From: Damien Sullivan (phoenix@ugcs.caltech.edu)
Date: Tue Dec 10 2002 - 13:29:29 MST
On Tue, Dec 10, 2002 at 04:12:22AM -0500, Eliezer S. Yudkowsky wrote:
> I don't know how to convey understanding. Sometimes people catch the
> pattern of what I say, or at least they seem to, but it seems more due to
> their own ability to fill in the tremendous gaps in what I say than to any
Learn to take smaller gaps.
I wonder if there's any relation to programming. Not that programmers are
magically better at explaning things. *cough* But there's some saying about
computers making philosophy honest. If you can explain something to a
computer -- write a program -- you understand _something_ concrete, at least.
I'm taking Group Theory Visualized from Hofstadter at the moment, where the
goal is to get an intuitive sense of group theory, with lots of pictures as
appropriate. Most of us aren't math majors, and we've got a musician too.
For my presentation, on characteristic and commutator subgroups, I took lots
of little steps, often referring back to stuff we knew, or repeating myself
and pretty much avoided any big jumps. It seemed to work pretty well -- at
the end of my half-hour, I think people actually knew what I was talking
about, as opposed to just having a definition.
Most of the books I'd tried looking at didn't have anything like that. Most
were pretty crappy (half didn't even give a clue as to why commutators are
called commutators.) One (Kurosh) gave me a lot of the clue I needed to
understand and pass on the material.
Course notes at
http://php.indiana.edu/~nccarter/m590f02/
if anyone wants to look. My stuff isnt' there yet, might not be for a while,
I'm better at drawing pictures than making them on a computer.
-xx- Damien X-)
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