This book builds up a mathematics in which multiplying two negative numbers gives you a negative, not a positive. The results are very interesting, particularly this: There are no complex numbers. The root of -1 is -1.
This is another example of something you never think to question, you always assume is "just the natural way", but which was a somewhat arbitrary choice and can be changed.
On a related not, check out the book "Negative Math": http://www.amazon.com/Negative-Math-Mathematical-Rules-Posit...
This book builds up a mathematics in which multiplying two negative numbers gives you a negative, not a positive. The results are very interesting, particularly this: There are no complex numbers. The root of -1 is -1.
This is another example of something you never think to question, you always assume is "just the natural way", but which was a somewhat arbitrary choice and can be changed.