Unknown unknowns and the Rest

Decades ago I learned of `unknown unknowns', `known unknowns', and the rest. As I remember, they were used by project managers to explain why their projects took longer and cost more than their funders expected. More recently, US Secretary of Defense has used the same terms.

Not long ago, someone — I cannot remember whom or what context — came up with a fifth category. It has stuck in my mind.

1. Unknown unknowns: a five year old child does not know that he does not know calculus. For him or her, calculus is an `unknown unknown'.
2. Known unknowns: an older child know he that he does not know calculus. For him or her, calculus is a `known unknown'.
3. Unknown knowns: a high school student starts to study calculus. He or she does not yet understand calculus. For him or her, it is an `unknown known'. (You will note that the focus of the first `unknown' shifts here from lack of knowledge of the general to lack of knowledge of the specific.)
4. Known knowns: after learning calculus, it becomes a `known known': it is both known to exist and understood.
5. A part of life: after learning calculus and using every day, a person may forget how much he or she knows.

Clearly, the last category applies to people, not to events. It indicates the problem of the expert, which is not knowing what a novice does not know.

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