Fabulous comment. Makes me think you're sandbagging us with this "I never learned linear algebra" schtick :) I was musing about this off and on yesterday and a

Fabulous comment. Makes me think you're sandbagging us with this "I never learned linear algebra" schtick :) I was musing about this off and on yesterday and another way of looking at it struck me. Linear systems are flexible in some (well, few) ways and rigid in others. The reason you can't build a model that just captures two points and then absconds without getting stuck with infinitely more is that, being linear, this stuff can't "bend". Another way of putting it (the sort of thing someone who has spent too much time around computing and not enough around geometry would say) is that the language of linear systems is expressive enough to express certain things but not others. The possible interactions are regimented. You can add dimensions to gain degrees of freedom, or equations to collapse them, but both "freedom" and "restriction" here have a pretty narrow meaning. I'm looking forward to learning about some of the magic things this theory can be made to do. It makes sense that something with such a regular, yet complex structure (complex by our standards anyway - mathematicians would no doubt chuckle) could yield some beautiful results, but that it found such a variety of real applications is surprising to me. More surprising in this respect than its older cousin, calculus, which starts off much closer to our naive sense of how reality works. Now for those matrix exercises.