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Very interesting article. On a related not, check out the book "Negative Math": http://www.amazon.com/Negative-Math-Mathematical-Rules-Positively/dp/0691123098
by edanm 16y ago
Very interesting article.
On a related not, check out the book "Negative Math": http://www.amazon.com/Negative-Math-Mathematical-Rules-Positively/dp/0691123098/ref=sr_1_1?ie=UTF8&s=books&qid=1277192051&sr=8-1 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.
- crazyjimbo 16y agoIt's also inconsistent if you assume that multiplication is distributive over addition: (-1 + 1) * -1 = -1 * -1 + 1 * -1 = -1 + -1 = -2 or (-1 + 1) * -1 = 0 * -1 = 0.
- deleted 16y ago[deleted]
- crististm 16y agosince when -1 * -1 is -1???
- edanm 16y agoPlease read my reply: I linked to a book which builds a Math where -1*-1=-1.
- crististm 16y agoI remember you can define algebras however you like with arbitrary commutativity and associativity rules but in this case you should also apply them and not assume they work in a certain way. If -1 * -1 = -1, this algebra disallows distributivity rule and the calculation only proves that.
- edanm 16y agoYour'e right, but you don't have to assume that multiplication is distributive over addition. You can build math without that assumption. It gets weird, but it's very interesting to see that so many things we take for granted about mathematics are really just conventions.
- crazyjimbo 16y agoVery true, but I like my numbers to behave like... well, numbers. You can define consistent algebras but I'd argue with you if you tried to call them numbers.
- jgrahamc 16y agoThis reminds me of the whole thing about the guy who invented a way of dividing by zero some time back. There's nothing at all wrong with coming up with mathematical systems, and nothing wrong with defining -1 * -1 to be -1. But you pay the price in terms of the consequences. http://blog.jgc.org/2006/12/midas-number-or-why-divide-by-zero.html http://blog.jgc.org/2006/12/midas-number-or-why-divide-by-ze...