[plt-scheme] 3rd-8th Grade

On Mar 20, 2006, at 5:13 AM, Matthias Felleisen wrote:

> 1. Just remember I didn't condemn pictures and images. I said they  
> don't scale.
>
> 2. To prove me wrong, design a backtracking algorithm and abstract  
> over its strategies.
>
> 3. I am a firm believer in graph-based (and that implies) picture  
> based `interpretation' of your data, your computation, etc. I very  
> much believe that the best cs and programmers are those who have  
> deep `geometric' intuition (and can express it well in a text-based  
> form).
>
> 4. Car is working out an idea of mine that presents class.ss based  
> computations via geometrical traces, because I believe in it.
>
> In all cases though, this is interpretation not synthesis. In the  
> opposite direction, it's limiting. -- Matthias
>

I suspect we've been talking past each other a bit. One area of  
mathematics that I really struggled with (maybe because I'm not as  
visual as I'd like to think) is the classification of semisimple Lie  
algebras. I could read through the proofs and think "Yes, that makes  
sense" without feeling particularly enlightened. When I decided to  
start focusing on 2 and 3 dimensions, and then asking how concepts  
like root systems fit into this simpler example, things started to  
make sense. But it's also possible to teach geometry in 2 and 3  
dimensions without giving much of a hint as to how it might  
generalize. Maybe that's the point.

===
Gregory Woodhouse
gregory.woodhouse at sbcglobal.net

"Nothing is as powerful than an idea
whose time has come."
-- Victor Hugo