A few of my friends and I were talking the other night about professors that had left a deep impression on them. And, I recalled Dr. Dan Garber at the University of Maryland Civil Engineering department around 1979. He taught me “Statics” and “Dynamics” classes and was a tough, but fair teacher. I would occasionally stop by his office to ask questions and often received jewels of wisdom (and fatherly advice). He was a wonderful teacher.

The jewel that I remember the most clearly was a response to me complaining that there was just too much to learn. He smiled and said something like “Let me draw you a picture…” At which point he drew a small circle and said “the area in the circle represents how much you know.” He then pointed to the perimeter of the circle and said: “And, this is how much you THINK you don’t know. You know, the unknown and mysteries that you can see, but do not yet understand.” And then he added the kicker: “And, as your knowledge grows, so does the perimeter of the circle and your realization of how much more you need to learn. In other words, kid, it only gets worse.”

While simple and possibly trite, this image has stayed with me and has been a good reminder whenever I start thinking that I have it all figured out. π

**Added**: Note: A couple of people have commented “*doesn’t the yellow circle represent your knowledge better than the blue circle?*” Answer: “No.” π First, the total body of knowledge is roughly infinite and thus needs to have infinite dimensions, and is therefore represented by the infinite plane that the circle is drawn on. The area inside the circle represents your current knowledge. In this metaphor, it would need to be an area covering gained knowledge, not a line with zero area. As you grow older and gain more knowledge, the circle expands and the area grows. [Obviously, a more sophisticated model would be n-dimensional and much more uneven than a circle, but let’s not go there. ;-)] The yellow circle is the edge between *what you know* and *what you don’t know*. You can think of the edge as your `knowledge horizon.’ Beyond the yellow is the stuff that you don’t know. And, so the point is that as your knowledge grows (area in the circle), your `knowledge horizon’ also grows, and thus your perception of *how much you still have to learn* grows too.

Again, it’s simple, maybe a little trite, and cutesy, but it reminds me of Dr. Garber’s kind, fatherly mentoring and reminds me not to get carried away with my own brilliance. π

Two questions:

1: Could it be you made a mistake in the image? Seems to me the little yellow line should be what you do know and the big blue ball is what you DON’T know? Or am I reading it all wrong? Anyway, great advice (so I do get it just not the picture)

2: what are you doing on your birthday? We are in SF that weekend…

π

I’d draw it as a bunch of polka-dots, getting bigger over time and occasionally merging.

And I’d label the tan area “what I don’t know I don’t know….”

There must be an area for What you don’t know you don’t know. That has to be the largest area of all, think about it.

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