Consider Figure 1 and Figure 2.
How do these figures 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 people.
(Alice) One who knows and knows that she knows . . . Her horse of wisdom will reach the skies.Adapted fromWikipedia (2019)
(Bob) One who knows, but doesn’t know that he knows . . . He is fast asleep, so you should wake him up!
(Carol) One who doesn’t know, but knows that she doesn’t know . . . Her limping mule will eventually get him home.
(Dave) One who doesn’t know and doesn’t know that he doesn’t know . . . He will be eternally lost in his hopeless oblivion!
Dave suffers from overestimating his knowledge. He thinks he knows the rectangle B in Figure 1, while in fact he doesn’t (or he thinks he knows some rectangle C in the Unknown Quadrant). Let’s now turn to Alice
(Alice) One who knows and knows that she knows . . . Her horse of wisdom will reach the skies.
What is this horse of wisdom that will reach the skies? It might be an airplane! Alice 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? Not necessarily. Let me introduce a few other characters.
(Another Alice) 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 perhaps.
(Eve) One who knows and knows that they might not know . . . Their friendship is a treasure.
But what does this mean? It means that Eve has intellectual humility.
Eve knows the fallibility of their knowledge. They hold their opinions and beliefs loosely.
(Frank) One who knows and knows that he does not know . . . His advice is a treasure.
Frank knows the extent of his 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.
The way Frank sees it, the volume of knowledge contained in his open and hidden quadrants is 1. He estimates the size of his blind quadrant—assuming “others” include the presently dead—to be one trillion or more. To his unknown quadrant he assigns an infinite or pseudo-infinite volume.
(Grace) 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.
Should we be like Eve, Frank, and Grace? This brings me to Heidi:
(Heidi) One who knows and knows how to know—and who also knows that she does not know how to know.
Knowing how to know involves at least the character traits exhibited by Eve, Frank, and Grace. And Heidi resembles Frank in particular. If only I could be more like Heidi.