Crazy Eddie
As a brief cultural note, today, I happened to be looking something up on the Atomic Rockets Future Mythology page, and was reminded of Crazy Eddie.
(The one from Larry Niven & Jerry Pournelle's The Mote in God's Eye, obviously. Even if, sad to say, that is no longer the one that leads the Internet's search results for the name.)
Feel free to read the page for yourself, or better yet read the original book which is well worth your time, but to sum it up, Crazy Eddie is a cultural anti-hero who keeps trying to solve problems ("doing the wrong things for excellent reasons") and always fails, making things worse. Ultimately, he represents the Motie belief that Not All Problems Have Solutions, and why idealistic attempts to solve problems are categorically inferior to pragmatic concessions to their inevitability.
This is contrasted to the humans who make contact with them. To deliver the appropriate quotation:
“I am not a man, and there doesn’t got to be a way. And that’s another reason I don’t want contact between your species and mine. You’re all Crazy Eddies. You think every problem has a solution.”
So here's how this relates to the 'verse:
The eldrae, with their hypomanic temperament and erratic genius and strongly antipragmatic philosophy are, in terms of Crazy Eddie-dom, to humans as humans are to Moties.
Because they really do believe every problem has a solution. Which is when confronted with supposedly difficult choices, or stereotypically Hard Men Making Hard Decisions, or those annoying Trolley Problems, they will turn to you and say, "Well, I would simply do the Right Thing," and if pressed, add "The answer is to take a third option, obviously. You have posed an artificial false dilemma, but in real dilemmas, you apply a little cunning and escape the damn dilemma. It's easy if you think about it~."
That this, and that they somehow make it work for them, usually renders the less Crazy Eddie by temperament incoherent with irritation is something they will never fully understand.