Sphinx and Great Pyramid

Book interview: Johnny Ball, ‘Wonders Beyond Numbers’

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If mathematics is the objective language with which to describe the universe, then ‘Wonders Beyond Numbers’ is its travel guide. Who better than Johnny Ball to take us on a magical tour of everything mathematical?

When we look at the world in terms of technology, engineering and mathematics, it’s tempting to assume that modern thinking has rescued the past from the dark shadow of a cloud of ignorance. But as Johnny Ball says: “Nothing could be further from the truth. In fact, the age of the Ancient Greeks was pretty amazing, and as for the Egyptians – despite not knowing much about them – the ruins that they left behind are amazing, too. If you look at the construction of the Great Pyramid at Giza, this was done by constructing huge ramps of sand in order to elevate these huge blocks of stone, after which they took the ramps away. Now this was a massive feat of engineering.”

The Pyramid is one of the starting points of Ball’s new book ‘Wonders Beyond Numbers’, which offers ‘a brief history of all things mathematical’. It has been described by no less a figure than the popular mathematician Ian Stewart as “a winner”. With some justification. In a shade under 500 pages, TV celebrity and autodidact maths expert Ball tells us just about everything we need to know about his world. From the first telescopes to Alan Turing, Pythagoras to Max Plank, from Galileo to Gödel, it’s all here.

It’s entertaining, enriching and, above all, consistent with the entertainer’s endless sense of fun, entirely readable. Even if you know nothing of mathematics – and at this point Ball inserts his hope that most engineers will have at least a mild obsession with the subject – you will come away better for the experience of reading ‘Wonders Beyond Numbers.’

Ball is probably best known for his unstinting work as a TV presenter, popularising mathematics in programmes such as ‘Think of a Number’ (the associated books still sell by the tens of thousands, especially in China, where elementary mathematics is still taught ‘the proper way’). Despite having no formal university education, the former stand-up comedian, who is approaching his 80th birthday, regularly lectures to enthralled audiences of all ages.

An inspiration to a generation of young engineers, Ball says he never gets tired of hearing the words ‘I became an engineer because of you’. “One day, of course, someone will come up to me and thump me while they are saying it. But it hasn’t happened yet.”

As Ball says, ‘Wonders Beyond Numbers’ tells one of the greatest stories of all. “Without maths we simply can’t understand the world around us. It is the language of the physical world.” His book explains how over the millennia we have built up an understanding of shapes, numbers and patterns, leading to the technological world we live in today.

“Galileo said that everything in the universe is written in the language of mathematics,” and this is Ball’s primer to that language. When the maths gets tough, as it sometimes does, there are handy sidebars in the text that delve into greater depth. When it gets even tougher, there are ‘wow factor’ appendices for the aficionado.

‘Wonders Beyond Numbers’

We read it for you

“The ocean of mathematics is full of amazing things and extraordinary stories of the heroic people who opened up this world of wonders to us,” says Johnny Ball in his superb book on the subject.

‘Wonders Beyond Numbers’ is simply a complete history of mathematics, from the earliest of mathematical legends to the modern possibilities of infinity. And because it is by Ball – who many of us will remember for his ground-breaking kids’ TV shows such as ‘Think of a Number’ – it’s written from the viewpoint of a man whose complex, brilliant mind loves nothing more than to entertain and have fun, while sneaking in some good old-fashioned book learning.

It helps if you like maths, but even if you don’t ‘Numbers Beyond Wonders’ will leave you mesmerised because, as Galileo said, “everything in the Universe is written in the language of numbers”. Fantastic stuff.

Maths is only one part of Ball’s rich tale of how we got to where we are today. His text bristles with extraordinary characters who most definitely existed (such as Kepler and Copernicus) as well as those who possibly didn’t (such as Pythagoras). We are treated to humorous anecdotes about mathematicians who were so insecure about their discoveries that they had most of their books burned, through to builders of ‘impossible’ structures and even a painter, who on discovering the world of maths, put down his brush never to pick it up again.

The inspiration for Ball’s book goes back to Jacob Bronowski’s 1973 television documentary series ‘The Ascent of Man’. “This is because he discussed the whole of the history of mankind and its development. I have done the same thing, only with maths. But I have illustrated this with examples from architecture, Renaissance art and all those things. And what you find is that if you get an understanding of the mathematics and are not scared of it, little bits of it will illuminate the situation for you and will help you understand it better.”

These ‘little bits’ are drawn from “following a historical tack”. On p216, Ball treats us to the background of the grid system of Elizabethan maths, which in fact dates back to the Library of Baghdad many centuries earlier, the name of whose long-​term chief librarian Al-​Khwarizmi gave us the word ‘algorithm’.

Try as you might, you won’t find any statistics here, and this is because “while I am fascinated by every aspect of mathematics, I can’t tolerate statistics”. Ball tells a story about how he was once a roommate of the British statistician Frank Duckworth (who along with Tony Lewis devised the target resetting formula for one-day cricket matches), before dismissing the subject altogether.

“Machines are perfect for doing statistics, shuffling numbers around and giving an answer. Today at least a third of the school curriculum is devoted to this sort of maths and it is soul-destroying.” He throws down the gauntlet by claiming he could teach statistics to a 13-year-old “in one term. Finished. In half of one term. And that would be all they need to work in the statistical world of marketing and training and things like that. It could be taught so quickly. But we’re pedantic about it and I can’t stand it.”

This last statement will come as no surprise to those familiar with Ball’s penchant for shooting from the hip. Pro-nuclear power and with little time for the conventional arguments for climate change, the former rector of Glasgow University clearly cares deeply about education, but doesn’t seem to care about upsetting the establishment. It follows that ‘Wonders Beyond Numbers’ is also something of a howl of pain from an elderly polymath who deeply dislikes the way in which mathematics is broadcast on TV today. “It’s awful. The BBC should be the best educator in the world, but the way in which the subject is presented to children has been destroyed. It’s criminal.”

‘Wonders Beyond Numbers’ by Johnny Ball is published by Bloomsbury Sigma, £16.99

Archimedes: the greatest Greek


Archimedes was, beyond doubt, the greatest mathematician, engineer and scientist of the ancient Grecian age. Today he is rated on a par with Newton and Einstein, but for me, considering the age in which he lived, his achievements were even greater than theirs especially in mathematics and engineering.

In the most famous Archimedes legend, he jumped out of the bath and ran down the street in the nude. King Hiero (who was Archimedes’ cousin) hired two jewellers to make him a crown from a bar of pure gold. When he saw the result he was thrilled, until someone whispered in his ear that the jewellers were not completely honest and may have substituted less valuable silver for some of the gold, which they’d kept for themselves. The problem was, how could he prove it without bashing the crown back into its original gold bar shape? Hiero turned to Archimedes for help, but even he had no idea how to solve the conundrum – until, one day, as he climbed into the bath, water slopped over the sides.

In a flash, Archimedes was out of the bath and running down the street crying ‘eureka’, while everyone else cried ‘you streaker!’ Eureka means ‘I have found it’ in Greek. But what had he found? Inspired, he took the crown, a bar of gold identical to the one used by the jewellers and an urn full to the brim with water. He immersed the bar into the water, forcing some of it to flow over the brim. When he took the bar out the level was much lower. The crown then displaced more water than the bar, proving that it had greater volume and must therefore contain lighter metal, only more of it, to bring the weight up to the same as that of the bar of gold. The king confronted the jewellers who confessed their fraud, lost the gold and their heads as well.

Edited extract from ‘Wonders Beyond Numbers’ by Johnny Ball, with permission.

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