Some years ago, a friend gave me a lesson I’ll never forget. He drew a circle on a piece of paper and said,
“The area within this circle represents all the knowledge you possess.
The area outside the circle is the unknown.”
Then he pointed to its round circumference and said,
“The edge of the circle--its circumference--represents the boundary between what you know and what you don’t know. The length of that boundary represents the amount of uncertainty in your life.”
Then he drew a larger circle around the circle and said,
“When you learn more, your circle of knowledge gets larger. But so does its circumference. Meaning, the more knowledge you gain in life, the more uncertainty you'll have.”
Then he said,
“But there's a caution.
If the shape of your knowledge isn’t round--if your knowledge isn't 'well-rounded'--then the length of the line--your uncertainty--will grow faster than your increase in knowledge. Therefore, the way to minimize the amount of uncertainty in your life compared to your knowledge is to have 'well-rounded' knowledge.”
Out of all the flat shapes in the known universe, a circle has the greatest area for its given circumference. Any other shape has a greater amount of circumference relative to its area.
Because my friend isn't an engineer, he didn't point out another property of circles. The following is a series of equations followed by summary statement, which I'll explain.
The calculations above show that the area of a circle (knowledge) grows faster than its circumference (uncertainty). In the example above, when the area of a circle is doubled, its circumference increases by a ratio of 5.013 / 3.545 = 1.414, which is far less than 2.
This means that as you learn at a certain rate, the uncertainty in your life increases also, but by a slower rate. As you learn, you keep getting further ahead of your uncertainty!
Now, isn't that nice!