This Toothpick Contains Everything Ever Said (Infinity Part 3)

The Rest Is Science

Goalhanger

Science, Physics, Mathematics

4.5 • 1K Ratings

🗓️ 6 April 2026

⏱️ 50 minutes

🔗️ Recording | iTunes | RSS

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Summary

What happens when you finally reach the end of forever? And what exactly is the difference between Omega and Aleph-null? Professor Hannah Fry and Michael Stevens (VSauce) return for the final (possibly not) chapter of our infinity series, unpicking the frankly absurd mechanics of multiple infinities. They reveal how mathematicians don't just measure the endless void, but actively organise it, exploring the bizarre gap between the sheer size of a boundless set of numbers and its actual order. Following Georg Cantor's mathematical meltdown, this episode tackles the mind bending rules of the infinite, why Aleph-null is just the baby of the infinite family, and how jumping to Omega requires a complete rewiring of human logic. ------------------- For more information about Cancer Research UK, their research, breakthroughs and how you can support them, visit ⁠⁠https://cancerresearchuk.org/restisscience⁠⁠ Cancer Research UK is a registered charity in England and Wales (1089464), Scotland (SC041666), the Isle of Man (1103) and Jersey (247). A company limited by guarantee. Registered company in England and Wales (4325234) and the Isle of Man (5713F). Registered address: 2 Redman Place, London, E20 1JQ. ------------------- Find The Rest Is Science all over the internet by ⁠⁠clicking here.⁠⁠ ------------------- Video Producer: Adam Thornton + Oli Oakley Video & Social: Bex Tyrrell Producer: Simona Rata Senior Producer: Lauren Armstrong-Carter Head Of Digital: Samuel Oakley Exec Producer: Neil Fearn Learn more about your ad choices. Visit podcastchoices.com/adchoices

Transcript

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0:00.0	Welcome to The Rest is Science. I'm Hannah Fry.
0:03.1	And I'm Michael Stevens.
0:04.3	And we have been talking for a long time about infinity.
0:08.7	But we're still talking about it.
0:10.6	We're still talking about it.
0:11.7	I don't know.
0:12.3	This series might become endless.
0:14.4	Or maybe third times the charm.
0:16.8	We'll see.
0:17.1	Maybe third times the charm.
0:18.2	I think they will end because we have decided we're done.
0:21.7	They certainly won't end because we've covered all the numbers.
0:25.6	No, no, certainly not.
0:27.6	The thing is there's just so much delight to discover.
0:30.3	There's so many strange weirdnesses once you allow your mind to wander into the depths of infinity.
0:35.9	Not only are there a lot of strange weirdnesses,
0:39.4	but there's a lot of different ways to talk about each strange weirdness. And sometimes I'll find
0:46.4	a whole new way of describing a trans finite number and I'll be like, that is so much clearer
0:51.1	than what I've ever heard before. I'm so glad I heard it. But I wanted to start with an object, okay, to kind of like cleanse our palettes. So we're going to talk about something that's physical and real. Are you ready, Hannah? I am. Absolutely. I have here a toothpick. You see that? Not what I thought you were going, but sure. This is a toothpick, but guess what?
1:11.6	Tell me.
1:12.4	Everything that could ever be said is on this toothpick.
1:20.5	Tell me how.
	...

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