By Ian Stewart
Published: 7:00AM GMT 27 Oct 2009Maths makes it: genetic breeding yields a better class of carrot
Like many amateur guitarists, I’d always wondered how to play the opening
chord of A Hard Day’s Night. Over the years, I spent hours trying to
reconstruct it, but there was something very odd about it: no matter how
hard I tried, I could never get it quite right.
In the end, the key to the mystery turned out not to be music, but
mathematics. Five years ago fellow Beatles fan and mathematician Jason Brown
of Dalhousie University analysed the chord using a method called Fourier
analysis, which splits sounds into their basic components. It turns out that
the Beatles used a piano as well as their guitars.
It’s not just music that has benefited from a little mathematical knowhow
recently. On the sports pages, there has been a bit of fuss about a new type
of football, which actually travels in the direction intended. What the
reports don’t say is that the design is based on a field of maths called
computational fluid dynamics, which uses complicated equations to work out
how the air flows past the ball, equations which take into account not just
the pattern of the panels, but even details of the seams.
That’s the strange thing about maths. Save for the odd occasion when you want
to split the bill at a restaurant, it seems infinitely removed from everyday
life. So it comes as a surprise to discover just how much maths is lurking
in everyday objects – such as footballs.
We know that maths and technology go hand in hand: the inner workings of
Google’s search engine, for example, rely on several areas of advanced
maths, such as network theory, matrix algebra and probability theory. The
researchers there are highly incentivised to make their work as accurate as
possible: improve the maths behind the equations, and oodles more cash
floods in from more effective advertising.
But let’s think about something more down to earth: a supermarket vegetable
aisle, for example, and in particular, the carrots. The carrot is the second
most popular vegetable in the world, after the potato. There are hundreds of
varieties, differing in colour, taste, resistance to disease, and ability to
survive for weeks in a lorry while being lugged across half of Europe.
All of these types of carrot have been specially bred. One method is to
cross-breed different varieties and see what you get; a more modern
innovation is genetic engineering. Both rely heavily on maths: it’s used in
the statistical calculations required to decide which breed is best, and in
the design of the trials that provide the necessary information.
Now, I’d be the first to admit that when you are buying carrots, you don’t
need to do that sort of maths. But someone has to, otherwise there wouldn’t
be any carrots for us to buy. Old-fashioned breeds don’t work when you have
to sell millions of carrots every day. No maths, no veggies.
Anyway, once you’ve lugged that bag of carrots over to the car and dumped it
in the boot, you notice that you’re nearly out of petrol. No problem: the
supermarket sells that, too. You don’t need to know any maths to stick the
nozzle in your car – but without a lot of very difficult maths indeed, there
wouldn’t be any petrol in the pump.
Early in September, British Petroleum announced the discovery of a massive new
oilfield in the Gulf of Mexico, but you don’t find oil seven miles down by
drilling wells at random: you have to know where to look.
Given an accurate map of the rock under the ground, geologists can recognise
places where oil may be trapped. But how do you make that map? You make loud
bangs at the surface and listen to the returning echoes. By doing the right
maths, you can then work out where the different layers of rock are.
It’s a complicated problem, because the echoes from all the different layers
of rock interfere with each other. It’s a bit like trying to work out the
street plan of a city by shouting loudly and listening to the sounds that
bounce off the walls. It has taken decades of work by specialist
mathematicians to come up with methods that are practical and accurate: one
big oil company now does a quarter of a million of these complex
calculations every day.
For centuries, maths has been the main driver of science and technology, and
the results have transformed our world. My wife and I have a new grandson,
and a few months ago we were able to watch a DVD of him before he was born,
made using an ultrasound scan. This employs sound that is so high-pitched
that the human ear can’t perceive it. And it works much like oil
exploration: the equipment listens to the echoes, and uses maths to
reconstruct the shape that must have produced them.
Modern medicine uses many different scanners – CT scans, PET scans,
ultrasound. Their common feature is that they use maths to calculate the
shape of whatever is being scanned, by analysing the signals that the
equipment is designed to detect. The mathematical basis of CT scans was
worked out more than a century ago by Johann Radon, a pure mathematician who
had no idea that his work – suitably tweaked – would routinely save lives
long after he was dead.
Today, medical researchers are developing mathematical ways to detect cancer
more accurately. Under a microscope, cancer cells look different from
healthy cells, but it takes a trained eye to tell the difference. The
mathematics of fractals – very complex geometric shapes – is just what the
doctor ordered, helping to capture the difference between the shape of a
healthy cell and a cancerous one.
As if that wasn’t enough, maths plays a big part in keeping the environment
healthy, too. An example is climate change. Even to detect it, you have to
compare what is actually happening with what would have happened if the
planet had been left to its own devices. But we can’t rerun the planet’s
history, so we have to deduce what would have happened without human
intervention. One way we can do that is to model the climate mathematically.
So yes, our fancy electronic gadgets – mobile phones, DVD players, digital
cameras, the internet, satnav – rely on a lot of maths. And yes, we use it
to make sure that aircraft stay up, Formula 1 cars drive very fast, and
gigantic towers don’t collapse. But we seldom realise the extent to which
maths has invaded every corner of our lives. It shows up in politics, in
opinion polls and focus groups. It controls traffic lights, gets crowds
safely into and out of sports stadiums, designs the lenses in our
And the reason we don’t notice it is that, entirely sensibly, the maths is
kept behind the scenes. If I’m buying carrots, I don’t want to have to learn
about the mathematics of genetic trials. If I’m putting petrol in my car, I
don’t need to know how to solve the inverse problem for seismic waves. But
if I want to understand how my world works, I do need to appreciate that the
maths is there. Otherwise, I’ll think that the subject is useless. And if
too many of us do that, soon there won’t be enough mathematicians to keep
Professor Stewart’s Hoard of Mathematical Treasures. Published by Profile (RRP
£11.99) is available from Telegraph Books at £10.99 + £1.25 p&p.
Call 0844 871 1515 or visit books.telegraph.co.uk. He will be speaking at
the Royal Society on November 5 at 6.30pm.
Data, patterns and creativity lead to inspiration. Look around you, it is everywhere!