Bloody hell, What a book!!
I did a maths degree over 20 years ago and I often wonder why I did. But then I read a book like this and it all makes sense. This book was perfect; full of interesting history, facts and ideas that made my head spin and yes, the pure beauty and wonder of maths shined through. (Really, it did!)
I haven't just read this book I have thought about it for days. I feel like I have re-connected with an old weird friend who I last chatted to over 20 years ago. I think it's both the humour and the passion of the writer which makes this book outstanding for me. Yes, parts of it are funny because mathematicians through history are completely bonkers. I grabbed it off the shelf in the library at the last minute and the first thing I am going to do after I return it is buy myself a copy.
It starts with the history of counting and how some tribes in the world have no numbers greater than two in their language.It talks for a while on different counting systems and how an ancient people from Babylon had a number system based around 60. (They left us with the system we use for time. 60 minutes in an hour.) It moves on to the first writing, which was accountants tallying up pints of beer. Counting was perfected as an art form by the Japanese and Chinese on the abacus and the notation was developed by the Indians . The Indians were the first people to use zero. The concept of using a symbol to show the idea of nothing was beyond the Greeks, Chinese and Babylonians.
Roman Numerals were no good for addition and the fight to get the Arabic /Indian number system into the West was interesting because during the 7th century the West had just started fighting the Islamic world. The West was envious that their grasp of mathematical notation was better and hence science, engineering and astrology was so much further advanced in the Islamic world It all came down to their representation of 'nothing' and their simple number placement which we take for granted now.
Indians call 'Slumdog Millionaire' 'Slumdog Crorepati' due to having a unique counting terminology and a system which goes back to Buddha. Buddha was the first philosophical mathematician who sat around thinking about very small and very big numbers. Now it has been proven that he got his estimates for the size of an atom and the size of the Universe almost correct. Buddha was the first, and probably only, man to hold a perfect image of the smallest and largest objects known to man in his mind without any mathematical proof.
The book then moves away from numbers and into my favourite world of geometry and shape. He talks about the beauty and sophistication of Islamic tiles as a representation of God through art and then moves on to the 50 pence piece. British mathematicians and members of the blind community lobbied for the 7 sided coin, which was the first curved heptagon coin in the world.
I love the bit on how paper folding is the only way to prove mathematical problems which completely stumped the Greeks. The Delian problem is one such mind bender
I loved this because it was all new to me and made me realise how folding a piece of paper can solve problems which the Greeks couldn't solve. (How sad am I.)
The book is still not even half through at this stage and I'm in total awe and think my head is going to explode with information but I take a deep breath and carry on.
We move on to shapes that have no volume and infinite surface area. They are called Menger Sponges and kind of freaked me out. ( Like when you put a mirror on your head and look at yourself in another mirror.) Some maths nutter in the States decided to make a third level Menger Sponge out of 66,000 business cards. They are painstakingly created from small 3D units and took her and her friends over 7 years to make. (again it all goes back to origami.) This woman is a complete and absolute mentalist.
If she made a level 4 Menger Sponge it would take over a million cards and weigh a ton, hence it couldn't support its own weight. She didn't attempt it. In the world of pure maths a Menger Sponge continues for infinity, in reality it stops after the number 3.
The book then went on to talk to people who were banned from casinos because of their mathematical wizardry at the poker table. A pretty useful skill.
The golden ratio was also covered. This ratio is the number of life, beauty and science. It's found in art, architecture, graphics, photo composition, personal beauty, dental cosmetics, the stock market (?) and the graph of a heart beat. It's also the same ratio we use when converting kilometres to miles.
Eddy Levin with his golden gauge was pretty mental! Mr Levin was a dentist from North London who decided to use this gauge to help him make false teeth in the best proportion. His gauge is totally ridiculous but proves the point about how many things are created in this ratio.
I love how the gauge is so UGLY but the proportion he is measuring is the height of balance and beauty!
The best part of the book was at the end. (If you are still here this is the bit which really got me going!)
In my degree I loved spherical geometry. This is simply drawing shapes on balloons and globes and seeing what happens to lines and angles.(Plotting trajectories of aeroplanes round the world and that kind of stuff.) I loved all this nonsense but then we also moved on to think about hyperbolic space. Hyperbolic space is constant negative curvature. A shape which never joins up to itself and also has a vast surface area. (like a pringle in its simplest form.) Wonderful things happen in hyperbolic space but it was all beyond me at university because I couldn't imagine the structure. We never had models to work with. No one ever told me that sea coral, lettuce, even delicious CURLY KALE are all simple hyperbolic structures. Natural objects often need to maximise their surface area so they can take in sunlight and nutrients efficiently.
Now the great thing is in 1997 a mathematician decided she wanted to learn more about hyperbolic structures so she could teach the subject better. Many of the students were also having problems getting their heads round the subject, so she decided to crochet herself some! She took the geometry world by storm. No one had ever thought of this simple solution before. (I suppose not many mathematic professors crochet in their free time.) She is my hero and I might begin to crochet my own structures soon. I might finally be able to understand something that I never thought I would.
What a book! Thank you Alex Bellos for writing this. You have inspired me and reminded me why, underneath it all, I still am completely in love with and in awe of maths. Right , I'm off to find my crochet hook.
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