Data compression programs seem at times to work magic. Squeeze that file and if it's text it will likely become less than half its original length. A spreadsheet, a picture, or a piece of music often map to under a tenth of their original dimensions. Yet it's easy to prove mathematically that not all files can be compressed (if one doesn't throw away information).

In the same way, clever notations and problem-solving techniques seem at times to collapse complexity as though by magic. We admire, publicize, share, and pay big bucks for such brilliant hacks. Yet just as with data compression, not all problems can be made simpler. Some are intrinsically difficult.

Perhaps most of the real challenges of life are like that. There may not be any short cuts, any genies in bottles, or any answers in the back of the book. Such problems may never be completely solved. They take patience, hard work, and experience to make progress on. That's the best anybody can do.

Thursday, February 17, 2000 at 06:11:50 (EST) = Datetag20000217


(correlates: EngineeringVersusScience, HippocraticHardships, BookCoverJudgment, ...)