Copyright: 2000

Publisher: Viking

ISBN: 067088457x

Mathematics is a fascinating field but alas a field in which I am not an expert.  Nevertheless I enjoy reading books like Zero: The Biography of a Dangerous Idea. Charles Seife is the interesting author of another book I read, Decoding The Universe.  In Zero he manages to pack an amazing amount of history of math, mathematicians and their effect on the world into a relatively short book.  He does it with an engaging narrative and brings it down to a level just low enough where a mere lay person can understand the significance of the number Zero in history.

Notes

  • The first civilization to use the zero was the Babylonians
  • Much of western civilization spurned the concept of zero for many years while the eastern cultures were busy building entire mathematical systems around the recognition of it's importance as a number.
  • Golden Ratio: Divide a line such that the ratio of the small part to the large part is the same as the ratio of the large part to the whole.
  • Dividing each number of the Fibonacci sequence by the preceding number yields a set of numbers that approaches the Golden Ratio.
  • Leonard of Pisa was better known as Fibonacci
  • Algebra comes from Al-jabr wa'l muqabala a treatise by Al-Khowrizmi on how to solve equations.  (Note that Al-Khowrizmi can be mis-pronounced algorithm by westerners!)

Zeno's Paradox

Zeno postulated that nothing in the world can move.  His paradox states that if a tortoise has a head start, even swift Achilles can't catch him.  Let's say the tortoise starts off a foot ahead of Achilles and that Achilles runs 1 foot per second.  The tortoise only runs 1/2 foot per second.

After one second, Achilles has run 1 foot, however the Tortoise is no longer there, he has travelled half a foot.  Achilles can cover that half foot in a half second.  But by the time he gets there, the Tortoise has now moved 1/4 foot ahead.  Once again, Achilles can cover that distance in 1/4 second but now the Tortoise is 1/8 of a foot ahead.  No matter how fast Achilles goes, he can never catch the Tortoise.

Zeno of course didn't understand limits!

Conclusion

If you like reading books about math and science you will love this book.  It brings a wide range of topics into the realm of the layman.  Seife covers everything from Aristotlian philosophy and it's relation to mathematics all the way through to string theory and how it can help explain the beginning (and end) of the universe.