# To Infinity and beyond

4 6 Share TweetQuestion: What’s bigger than bazillion? Answer: Infinity!!! But Infinity is one of those words that’s really hard to define – What exactly does it mean to say that something is Infinite? Is Infinity even a number?

### What is Infinity?

Imagine that someone tries to get you to define infinity by asking you to name an infinitely big number – How should you answer?

999999999999999999?

9999999999999999999999999999?

9999999999999999999999999999999999999999999999999999?

No, clearly none of these are infinitely big numbers! In fact, as soon as you try and say a specific number, there’s no way you can really be talking about something that is infinite – You can always just add another digit to what you’ve said to make it bigger. The problem reminds me of that game you play as a kid where you dare someone to do something (actually, come to think of it, I still play it now):

‘I dare you to do it’

‘I double dare you’

‘Too bad because I triple dare you’

‘You lose sucker – I dare you a million times!’

‘No you lose! I dare you infinity times’

‘Well I dare you to do 50 press-ups infinity times plus one – Beat that Grandad!!!’

So, if infinity isn’t a number, what is it? Well, people usually think about it as a concept instead. Infinity is something so big that it has no end. This is a pretty vague definition but, as we’ve seen, trying to pin things down leads to problems!

### Achilles and the Tortoise

One of the first Philosophers to look at the concept of infinity in detail was Zeno of Elea. Zeno lived in Ancient Greece from c. 490 BC until c. 430 BC. He told several paradoxical stories about infinity and the story of Achilles and the Tortoise is one of them:

Imagine that Achilles is having a race against his slowest friend, Mr. Tortoise. Because Achilles is so confident that he’ll win the race, he gives the tortoise a head-start of 100 meters. So the race begins and both Achilles and Mr. Tortoise run as fast as they can. After a little time, Achilles has run 100 meters. But during this time, Mr. Tortoise moves forward a little too (we’ll say 10 meters). Now imagine that Achilles runs the next 10 meters to catch up with the tortoise – But by the time he has run this distance, Mr. Tortoise will have moved a little farther on again. And because this process can go on and on, it looks like however far Achilles runs, he will never catch up with the tortoise – It will always take Achilles some time to reach the point where Mr. Tortoise was before, and by the time he reaches that last point, the tortoise will have moved on a little bit! So the story states that while the gap between Achilles and the tortoise might get smaller and smaller, Achilles will never be able to catch up with his green-shelled friend!

Whilst it may not be clear straightaway, the problem Zeno expresses in his story relates to the concept of infinity – Namely, the problem involves Achilles trying to complete an infinite number of tasks in order to catch up with the tortoise. By the time Achilles reaches point 1 (the point at which the tortoise starts the race), the tortoise will have reached point 2. And by the time Achilles reaches point 2, the tortoise will be at point 3. And by the time Achilles reaches point 3, the tortoise will already be at point 4. And so on to infinity. So, in the story, it looks like Achilles must somehow complete an infinite number of steps (reaching points 1, 2, 3 etc.) in order to catch up with his friend.

But Zeno’s story is clearly absurd – We all know that Achilles would easily be able to catch up with the tortoise in real life! So what’s wrong with the story? Post your answers in the comments below, I need your help and infinite wisdom to answer this paradox!

Prophecy Number 9: ‘A bazillion fresh analogue tunes await us’ – Want to learn more about the analogue future? Head to the Microsite, take part in our Shoot Your Prophecy Competition and download the Future is Analogue posters!

written by tomas_bates on 2011-04-22 in #lifestyle #future #prophecies #paradox #analogue #beyond #infinity

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