From Zero to Infinity

Zero to Infinity
 Beyond Every Extreme are the Ultimate All or Nothing
Zero the biography of a dangerous idea     Zero: The Biography of a Dangerous Idea / Charles Seife

Starting with the Egyptian and Greek geometricians Seife relates the history of a number with very peculiar properties and its polar opposite, infinity. That makes this a book about nothing and everything. He uses it to mathematically prove that Sir Winston Churchill was a carrot and includes instructions on how to “make your own wormhole time machine.” For the most part he uses drawings rather than mathematical formulae to illustrate concepts, making this a very accessible book for the non-mathematicians among us.
 

The infiinite book      The Infinite Book: A Short Guide to the Boundless, Timeless, and Endless / John D. Barrow 
 
A breezy look at Infinity, or as Professor Barrow, titles his first chapter, Much Ado about Everything. “… for something that you can’t buy on the internet,” he writes, "‘infinity’ is strangely ubiquitous. It turns up in church sermons, mathematics lectures at all the best universities, popular science books, about ‘Life the Universe and Everything, and mysticism the world over, while historians remind us that people have been burnt at the stake for talking about it. It is at once the staple of the mystic contemplation of reality – ‘make me one with everything’ as the mystic said to the hamburger vendor – and the familiar territory of science fiction and fantasy.”

Barrow recounts how infinity is different from just a really big number, what it would be like to run a hotel with an infinite number of rooms, why the sky is dark at night, the three flavors of infinity, how Gregor Cantor was able to count and explain why one infinity was larger than another, the logical, philosophical, and theological implications or infinity, paradoxes by Zeno, Galileo, Albert of Saxony and others, the possible sizes and shapes of the universe, time travel, and eternal life in a fascinating (but finite) 328 pages.