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Why does thinking about infinity make my head hurt?

infinity 01

Now that Discovery World Tropical Forest has closed for redevelopment, everyone is asking about the new science centre. With 50 new interactives, there’ll be lots for you to discover. Leading up to the opening in December we’ll explore some interesting topics that you may find in our new science centre. We start with this brain bender ... read on!

First there was Te Kore, the void. Before matter, before time itself; just the potential of being. This time before the Big Bang was a space without boundaries – infinity.

We have all heard about the idea of infinity, but why do we struggle to comprehend it?

Infinity isn’t something we can observe, and that makes it hard, because in our everyday lives almost everything is observable, and finite. One of the most fundamental concepts in our lives is that things begin and end, and this is intrinsically tied to the idea of time. As time passes, things change. But if something is infinite, it sits outside of time – it goes on forever, both forwards and backwards. By definition, it cannot end. So, infinity before matter – Te Kore – is still there. But since the Big Bang there is finite matter around as well, and that is what we see.

This is one reason infinity makes your head hurt – we never see it and have no easy way to represent it.

But this will make your head hurt even more. Many things are infinite, but they are not all equal. Infinity turns up a lot in maths, and there is one neat mathematical example that shows the inequality of infinites.

Let’s imagine all the whole numbers (a number without a decimal place, like 1, or 100, or 32 607 – whatever). There is an infinite number of whole numbers, but they are countable. If you had an infinite amount of time you could keep counting them, forever.


There are also real numbers (a number with a decimal place, like 1.2, 100.34 or 32 607.1). A recurring decimal number can have an infinite series of digits after the decimal point, eg 572.9999…  And while the whole numbers are countable, the real numbers are not. Without delving into some mind-bending maths, simply said, there is just no algorithm for counting them.

Thus, these numbers are endless; there is an infinite amount of both… but they are not equal.

So that’s infinity, in a nutshell.

In the Museum’s new science centre we’re going to offer a way to imagine infinity. When we open in December, come and check out our Infinity Room to find out if you can see to the edge of endlessness.