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How To Build A Brain And 34 Other Really Interesting Uses Of Mathematics by Richard Ewes

01/05/2011. Contributed by Geoff Willmetts

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pub: Quercus. 223 page illustrated indexed hardback. Price: GBP 9.99 (UK). ISBN: 978-1-84916-480-1.

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Considering how much mathematics is part of our lives, it always strikes me as amazing why so many people are scared of it. As such, I’m all for books that can explain maths simply and not intimidate the reader. ‘How To Build A Brain’ will not give you information to turn you into a Frankenstein but it will show you the importance of numbers and how to manipulate them and how they are used in the life you lead.

Amongst the things I didn’t know but learnt from this book are that mathematics derives from the word ‘mathematikoi’, the name for a group of people for forsook personal possessions and ate a vegetarian diet. The proof for Pythagoras’s theorem about the square on the hypotenuse being graphically shown and even applied to three dimensional objects, something you don’t usually see. Arithmetic is derived from the book title ‘Arithmetica’ by Diophantus about number theory. Fermat’s last theorem being solved in 1995 or rather proven to be unsolvable by Andrew Wiles. Why the number that makes up Pi, the Greek letter chosen as being closest to the word ‘periphery’, is a number that never repeats itself over nearly 68,000 digits calculated so far.

The more you read this book, the more you will understand how so much of the world about you can be seen in the form of numbers and mathematics. Then again, when you consider the computer games you play depends on such a realisation, why should you be surprised? Having it explained in a way that anyone can follow should give you better appreciation. You probably employ maths without realising it. I mean, you must have figured how long it would take you to get anywhere by knowing the distance and how long it would take to get there by walking or in a car. Calculus is only one step on from this but all it does is break down the distance to a smaller distance for precision and ignore the acceleration completely.

One thing your kids will love is playing with fractals and the shapes they make. A later chapter progresses into how to make a spiral repeating progressively smaller squares and a simple arc line. If you’ve ever wondered how to do this simply for, say, a decoration then you’ve got a good way at your fingertips.

Other demonstrations included show you how to calculate your bank account compound interest, such as it is at the moment. If you’ve ever wondered how Sudoku evolved then you’ll be also interested in its origins and the name derived from Suuji wa dokushin ni kagiru also the game itself was created by an American called Howard Garns in 1979. The more you read on, the more you will appreciate how understanding combination patterns also shows that some are impossible to solve.

There are a lot of chapters, which I should point out are about six pages long, devoted to geometry. In some respects, I often found this dry at school but here the explanations make a lot more sense starting with Euclid and moving into areas which we as SF fans are more conversant with like the shape of the universe. Thought is also given to various knot shapes and how a square is really a circle. Don’t scratch your heads with that one, it’s no Zen but how it can be stretched out and you need to read the book for this. If you want your imagination to work over-time on three-dimensional shapes also bear in mind polygons are the principle of design in computer game graphics.

Author Richard Elwes points out that Georges Polti says there are only thirty-six possible plot-lines. My current tally is seventy-seven and I’m trying to water that down. If you wonder what that has to do with maths then it’s more to do with getting things down to basics.

There’s a fascinating study of how to make room for one more in a full hotel although I think moving people around all the time would stop in a minute if a guest stopped and asked another guest what was going on.

If code-breaking is your thing then seeing the statistics for letter frequency is fascinating and is understandable why not only in espionage but the means to make a password or even a website accessible difficult. I say difficult deliberately because Elwes points out that number crunching computers can solve any code eventually, but it depends how old you are when it does so, let alone understand the message.

I’ve commented a lot on probability in the past but it can also be applied to psychology in getting captured criminals to grass up their partners-in-crime to get a lesser sentence. Chapter thirty reveals it’s a no-win situation for the criminal because it depends entirely on how much trust they share and what makes someone have criminal intent works from not fully trusting anyone.

For those who have the urge to bet in casinos, the demonstrations of odds in practice should show you that the house has the edge when it comes to taking your money. There is also a section on statistical probability which although sounds a mouthful shows that the odds of anything falls into a Gaussian distribution curve. When it comes to computers though I do wonder why Elwes covered binary but not hex (base 8) which is also used. He does make it plain that the Roman numeral system was a drawback to doing mathematics and why we switched to Hindu-Arabic symbols because it depended more on number repetition.

The length of my review should indicate that even at my age, I’ve learnt a lot from this book. I wouldn’t recommend it for pre-teens but above that I can see teenagers and adults digging into this book for insights on all manner of things related to maths. A great learning experience.

GF Willmetts

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