Spectacular numbers with strange powers

Although this may make you want to smack your head against the wall repeatedly, the fact of the matter is; everything is maths. From your phone to your house, the tiny particles that everything is made of and the giant, swirling galaxies that dot the infinite universe; all of that is based on numbers.

But before you start throwing tomatoes at the screen, as you are part of the large majority of people who hates numbers and their evil behavior, don’t worry, no formulas or tests today.

It’s strange though, isn’t it, this anger towards something that is so vital to our lives, and that mathematicians are seen as strange wizards with their nerdy number magic. So today, we look at magic numbers that rule your life, and possibly death.

Let’s start with a nice safe one; ten.

We all like ten, it’s the girl next door of mathematics; you get ten, you know ten, ten is your friend. But why is this? Why are we so comfortable around those lovely rounded tens, twenties and hundreds but it all gets so murky when you veer away from them?

Well the simple answer is; habit. The only reason we work in tens is because we have ten fingers and it just became common practice to do it like that. These are called “bases”. A base is just how you decide to group your numbers.

We work in base ten so you have the numbers zero to nine, if you add one more to nine then you complete a group of ten, and so you move onto the next group.

So if we worked in base four, you’d have the numbers zero to three and when you add one more then you complete a group of four.

We feel like 10 is logical but an alien society is just as likely to work in some other base. It wouldn’t be a problem though, we could easily “translate” it into friendly looking tens.

Many cultures have used other bases, either partially or completely. French for example, mixes in base 20 with base 10.“Quatre vingt dix neuf” is 99 but translates as “four twenties and nineteen”.

The Oksapmin people of New Guinea have a base-27 counting system, with each number being named after a separate body part, which is how they keep track things.So, I’ll have ear apples, elbow carrots and belly button slices of bacon please.

Probably the most important number of all time is zero.

It seems like such an obvious thing to us but it was missing from many early counting
systems.The Sumerians were the first people to develop a counting system but it was all about keeping stock of cattle and horses so you didn’t need a number for something that you didn’t have.

It was Brahmagupta, an Indian mathematician from the 7th century who formalized zero by representing it as a dot under a number. He also wrote rules about its use.

It reached the west through trade from Arabia, with the Arabian mathematicians making great advances in many areas of mathematics and Mohammed ibn-Musa al-Khowarizmi creating equations which resulted in zero, or algebra, as it is now known. The word zero itself is from Arabic, along with algebra, algorithm and average. Without zero, we never would have been able to create binary code, which gave us computers. So life would be very different today; I would probably be shouting all these facts in some town square somewhere and then maybe burnt as a witch.

Can you tell me what these numbers have in common?
2, 3, 5, 7, 11, 13, 17, 19?

That’s right, they are prime numbers. A prime is a number that only divides by one and by itself, we don’t include 1 as a prime.

Now, for non-mathematical people, you might think? Who cares? Why does everyone talk about primes like they are so important? The thing is, prime numbers are like elements in chemistry; they are the building blocks that everything is made of.

2,3,5… these are just like Hydrogen, Helium, Lithium and so on. Every non-prime, or composite number as they are called, can be made by multiplying two prime numbers together. Fifteen, for example is 3 x 5. Ninety-Four is 2 x 47. What’s more, all even numbers are the sum of two prime numbers. Ninety Four is 89 + 5

The multiplication of primes may just sound like a dull quirk of mathematics but it has a very real benefit for us internet users; security.

Multiplying two primes together might be easy but working backwards is very very difficult. If I give you a number and tell you to work out what primes it’s made up of, you basically have to try out all the combinations until you find the correct one; there is no formula.

If it’s a small number, that’s not so bad but when you get up into something that’s hundreds or thousands of digits long, yeah… good luck with that. So internet security, which is active when you see HTTPS at the beginning of a web address, uses this quirk of mathematics to encode your sensitive data; you need the correct key in order to solve this prime multiplication problem each time. Finding new prime numbers can be a rewarding business since there are a range of prizes on offer, with hundreds of thousands of dollars being offered for ones over 100 million digits long.

The current record holder for the world’s largest prime number was only just discovered in January 2016 and the number itself is over 22 million digits long.

Although we picked 10 because of what our hands look like, there are some numbers that are important throughout the universe, such as 3.14… or Pi. Carl Sagan, the famous astrophysicist, wrote a novel Contact, which became a big movie.

When humans find the number Pi in a radio signal from the stars, we know it’s a sign of intelligent life because this number must be universal to everyone, regardless of how many fingers the alien species has.

Pi is actually quite a simple concept. If you take a circle and divide its circumference by its diameter, then you always get the same answer because this is just the ratio that makes a circle.

It’s everywhere; car tyres, coke cans, actual pies impressively round. And it’s been invaluable for all of science, and has led engineering advances for thousands of years.

There are other constant numbers like "e", which is 2.718, that is used for many things but famously on working out interest in banking. I’m sure we all have a lot of interest in banking. But one constant that is much more exciting is Phi; the golden ratio.

The number is about 1.618 and it’s all about proportions.

Take a rectangle if it is a perfect rectangle the long side will be 1.618 times longer than the short side the golden ratio.

The reason we’re so interested in it is that is seems to appear in nature all the time, especially when you apply it to spirals; the seeds of a sunflower, the swirl of a galaxy, pinecones, hurricanes this all obey the golden ratio.

You can see examples of the golden ratio in ancient buildings and a huge number of paintings.

It’s often been suggested that it is the number of pure beauty and that a face with features matched in the golden ratio is going to be the most universally popular, so make sure you have a ruler out ready, next time you’re on tinder.

Even if you are one of the many people who would rather lick a toilet bowl than work out a percentage, it’s good to know that maths is out there, doing its job, even without your help and appreciation, you ungrateful little monkey. And of course, even though it’s not on this list, all of us know which number is really the secret answer to the universe, don’t we?