Consider Figure 1 and Figure 2.
How do these relate? Knowns, the top row of Figure 2, can either live in the Open Quadrant or the Hidden Quadrant. Unknowns, the bottom row of Figure 2, in the Blind Quadrant and Unknown Quadrant. The following poem by Ibn Yamin distinguishes four kinds of men (women, non-binary).
(1) One who knows and knows that he knows . . . His horse of wisdom will reach the skies.Adapted fromWikipedia (2019)
(2) One who knows, but doesn’t know that he knows . . . He is fast asleep, so you should wake him up!
(3) One who doesn’t know, but knows that he doesn’t know . . . His limping mule will eventually get him home.
(4) One who doesn’t know and doesn’t know that he doesn’t know . . . He will be eternally lost in his hopeless oblivion!
The fourth type suffers from overestimating their knowledge. They think they know the rectangle B in Figure 1, while in fact they do not (or they think they know a rectangle C in the Unknown Quadrant). Let’s now turn to the first type.
(1) One who knows and knows that he knows . . . His horse of wisdom will reach the skies.
What is this horse of wisdom that will reach the skies? I think it’s an airplane! Person (1) is your typical successful business person or popular academic. Their knowledge takes them all over the world for lectures, meetings, conferences, and whatnot. Is this the goal we should strive for? I don’t think so. Let me introduce a few other characters.
(1*) One who knows and knows that she knows even among those who know . . . Her knowledge is a treasure.
This is what I’d call higher knowledge. Familiarity with étale cohomology for example.
(5) One who knows and knows that they might not know . . . Their friendship is a treasure.
But what does this mean? It means that this person has intellectual humility.
They know the fallibility of their knowledge. They hold their opinions and beliefs loosely.
(6) One who knows and knows that he does not know . . . His advice is a treasure.
This person knows the extent of their ignorance.
He knows the continuously expanding vastness of the Blind Quadrant compared to his own Open and Hidden quadrants. And he knows the incomparably greater vastness of the Unkown Quadrant compared to the Blind Quadrant. He realizes that his knowledge is but a candle of light in unbounded darkness.
(7) One who knows and is grateful for what she knows . . . Her generosity is a treasure.
She knows she’s lucky to know at all, considering the fragility of life.
Are (5) – (7) worth cultivating? What about (1*)? This brings me to the last person.
(8) One who knows and knows how to know—and who also knows that they do not know how to know.
Knowing how to know involves (5)-(7) and possibly more. And (8) as a whole examplifies (6) in particular. Can we make (6) more explicit? I think so.
Let’s say the volume of knowledge contained in my open and hidden quadrants is 1. Then I’d estimate the size of my blind quadrant—assuming “others” include the presently dead—to be more than one trillion. The size of my unknown quadrant? Pseudo-infinite, at least.