Math Formula

Wednesday, November 23, 2011

I Know That I Know Nothing

I know that I know nothing -- Socrates, Greek philosopher
Yes, I know, I used that quote in my last week's post about my first year in Bosnia already, but it is also related to what I want to talk about today.

The final sentence there is: "... having learned a few things already. At the same time, I know that I know nothing." After I learned a little bit about local habits, I reached a point where I knew enough to know that there is much and more to come. In fact, I tend to think that this is true about pretty much everything one learns.

Since I once ago took some courses in economics and economist are very fond of curves (the ones on diagrams, of course, what did you think??), I tried to compress and summarize my thoughts in a small graph.

On the x-axis, there is the "actual knowledge" in red, compared to "perceived knowledge" (by you, not by others) in blue, both as they are developing over time.

The actual knowledge does steadily increase over time. Of course, this is a huge over-simplification, because learning curves are different in different fields; the improvement might not be as steady as pictured out but stagnate or sometimes even decline (that is, you forget something); there are several difficulties related to accurately measuring knowledge. Yet, I think the fundamental principle remains more or less the same: Your actual knowledge does grow over time.

The perceived knowledge, however, does not. Depending on one's personality, perceived growth of knowledge is similar to the actual, or might even out-perform it. (Raise your hand if you never learned something new, thought you are a super-hero and natural talent after day 1 - just to fall flat on your face on the 2nd.)

In my understanding, this parallel growth of actual and perceived knowledge continues, until one of the following things happens:
  • You fall flat on your face
  • Your knowledge is challenged, particularly in fields you were not yet that profound in (e.g., an exam)
  • You meet, or read something from, somebody who you think you can learn something, just to be surprised how much there is still too learn
In any case, your perceived knowledge drops immediately, which actually is quite irrational a thing. You know that you've learned something already - on the other hand, only now you found how much more complex that field of knowledge actually is, and how much more there is still too learn.

Some people just give up on the sight of the remaining part of the path. Maybe you know the Simpsons episode where Homer tries to climb up the Murderhorn, at one point looking up to the top of the mountain like this (source:

However, as I pointed out above: I'm quite convinced that this is simply part of the way to mastering any subject. Again and again, you will encounter such peaks of perceived knowledge - just to find that there is more to come, the actual top of the mountain is even farther. In such moments, just visualize one of the pictures from above (yes, both the curves and Homer may do) and remember: Your actual knowledge is still increasing. Yet, even who was believed to be one of the wisest men of ancient Greeks knew - that he knew nothing.

P.S.: I'd be interested in some other literature which covers that topic or goes into a similar direction, so I'd be very grateful for all links or suggestions.

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