You do remember Donald Rumsfeld, don’t you? Famous (or infamous) for many things, including the distinction between known unknowns and unknown unknowns, not to mention known knowns and unknown knowns. Confused yet? James Harbeck—whom I’ve cited a dozen times in this blog—recently wrote a fascinating post about these terms and concepts.

The confusing cross-product here can be organized and clarified in what I would call a Punnett Square, though Harbeck tells me it’s a Greimas Matrix, which I had never heard of before.

But Harbeck cautions us not to read too much into this organizational scheme:

Putting things into tidy diagrams and taxonomies can be rewarding, but it doesn’t necessarily add information any more than organizing your bookshelf adds information about what’s in the books.

But the real payoff comes from Harbeck’s lovely explanation of the use of this organizational tool in linguistics, particularly the taxonomy of speech sounds. The explanation contains a lot of useful examples, so please read it—and read it carefully, not like a random post on social media. And do notice that he includes one of my favorite quotations! It’s from T.S. Eliot:

We shall not cease from exploration 
And the end of all our exploring 
Will be to arrive where we started 
And know the place for the first time.

Categories: Math, Teaching & Learning