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WORTH THINKING ABOUT: LEARNING THINGS BACKWARDS AND FORWARDS "School curricula reinforce the impression that logical subjects like math and science require starting with basics and progressively adding more sophisticated conclusions and applications. "But the very nature of logical laws make it equally feasible to work backward from conclusions, or observations, to hypotheses. Deduction and induction are entirely complementary. "In reality, scientists and mathematicians do not do their crafts in the linear, progressive way their subjects are usually taught. "Practitioners commonly start with a flash of insight (the stereotypical light bulb lighting), a hunch, a dream, a guess, an elaborate hypothesis or postulate, and then work backward, forward, and around it to try to make it fit with established knowledge. "Physicists or engineers commonly try using complex mathematical gadgets to solve the problems that interest them without knowing or caring how the math was logically derived. "Experimenters tinker in laboratories and make surprising discoveries that theoreticians then labor to try to explain logically. "Alternatively, theorists like Einstein come up with wild new theories like relativity that experiments may have to struggle for decades to find a way to test and prove. "Scientific knowledge does not grow incrementally down a predictable track. Rather it grows volcanolike, sometimes oozing in patient rivulets, sometimes erupting in fiery ferment, and occasionally exploding, blowing away the rock of established truth. "Pedantic, linear teaching rarely conveys the true drama and mystery of the human quest for knowledge. "School plods where human imagination naturally leaps." From "School's Out," by Lewis J. Perelman; you may be able to find it through <http://www.amazon.com/exec/obidos/ASIN/newsscancom/> (We donate all revenue from our book recommendations to Literacy Action, in support of adult literacy programs.) NewsScan Daily <http://www.newsscan.com/> janet paterson 52 now / 41 dx / 37 onset 613 256 8340 po box 171 almonte ontario canada K0A 1A0 a new voice: <http://www.geocities.com/SoHo/Village/6263/> <[log in to unmask]>