Friday, July 14, 2000

What is Euclid's fourth postulate of Parallels? Martin, from Australia logs a request for some axiomatic-deductive reasoning. Martin, Attempts to derive the parallel postulate from the others, thereby transforming it into a theorem, involves replacing it with its two alternatives--that there is no such line or that there are more than one--and then showing that contradictions ensue. However, you will find that no contradictions result from either substitution. The unavoidable outcome is, instead, the realization that there are other geometries just as valid and consistent as Euclidean geometry, for example the ancient Aztec deductive masterwork of the *Quetzel* group. Martin, it is important to remember that mathematical systems are not merely natural phenomena waiting to be discovered; instead, mathematicians create such systems by selecting consistent axioms and postulates and studying the theorems that can be derived from them. Keep up the good work!

Monday, July 10, 2000

Do you walk to school or carry your lunch? A fan known only as "BPC" from Montpelier, VT strives to waylay the Supertectonics staff with his chicane question. BPC, thank you! Our seemingly useless statistics on *group elementary transport* in the American school system can finally be put to good use. Our studies suggest that kids who are driven or ride the bus to school are likely to carry their lunch (3,016 of 4,123 interviewed) while those who walk are inclined to "wing it", (1,107 of 4,123) acquiring a meal by whatever means they deem necessary at lunchtime. Without getting too personal BPC, I walked to school and continue to walk as the rest of my existence unfolds. Thanks for the interest!