READ WITH CAUTION: This Story Will Keep You Awake at Night

Hear me now and hear me well! The following story – an account of many things paradoxical, a muse on the very existence of space and time as we know it, a pondering of the mysteries of life which may never be solved – will keep you awake at night. Turn back now else face endless head scratching and mayhap even stare down the very path to madness.

Ye have been warned. Don’t you remember? I wrote a story a few weeks ago with a title begging all of you not to read it, and yet it’s my most read story…

So I suppose the warning is useless then.

Still here? Very well! Come with me as we journey through the complexities of the human mind and the universe beyond!

Many years ago, I worked with a man who told me a joke. The joke was terrible. And it changed my life.

It went something like this:

An infinite amount of mathematicians walk into a bar. The first one says: “Can I have a pint of beer please?” The second says: “Can I have half a pint of beer please?” The third says: “Can I have a quarter of a pint of beer please?” The barman says: “I’ll stop you there,” and simply serves two pints of beer.

At the time, I had eagerly awaited the punchline, before being told that the punchline was that the barman would simply serve the two pints.

‘But two pints wouldn’t be enough for an infinite amount of customers!’ I had cried.

‘Yes it would,’ Steve (the jokester) had said. He had a smug look on his face. The kind you wanted to slap off. ‘If the volume keeps halving, the second pint glass would never fill, so they'd have more than enough. It’s simple maths.’

‘But…’ I’d stammered. ‘But it would! If you kept adding to it, surely eventually it will fill up!’

Steve just continued to smirk, and added in a good amount of eye-rolling and head-shaking at my constant claims that that pint glass would eventually fill up, and in fact spill over.

Alright, I hear you. I have this unique way of sneaking into my readers’ thoughts. And you there, yes you. You’re thinking I’m wrong. Mathematically, if the amount the barman filled into that one pint glass kept on halving (and assuming the customers could take such tiny and precise sips and didn’t mind sharing their glass), the total volume of the liquid would in fact never reach the top of the glass, and the infinite number of mathematicians would be satisfied. I’m the idiot, there’s no way I can prove to you otherwise and you’re about to click off of this story and go and do something much more worthwhile with your time.

But wait. I promise you – actually I guarantee – that I can change your mind. And by the end of this story, you’ll be left awake tonight staring at the ceiling and questioning existence itself.

But before that, let’s rewind my story a little. You’ll like this, I swear.

I once worked at a hotel. Beautiful place, and totally unique. You’ve probably heard of it. It was the Hilbert Hotel (Google it). The Hilbert Hotel is the infinite hotel. It has an infinite number of rooms and can accommodate an infinite number of guests.

Supposedly.

You see, there are a few problems with this, and they highlight the problem with the concept of infinity. And ultimately, it will be the first of my evidence for why that damn pint glass would eventually spill over.

On my very first night at the Hilbert Hotel, an infinite number of guests came to check in.

I sniggered. I looked at my manager, David, who had begun to sweat a little.

‘What are we going to do then?’ I asked him.

He took a deep breath in and then chuckled a little. ‘Don’t you worry, lad! The entire concept of infinity might be a little tricky for our human minds to fully understand, but as there are an infinite number of rooms in this hotel and an infinite number of folk outside demanding a room, we shall be able to accommodate them.’

‘How?’ I asked, intrigued as to how on earth David was about to manage this.

‘Well…’ he returned. ‘It's just like having ten rooms and ten guests, isn't it? When we’ve got all of these people into their rooms, the infinite hotel will be… full.’

Full? I thought then. Full!? How could an infinite hotel be full?

But I watched on as an endless stream of guests made their way into the hotel. They were quick enough, walking by Rosie, another of the hotel attendants who held out their room key to them, looking at their room number and prancing on their merry way.

‘Come with me, lad,’ David said. He put an arm around me and explained that however it was possible for an infinite number of people to pass by before our very eyes, it indeed wasn’t for our very eyes. ‘Let’s just go through to this room here for a minute, and when we come back, the infinite number of people will have hopefully gotten to their rooms.’

And he was right. When we arrived back in the lobby, the infinite amount of pegs which usually held the infinite amount of keys… were empty.

‘But…’ I stammered. ‘How… that doesn’t make any…’

David simply patted me on the back and chuckled. ‘Ah, my boy! The mysteries of the universe are beyond the realms of our simple and human minds. How about a cup of tea, eh?’

‘Sir!’ Rosie interrupted. She’d just hung up the telephone. Her face had gone as pale as an infinite mathemetician who had received his drink and found that there weren't an infinite amount of seats in the bar. ‘We’ve erm… we’ve got a slight problem.’

‘What is it?’ David asked calmly, although I thought I did detect a slight tone of worry in his voice.

‘A gentleman just called,’ Rosie said. ‘He’d like a room. How on earth will we manage? I’ve just given all the infinite keys away!’

David didn’t worry. He simply chuckled again and walked calmly over to the hotel’s Tannoy system. He pressed the button down before making a request in his most charming voice.

‘Ladies and gentlemen, this is the hotel manager. Thank you for choosing the Hilbert Hotel, where we aim to please you infinitely. If I could make a small request – could each guest please move to the room number one above where you currently are? That would help us make room for another guest. Thank you!’

Almost automatically, I heard the infinite doors of the hotel swing open, a pounding of an infinite number of footsteps, and the swinging closed of an infinite (minus one) number of doors.

(This begs the question... what exactly is infinity minus one? Ah, on with the story!)

The new guest arrived shortly afterwards and was happy to move into room #1. The day was saved, and for the second time that day, the infinite hotel was full.

‘Genius!’ I spat out then. ‘Outstanding, Sir! But it still doesn’t make much sense to me…’

I was interrupted by Rosie once more, who slammed down the telephone she’d just been talking into, and looked at David and I with sheer horror on her face.

‘What’s wrong?’ David asked her.

‘There’s a bus coming,’ Rosie said.

‘What kind of bus?’

‘A big one.’

‘How big?’

‘Infinitely big.’

‘Infinitely big?’

‘Yes Sir, it’s an infinitely long bus with an infinite amount of seats.’

‘Well, who’s in it?’

‘An infinite amount of people.’

‘An infinite amount of people?’

‘Yes Sir. Plus the driver. And they’d all like a room.’

‘Well, call them back! Tell them we’re full!’

‘Well, that’s the thing, Sir.’

‘What’s the thing?’

‘We’re an infinite hotel. With infinite rooms. And you placed that advert on the TV, remember? You said you had an infinite amount of money and could place an infinite amount of adverts.’

‘Yes, yes. What of it?’

‘Well, Sir. You have an infinite amount of people who have seen an infinite amount of adverts infinitely promising them that you have infinite rooms at your infinite hotel… what do you suppose will happen if they all think they’ve been lied to?’

‘Good God!’ David gasped. ‘An infinite number of lawsuits! It’ll cripple the business indefinitely!’

‘What can we do!?’ Rosie cried.

‘Think… think… think…’ David mused while pacing.

‘I know what we can do,’ I piped up here. To me, the answer was obvious.

‘Well, boy!’ David cried. ‘Tell me! Tell me what we can do to solve this impossible situation!’

‘Can I use the Tannoy?’ I asked. I’d always wanted to. Here was my chance! David looked at me with suspicion, but just then, the infinite bus pulled into the car park, its door opened and David motioned a hand to me, inviting me over to the speaker.

‘Yes, yes! Be quick, boy! Quick!’

I pushed the button and cleared my throat.

‘Ladies and gentlemen, thank you for choosing the… erm… Hilton – no! Sorry, the Hilbert Hotel. Uh… we have a somewhat unusual problem and we’d like to make one last request of our guests today. Could each of you please move to the nearest room of the first even number up from yours? This will help us immensely. Infinitely, you might say! Haha… erm… thank you.’

‘Outstanding thinking!’ David beamed. ‘Remarkable! You’ve saved the day, my boy! Now we just need to make sure we move each of these guests on that damn infinite bus into all the odd-numbered rooms!’

And they did. They all strolled in, one by one, taking their key with a smile from Rosie before marching into the infinite corridor and into their room. And after a quick stroll in and out of the lobby, for the third time that day, the infinite hotel was fully booked.

But I knew then what I know now. The same thing you’re thinking as you read this. All of this is simply impossible! How could we have two sets of infinite numbers of people come into the hotel? And that other chap, the one who came by himself, if he left would there still be an infinite number of people in the hotel as there was before he arrived?

At the time, I thought of it this way – whatever mystical and magical force was able to make that hotel with its infinite number of rooms, could well have made the rooms with people already in them. What happens then, when that infinite bus arrives with infinite people looking for rooms? Has the Hilbert Hotel with its infinite rooms... run out of rooms? Could it be that there are two (or more) different types of infinity?

It’s a head-scratcher, I know.

Except it isn’t. And let me tell you why. But before that, allow me to tell you how I quit my job at the Hilbert Hotel. It happened only three seconds after that infinite bus arrived.

‘Sir! Sir!!’

Rosie slammed the telephone down once more. Now she looked as though she'd swallowed an infinite amount of hamsters.

‘What is it?’ David asked, calmly. ‘Surely there cannot be any problem that we can’t solve now!’

‘I wouldn’t be too sure…’ Rosie said. Her voice was shaking.

‘Well, what is it?’ David asked. ‘What’s the problem?’

‘More buses are coming,’ Rosie said.

‘Buses?’ David spat. ‘Plural? Well, how many?’

‘An infinite number.’

As soon as David’s eyes turned to me, I told him I quit.

***

Before we get back to Steve and his pint glass theory, I want to share some musings with you that will help you to understand how I defeated my nemesis (oh yes, spoiler alert, I will indeed defeat Steve in this story).

Here’s something I always thought of, ever since I was a child. Was there ever a beginning of time? Hear me out! That sounds a bit silly, or a bit science-fictionish, I know.

Of course these wasn’t a beginning of time! Time just runs, and that’s it.

Alright, so if we had some sort of cosmic video recorder that had been recording for all of time and we pressed rewind on that video… it would never stop? It would just rewind forever? Because time is infinite, both ways? Then how did we arrive here, at this point in time, with you reading my story?

So then, there must have been a beginning to time! But there couldn’t be! Because what was before time? There couldn’t be anything before time! How would time have begun if there wasn’t anything there to start it?

Here’s a theory. Don’t laugh at it, because it’s a proper scientific theory.

Time doesn’t exist.

It’s an illusion of sorts. Something our feeble minds do to try and make sense of the unfathomably complex universe around us.

Sound nutty? Consider this:

We have no accurate way of measuring this thing we call time. Clocks? Ha! Haven't you noticed they always eventually go off by a few minutes? Digital clocks that aren’t connected to the internet? Same story. Clocks that are connected to the internet?

Same. Story.

The internet adjusts the time all the… well, time.

And what are we actually measuring when we examine what time it is? How long before one event happened did the next thing occur? What if the whole universe just…

Stopped.

…?

Everything stopped moving. But it was all still conscious, somehow. Would time still exist then?

We only ever measure physical changes when we measure time. So, does it exist if none of us can actually measure it or even describe exactly what it is?

I guess what I'm saying, is that for infinity to exist, time and/or space must exist, because the concept of infinity can exist only within the concepts of time or space. However, if we can't prove infinity, how can we prove time or space?

So time might not exist. But I put it to you, reader, that space doesn’t exist either. And by the end of this story, you’ll either agree with me…

Or be wrong.

***

Alright, let’s get back to Steve. Because you’re dying to know, aren’t you? You’re dying to know how I defeated my nemesis and what my proof is. My proof that that pint glass would spill over.

Well, I slapped him. In the face.

You didn’t expect that did you? But read on! Because this is my proof.

‘You… you just slapped me!’ Steve stuttered.

‘Did I?’ I asked, with a grin. ‘Are you sure?’

‘I’m telling Gemma!’

Gemma was our manager. Sure enough, he ran to her office and I was called in to discuss the matter a few minutes later.

‘Steve said you slapped him!’ Gemma fumed. ‘In the face! I’m very sorry, but we cannot and will not tolerate that here, so I’m afraid I’ll have to fire you.’

‘That’s fine,’ I said. ‘I’ll accept a firing. If Steve is sure I slapped him.’

‘I am!’ Steve cried. ‘I’m very sure!’

‘Are you?’ I asked, turning to face him. ‘Are you really? Because if you’re sure I slapped you then you’re also sure that that pint glass would have spilled over.’

‘What’s this?’ Gemma asked. ‘Pint glass?’

‘Oh…’ Steve said. ‘It’s erm… it’s nothing really, it’s…’

‘For me to have slapped you,’ I interrupted. ‘My hand would have had to have travelled from where it was to your face, wouldn’t it?’

Steve screwed his face up quizzically and nodded. ‘Well, yeah, of course…’

‘It would have had to have travelled one hundred per cent of the way to your face, yes?’

‘Well… yeah, of course, but…’

‘But for it to travel one hundred per cent of the way to your face, it would have to first have travelled fifty per cent of the way there, wouldn’t it?’

‘I don’t see what this has got to do with…’ Steve blurted.

‘And,’ I interrupted. ‘For it to have travelled fifty per cent, it would have had to have travelled fifty per cent of that fifty per cent. And also fifty per cent of that one. And that one. And that one.’

Both Steve and Gemma looked completely bemused, but neither of them spoke now.

‘You could say that this distance always halves. Infinitely, yes? Into tiny fractions imperceivable to the human eye or mind. But mathematically, it’s what must happen for my hand to reach your face. According to maths, and to your theory about that pint glass never filling, my hand did not reach your face and I never slapped you. Unless I’m right about that pint glass, of course?’

Steve stood for a moment, staring at the wall. He looked as though he was about to vomit, and I thought he was because he opened his mouth, but all that came out were six glorious words.

‘I guess he never slapped me.’