I’ve just completed The Book of Nothing by John D. Barrow, which as you may guess is a book about nothing. The book is really divided into two parts – the first describing the history of the number zero in maths and the second looking at nothing (the vacuum) in science.
The book looks at different numeral systems and the advent of the number zero. It took a surprisingly long amount of time for zero to appear – to have a digit which represents nothing.
The first half of the book goes into a lot of detail about how number systems evolved in different cultures – roman numerals, "modern day" arabic numerals, and numbers in different base systems (e.g. Mayans and base 60).
There’s a lot of stuff to get you thinking. I particularly liked the Zeno paradox. It goes a bit like this:
There is a man and a turtle. The man walks at 400 metres per hour. The turtle walks at 40 meters per hour.
The turtle starts the race 400 meters in front of the man.
By the time, the man has travelled 400 metres, the turtle will have travelled 40 meters so will be 40 meters ahead.
The man travels another 40 metres, but by then the turtle is 4 meters ahead.
The man travels another 4 metres, but the turtle is 0.4 meters ahead.
And so on…
The man can therefore never overtake the tortoise.
The trick of this paradox is that we’re tending towards a certain point (444.44m) in increasingly small amounts. We can iterate the above statements an infinite number of times, each time the difference in length tending towards zero.
The second part of the book focuses on zero or nothing, in science. It talks about the vacuum and the ether in history, but goes on to discuss "vacuum energy" or dark energy, and how it can answer some of the fundamental questions about our universe.
This book combines a lot – mathematical history, religious philosophy and scientific theories. Barrow goes to quite a bit of length to try and show the beauty of zero and mathematics – there are quotations and poetry dotted all over the place.
I personally found the first half of the book much more interesting than the second; the end of the book was quite technical and the book lost me a few chapters before the end. Which half of the book you enjoy will probably depend on your own area of interest, but this is certainly a book of two halves.
An enjoyable and interesting book.