[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
>

Okay, maybe just one (or two) other thoughts before I head off to the  
office. Even with all the nice geometric intuitions we might have  
into Lie algebras, once we pass to n-dimensions (i.e., try and make  
it scale), we end up reasoning about certain pseudograpahs known as  
Dynkin diagrams. The human (or at least, this human) mind doesn't do  
well with n dimensions. An interesting fact about geometry in two  
(complex) dimensions is that it is easy to "algebraize" by passig to  
the quaternions, but you hear little about the Cayley numbers  
(octonians) these days, primarily because they don't even form an  
associative algebra. What may seem a natural correspondence in low  
dimensions may be difficult to generalize.

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

"We ascribe beauty to that which is simple."
--Ralph Waldo Emerson