How maths makes the world go round – Telegraph

By Ian Stewart

Published: 7:00AM GMT 27 Oct 2009

How maths makes the world go round

Maths 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
spectacles.

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
everything working.

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!

Triathlon Training, Security Guards and Football « Aric In Training

You might be wondering what triathlon training, security guards and football are doing in the same headline of this post.  They certainly don’t have much in common do they? Just keep reading.

When I left the house this morning for work, I planned on having my first speed workout for running this evening.  Last night, I programmed the Garmin 305 with the distances and paces so that I could accurately measure the 3×800’s at 10:00 pace.

So, after work, I hit the gym like I usually do.  This gives me a moment to wind down and start focusing on my run.  It also gives me an opportunity to change, foam roll and stretch.

Challenge Number One

After I stretched out, filled my water bottle and started packing up my gym bag, I suddenly realized that my Garmin 305 was no where to be found!

“Oh no! Where is it?”

Well, since it wasn’t on in its usual home on the strap of my gym bag, there was only one place it could have been.  You see I was really tired last night and didn’t prepare my gym bag the night before like I usually do.  Since I had programmed the workout into it, my tiredness apparently prevented me from at least staging it with the rest of the running stuff.  AND, in my haste to get out the door this morning for work I left it on my desk.

“oh, pooh! A lot of good it does me there!”

Anyway, perseverance is a triathlete’s middle name.  We don’t let these stupid little things interrupt our training addictions.

I had my Polar heart rate monitor with me, so I could, at the least, record heart rate, kcals, and time.  From that I could extrapolate pace.  Also, I know my heart rate zones so I know how hard to run, when to rest etc.

Challenge Number Two

After  I arrived at my usual running spot, I had this crazy idea to head over to a nearby high school and run on their track.  This would help eliminate the problem of trying to guess how far I ran. At the track, I could  calculate my pace better as the goal was for each 800 to be in 5:13.

Well, the giant school bus out front of the school and all the traffic around the school should have been an indication to just keep driving. But no, I found a secret parking spot on a side street and heading toward the track.

But then I noticed the gate to the track was locked and a big truck parked on it.  Hmmm…. something is fishy and it isn’t tuna!  Then I noticed the stadium lights were on.  I thought that was pretty nice of them to turn the lights on for me.  But, I kept walking and noticed that the next gate was locked too.

You have to remember that I am wearing dark sunglasses, a white hat, black track pants and a dark blue shirt.  I am certain I would be suspicious of me too.  The security guard definitely was!

Just after I noticed a number of camera men stationed around the track and the high school football team on the field, did I hear the security guard screaming at me.  Something about trespassing…  but I couldn’t tell because all I saw in slow motion was the long, billy club come out of her holster and it started swinging in my direction. (I think she thought she was Clint Eastwood; kill first, then ask questions).

I asked her why the gate was open and what the event was.  Apparently, everyone in Goleta knew there was a game tonight but me.  I live in Santa Barbara so, go figure.    Swinging the club, she asked me to leave or else she will call the police.  This is ironic because during this entire 30 seconds, about a dozen other people came through the same gate and hopped the fence right in front of her which made the camera guy yell about disrupting his shot.  Sure, pick on the dude from Santa Barbara.

In retrospect, this problem gave me an idea… create a calendar of availability for all of the tracks in the greater Goleta and Santa Barbara area.  I certainly would like to know when I should avoid going to a track due to an event; could have saved me the pleasure of meeting Bertha and her billy club.

Finally, The Run

At this time, I felt like this run was doomed from the moment I realized I left the gps on my desk.  However, I was there, the car was in a safe place and I had a lower middle class neighborhood in Goleta to explore.  So, I started out running a route that I had run before.

The idea was to get my heart rate up for about a half mile, then recover and repeat.  Since I had no indication of distance or speed, this structure went out the door rather quickly.  I did continue to run until the heart rate reached 180, jogged until it came back down to 160, and then ran to 180 again.

In the end, I only did this three times, covering 2.36 miles in 26:08 (11:04 pace, 165/181 hr).  While I didn’t go as far as I wanted, at least I didn’t let the circumstances prevent me from getting in a workout.

Now you now why triathletes have such perseverance.  You also now know what triathlon training, security guards and football have in common.

If you are interested in more about my experience with running, please check out From Office Potato to Runner, Part 1

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Commentary concerning tonight’s attempt at a speed workout. It was doomed when I left the house for work. I persevered though.

Community, Huh?

Communities can take on numerous forms. Whether it is a community of athletes, a community of scientists, or even a community of geographic location, similar interests bring people together.  In fact, one individual can be a part of many communities at the same time.

From the Maya civilization to the British Empire and the foundations of the United States of America, community is a huge concept that everyone needs to be a participant of.

It is through the community that we find our friends and network with people that not only share ideas, but help us when we are down.  You see, the power of the community is infinite.  As I discussed in my post on collaboration, one person cannot succeed alone.  Many persons can build a monument and shape the country we live in.

Here are a few things that I think make communities so wonderful:

1) Support those around you the best you can.

2) Be there to enable to someone to find their dreams.

3) If someone needs a meal, spare a can of soup at the least.

4) Offer someone an ear and a shoulder to cry on… be human.

5) Everyday, make someone smile and share one idea.

I would like you to make a list of all of the communities that you are involved in.  If you feel like it, please leave a few in a comment.

Here are a few of my communities:
A) Triathlon B) Photography  C) Blogging D) Social Media E) Analytics

If you really are saying, “Community, Huh?”, you have work to do.

Posted this over at my wordpress blog. Enjoy!

Balance, Don’t Forget It!

Balance is one of those things that I think a lot of people go through life without. It applies to just about everything and can be hard to achieve. In fact, we often forget to look for the balance in every situation.

Here are some examples:

1) Horseback Riding – The rider must balance their weight on the saddle. Lean too far right or left and you risk falling off. Lean too far forward descending a steep hill and you risk tumbling forward, horse and all. Constantly maintaining balance in the saddle is the key to happy horses and happy riders.

2) Triathlons – During a triathlon, the triathlete is balancing speed with energy exertion, meaning that you want to finish in the fastest time possible but still have energy left to make it across the finish line. Fail at fueling your body correctly or pushing yourself too hard and your performance will show it. Balance the speed and energy to be a successful triathlete.

3) Swimming – The key to moving through the water is perfect balance, which creates minimal drag. Michael Phelps (sorry, you can’t talk about swimming and not mention him) is somewhat of a scrawny guy, but his success comes from finding the most streamlined position and movements in the water. Phelps does not need power when he is not losing speed to drag; he just needs enough to maintain. Balance makes you a happy, efficient swimmer.

4) Nutrition – Eating lots of one thing, really doesn’t work for the human body. In fact, the phrase concerning moderation is right on. Eating a balance of vegetables, fruits, proteins, and fats is the key to feeling great and losing weight.

5) Personal and Professional Life – Working too much can lead to burn out. Not working enough can lead to bankruptcy and foreclosure. Not having enough fun can lead to depression. Not exercising enough and eating too much can lead to obesity. I think you know where I am going with this. Life balance is about getting paid to do something you enjoy, hanging out with the people that make you laugh, going to the symphony, and even sweating a lot playing basketball or running through the neighborhood. Finding balance in life can be difficult and many die never having it.

As you are reading this, ask yourself, Where is the balance in this moment? Is the lighting just right? Is your chair comfortable? What can you do to bring balance to the moment?

When you get up tomorrow, keep balance in mind all day. Observe your world and find the places that you may have forgotten where balance exists or needs to exist.

DON’T FORGET IT!

Balance, Don’t Forget It!

Balance is one of those things that I think a lot of people go through life without.  It applies to just about everything and can be hard to achieve.  In fact, we often forget to look for the balance in every situation.

Here are some examples:

1) Horseback Riding – The rider must balance their weight on the saddle.  Lean too far right or left and you risk falling off.  Lean too far forward descending a steep hill and you risk tumbling forward, horse and all. Constantly maintaining balance in the saddle is the key to happy horses and happy riders.

2) Triathlons – During a triathlon, the triathlete is balancing speed with energy exertion, meaning that you want to finish in the fastest time possible but still have energy left to make it across the finish line.  Fail at fueling your body correctly or pushing yourself too hard and your performance will show it.  Balance the speed and energy to be a successful triathlete.

3) Swimming – The key to moving through the water is perfect balance, which creates minimal drag.  Michael Phelps (sorry, you can’t talk about swimming and not mention him) is somewhat of a scrawny guy, but his success comes from finding the most streamlined position and movements in the water.  Phelps does not need power when he is not losing speed to drag; he just needs enough to maintain.   Balance makes you a happy, efficient swimmer.

4) Nutrition – Eating lots of one thing, really doesn’t work for the human body.  In fact, the phrase concerning moderation is right on.  Eating a balance of vegetables, fruits, proteins, and fats is the key to feeling great and losing weight.

5) Personal and Professional Life – Working too much can lead to burn out.  Not working enough can lead to bankruptcy and foreclosure. Not having enough fun can lead to depression.  Not exercising enough and eating too much can lead to obesity. I think you know where I am going with this.  Life balance is about getting paid to do something you enjoy, hanging out with the people that make you laugh, going to the symphony, and even sweating a lot playing basketball or running through the neighborhood.  Finding balance in life can be difficult and many die never having it. 

As you are reading this, ask yourself, Where is the balance in this moment?  Is the lighting just right?  Is your chair comfortable? What can you do to bring balance to the moment?

When you get up tomorrow, keep balance in mind all day.  Observe your world and find the places that you may have forgotten where balance exists or needs to exist. 

DON’T FORGET IT!