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I think a better measure of understanding is how well you are able to explain it to a layperson. As Einstein once said, "If you can't explain it to a six year o
by bdhe 15y ago
I think a better measure of understanding is how well you are able to explain it to a layperson. As Einstein once said, "If you can't explain it to a six year old, you don't understand it yourself."
As a researcher, who has also TAed classes, it takes a lot of effort not only to teach a particular topic, but also simultaneously present the crux of the idea as well as the right way to think about it and its place in the context of other information. And learning to think about everything with these in mind will make you understand things much much better. In particular, one of the most challenging things is not to explain breakthrough ideas to cutting-edge researchers but rather explaining breakthrough ideas to complete outsiders and laypeople.
- qq66 15y agoEinstein may have said that but it's just not true. How do you explain the Higgs boson to a six-year-old? If you succeed, it's because you made an analogy so simple that it has no meaning.
- chrismsnz 15y agoMaybe that's because we don't understand it fully?
- qq66 15y agoThere are plenty of things we understand fully (e.g. translation lookaside buffers) that are impossible to explain to a six-year-old.
- aristus 15y agoOff the cuff, I would come up with something involving parking valets and the pegboard for keys. It would illustrate the important bits of the mechanism and its purpose. I don't know if you would dismiss that as meaningless analogy, but explaining TLB (or Traveling Salesman, or functional decomposition, etc) to kids is not impossible.
- xyzzyz 15y agoThere are things in mathematics that I find difficult to explain even to someone who finished freshman calculus and linear algebra courses. How should one explain singular homology to someone without strong background in topology, algebra and pure math itself? Same thing with theory of sheaves, for instance. These things are not terribly difficult themselves (but they're no easy, I admit), but the amount of time required to explain what they're really about is breathtaking.
- aristus 15y agoI don't know anything about those so I can't say. Not everything has a facile real-world analogy, and there may be long chains of dependent concepts to get through first. Here's the thing, though: if you make an honest effort to explain something like that to a lay audience, you may fail. Or you may not. Or you'll give them a workable, but incomplete and strictly wrong idea. Either way you yourself will end up with a deeper understanding. A huge part of "real" mathematics is finding isomorphisms. Teaching is more or less finding isomorphisms between new concepts and concepts that the student already has.
- gridspy 15y agoSure you can handwave certain parts of your explanation, but if you don't understand the material yourself then simplifying it accurately is very hard.
- deleted 15y ago[deleted]