Things to Make and Do in the Fourth Dimension

by Matt Parker

It’s a shame that most people think maths is just what they were subjected to at secondary school: it is so much more than that.

As the Nobel Prize-winning physicist Richard Feynman allegedly said of his own subject: ‘Physics is a lot like sex; sure it has a practical use, but that’s not why we do it.’

Mathematicians hold multiplication in higher regard than addition because addition predictably tells you how big a number is, whereas multiplication tells you a bit about its personality.

Because adding up the factors of each of the numbers gives you the other number, 220 and 284 are considered to be intimately linked, and have earned the name ‘amicable numbers’.

The square of every prime number is one more than a multiple of 24.

Trying to hide won’t do it any good either: as 3D creatures, we can see the entire 2D world set out in front of us like a blueprint – which is exactly how the 4D creature in the Alan Moore story describes the 3D world.

So I bought ten thousand dominoes.

But in the ugliness of the Bernoulli numbers lies a strange type of beauty.

This is why Ada Lovelace wrote the first ever computer program to calculate the ‘Numbers of Bernoulli’. It’s a beautiful thing to behold.

Of course, the sum of all the positive whole numbers is infinite, but if you can somehow peel that infinity back out of the way and look at what else is going on, there’s a −1⁄12 in there.

I think a 4D hat is a good place to finish our journey through topology.

This is the basis of what is known as the sausage conjecture.

Romance isn’t dead, just digitized.

(Setting the Earth’s atmosphere on fire is widely regarded as a ‘very bad thing’.)

It’s an illusion that text messages work so well. There is just a lot of maths fixing the errors before the user even notices.

My mum had by chance knitted me the world’s first error-correcting scarf.

If you could have negative-four ducks and you introduced them to five positive ducks, they would cancel out with a bang, leaving one solitary very confused duck.

The square root of a negative number had the decency to go away again before the final solution to an equation, but what did it mean while it was there?

The mathematician Erdős was in the habit of calling children epsilons because they are very small but non-zero humans.

This is because infinity is like a loose thread on the coat of mathematics. If you start pulling on it, not only is it longer than expected, but everything else starts to unravel and suddenly you’re standing there, mathematically naked, wishing you could push that thread back in and continue happily ignoring it.