cankun.me
Jul 21, 2026 · 9 min read /

The Shape of Not Knowing

Rumsfeld sorted ignorance into three kinds, a fourth completes the matrix, and Polanyi and Wittgenstein show how a conversation can move through it.

A lone traveler stands on a rocky edge while a narrow path disappears into luminous mist

In 2002, answering a question about evidence linking Iraq, weapons of mass destruction, and terrorist organizations, Donald Rumsfeld sorted uncertainty into three kinds: the things we know we know, the things we know we do not know, and the things we do not know we do not know. The briefing transcript is worth reading in context, since an elegant distinction can still be used inside a disastrous argument. Even so, the distinction outlived the argument around it because it gives ignorance a usable shape.

If you lay Rumsfeld's categories out as a two-by-two matrix, a fourth cell appears:

AwarenessI know itI do not know it
I am aware of itI know that I knowknown knownI know that I do not knowknown unknown
I am not aware of itI do not know that I knowunknown knownI do not know that I do not knowunknown unknown
The Rumsfeld Matrix separates whether something is known from whether that state is itself recognized. See also this applied walkthrough.

The top row is straightforward to talk about. What you know you know can be stated directly, and what you know you do not know can at least be phrased as a question. Ordinary question-answering systems are built for those two cells: hand the system a proposition to confirm or a gap to fill, and let it work.

Conversations get harder, and more interesting, in the bottom row, which holds what I cannot simply type into a prompt. Sometimes I have a real distinction in mind without the words to name it; other times I am missing an entire region of possibility and do not even know what question would reveal it. From the outside, both failures look like silence, yet they call for opposite kinds of help.

A map is not an inventory

Putting unknown unknowns on a map involves an obvious paradox: the moment I can name a specific one, it is no longer wholly unknown. At best I can mark a frontier where my current vocabulary and model probably fall short.

That is why the matrix works better as an orientation device than as a complete inventory of mental contents. Instead of cataloging everything waiting to be discovered, it points to where the next conversational move should go.

Without that orientation, a list of known unknowns can create a peculiar kind of overconfidence, feeling comprehensive precisely because everything outside the list is invisible. A map of ignorance only earns its keep when one of its symbols means not “miscellaneous unanswered questions,” but “the frame itself may be missing something.” And the fourth cell, the unknown known, is just as important from the other side: it reminds us not to treat whatever was left unsaid as something that was not known.

We know more than we can tell

Michael Polanyi built The Tacit Dimension around a single observation: “we can know more than we can tell.” People often reduce that line to physical or perceptual know-how, like riding a bicycle, recognizing a face, or sensing that an argument is wrong before locating the broken step. Polanyi's point cuts deeper than that, though. Articulation is not a transparent export operation that copies ready-made propositions from the mind into language; some of what we know exists first as skilled discrimination, attention, timing, or recognition.

You can see this clearly in aesthetic judgment. Someone says a transition feels cheap, and when you ask what easing curve they want instead, they have no idea how to answer. Show them linear motion, ease-out, spring motion, and a staggered entrance side by side in tiny scenes, and the answer is often immediate. Nothing was retrieved from memory; a concrete vocabulary was offered, and recognition picked what fit.

That is one form of unknown known: not a finished proposition hidden away in the mind, but a capacity for judgment that becomes legible once the right contrast appears. Asking another open-ended question (“Tell me what you want”) just repeats a demand the person cannot meet on their own. The useful move is to lend words by offering a small set of named distinctions, concrete enough to feel, that the person can point to, reject, or revise.

Tacit knowledge does not exhaust that cell, of course. Unexamined habits, inherited categories, bodily warnings, and assumptions a person has never needed to state belong there too. Polanyi does not give an exhaustive definition of the quadrant, but he explains why it cannot be flattened into ordinary missing information.

Meaning arrives in use

A complementary line of thought comes from Ludwig Wittgenstein's later work (Philosophical Investigations appeared before The Tacit Dimension, though I am following the logic of the problem here rather than the calendar). If a word's meaning were a private mental object stored behind it, then finding the right word would mean matching a label to that hidden object. Wittgenstein instead turns attention toward how words function in practice, a shift the Stanford Encyclopedia of Philosophy summarizes as moving from meaning as representation toward meaning as use: look at the activities in which a word does work, the contrasts it draws, and the judgments it makes possible.

In practice, that is why a concrete example helps more than a synonym. “Spring easing” becomes useful when you place it in a miniature language-game: a panel overshoots its resting point, settles back, and feels as if it has physical mass. The scene is not mere decoration around a definition, but part of how the expression gets its grip.

Wittgenstein's discussion of aspect-seeing takes this a step further. In the duck-rabbit illusion, the ink marks on the page do not change when your perception flips from duck to rabbit; what changes is the aspect under which you see them.

One ambiguous black-ink animal head that can be seen as either a duck facing left or a rabbit facing right
Duck or rabbit? Read the two projections on the left as an open bill and the animal faces left; read the same lines as long ears and it faces right. The marks remain fixed while the aspect changes. Original illustration generated for this essay.

Later commentary connects seeing an aspect with seeing a meaning, which is close to what a productive conversation often does. Rather than just adding another fact, it reorganizes an existing situation so that its parts become easier to name, see, or test.

Polanyi, Wittgenstein, and Rumsfeld's matrix do not form a hidden unified theory, and I am not trying to force them into one. My interest in putting them together is practical: the matrix helps locate where a conversation is stuck, tacit knowing explains why asking for explicit recall may fail, and meaning-in-use and aspect-seeing suggest how concrete examples, contrasts, and probes can change what someone is able to recognize and say.

The two dark cells need opposite help

When I know what I like in practice but cannot describe it, my experience already constrains the answer; I just need candidates rich enough to react to. For that kind of unknown known, the helpful conversational move is to lend words.

When I am entering an unfamiliar field whose main options I have never encountered, no candidate is waiting inside me to be recognized. Asking me which architecture, research design, or career path I prefer only forces me to pick from whatever few names I happened to bring into the room. For an unknown unknown, orientation has to come before preference: the helpful move is to give a tour of the nearby option space, what each region is built for, what it costs, and which direction seems to fit.

Put simply, an unknown known calls for recognition rather than recall, while an unknown unknown requires orientation before choice.

The top two cells carry their own obligations as well. What is already settled should be confirmed and compressed so it does not take over the conversation. Named gaps should be met by identifying what evidence, reasoning, or experiment would resolve them; when that probe is cheap to run, it is better to run it directly than to ask the user to speculate. A four-cell map should produce four behaviors, not just four labels.

Nor can these moves be reduced to a closed checklist. Articulating taste, discovering capabilities, and weighing open decisions are useful cases, but another topic might call for exposing a hidden assumption, changing scale, offering a counterexample, drawing a distinction, or running a premortem. Across all of them, the goal of aspect-seeing is to take some relevant part of the problem and make it easier to name, see, or test.

A conversation should leave a trace, kept light enough to redraw

Once you use the matrix to guide a real discussion, it needs state, and that state has to stay light enough to redraw on every turn: a fixed skeleton with one short phrase per entry, more like a card than a document. If the map grows too long to take in at a glance, you stop redrawing it, and it stops working as live state. Within the card, I use four marks:

  • ✓ settled
  • ? a named question
  • ! a recognition candidate
  • ~ an unexplored frontier

Rather than acting as confidence scores, these marks track what kind of work remains. A ? can be answered or explicitly deferred, and a ! can be recognized, rejected, or refined. A ~ cannot be “solved” in an exhaustive sense; it is either explored into something more concrete or honestly retained as residual darkness.

Resisting the urge to turn every mark into a ✓ matters, because tidying up the card is not the same thing as knowing everything. Before wrapping up, a good conversation tries one deliberate frame-break by naming a plausible missing aspect that, if real, would change the conclusion. If it matters, the discussion keeps going; if not, it stays on the record as an acknowledged boundary rather than getting papered over with a manufactured answer.

The final artifact should not be the matrix card itself, which is just the working receipt showing how the discussion moved. What the user leaves with should be a concise brief: the vocabulary they recognized, the choices they settled, the gaps they deferred, and the darkness that remains, written clearly enough to paste into a future conversation without reconstructing the whole path.

Turning the idea into a skill

I packaged this workflow as an open-source agent skill called known-unknowns.

The skill gives an agent a straightforward conversational loop. It opens by drafting the whole map at once from the topic and whatever domain knowledge applies, tagging every inference as a guess. That initial draft is meant to be a bit presumptuous, since a wrong map draws corrections faster than a blank interview draws answers. From there, the agent works one cell per turn, starting wherever the map is darkest but still useful. In each turn it contributes something concrete before asking anything: lending vocabulary, touring an option space, running the probe a named gap allows, testing an assumption, or choosing another move that prompts aspect-seeing, followed by a single question. On the next turn, it redraws the map so anything the user recognized or corrected becomes part of the visible state.

That structure avoids two opposite ways conversations stall. A blank interview offloads all the work onto the person who came for help precisely because they did not yet have the words or the map, while an unbroken lecture fills space without letting the user's recognition steer. Pairing one contribution with one question keeps the loop tight: the agent supplies structure, the user supplies correction, and the map changes.

None of this promises to uncover every unknown unknown, which would contradict the whole point of the matrix anyway. What the skill does is smaller and more practical: it refuses to treat silence as emptiness, and it gives a discussion a repeatable way to approach what cannot yet be asked.