Each year, more and more scientists and philosophers are joining the quest to dissect and understand the phenomena. It appears to be an advanced form of mathematics that is being used, showing us theorems that are yet to be known.

But how would we ba able to withstand direct communication? I think it would be life-shattering. A more intelligent race would send us clues first, to see if we were paying attention. THEN, maybe they would up the ante (if it is a "they"), to see if we were following the lines of this communication.

Like sending an invitation in the form of a note. It is not intrusive and depends only on the degree of participation involved.
Whatever it is, the intelligence seems to be able to gauge our understanding AND reply.