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AN INTRODUCTION

Welcome to

The Infinite Monkey Cage

Hello, I am Robin Ince.

And I am Brian Cox.

ROBIN: Growing up in the 1970s and 1980s, our interest in space, technology and strange undersea creatures with terrifying tentacles or the ability to eat their own brains came from a mixture of Look and Learn magazine, The Six Million Dollar Man and Arthur C. Clarke’s Mysterious World.

BRIAN: We were kids in the Indian summer of the space race, a little too young to remember the Moon landings, but the excitement of exploration still enthused us all. (I myself still own a Space 1999 outfit.) It was a time of Cold War danger and anxiety, but also of immense optimism and confidence in the promise of science and technology.

R: Sadly, Brian could never become an astronaut because he is too tall and I could never be one because I am too chatty… and short-sighted… and not very patient when it comes to misbehaving machines. So there is no way Apollo 13 would have returned to Earth if I’d been in there gallumphing about and kicking whatever bit of kit that refused to operate as I wanted it to. I am one of those unfortunate humans who believes that objects misbehave with the specific intention of ruining my day. I am likely to be found dead from a heart attack after a blazing row with an inanimate object.

B: Whilst Robin’s inability to operate machinery led him to become a comedian, via a degree in one or other of the humanities at some university or other, I became a particle physicist after a short detour via the music industry. Although even then I was primarily interested in programming the Roland MC-300 Micro Composer and only transferred my interest to sex and drugs and rock ‘n’ roll when my midi cable became frayed.

R: In the early 1980s, television was our teacher. Carl Sagan’s Cosmos is one of the main reasons why The Infinite Monkey Cage exists. Opening with the music of Vangelis, the composer who would also score Blade Runner – a film Brian loves as he now knows why he has the same dream about unicorns every night – Sagan’s ‘spaceship of the imagination’ travelled through nebulae and star systems. Music fades, camera pans across a cliff face and zooms into Carl Sagan, and we twelve-year-olds sat up, wide-eyed and eager, and heard the words:

‘The Cosmos is all that is, or ever was, or ever will be.’

And thus we were snared. Within minutes, we would know that we were all starstuff, that the stuff of us was the stuff of the stars. The atoms that were currently gathered to form the shape and minds of us had been forged in the furnace of stellar nurseries.

B: Carl Sagan was a pivotal figure for us because he made vivid the link between our science and our humanity. We are a part of the Cosmos, Sagan told us, and our fate is deeply connected with it. Science is devalued when separated from culture, and our experience of living is diluted when we become separated from science, because science is a necessary but not sufficient part of our exploration of what it means to be human. It is not possible to have a meaningful discussion about our place in the Cosmos without knowing its size and scale, without knowing that we are made of it and will return to it, without acknowledging the deep mysteries that await us as we push our understanding ever further back to the beginning of the Universe, 13.8 billion years ago.

Science is often celebrated because it is useful, and research is funded because it provides us with objects of perceived value. The true value of science is that it allows us to acquire reliable knowledge and teaches us humility. Your opinion is irrelevant in the face of nature; imagine the improvement in modern-day political discourse if that single sentence were seared into the forearm of every politician as a cow is branded with the mark of its owner?

Having said that, aircraft, mobile phones, medicine, electric light, refrigerators, vaccines, computers and radios are useful things, and Robin would struggle without the synthetic fibres that strengthen his book-filled rucksack.

We are a part of the Cosmos, Sagan told us, and our fate is deeply connected with it.

Raymond Baxter, the first presenter of Tomorrow’s World, seen here in 1970 with an innovative doll that can walk, talk and sing.

R: Tomorrow’s World told us of what was to come, and though often mocked for its adventurous predictions involving round cars on wheeled stilts, much of what was featured on the programme was accurate, intriguing and inspiring. Returning to it now, we are reminded of the speed of change. The unwieldy home computer of 1967 contains far less data-processing capacity than one of the twenty-first century’s fancier and, predominantly, pointless, wristwatches.

‘Imagine a world where every word ever written, every picture ever painted and every film ever shot could be viewed instantly in your home via an information superhighway, a high-capacity digital communication network… it sounds pretty grand, but in fact this is already happening on something called the internet’

Kate Bellingham told us in 1994.

1994!

Imagine a world without something called the internet. Imagine how hard it would be to shop, watch or destabilise democracy and seed disinformation.

William Wollard, former presenter on Tomorrow’s World, seen strolling up the roof of St Pancras Station in London in 1970, made possible through the cunning invention of Herbert Stokes’ ‘Roof Shoes’.

B: As children, the divide between science, pseudoscience and plain nonsense was not as marked in our minds as it is now, but perhaps paradoxically the lines were more clearly drawn in public discourse. In his book The Demon-Haunted World, published in 1995, Carl Sagan wrote: ‘I have a foreboding of an America in my children’s or grandchildren’s time – when the United States is a service and information economy; when nearly all the key manufacturing industries have slipped away to other countries; when awesome technological powers are in the hands of a very few, and no one representing the public interest can even grasp the issues; when the people have lost the ability to set their own agendas or knowledgeably question those in authority; when, clutching our crystals and nervously consulting our horoscopes, our critical faculties in decline, unable to distinguish between what feels good and what’s true, we slide, almost without noticing, back into superstition and darkness.’

Sagan would have been horrified if his editor had said, ‘Carl, perhaps remove the grandchildren line…’

R: Having said that, to an inquisitive child in the 1970s, science was not only NASA and Einstein, but also Bigfoot and the Bermuda Triangle. When not leafing through David Attenborough’s Life on Earth, I might be reading The Unexplained magazine or Chariots of the Gods?, a book that didn’t ask if Neil Armstrong was an astronaut, but went further and asked if God was one.

The mind of a curious child was as open to questions of Bigfoot as it was of black holes; at that time, after all, the physical evidence for both was nil.

Made in 1967, the Patterson-Gimlin Bigfoot film was the Blair Witch Project of its time, the juddering graininess giving it a disconcerting authenticity. Why juddering graininess makes evidence more persuasive, I have no idea. It looks very like a biggish man in a gorilla costume wandering through a partially cleared woodland, but could it really be so simple?

According to the TV documentary, Chinese scientists had examined the footage and decided a man could not walk in such a lumbering manner. I myself have tried to walk in that way, both in and out of my gorilla costume, and I’ve found it surprisingly easy, but then, that might be evidence of a recessive Bigfoot gene revealing my family’s shameful Sasquatch dating past. Eventually, evidence-based investigation by author Greg Long revealed the truth of the Bigfoot film.

Retired labourer Bob Heironimus saw a documentary about the ‘Bigfoot hoax’ in 1998 and decided now was the time to own up that he was the human in the costume, bulked out by American-football shoulder pads and encased in a very smelly and claustrophobic mask that he had not enjoyed wearing at all. Those sceptical of scepticism may consider that this is a typical attempt by the National Parks Service to cover up their family of Bigfoots, but the next stage of investigation reveals the reason why you must avoid using anyone with a prosthetic eye when attempting to pull the wool over other people’s functioning eyes. The Bigfoot’s right eye reflects sunlight when looking at the camera because Bob had a glass eye. The sceptic sceptic may still declare, ‘but how do we know the Bigfoot has not developed glass-eye technology?’ and the mystery can continue if they’d like it to.

Still from the famous Patterson-Gimlin Bigfoot film made in North Carolina in October 1967.

Wilderness explorer C. Thomas Biscardi claimed to have captured Bigfoot on camera in northern California in 1981. He had been searching for the legendary ape-like creature for nearly a decade.

Another supposed ‘sighting’ of Bigfoot.

B: We recount this story for two reasons. One is to provide a glimpse into the confused and dusty book repository of Robin’s mind, where the windmills cannot turn freely because their mechanisms are clogged with VHS tape.

But it also illustrates what we hope The Infinite Monkey Cage is about; seeking evidence for working out why you believe what you believe and being open to changing your mind if the body of evidence leads to a different conclusion.

R: We currently live in a world where the quantity of information doubles with increasing speed. We can be overloaded by the extraneous. We can be misled by many groups and individuals who project the illusion of authority. For the open-minded and sceptical, the entire day can be lost just trying to work out if the front page of a newspaper is accurate. Dogma can be alluring when open-mindedness is so bewildering. It is troublesome to realise that nothing is 100 per cent right, but there are things which are the least-wrong version of events or ideas. Over the almost 100 episodes of The Infinite Monkey Cage we have recorded so far, we have tried as often as possible – whether dealing with race, climate change or cosmology – to demonstrate that the elasticity of an idea is determined by the evidence available. Where there is no evidence, you can stretch an idea as much as you want, but in this case the idea may be of little practical use and not one to inform your decisions.

Of the two of us, I am probably more sceptical when it comes to the views of scientists, though Brian may say that’s because I don’t understand the equations. We’ll explore some of our more incendiary stand-up rows later in the book.

B: I hope that Monkey Cage also goes a long way to erasing the myth that science is a cold endeavour, where humans with an emotional range that barely goes from A to B sit and count things and make graphs from the results and then state their discoveries with error bars in a monotone drone. As Albert Einstein wrote, ‘with logic we can go from A to B, with imagination we can go wherever we want.’ As many of our guests have demonstrated in their work, imagination and passion are vital to understanding. We need to maintain our childhood desire to keep pulling at the threads of our understanding: ‘But why? But why? But why?’

‘I want a liquid mirror on the dark side of the Moon please. Get one of the really massive craters, and have a really really massive telescope on the dark side of the Moon. Just think what you could do with that!’

Professor Catherine Heymans

Series 16, Episode 1 (3 July 2017)

R: In the radio series we hope to ignite or reignite people’s passions. We hope that people finish listening to each episode with a desire to know more and see more, to lie in the grass and look at the stars, to view Saturn’s rings through a telescope, to imagine hopeful possibilities for the future and ponder how to remove the obstacles to a better tomorrow.

When we started thinking about this book, we wanted to create an annual just like the Look and Learn annuals that excited us as children. This is not a book of conclusions, but it is, we hope, a book of benevolent spikes and spurs that will make you want to look more deeply into the subjects we cover.

Brian concludes: We are both fortunate to be in the position of making a living from being curious. From the evidence we have so far, it would seem we are a rare species; a species aware of itself and interested in its surroundings beyond the needs of survival. Our ambition is that, one day, this book will be casually discarded on a graphene table amongst the reading materials in the arrivals lounge on Mars.

The Mars Pathfinder mission was an important first step in rovers for NASA. A 1997 mission included the first successful rover on Mars, called Sojourner, which spent 83 days of a planned seven-day mission exploring the Martian terrain, acquiring images, and taking chemical, atmospheric and other measurements.

A QUESTION

Why is the programme called

The Infinite Monkey Cage?

Someone suggested we called it ‘Top Geek’. From that point onwards, we were determined to find an alternative by any means possible. ‘Top Geek’ suggested a show where Brian got overexcited to the point of Freudian excitation as he test-drove particle accelerators while wearing very tight jeans.

So I sat in a room in Levenshulme with an A4 pad and sought to escape my Richard Hammond fate by dreaming up every possible alternative, writing down every dismal proton pun or alliterative coupling of cosmology and comedy. From Fermat’s Penultimate Theorem via Einstein A-Go-Go to Cosmic Asides, the list was many and awful. Sometimes the key to writing is to put everything down, including the horrors that you might have to resort to if your brain doesn’t offer you something better.

Fortunately, I never got as far as Planckety Planck, Celebrity E=MC Squares or Custard Pi.

In fact I came up with ‘Infinite Monkey Cage’ quite early on. It was the Sasha’s idea to add ‘the’ at the beginning so that we became more definite – it is always useful in such an uncertain universe to find any way possible of making your existence more concrete, especially when so much of us is just empty space reliant on string forces.

I like thinking about infinity.

I hate thinking about infinity.

It gives me cosmological vertigo.

Apparently this was a new malaise of the late nineteenth century. With the Earth uncentred from the Universe, Darwin showing our familial proximity to chimpanzees and rapidly increasing technological advances, the magnitude of it all became dizzying. So much so that this was given as one of the reasons why Gauguin went to Tahiti and pretended that all its female inhabitants were topless for most of the day.

I can’t remember when I first found out about infinity, but it made me wobble every time I thought about it. I would imagine the Universe had existed forever and I would start to topple. I would imagine travelling in a straight line in my pencil-drawn rocket ship and seeing no end in sight.

Eventually I was saved by hearing about the Big Bang, which put the whole idea of infinity into some perspective. At least our universe was now imaginably unimaginably vast.

But then I heard rumours that even with the Big Bang there was still room for a universe of an infinite size with all its associated ramifications. While thinking about that and watching the buses passing through Levenshulme, I thought of all those monkeys writing Macbeth or Titus Andronicus, as well as Fifty Shades of Grey, Delia Smith’s Cooking for One, the bus timetable for the Number 63 from East Dulwich to King’s Cross and all the works of L. Ron Hubbard. I had always been told that an infinite number of monkeys will eventually write the works of Shakespeare, but a jovial and intense mathematician informed me that they won’t eventually write the works of only Shakespeare, they will immediately write the works of Shakespeare and Milton and Dante and Chaucer and Ursula K. Le Guin, and every issue of 2000AD, Reader’s Digest and all the titles in the Mills & Boon collection.

I was wobbly again.

This infinity sure seemed big.

So I thought of a cage so big that it contained an infinite number of monkeys – and mused over whether that could even be a cage – and I imagined it as a flippant description of a vast universe. As we were hoping our new show would find time (if time exists) to cover everything in the known universe at least, this seemed like a lightly enigmatic title.

I came up with ‘Infinite Monkey Cage’ quite early on. It was Sasha’s idea to add ‘the’ at the beginning so that we became more definite – it is always useful in such an uncertain universe to find any way possible of making your existence more concrete, especially when so much of us is just empty space reliant on string forces.

It is an interesting question as to whether the ‘The’ at the beginning of The Infinite Monkey Cage is necessary. If we assume that the monkey cage in question is our universe, some important cosmological caveats are in order. Firstly, we do not know whether the Universe is infinite. We can only say that there is more of it than we can see. The part we can see is called the Observable Universe, and it currently contains around 2 trillion galaxies; not an infinite amount of territory for monkeys, but quite roomy. The number of accessible galaxies is falling, however, because we live in an expanding universe. As space stretches, the distance between galaxies that are not bound together by gravity increases. In a few tens of billions of years, the distance to most of the galaxies we see today will be increasing so fast that the light emitted from them will no longer be able to reach us, and conversely we will never be able to reach them. Their images will fade and redden until they are no longer visible. In the far future, the Universe we see through our telescopes will consist entirely of our local group of 50 or so galaxies, which will most likely have merged into a single super-galaxy. Beyond, there will be only darkness. Unless textbooks survive from the distant past, the cosmologists of the future will find it impossible to imagine the scale of the Universe beyond their horizon, or indeed have any inkling that such a thing exists. The accessible part of the cage will consist of a single galaxy, surrounded by a great all-encompassing void.

Secondly, the question arises as to whether there can be more than one infinite cage. It seems that there should only be room for one, but that is not necessarily the case. As we’ll see in the section that discusses Hilbert’s Grand Hotel, infinity is a slippery subject. There is a cosmological theory known as eternal inflation which leads to the idea of an inflationary multiverse. Our universe could be a single ‘bubble’ universe amongst an infinite sea of universes, each with potentially different low-energy laws of nature. Some may contain monkeys, others may not. Grammatically speaking, then, if our reality is really the multiverse of eternal inflation, the prefix ‘The’ may be necessary if we intend to refer to our specific monkey cage, rather than the infinitely many monkey cages that may exist.

From our first episode, we started to get emails and letters with listeners’ conjecture on what exactly was meant by an infinite monkey cage. This was on top of the complaint we received from an angry animal rights activist who wrote that ‘yet again, the BBC is celebrating animal cruelty and vivisection. Who spends their time imagining monkeys crammed in a cage?’ We wrote back to explain that an infinite monkey cage is roomy. We heard nothing more.

By week three, we were receiving letters complaining that the show was another of those arrogant shows that thinks you can prove anything with evidence and that the very title was based on a lie.

‘The idea that an infinite number of monkeys would write the works of Shakespeare is rubbish, as a recent experiment has proved.’

This was exciting news. A maverick scientist had gathered together an infinite number of monkeys? Surely we would have heard. It’s hard to be surreptitious with an infinite number of monkeys. It’s the noise and the smell.

Sadly, the experiment was somewhat smaller. One typewriter and six monkeys at Paignton Zoo. After a month, they had broken the typewriter and done a poo in it, and not so much as a disembowelling scene from Titus Andronicus was found. We attempted to explain that six monkeys really wasn’t enough, it was too far from an infinite number of monkeys – but to no avail. The correspondent was certain that at the very least it would be an accumulating system:

10 monkeys = a leaflet on banana safety.

100 monkeys = an article for GQ on aftershave.

1000 monkeys = a simian version of 50 Shades of Grey (Langur).

Just as with the complainant who was annoyed that we had no ghosts on the panel for our show, eventually the fury faded into an email memory, to be archived and trashed when in need of a new memory.

INFINITY

‘Infinity always gives me the urge to scratch my head. Perhaps it’s a rash. I worry about infinity,

it is much bigger than my brain.’

Professor Carlos Frenk

Series 10, Episode 5 (5 August 2014)

First, let us convince ourselves that the concept of infinity makes sense. Consider adding an infinite number of numbers together:

This is called a geometric series. At first sight, you might guess that adding an infinite series of numbers together one after the other, forever, should lead to an infinitely large number, but this isn’t necessarily the case. For this particular series, the result of adding them all up is 1. You can see this by using a little simple algebra.

Let’s call the sum of this series S:

Now consider a different series; the original one, but with each term divided by 2:

Now subtract S/2 from S. Every term in the series disappears except the first term in S:

Adding an infinite series of numbers together is something that we can do, at least in this example, and get a finite answer.

The type of infinity we’re thinking about here is an infinite set of fractions; ½, ¼, ⅛, and so on. How many of these fractions are there? An infinite number, and we assumed this in our proof because for every fraction in the infinite series S, other than ½, there was a corresponding fraction in the infinite series S/2 to cancel it out. But this raises an interesting question. We subtracted an infinite number of fractions from an infinite number of fractions and we had one term left: ½. Does this mean that there was one more fraction in S than in S/2? The answer is no; the two infinites are precisely the same. The first mathematician to think about what we mean when we speak of an infinite set of numbers was the German mathematician Georg Cantor, at the end of the nineteenth century.

Consider, for example, the set of all integers; 1,2,3,4 … We could imagine making a table of the integers by writing them all down in a vertical column from 1 to infinity. We could then write each of the terms in our set S alongside in a neighbouring vertical column. Each fraction – ½, ¼, ⅛ – would be paired up with an integer, all the way down the list. We could do the same for our set S/2; the column would begin with ¼ rather than ½, but it would carry on all the way to infinity. This one-to-one correspondence between all three sets of numbers is the reason why Cantor claimed that the three sets have the same ‘infinity’ of numbers contained within them. Mathematicians would say that the sets have the same cardinality.

There is certainly something odd about these infinite sets, because they don’t behave as we might expect. Notice, for example, that the set S/2 is a subset of S, because S contains every entry in S/2, but it also contains ½. And yet S and S/2 are the same size! This counter-intuitive nature of infinite sets led to one of the great Infinite Monkey Cage arguments that took place between Brian and comedy producer John Lloyd in the form of Hilbert’s Grand Hotel paradox.

John Lloyd: Infinity plus one is just intellectual brain bending and I cannot see the use of it. Infinity is a word. That belongs to the wordy people like me and Robin. The point is you cannot place a numerical value to infinity and therefore you cannot add a plus one to it or a minus one.

Brian: There are either an infinite number of numbers or there aren’t. I don’t see what the problem is?

John: There aren’t an infinite number of numbers, because you can always have more than infinity and so infinity is a meaningless concept.

Series 9, Episode 4 (9 December 2013)

Hilbert’s Grand Hotel has infinitely many rooms, and they are all occupied. What happens if a further guest turns up unannounced? The guest in Room 1 can be moved into Room 2, the guest in Room 2 can be moved into Room 3, and so on, freeing up Room 1 for the new guest. There is always room in Hilbert’s Grand Hotel, even when it is full. We haven’t increased the size of the hotel, and yet we’ve accommodated another guest. Using the language above, we can say that the cardinality of the set of rooms in Hilbert’s Grand Hotel is the same as the cardinality of the set of guests. Notice that this implies that we can slot an infinite number of extra guests into Hilbert’s Grand Hotel, even when it is full. To see this, note that we could have moved the guest in Room 1 to Room 2, the guest in Room 2 to Room 4, the guest in Room 3 to Room 6, and so on. This frees up ALL the odd-numbered rooms, and since there are an infinite number of odd numbers, the Grand Hotel can now accommodate an infinite number of new guests. The reason for this strange state of affairs is that the number of odd rooms is not smaller than the number of even + odd rooms. Both sets have the same cardinality.

Figure 1

As an aside, there are sets with a different cardinality to the integers. Consider, for example, the set of infinite binary sequences; 0000000000…, 1111111111…, 0101010101… and so on. Cantor imagined laying these out in a vertical table, just as we did for our sets S and S/2, against the column of integers. Now imagine constructing a new binary sequence by changing all the digits in a diagonal line down the table; when there is a 1, swap it for a 0, and when there is a 0, swap it for a 1 (see Figure 1). The resulting sequence is not in the table; it can’t be the same as the sequence in the first row because the first digit has been flipped. It can’t be the same as the sequence in the second row because the second digit has been flipped, and so on. Every row will differ from the new sequence by at least one digit, claimed Cantor, because there are more infinite sequences of 1s and 0s than there are integers. A mathematician would say that the infinite set of binary sequences has a cardinality greater than the set of integers.

Infinity exists in mathematics, and as we have seen there are different sorts of infinity. We might ask whether there are infinities in the real world, and the answer is that we don’t know. The Universe may or may not be infinite in extent. The part of the Universe we can observe is certainly finite, and cosmologists refer to this as the Observable Universe. The most distant objects we can see are objects from which light has been able to travel during 13.8 billion years, which is the age of the Universe. You might be tempted to say that the Observable Universe is 27.6 billion light years across, but this is not correct because the Universe has been expanding throughout this time, and the objects have receded from us. Because we know how much the Universe has expanded, we can calculate the diameter of the Observable Universe today; it is just over 93 billion light years.

There are around 2 trillion galaxies in this observable sphere centred on the Earth, but this is very likely to be a small fraction of the entire Monkey Cage. Whether it is a finite subset of an infinite cage is an open question.