Joe N.: Thanks for all the information about Alberto Martinez and "Negative Math". Let me try and get hold of the book.
GSC > GS Chandy says: > >Rather late in the day (I'm sure), I must confess > that I do not 'get' what you mean by the 'Martinez > road'. > > Author of "Negative Math": > http://www.amazon.com/Negative-Math-Mathematical-Rules > -Positively/dp/0691123098 > > He simply shows that the algebra we learn in school > is not the only possibility -- more a philosophical > point than practical. > Regarding the business of why (-) x (-) = (+), the > answer in this book is "well, that's a choice, there > are other possibilities," and he begins to explore > that a bit. > Obviously its not a bad choice, but people have been > confused for eons thinking it should be more obvious > somehow (of course it can be "proved" as well, given > you accept certain other axioms.) Not quite at the > level of math infamy as the fifth postulate, but > along those lines. > > >Indeed, Mazur's 'virtuous circles' ("virtuous > cycles", I would believe) are only a (relatively > small) portion of 'deeper understanding: > > I was too hard in my words, its a good discussion in > "Imagining Numbers", but he never points out the > other possibilities. > > Cheers, > Joe N