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‘Because you have to. Okay? If you didn’t trust me, you wouldn’t have followed me out of the hospital. Now, I will come and see you tomorrow. Do you have food and drink in the house?’

I nodded and squinted in the heat. It was really hot. The kind of day you could feel your skin cooking in real time.

‘Good. Stay. Just to be safe.’

‘Safe from what?’

I thought he was going to enlighten me. But he didn’t. He just said: ‘Safe from yourself.’

‘Why? What will I do to myself?’

‘You have been given talents that you are not yet adjusted to. This is a dangerous time for you. Anything could happen. But I will come and see you tomorrow.’

‘I don’t want you to come tomorrow.’

What I really meant was: I want things to be normal. I wanted to subtract every new addition. Including Alberto. I was, in short, more than a little frightened. And my response in fear was denial.

He handed me a scrap of paper with a number scrawled over it. ‘For when you change your mind.’ Not if, but when.

And then he drove away, and I stared up at the billboard of the Eighth Wonder resort and the little inset photograph of an immaculate hotel room. It looked perfect, but its perfection now troubled me. I wondered why it bothered me, when I had so much else to come to terms with. But it did. Just until I turned my back to head indoors.





The Infinite Hotel

When my old maths tutor Mr Sole told me there was something bigger than infinity I laughed. Then he gave me a thought experiment which helped explain Set Theory. I probably spoke about it in maths. The one about the hotel that the long dead German genius David Hilbert came up with as a way of explaining what Cantor was on about with his transfinite numbers. The one that has blown several minds to oblivion. That is childishly simple and devilishly complex all at once. It basically proves that a true infinity can’t really be grasped. It goes something like this:

Imagine a hotel of infinite rooms. Each room has a number, as hotels normally do. Room 1, Room 2, Room 3, Room 4…On and on and on and on for ever. Imagine now that every single one of these rooms is full. That’s right. It’s a popular hotel. An infinite number of people have filled an infinite number of rooms. Now, someone new arrives at the hotel. Let’s call her Marjorie. She is tired. She has had a long flight. Her legs hurt. Her veins are playing up. She needs a room.

Now, what does the hotel receptionist tell her? He can hardly say that the Infinite Hotel has no more rooms, can he? Marjorie could get on TripAdvisor and take the place down. CALLS ITSELF THE INFINITE HOTEL???????!!!!! MORE LIKE THE FINITE HOTEL!!!!!! WHAT A JOKE!! (One star.)

No. The receptionist budges everyone up a room. So the guy in Room 1 moves into Room 2 and the honeymooners in Room 2 hop next door to Room 3. Okay, it’s not the best system, but just go with it. Anyway, the end result is that Marjorie gets her room and everyone else still has a room. So, the hotel is now infinity plus one:

∞ + 1 = the hotel

The original hotel wasn’t large enough so there were limits to its infinity. But then what if more people came along? What if another infinity of people came along in an infinite aeroplane and had an infinite number of taxis pick them up to transfer them from the airport? Then we’d have:

∞ + ∞ + 1 = the hotel

Bottom line: infinity comes in sets. There can be a bigger infinity. Infinity can be doubled and trebled and quadrupled and quintupled, etc. There can be an infinity of infinities. Even without any new guests at all the Infinite Hotel had different sizes of infinities. An infinite hotel surely has an infinite number of odd numbers, but it also has an infinite number of even numbers, and in any hotel the total number of rooms is larger than the total number of odd (or even) numbers on their own. You really can go beyond infinity. Buzz Lightyear was the secret genius in Toy Story.

Why do I keep talking about this? Because it is frightening how quickly a belief system can change. And because believing in extra-terrestrial life on Earth was beyond infinity for me. When you get to my age, you feel like you have nothing major left to learn. You have accumulated all the knowledge that can serve you. Your hotel is full. I had reached the limits. And I simply wasn’t ready for that extra room. And it was an earthquake inside me, only comparable with grief. But grief was the death of a person, this was the death of everything I had considered reality. And when you get older, as you wrote in the letter, it becomes harder to break patterns. So I was in the rubble. I had no idea who I was or what world I was living in. I felt reborn. And like every new baby I wanted to cry. Or scream.





The Peculiarities

I wandered around the small house.

Unusually for me I didn’t need to sit down every two minutes. I had energy. But though I felt reborn, I wasn’t really – there were still enough dull aches and quiet creaks to make me understand I was still in my seventies – but I was more alert and alive than I had been in years.

This is a dangerous time for you.

I switched on the television to try to shake Alberto out of my mind. I found a news channel in English. The reporter was one I had never seen before but I somehow knew he was in the middle of a divorce. He was talking about forest fires thousands of miles away.

It was upsetting news, sure, but the kind I’d seen hundreds of times before, which I’d normally gawp at like another piece of bleak twenty-first-century moving wallpaper. But this time, as I stared at the yellow diggers and logs stripped of their branches, I felt an unprecedented nausea that caused me to gag. I had a strange queasy hunger sensation, and my mouth was suddenly filling with saliva. It was as if someone had just forced me to eat soap. I switched off the TV and rushed to the tiny mildew-speckled bathroom and retched over the sink.

I was actually sick.

Not from anything I had eaten but simply from watching the news, as if the devastated landscape I had just witnessed on the screen had provoked a direct internal reaction. Unlike at home, I had no mouthwash here to rinse away the taste. I brushed my teeth.

I am sorry. I should have warned you before saying all that. But after I was sick, I felt fine and healthy again.

Then another peculiarity happened. I noticed the cars going by on the road all had their own sounds. I was never into cars. My son Daniel when he was about five could differentiate between different car headlights. Even in the dark he knew the cars when we were driving back from his grandmother’s house. ‘Ford Cortina,’ he’d mutter from the back seat, in a kind of trance. ‘Vauxhall Cavalier…Metro…Ford Sierra…’

I couldn’t identify every model in the way Daniel could have done, but I pictured every car. Just from the sound. Right down to the shape and colour.

I don’t even know if it was actually from the sound. It might be best explained as a feeling of déjà vu. But in reverse.

So I looked out of the window and thought yellow car and sure enough the next car that passed the window would be yellow. Blue car. Blue car. White taxi. White taxi. Large gleaming red-and-yellow bus. Large gleaming red-and-yellow bus. It was very, very odd and very, very far beyond anything that I could explain. And then I felt a little thirsty. So I went to the fridge and pulled out the bottle of orange juice. That makes it sound like a normal thing. But this wasn’t a normal thing. This was a very unusual thing. In fact, it was so unusual I think I will give it its own chapter.





The Infinite Pleasure of Orange Juice

I took a few gulps and closed my eyes, as committed as a wolf howling to the moon. I have drunk orange juice for most of my seventy-two years – and even freshly squeezed orange juice on many occasions – but I can honestly say that I have never really noticed it. Orange juice was the water of fruit juices, I used to feel. It kind of just existed. Part of that same category of food that includes vanilla ice cream and tea-and-toast that was perfectly lovely in a neutral, take-it-for-granted kind of way.

But this was different. This was the most wonderful drink I had ever tasted. The competing but perfectly balanced sweetness and bitterness was as complex as the finest Zinfandel. I savoured every mouthful. I ended up finishing the whole bottle.

The odd thing was that the last time I’d drunk it, it had been nice but perfectly forgettable orange juice. Now, it was ambrosia from the gods. It felt like the whole purpose of life was just to enjoy the experience of pouring a liquid extraction from the vesicles of a divine citrus fruit into my mouth. Immense relief and release. Even more quenching than that feeling as a child, after playing tennis with my old friend Sarah in the heat of July, of glugging a full glass of water.

That orange juice was, quite simply, the very best thing I had ever tasted.

‘That was enjoyable,’ I told myself, out loud, because it felt so important that it needed to be voiced.

Are sens

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