The Infinite Monkey’s Guide to... Infinity

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Hello, I'm Brian Cox.

I'm Rob Lince, and this is the Infinite Monkeys Guide 2.

Every now and again, our show has moments of furious confusion.

And one of the

confusion is just a la la la la.

Haven't got a clue what he's talking about.

Is that what that look is?

La la la la.

I've been looking at this face for the last more than a decade.

And furious confusion, I think, defines that look beautifully.

That's what it is.

I'm very much confusion in a hammock.

Just kind of, woo.

Yeah.

But sometimes we have had guests who've not had as much time to get into the hammock of confusion and are in the conflagration of confusion because our brains are big enough to fit in the simple symbol for infinity.

But when it comes to actually contemplating the infiniteness of infinity or infinities, then we do start to get a little bit dizzy from cosmological vertigo.

Do you ever get cosmological vertigo?

No.

There must be something which you've contemplated that has just made you have, you know, that kind of.

Yeah, I joke.

I mean, the idea that two trillion galaxies by some measures.

It's an estimate, of course, of how many galaxies there are in the observable universe, the part of the universe we can see.

And then you think one of those galaxies, the Milky Way, our galaxy, 400 billion suns, give or take,

takes light around 100,000 years to cross it.

And that's one of the many hundreds of billions, even thousands of billions of galaxies that we can see in the sky.

Yes, I agree.

You know that bit when you're putting together the picture in your head and then suddenly it becomes so massive and you just think, oh, I'm slightly off kilter now.

400,000 million suns in one galaxy.

It is impossible to picture.

You need every day, you need to make that noise that Keanu Reeves makes in the first Matrix movie.

That bit where he goes, Woo!

You know, that kind of just noise is very required.

When we first did a show about infinity, I found that I think it's a New Yorker cartoon.

I think it's one of the greatest cartoons of all time.

It's the number eight at the therapist.

And the therapist says, just lie down on the couch.

And he goes, if I lie down, we're going to be here forever.

Well, here is the great cosmologist, hugely popular guest on the show, Carlos Frank, contemplating infinity.

Infinity always kind of gives me

the desire to scratch my head.

Infinity is big.

Big, big, big.

And

the uh, so I worry about infinity.

It's much bigger than my brain, I'm sure, of that.

So it turns out, sadly, for me, and I hope for most of you, that if these ideas of inflation are correct, then because inflation is associated with these quantum things and quantum things fluctuate all the time, then it may well be that once the mother of all big banks happened and inflation then followed, that as part of inflation, there were more quantum fluctuations that created a new universe distinct from ours, which inflated as well.

And because there was still some leftover of this vacuum energy I was talking about before it would fluctuate again and again and again and again and again and we could be in a situation where there isn't one universe or two or three or any number I can count but an infinite number of universes but that's bad enough trouble is if these ideas are correct

there are an infinite number of universes being born all the time.

Right now we need to deal with this.

So Brian, how many infinities are there?

I know there's a kind of infinity you have between say one and two where there's an infinite number of fractions.

What are the others?

It's one of the most counterintuitive ideas that there are different sorts of infinity.

It goes back to great mathematicians, Cantor.

It was those others that led to a heated debate, which is unusual on Monkey Cage, isn't it?

A heated debate when legendary comedy producer John Lloyd met legendary astronomer royal Lord Martin Rees.

And John Lloyd became affronted to discover that there are so many infinities.

But first,

they had to deal with an infinite number of big bangs leading to an infinite number of universes.

And that's before they got on to the infinite number of potentially infinities.

It's not hurting yet.

If it's not hurting yet, you're not listening properly.

So here they are, Martin Rees and John Lloyd debating

the idea that there should be different types of infinity.

Martin has said before that it's slightly embarrassing in science that 95% of the universe that we're in is unaccounted for.

Only 5% we know something about, and the other 95% is two madey-uppy things called dark matter and dark energy.

So

I mean, it could be anything, could it be?

Ryan?

They're not madey-uppy in the sense that we've observed their influence on the universe.

Well, no, I'm just saying that we don't know what they do or where they are, and therefore what other theory, you know, if I produced a comedy show that was only 5% funny, I think I probably

wouldn't be sitting here now.

Most things in the universe, most things in this room don't shine.

So why is it in the universe?

No,

I'm just saying that most things are dark in the universe, just like that.

My point was that I thought that maybe the ninety-five percent that we don't know about is where all the parallel universes are.

But that would only allow for twenty of them, which isn't enough.

Very large numbers that are interesting.

That's interesting.

Martin, I I believe there have been theories where the the influence of maybe extra dimensions in the universe are causing those deviations from Newtonian gravity.

Well, extra dimensions are, of course, fascinating.

Most people suspect that if we were to divide up space very finely indeed, on a scale much, much smaller than atoms, chop it up very small, then what we think of as empty space becomes very complicated.

What we think of as a point in our space may even be a sort of tightly wrapped origami in five extra dimensions.

This is what string theorists think about.

But some people think that there may be some of these dimensions which aren't wound up so tightly, and

it may be that we see some evidence for them in accelerators.

But more spectacularly, it could be that there are some that aren't wound up at all.

And if that's the case, then there could indeed be another universe which is alongside ours, but separated by a small distance in the fourth dimension, and we're not aware of it.

Just like if you imagine a whole lot of ants crawling around on a sheet of paper, that's like their two-dimensional universe, they might be unaware of another population of ants crawling around on a parallel sheet of paper.

It could be that we are in our three-dimensional world and we are in a space-time that's embedded in some extra dimension, and there are other space-times also embedded in it.

This is really fabulous, but it is, you know, it's science fiction and fun.

Speculative science.

Speculative science.

Somebody said there is speculation, there is wild speculation, and then there's cosmology, isn't that right?

No, 50 years ago,

we didn't know if there's a Big Bang at all.

We knew nothing about cosmology.

Now we can talk with confidence about back to when the universe was a nanosecond old.

That's huge progress.

And if we think of that progress you made in the last 50 years, then 50 years from now, I suspect we will have got back far enough to be able to understand the Big Bang well enough to say whether it was the only one, whether it was one of many, and whether the other Big Bangs cooled down to be governed by the same laws as ours or not.

I should mention that there is an idea called eternal inflation, which is the idea that our Big Bang started with some very rapid expansion called inflation,

but that these Big Bangs keep popping off all the time in some infinite substratum that goes on forever.

So it's rather like the old steady-state universe, but on a much grander scale.

And this I love, because I've been saying, I'm going to really step out of line here.

I've been saying for 10 years that the Big Bang theory theory will not stand out.

It will not be here in its current state in 10 years' time.

And you've already mentioned that there might be some other Big Bangs and this eternal expansion thing, and there's a thing called quantum fluctuation, isn't there, as well, which is quite interesting.

And it's starting to come apart at the seams, this Big Bang thing.

Because there are a lot of...

No, that's not true at all.

It's just.

No.

But you're saying the steady state.

I like the steady state theory.

I like Fred Hoyle.

And I think that.

Well, it was completely wrong in the form that he proposed.

Yes.

Well, it's coming back to deciding that there's...

But No, it's coming back on a quite different scale.

The point is that

in science, what happens is that there are speculative questions, and as they get settled, new issues come into focus

and new questions which you couldn't have posed before.

So we've settled most of the questions we debated 40 years ago, but we are now addressing questions that couldn't have been posed then.

And 40 years from now, it'd be another set of questions.

That's the nature of science.

New science doesn't sort of overthrow the old, it transcends the old.

Now, Brian often wonders what an infinite universe would actually look like.

Well, no, I know, because our universe could well be infinite, and I know what it looks like.

Well, you know a bit of what it looks like.

You haven't got the full picture.

No, that's true.

If you have got the full picture, start showing it to us.

You'll probably win a prize.

But you also like to be drawn into ecumenical matters.

And that is how we ended up discussing how a universe without a beginning may affect religious faith with screenwriter and theologian Katie Brand.

If, for example, it is shown through doing physics that the universe is eternal, for example, does not have a beginning in time, what do you think it would mean to people who think about religion?

As in, there was no point at which the universe didn't exist and therefore there can't really be a creator.

Yeah, well,

does that follow?

That's my point.

Well, I mean, I'm not now religious, and in fact, I became an atheist on a pilgrimage to Rome.

Yes, and I did did meet the Pope at the end, and it felt like the closer I got to the Pope,

the more atheist I became.

That's what I originally said.

So it was embarrassing when I did finally meet him.

But so I can't answer from a personal point of view because I would just find it very exciting because I'm now an atheist and I would just find it fascinating because I find all of this fascinating.

But I do think, you know, a lot of Christians have tried to combine the idea of evolution with the idea of guided evolution, and that all of these scientific discoveries have been kind of folded into religion for the more open-minded or intellectual perhaps people who have religious beliefs.

So, personally, I would think that what would happen, I'm sorry to disappoint anyone who's a very militant atheist, is that religious people would simply find a way to fold that into their existing story.

And I think probably a lot of humans would be comforted by that.

But I think it's hard to know because what I'm trying to understand is how radical would it be for humans, just sort of on a lay person's level like me, if you did discover the theory of everything, or would it just be sort of felt to be

a kind of

another layer of very complicated physics that most people don't really engage with?

Or would it be sort of front-page news, like as if an alien had landed in someone's back garden in Richmond?

When you say front-page news, when we look back, Einstein was front-page news, and there were, in the 20th century, in the first half, science often was front-page news.

And there's still science going on that should be front-page news.

But unfortunately, our media has decided that that is not as immediately kind of tacky and sticky and so it's all out there so I think that's part of it as well is to say there are brilliant and wonderful ideas and this is far more interesting than your particular attack on you know Harry and Megan or whatever it might be

it's interesting isn't it how Harry and Megan can be both royal and not royal

now quite often we've heard that mathematics is a pursuit that can turn people quite mad and indeed there is a rich history of people who trying to comprehend a world of numbers just eventually.

That was almost very funny.

Did you say cantern?

I thought you said cantor.

Oh, can you say cantor people quite.

I thought that's an extremely clever thing.

If we get to that level of pun, which I think we may well have done again by chance, then perhaps we've finished our work here.

Cantor had a very famous concept of different infinities,

had long, long discussions with David Hilbert, the great mathematician.

And again, one of my favourite things that we've discussed in Monkey Cage, Hilbert's Hotel.

Yeah, the finest thing that we put into that book we did was the TripAdvisor's review of Hilbert's Hotel and the various issues with continually having to get out of the room that you'd booked and move to the next door.

Is this one not?

It's the idea that you can have a hotel with an infinite number of guests and not be full.

It's a parable.

21st century Britain.

But if it is full, then what happens is someone turns up and then as long as you move one more room, it turns out there is another room.

Is that profit?

Yeah.

And not surprisingly, John Lloyd.

He disagreed with mathematician Simon Singh.

My argument about infinity is this, Simon.

Infinity is a word, that belongs to the wordy people, like me and Robin, the word creatures, and not to the numbery people.

Oh, you can have two as well, then two is a word.

No, no, no, two is a numeral.

But the point is, you cannot place a numerical value on infinity, and therefore you cannot have a plus one to it or a minus one.

No, but it was just proved that you could, so we can stop.

It's been proved.

That's not proof.

That's a problem with you, Bob.

That's just word for proof.

It's gameplay.

But you absolutely take infinity as something which

could be bigger.

But you're right.

You're right in that whenever I say.

No, he's not.

No, no, no.

He's right in as much as whenever I say, so I'm going to talk about the number infinity, somebody always corrects me and absolutely right to correct me that infinity is not a number.

It's a concept.

And we can play with that concept using mathematical ideas and so on.

But as you say, in a concrete way, it's not a number.

There are either an infinite number of numbers or there aren't.

There are.

I don't see

where the problem is.

No, there aren't.

There aren't an infinite number of numbers, right?

Because you can always have more than infinity, and therefore, infinity is a meaningless concept.

See, I'm annoyed now because I'm thinking about the infinite number of monkeys, and you get them all together, and then you go, what have they written?

And you go, they've written the Dew of Malta.

But that's by Marlowe.

We didn't have enough monkeys.

You know, the whole kind of thing is a disaster.

And now to ensure that this show is a Mobius strip, we find ourselves back to roughly where we began.

Just how many infinities are there?

Here's mathematician Vicki Neal talking big, big numbers.

What's the difference between a big number and a big, big number?

Well, it's much like infinity.

You know, there's

big, and then there's biggie big, and then there's bigness big, and then there's the notorious BIG.

Is there a number so big that you can't fit it in an infinite cage?

No.

How big is your infinite infinite cage?

What kind of infinity do you have?

No, we're not doing that again.

No, no, no, no, no.

I refer you to series nine.

What about the smallest infinity?

The smallest infinity is the number of real numbers.

Is that the smallest infinity?

No, no, no, no, no, no, no, no, no, no, no, whole numbers.

Whole numbers.

Real numbers.

Whole numbers.

There are masses.

There are loads of whole numbers, but there are loads and loads of real numbers.

Yeah, loads of numbers.

Oh, yes.

So if I had a cage that was just big enough to fit the infinity of real numbers in it.

That would be huge.

That would be be huge.

Yeah.

But whole numbers, then I could, it wouldn't fit the infinity.

That would just be quite big.

It wouldn't fit the reality.

It's not that huge because you can quite easily, there are an infinite number of infinities that are even bigger than that.

Yeah.

So the infinite cage is really, yeah, problematic.

If we were small, treating the numbers humanely, could we make it smaller?

The Infinite Monkey Cage episode we took all of these clips from are available on BBC Sands and the Infinite Monkey Cage back catalogue.

Now next week you're in charge of the show.

So you've sent us long lists, wonderful emails about the things you found most surprising over 15 years of the Infinite Monkey Cage.

Sadly enough the main thing that I've seen on the list is the fact that I have aged at an incredible rate and you haven't changed one bit.

Apart from the fact you're a bit thinner.

Which is hard, really, to contemplate because it's a radio show, so I don't know how they'd know this.

I just think they hear my old beard all filled with like like kind of blackbirds that live in it, rustling against the microphone every now and again, and they hear the tightness of your skin sometimes ping.

Yeah, you are morphing into a kind of a sort of Alan Moore, somewhere between Alan Moore and the subject of a limerick.

In the infinite monkey cage,

in the infinite monkey cage.

Till now, nice again.

We hope you enjoyed that.

And here is another.

We enjoyed it, you can hear in the background.

So we hope you enjoy this podcast that also comes from the BBC that's coming next.

Can you just tell me who he is?

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Has he got any distinguishing features?

His anonymity.

What's his name?

Banksy.

I'm James Peake, and I'm on a mission to find out how Banksy became the world's most famous and infamous living artist.

He could literally be anyone.

Banksy essentially humiliates the art world.

With dealers, critics, and someone who once worked deep inside Banksy's secret team.

Do you wish you didn't know who he was?

Sometimes I wish I'd never heard of Banksy.

The Banksy Story with me, James Peake, on Radio 4.

Listen now on BBC Sounds.

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