From the point of view of Philosophy, one of the great known unknowns concerns the nature of Knowledge itself.
Another related known unknown is why the Indo-Europeans developed Being with the qualities of Knowledge, but which is an illusion. And what is the relation between this unique indo-european development and the fact that Indo-Europeans have been a dominate player on the world stage throughout known human history.
Metaphysics is the core of Philosophy and it is made up of Epistemology and Ontology. It is interesting that in the Indo-european languages the most broken roots are those of Being and Having. We can argue that Having is a way of approaching knowledge. We say we “have” knowledge. So the question is whether having knowledge is just as illusory as Being’s perdurance. It could be that the split between Knowledge and Being is a symmetry breaking that does not exist in truth, in reality. The standing of existence is perhaps unified in this respect unlike the standing toward the world of Being/Knowing.
So in essence the greatest known unknown is the standing of knowledge itself. But even if we knew the standing of knowledge itself, then there is the question as to how something could be first an unknown unknown then a known unknown, then a known known. And for that matter what is the relation between known unknowns and unknown knowns. Our question here is about known unknowns. But are there unknown knowns as well. We have a whole discipline that deals with the unconscious which would answer yes. What happens when things are pushed into forgetfulness or even into oblivion, do they actually become unknown unknowns again or are they unknown knowns.
So if we were to list some unknown knowns what phenomena would we include? On the one hand we think we can forget and even lose completely what is known into oblivion, but is this true? Are there not always some trace left. For instance, the example given in another answer of Göbekli Tepe. It was in oblivion for us but now it has come back. We knew it once in our history, and even built it, but we covered it up, and now it is back to haunt us with our own ignorance of our own prehistory and origins. We are in a similar position with the deciphering of the Egyptian Language and the Sumarian Languages, we can no longer count their civilizations as forgotten in the mists of time, but much of it remains, and can now be understood but it has still not been completely incorporated into our own notions of our history which starts in our common consciousness with the Greeks, when they were just one step in a long line of various civilizations that have come and gone and left their mark in us.
But ultimately we must track back to the unknown unknowns that loom all around us, like the multiverse within which we are now thinking our universe must be embedded. It is something that will always probably be pure speculation. But that is our way of dealing with an unknown unknown, we make something up. Or like Dark matter and Dark energy. These are names for we know not what, and may never know. Unknown unknowns when they first arise are seen as discrepancies in our data, then we name it, and then we spend a long time not knowing how to proceed to make them unknown knowns. Unknown knowns are the next stage where we really know what is unknown, for instance in Quantum Theory where we have tons of proof that things work a certain weird way but cannot understand it. But eventually these transition into known unknowns, i.e. things that are well defined gaps in knowledge like for instance P=NP or other conjectures that are not yet proven. People work toward the answers, and everyone knows exactly what remains unknown, and they also will be able to recognize when the problem is solved because it is very well defined. Finally there is known knowns where we solve the conjecture and we know the answer, and then it is just a matter of making it more accessible to others as another piece of knowledge among myriad others. But even then we still do not know what knowledge itself is despite being intimate with it, and also we hardly understand its context which is Life, Consciousness and the Social.
Now since there seems to be a series here by which things come into existence, then it behooves us to attempt to understand it in terms of the emergent event. Lets guess that the kinds of Being are what separate these varioius relations between known and unknown.
Oblivion = Ultra Knowledge = Singularity = Learning^4 = no traces = unknowable
Unknown Unknowns = Wild Knowledge = Lost = Learning^3 = Forgotten
Relflexive Special System
Unknown knowns = Hyper Knowledge = Exploration = learning to learn
Autopoietic Speical Systems
Known unknowns = Process Knowledge = Learning
Dissipative Special System
Known Knowns = Pure Knowledge = integrated into the body of knowledge.
knowns = comprehended eventities and facticity concerning states of affairs.
This is the basic structure of the Emergent Event expressed in terms of epistemology rather than ontology. It shows how the Special Systems intertwine with the Meta-levels of Knowledge that relate to Bateson’s meta-levels of Learning (Steps to the Ecology of the Mind). Knowledge has perdurance in the sense that once something important is known, try to forget it, it is very difficult. Thus knowledge is the most stable thing in our experience, yet we really do not possess it because we don’t know where it is when we are not expressing it in the appropriate context at right time. We say we have knowledge but where is it? We don’t know where it is when it is not needed. We say in memory, but there is a lot of memory that is not knowledge. Much of memory has to do with memories of sensations. But where is it that the stable pieces of knowledge are kept?
We know that Knowledge is part of an emergent hierarchy which goes something like this:
Knowledge is the central element in this hierarchy with regard to the individual which are the levels in Bold, while the interleaved hierarchy is social. Unlike the emergent Hierarchy of the schemas that have a gap in the middle where the special systems appear, in this case the central position is taken by knowledge with its odd mixture of perdurance and lack of whereness. Knowledge is also key to our process of Experience. Following Plato Kant concentrates on Reason, and the role it plays as central, but much that we know from experience is unreasonable. And part of it is the sexual sense of knowing as a euphemism for sexual experience. Knowledge is wider than reason and ultimately more important to our survival even though reason plays a key role.
Now if knowledge plays this key role and its perdurance is unquestioned, then our real question is why there is a detour into Being within the Indo-European tradition. We should not kid ourselves that there is not illusion in cultures that only have existence, that is why we call emptiness and void interpretations of existence. There is dukkah, maya, dunya that covers over existence too, but in our case there is an extra level of illusion that produces delusion especially when mixed with action on the basis of illusion. And in this case two wrongs do not make a right, but it really carries is only further astray.
I am going to speculate that when you have two levels of illusion, basic illusion that covers over existence as interpenetration and advanced illusion that sees perduence in things by postulating a substrata that perdures as things change we get by the layering of illusion (dukkha, maya, mara, dunya) that we get a mirroring effect within illusion itself, Illusion becomes reflexive. Now illusion itself is already very complex and tricky without this reflexive quality, so when we get the mirage of the mirage, so to speak, i.e. raise illusion to a power then we get something very complex, as well as something contradictory to experience where we see that the only thing that does not change is change itself, and paradoxical due to the reflections of contradiction in the reflexivity, and absurdity in which paradoxes reflect each other.
Now if this were true, then we would see that Being is really a mirroring of Existence because Existence is composed of the Special Systems seen as supra-rational, but Being is building up a similar hierarchy within the reflexivity of illusion going from contradiction to paradox (which we know from Spencer-Brown and Hellerstein are twinned and entwined) to Absurdity where paradoxes are twinned and entwined.
So Being is an artificial mimicking of Existence within illusion. That is an interesting result, which if true would have broad implications for our understanding of the Indo-European linguistic project that produced Being as a unique and anomalous linguistic structure.
This reminds us of the myth of Nephele, where Zeus gets wind that someone wants to have an affair with Hera, and so he makes a duplicate copy of Hera called Nephele, whom that character makes advances toward and is then caught and punished. But now there is the problem of two Heras running around the original and the copy. Hera forces some mortal to marry Nephele to get rid of her. But what this story does is it places mirroring as a feminine theme to the extent that there is in the myth self-mirroring (cloning) and all the problems that produces. What you get is the interplay of the copy with the original, and in our case within the Western worldview that gives us Plato’s Divided Line which is basically the interspace between Existence and the doubled illusion of Being. Doubling of illusion does not take us back to existence, but into more and more rarified realms of self-deception.
Getting back to the question, we have seen that the meta-levels of knowledge can be conceived as the interplay between known and unknown reaching out from the unknowable and become an image of the emergent event, i.e. the transition from the unknowable to the known of something new, or something old and lost like an old civilization or a new continent as a frontier for exploration. Emergent events can either be generated internally by looking at the deeper assumptions of our theories, or externally by discovering new phenomena that are recognized as completely new and actually existing even though they go against our whole way of looking at existence (super-conductivity when it was first found for instance). So if we talk about emergent knowledge then we do not need Being at all. But once we focus on ontology and project that it has the perdurence of knowledge, then the focus shifts to emergent eventities (ontic emergence) under the auspices of Being, and Emergence and Nihilism then become a pair of Nihilistic opposites which merely means that they are reflected in the complex mirrors of illusion upon illusion.