Dave, I'm curious...I know that technology and new methods have made critical thinking in math very sloppy...but has this "unlimited" memory made programming sloppy? I've also noticed that students (and myself too) find it faster to just try several things quickly instead of reasoning out a problem. I wonder about the end product of this type of thinking. The carryover into philosophy is scary.

We are probably of a generation that remembers and appreciates how to use our minds pre-computer times. (I remember using cards.) I wonder about this new generation.

When personal computers were new, there were a lot of predictions about using their power for math self-discovery-type programs. (What was the little turtle's name?) Then computers were taken over by business departments -- word processing, spread sheets, even email. I wonder...

In the early days I expressed one of my fears about writing to a computer teacher. She dismissed my questions as irrelevant. (I had noticed that people thought and wrote differently when they could cut and paste -- the thinking was more fractured.) Was I right? Or has the new generation learned to think deeply and wholistically using a word processor and typing? (Like I'm doing now -- notice my fractured, train-of-thought ideas? ;-))