to me that their descriptions were either, on the one hand, a collection of disjointed concepts ("essence, potential, possibility, talent, etc") or overly vague and abstract, unconnected to the practical experience of the elements ("internal statics of objects"). My reasoning was that, if for example Se essentially conflicts with Si, then the two must each have some essential quality that is responsible for this — the collection of traits otherwise seems like some kind of fluke or coincidence.
Although I have made considerable progress towards this goal, and I still expect to find a true system of definitions, it seems to me now that the original goal has to be modified slightly. Socionics has certain aspects, both formal and conceptual, that relate to quantum mechanics. In quantum mechanics you cannot assign all properties of a system (such as momentum and position) simultaneously: once you measure one aspect, your choice of what to measure makes the other properties somehow ill-defined or nebulous. This may also be the case in socionics, for example: from the point of view of Te, Ti is about simplifying, ignoring, or reducing information. But from an Fe point of view Ti is more about clarity and organization. These incompatible points of view are what result in quadra values, and compatibility and conflict.
This suggests that information elements must be defined at some level by their interactions. Normally definitions assume some pre-existing framework, and use language to specify some class or individual within that framework. This is the Ti approach. But in a more fundamental theory this may not be possible: if the IM elements are themselves prior to any information, how can they be specified? This is a paradox, and its resolution requires incorporating the dynamic Fe perspective as well.
In fact, information (literally "putting into form") itself is only made possible through an interacting complex of entities. Where there is no distinction between here and there, self and other, there is no transfer (nor anything to transfer) and therefore no information. Geometry and information are two sides of the same coin.