How to explain infinity to a 4-year-old

Summary

More or Less (BBC Radio 4)

Episode: How to Explain Infinity to a 4-Year-Old

Date: September 3, 2012
Host: Ruth Alexander, with guests Johnny Ball, Count Von Count, Tim Harford, Claudia and Ellie Howarth

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Episode Overview

This engaging episode tackles the profound question: "How do you explain infinity to a 4-year-old?" Blending playful interviews with serious mathematical insight, the More or Less team sets out to make an unfathomable concept approachable—while also paying tribute to Jerry Nelson, the late Muppet performer behind Sesame Street’s Count Von Count.

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Key Discussion Points and Insights

1. Introducing the Challenge (00:13–00:39)

• Host Ruth Alexander kicks off with an episode intended for both children and adults, leading with a listener’s challenge: explaining infinity to four-year-old Claudia Howarth.

2. Exploring Infinity with Johnny Ball (00:56–04:50)

Explaining Numbers and Infinity

• Ruth invites legendary maths educator Johnny Ball into the studio with Claudia and her mother Ellie.
• Claudia’s big question: "What is the number before infinity?" (00:52)

Using Sweets to Illustrate Counting

• Sweet counting exercise demonstrates how numbers keep going—there’s always "one more."
• Johnny Ball:
  “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.” (02:11)

Claudia’s Understanding

• Ruth tests Claudia’s grasp post-explanation:
  • Claudia Howarth: “It goes on forever.” (02:51)
  • Ruth Alexander: “That's wonderful. You've obviously explained it well, Johnny.” (02:54)

The Challenge of Infinite Concepts

• Johnny reflects on the rarity and difficulty of truly infinite things.
  • Johnny Ball: “Virtually everything we talk about is finite... but infinity goes beyond that.” (03:22)
  • He ties infinity to classic geometry: “The definition of a circle is an infinite number of points, a set distance from a central point that together make up that circle.” (03:58)

Memorable moment:

• Johnny Ball (humorously miscounting his sweets): “1, 2, 3, 4, 7, 5.” (05:05)
• Claudia Howarth (correcting him): “He got him wrong.” (05:17)

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3. Tribute to Jerry Nelson and Count Von Count (05:19–07:36)

Remembering Jerry Nelson

• Ruth notes the passing of Jerry Nelson, the puppeteer behind Count Von Count.
• Replay of a previous More or Less interview with the Count.

Interview Highlights with Count Von Count

• Why do they call you the Count?
  • Count Von Count: “Because I love to count things.” (05:59)
• First thing you ever counted?
  • “My fingers and my toes, my ears and then my nose, in that order.” (06:06)
• Favorite number?
  • “34,969. It’s a square root thing.” (06:17)
• Has a love of counting caused problems?
  • Anecdote about counting chickens before they hatched, discovering “five chickens, three turtles and two alligators.” (06:52)
• Counting vs. doing sums
  • Count: “A person who does sums counts and then adds those together. Is that correct?” (06:27)
  • Tim Harford: “Yes, I suppose it is.” (06:34)
  • Count: “I have done this, of course, but it's not really my thing.” (06:35)
• On being an elevator operator and mishaps with Kermit due to compulsive counting (07:07)

Memorable banter:

• Tim Harford: “Wasn't that a bit selfish? Your friendship with Kermit must have suffered.” (07:07)
• Count Von Count: “Yes, well, it was a minor setback in our relationship... I think we are still very good friends.” (07:21)

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4. Listener Puzzles and Fun Facts about 34,969 (07:36–09:01)

Decoding “Count’s” Favorite Number

• Ruth explains listener theories revealing:
  • 34,969 = 187².
  • 187 = 11 × 17; “a very fine number,” as one listener puts it.
  • 187 is 94² - 93² (also 94+93).
  • Noted by listeners: 187 is the US police code for murder—"Murder squared?" Playful speculation on the Count's symbolism.

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Notable Quotes and Memorable Moments

• Johnny Ball (on infinity):
  “You can’t have the number before infinity... it goes on forever.” (02:11)

• Claudia Howarth (age four, after learning about infinity):
  “It goes on forever.” (02:51)

• Johnny Ball (on human curiosity):
  “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.” (04:39)

• Count Von Count (on his favorite number):
  “34,969. It’s a square root thing.” (06:17)

• Count Von Count (counting misadventure):
  “As it turned out, what I thought were 10 chickens were, in reality, five chickens, three turtles, and two alligators.” (06:52)

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Important Timestamps

• 00:13 – Episode introduction and tributes
• 00:56 – Claudia’s question introduced
• 01:19–04:50 – Johnny Ball’s explanations and playful maths with sweets
• 05:05 – Johnny miscounts sweets; Claudia corrects him
• 05:19 – Count Von Count segment and tribute to Jerry Nelson
• 05:59–07:36 – Interview with Count Von Count
• 07:36–09:01 – Listener engagement with Count’s favorite number

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Episode Tone and Style

Friendly, playful, and inclusive—mixing gentle humor and genuine mathematical curiosity. The hosts honor children's inquisitiveness and nostalgia (through Sesame Street), while never talking down to listeners of any age.

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Conclusion

This episode manages to render infinity both approachable and wondrous, demonstrates how to introduce advanced ideas to young minds, and celebrates the joy of counting—whether that’s sweets in a studio or the never-ending numbers stretching into infinity. The tribute to Count Von Count is both touching and delightfully quirky, showing that sometimes the best mathematical explanations come wrapped in laughter.

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Transcript

[BBC Announcer]

Thank you for downloading from the BBC. For details of our complete range of podcasts and our terms of use, go to bbcworldservice.com podcasts

[Ruth Alexander]

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 amongst and a hero to us here on More or Less.

[Count Von Count]

The first thing I ever counted was my fingers and my toes, my ears and then my nose, in that order. Ah, ah, ah.

[Ruth Alexander]

Sesame Street's Count Von Count, whose Muppet master Jerry 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

[Claudia Howarth]

know what is the number before infinity?

[Ruth Alexander]

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 batted 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.

[Johnny Ball]

Right, can you help? What is the number before infinity? If your friends ask you what, what would you say to them?

[Claudia Howarth]

I think 100 or a million

[Count Von Count]

are

[Johnny Ball]

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.

[Claudia Howarth]

One, two.

[Johnny Ball]

Right.

[Claudia Howarth]

Three.

[Johnny Ball]

That's very good.

[Claudia Howarth]

Four, Five.

[Tim Harford]

Six.

[Claudia Howarth]

Seven and eight.

[Johnny Ball]

Have you got any more? No, but if I gave you another one, that would be. How many is that?

[Claudia Howarth]

Nine.

[Johnny Ball]

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.

[Ruth Alexander]

Claudia, you've heard Johnny's explanation. If one of your friends came to you with your question and said, what number comes before infinity? What would you tell them now?

[Claudia Howarth]

It goes on forever.

[Ruth Alexander]

That's wonderful. You've obviously explained it well, Johnny.

[Johnny Ball]

That's infinity.

[Ruth Alexander]

Congratulations. 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. Infinity is a difficult concept and as I think you found then, it's a difficult concept to explain as well because.

[Johnny Ball]

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. You know, 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 univers is or whether the universe goes on to infinity forever and ever. We probably will never know that.

[Ruth Alexander]

See, I was going to ask you that. You know, what is infinite? What is there that we know is infinite? I mean, numbers are, aren't they?

[Johnny Ball]

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 in the 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.

[Ruth Alexander]

I think it's very interesting how hard it is for humans to conceive of something that goes on forever.

[Johnny Ball]

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.

[Ruth Alexander]

Well, on that note, Johnny, thank you so much for your efforts. Ellie and Claudia, most of all, thank you so much for your positively mind expanding questions. Such a tricky question and you've got us all thinking very hard. So thank you very much indeed.

[Johnny Ball]

Claudia, I think you're wonderful. I'm going to count my sweets right. 1, 2, 3, 4, 7, 5.

[Claudia Howarth]

He got him wrong.

[Ruth Alexander]

Claudia Howarth, aged 4. She starts school for the first time next week. Now, the More or Less team were sad to hear that Jerry Nelson, the man behind the Sesame street character Count Von Count, has died, age 78. His mathematically gifted Muppet was interviewed on more or less three years ago as the children's television series celebrated its 40th anniversary. He was pretty much our favourite guest on the show ever. So here's another chance to hear Sesame Street's leading mathematician put through his paces in a typically rigorous more or less interview. Tim Harford's first question was straight to the point. Why do they call you the Count?

[Count Von Count]

Well, Tim, they call me the Count because I love to count things.

[Tim Harford]

And what's the first thing you ever counted?

[Count Von Count]

Ah, well, the first thing I ever counted was my fingers and my toes, my ears and then my nose, in that order.

[Tim Harford]

Do you have A favorite number?

[Count Von Count]

34969. It's a square root thing.

[Tim Harford]

Do you ever do sums or do you just count, count sums?

[Count Von Count]

Well, yes. A person who does sums counts and then adds those together. Is that correct?

[Tim Harford]

Yes, I suppose it is.

[Count Von Count]

I have done this, of course, but it's not really my thing.

[Tim Harford]

Now, Count, I want to talk to you about a word that begins with the sound of the letter A. It's called erythomania, which refers to a love of counting or problematic or compulsive counting. I have to ask, has your love of counting ever caused you problems?

[Count Von Count]

Well, yes. Once. I tried to count my chickens before they hatched. As it turned out, what I thought were 10 chickens were, in reality five chickens, three turtles and two alligators. The people who thought they were buying chickens were not amused.

[Tim Harford]

I seem to remember an occasion when you were working as an elevator operator. Your friend Kermit couldn't get off on the floor he wanted because you insisted on going all the way to the top to count every floor. Wasn't that a bit selfish? I mean, your friendship with Kermit must have suffered.

[Count Von Count]

Yes, well, it was a minor setback in our relationship. I often find this the case. People sometimes do not understand how important counting is, but we sorted that out. I think we are still very good friends.

[Ruth Alexander]

Count Von Count from Sesame street and Tim Harford. So his favourite number is 34,969. It's a square root thing. Well, that had us puzzled. 34,969 is 187 squared. But why 187? Well, a number of listeners sent in theories. David lees noticed that 187 is the product of two primes, 11 and 17, which makes 34,969 a very fine number. Indee being 11 squared times 17 squared. Watts, he asked, could be lovelier. And Simon Phillips calculated that 187 is 94 squared minus 93 squared. Neat when you consider that 187 is also 94 plus 93. But both Simon and Toby hinted at darkness behind the count's carefree laughter and charming flashes of lightning. 187 is also the American police code for Murder Murder Squared. Was the Count trying to tell us something? Do please send your theories, comments and questions to more or lessbc.co.uk and you can download more editions of this program at our website, bbcworldservice.com moreorless well, I guess that must be about the end of the program then.

[Count Von Count]

Here we go. 5, 4, 3, 2, 1.

[Tim Harford]

Ah ah ah ah ah.

[Count Von Count]

I love it.

[Ruth Alexander]

More or Less was presented by me, Ruth Alexander. The editor was Richard Varden.

[BBC Announcer]

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