How to explain infinity to a 4-year-old
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What is the main topic discussed in this episode?
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Hello and welcome to More or Less on the BBC World Service. I'm Ruth Alexander. This week we hope the programme will appeal to both little people and adults. In just a few minutes we'll pay tribute to one of the world's greatest mathematicians, certainly one of the most popular and a hero to us here on More or Less.
The first thing I ever counted was my fingers and my toes, my ears and then my nose, in that order. Ah, ah, ah.
Sesame Street's Count von Count, whose Muppet master, Gerry Nelson, has sadly died. But first this week, we've been asked to make some time for infinity.
Hello, my four-year-old daughter wishes to know... What is the number before infinity? Can you advise on a mathematically reasonable answer that I could explain to a four-year-old? Thanks.
One of the toughest challenges yet, for more or less. So confidently, I invited four-year-old Claudia Howarth and her mum Ellie into the studio and battered her questions straight on to someone else. Johnny Ball, a legendary British TV presenter who's made a career out of explaining maths to children.
Right. Can you help? Or infinity? If your friends asked you, what would you say to them?
I think 100 or a million.
Are big numbers, but they're nowhere near infinity. So, how can I explain it? I've got some sweets here. In fact, I'm going to give you some sweets. You've got some sweets, and I've got more sweets, because they're my sweets. But you've got some more now. You start counting yours.
One... Two. Right. Three.
That's very good.
Four. Five. Six. Seven.
And... Eight. Have you got any more? No. But if I gave you another one... That would be... How many is that?
Nine.
Nine. You'd have nine sweets. Right. You asked, what is the number before infinity? Well, as infinity goes on forever, you can't have the number before infinity because whatever that number is, however big it is, if you added one more, you'd have another number that's bigger. So you can't have the number before infinity. It goes on forever.
Claudia, you've heard Johnny's explanation.
How does the episode introduce the question ‘What’s the number before infinity?’?
If one of your friends came to you with your question and said, what number comes before infinity, what would you tell them now? It goes on forever. That's wonderful. You've obviously explained it well, Johnny.
And that's the infinity.
Congratulations. And that's very good. So, Claudia, you enjoy that suite. Ellie, what did you make of Johnny's explanations? Does this make sense to you? As much as infinity is ever going to make sense, I hope so. Because infinity is a difficult concept. And as I think you found, Ben, it's a difficult concept to explain as well.
It is, because virtually everything we talk about is finite. The number of molecules of air in the atmosphere is finite. They could be counted. There's a number you can't go beyond. But infinity goes beyond that. We talk about the big bang started the universe, and it seems like a model that works, but we don't know where the edge of the universe is or whether the universe goes on to infinity forever and ever. We probably will never know that.
See, I was going to ask you that. What is infinite? What is there that we know is infinite? I mean, numbers are, aren't they? Yeah.
If you have a square, it's got four sides, and it will fit into a circle. If you have a hexagon that fits into a circle, it's six sides, and it still fits into a circle. If you have an octagon with eight sides that fits into a circle, all well and good. How far can you go? How many sides can you have to a figure... that will still fit in a circle. Well, the definition of a circle is an infinite number of points, a set distance from a central point that together make up that circle.
I think it's very interesting how hard it is for humans to conceive of something that goes on forever and ever.
And it's wonderful that human brains will always want to stretch it and stretch it. So if you like, the human brain's thinking... will go on to infinity, hopefully.
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Chapters
4 chapters
1
What is the main topic discussed in this episode?
0:00–2:41
2
How does the episode introduce the question ‘What’s the number before infinity?’?
2:41–5:34
3
How does Johnny Ball demonstrate infinity using sweets and counting with a four-year-old?
5:34–7:53
4
Why can't there be a 'number before infinity' according to Johnny Ball?
7:53–9:32