The Number Zero

I read this thread some time ago and wanted to shed some light on some things. Now I'm not very good at math, but I doubt math is wrong. When I was in High school, not that long ago, I read a book called "Zero: The Biography of a Dangerous Idea" by Charles Seife. If you like history or math this is a nice book to read. The author goes over the history of math from the Babylonians to the Mayans to the Greeks and Pythagoras, so on and so forth.

The author talks about the "void" of zero. Zeno came up with a problem that the author claims plagued mathmaticians and philosophers for hundreds of years. It is often called simply "Achilles". It's a race between famed Achilles and a tortoise. The tortoise gets a foot start of Achilles, say for simplicity Achilles runs at a foot per second and the tortoise half of that, no matter how fast Achilles is he never passes the tortoise. We all know he would easily pass him but without zero no one could make it happen on paper. Every time Achilles would catch the tortoise the tortoise would quickly get ahead by a quarter, an eigth, a sixteenth, and so forth. It is a little trick to do with zero's cousin, infinity. Of course doing the math Achilles would pass the tortoise around 2 seconds.

The author goes into more complex ideas and paradox's about zero as the book goes on. Some neat tricks to do with zero goes as follows.
A=1 B=1
Bsquared=ab
It's obvious A equals itself Asquared=Asquared
Now subtract the two problems. A sq - B sq = A sq - AB
We can factor both sides of the equation; A sq - AB equals A(A-B). Likewise, A sq - B sq = (A+B)(A-B). Now we get...
(A+B)(A-B)=A(A-B)
So far so good, now divide both sides of the equation by (A-B) and we get A+B=A
Subtract A from both sides and we get B=0
WOW! However we set B to equal 1 so this means that 1=0.
Now we all know that one does not equal zero. Charles Seife goes on to make Sir Winston Churchill into a carrot by using this set of equations since he has 2 arms he has no arms, since he has 2 legs he now has no legs, he has no tapered points now he has 1 tapered point, and so on and so forth.

THIS DOES NOT MEAN MATH IS WRONG just that there are loop holes where we can do some funny and interesting things. Such as making your own worm hole time machine!

As I said I wanted to share some things about this book with people and hopefully some of you will enjoy this interesting and compelling book.

NOTE You don't have be a mathematical genius to read this, I read it and the highest math level I completed was a college trig course. For those that love math I'm sure you will like, or even dislike this book.

The book is available for only a few dollars if interested

reply to post by AudioGhost


I love these games. Sounds like a really great book.

S+F (or is that S=F ?)

reply to post by chr0naut


Thanks! Paradox's are good brain tweezers and make you think. The author points out the difficulty some people had with zero such as Pythagoras who was scared of a lot of weird things. Also it is a good length read, not too long and not that short. I lent it to my math teacher in college last year and he enjoyed it. He even said when he was in college he loved that sort of paradox zero and infinity give and the challenges they make. Who knows maybe one day these will be solved and we will have even crazier brain tweezers!