THE IRRATIONAL DIARY OF CLARA VALENTINE

THE IRRATIONAL DIARY OF CLARA VALENTINE

THE IRRATIONAL DIARY OF CLARA VALENTINE

Coralie Colmez

Coco Publishing

Copyright © 2022 by Coralie Colmez

You can reproduce and distribute as much as you want of this book as long as you credit it to me and do not make money from it. A free pdf is available on my website: www.coraliecolmez.com

Paperback: 978-1-3999-2221-0 

Ebook: 978-1-3999-2222-7 

First printing, 2022

Coco Publishing

To all the girls who love maths

Contents

How It Started

1 Number of Pairs in a Set

2 The Birthday Problem

3 RSA Encryption

4 The Hilbert Hotel Paradox

5 Sizes of Infinity… Plus Some Irrationality!

6 Liars and Truth-Tellers

7 The One-Time Pad Code

8 Fibonacci Numbers

How It Started

Thursday 6th October

Ok, here I go – I’m starting a diary. Because something totally amazing happened today and I can’t tell anyone. I can’t even tell M! I. Can’t. Tell M. Do you know when was the last time I didn’t tell M something? Never, that’s when!

She knows what's happened in my day a maximum of 75 seconds after I know about it. I notify her when I’m about to buy another 90s mesh top on Depop (so she can rein in my habit, but actually she always says I should do it), or when I've found a new show I like (so we can watch at the same time). I tell her what I’m having for dinner every day. I even text her my dreams in the morning, which is notably frowned on in most friendships but actually encouraged in ours. How can I keep something from her? I’ve already had to stop my fingers from phoning her without consulting me at least eight times. So for now, this is my solution – I’ll write it all down in here and hopefully that’ll be enough to keep me from blurting it out.

It’s so strange to think that when I woke up this morning, I had no idea that this day would turn out to be anything other than normal – worse than normal, dreary, even. I woke up to my alarm ringing just as I was having a dream that I was getting into bed, so that set the tone for the day. I dragged myself to school feeling just about exactly as if I hadn’t slept the whole night. I arrived with one minute to spare, only to be treated to the classic assembly speech about how we are the worst-behaved students the teachers have experienced in the entirety of their formidably long careers. Invigorating stuff.

I can’t believe it’s been only four weeks since the start of this school year. Everyone is already grey and haggard – you know, the February look. Except it’s October. Summer holidays are but a distant memory, and they weren’t even that great. Back in August, I was almost – almost! – excited for them to be over, and to be back in London with everyone. What was I thinking?

Well – I guess that what I was thinking was that this year would be like last year. I’d go to the park with M after school every day, and spend weekends watching movies featuring Leo back when he was still cute and trying out random alcohol combinations from the parental cupboards of whoever was hosting. I was forgetting that we’re applying to uni this year. Our teachers seem to believe that this means we are no longer allowed the basic human right of time in the day to feed ourselves and sleep. Instead, we are to spend every minute doing homework and finding ever more creative ways to massage our most minute life experiences into impressive-sounding achievements for our personal statements.

I was in a medium-to-bad mood all day, getting progressively worse as the hours dragged on. My last period was Further Maths. I sat next to Sayid, who was completely immune to the don’t-talk-to-me vibes I was emitting and kept chatting happily about his mother’s friend’s cousin’s wedding this weekend where there will apparently be an assortment of fit girls to meet.

When the bell rang I walked out quickly, rubbing my temples – the whole day had given me a headache. Outside was a light-less grey and drizzling mildly. The weather so closely represented my mood it was as if I had conjured it. All this to say that I was absolutely not prepared for the extraordinary thing that happened next.

I walked out of the door and in the corner of my eye I spotted Ty waiting to one side, looking all kinds of shades of gorgeous, his hair getting adorably curly in the rain. He was wearing all black – faded carpenter jeans, a soft T-shirt and a denim jacket. Unconsciously, I put my hands up to my own hair and confirmed what I already knew – rather than adorable curls, I was developing horrific frizz.

I gave Ty a tiny wave, wondering what he was doing there. And then – like we were in a film – he started walking towards me, so slowly and deliberately that it felt like the world was playing at half-speed. I was fixed to my spot, wondering if I was making a fool of myself and imagining things and he would turn out to be greeting someone behind me, but he walked right up to me, super close, close enough that when he talked in a low near-whisper I could hear every word as clear as the raindrops around us.

He opened his lips and they said, ‘Clara, I need your help.’

1

Number of Pairs in a Set

Thursday 6th October – starting again

Wait, let’s rewind a bit. I think we need some context – you know, for when people are looking over these to publish them after my death because I’ve become super famous and important. We can’t have anyone wondering, Who is M? Who is Ty? What is a personal statement? (Because by then statements won’t be a thing anymore as unis will have realised they are pointless. Can you tell mine is going great?)

So let’s go back to this morning. On Thursdays, I start with Physics. That’s followed by two hours of Maths with Mr Howard. Mr Howard is one of those teachers who I won't feel horrified at bumping into in the street a few years from now. He’s young – Dad says, ‘Who’s the child teaching you?’ He makes jokes. Occasionally they are funny. The best thing about Maths is that Mr Howard doesn’t make a seating plan, which means M and I can sit next to each other in our favourite seats, all the way at the back of the class.

I slumped down in my seat, in the aforementioned bad mood, and M did the same.

M: Bad morning?

Me: Not great. You?

M: … [a groan]

Me: What happened?

M: News depression.

Me: Ah. Is it the story about how more young people are unemployed than ever before?

M: It’s the whale with the plastic bags in its stomach. But thanks, now I can be depressed about unemployment too.

Me: Sorry. I saw the whale news, it’s so sad.

M: I read it this morning, as I was staring at the plastic bag that I used just last night to carry Maltesers and grapes home. I’m a monster.

Me: You’re not a monster.

M: I am though. Why did I get a plastic bag? I didn’t need one! I could have carried everything in my hands! I am personally responsible for that story.

Me: You haven’t used straws for years though. So you’ve saved lots of turtles.

M: Whatever. I killed a whale.

Me: You got us reusable coffee cups too, so that’s even more saved turtles. We’re probably reaching a whale-sized amount of turtles by now.

M: Ok…

Me: Ok?

M: Yeah.

Me: You need more? Umm… let’s do another park clean-up! Remember last time they said a species of bird had just been spotted that they hadn’t seen for 63 years.­­­

M: [sitting up a bit, looking perkier] Yes­­—

Mr Howard: Girls, sorry to interrupt what looks like a fascinating conversation, but do you mind telling me what we’re talking about up here?

M: Umm…

Me: We’re talking about surds.

Mr Howard: Ok Clara, and what is a surd?

M: Umm…

Me: It’s a root that you can’t simplify.

Mr Howard: So how about you come up here and put these in their simplest form?

I walked up to the board.      

Me: √49. This one is simple. 49 is a perfect square, it’s the square of 7, so the square root of 49 is just 7, √49 = 7.

Mr Howard: …

Me: √45. Here, I can factorise 45 inside the square root as 9x5, and then we can split this up into two multiplied square roots: √(9x5) = √9x√5. 9 is a perfect square and 5 can’t be simplified any further, so we get to √(9x5) = √9x√5 = 3√5.             

Mr Howard: …

Me: √(20+12). Here, you can’t split up a square root with an addition, only with multiplication, so I need to do the adding first: √(20+12) = √32. Then I go through the same steps of factorising 32 and splitting up the multiplication, which gets me to: √32=√(16x2) = √16x√2 = 4√2.

Mr Howard: [after a big sigh, gesturing for me to sit down] That was all very good – thanks, Clara. I expect you all to know the rules for simplifying surds like the back of your hands, because we will be using them all the time when we get to the next chapter [then he gave me one of those special teacher looks that mean bad things and good things at the same time].

M: How did you do that? I haven’t heard a word he said since good morning.

Me: I just, you know… listened.

M: Oh, that. Obviously I’m not going to do that.

Me: Well, do you want to hang out after school? I’ll tell you about surds if you feed me crisps.

M: I can’t believe I have to turn down such an exhilarating proposition, but I’m helping Mum at the youth centre.

Me: How did she get you to say yes to that?!

M: She was super sneaky. She totally took advantage of what I thought was a heart-warming mother-daughter conversation. I was complaining about the lack of interesting boys around and Mum said, Miracle, connections happen when you’re just living your life, not desperately searching for them.

(Side note: M has the kind of relationship with her mum where they talk about this type of thing, it’s totally mind-blowing. Oh and yes, her full name is Miracle, which is why everyone calls her M.)

M: I said that was easy for her to say given that she has a lot of connections already. Then she said What you need to do is put out into the world the energy that you want to get back, so if you do happy, interesting, fulfilling things, you’ll attract that type of person.

Me: Happy, interesting and fulfilling does sound like a great boyfriend to me.

M: Well, I don’t want a boyfriend. No offence.

(She said this pointedly, because, you see, I do have a boyfriend. He's called Sam and he’s very sweet and thoughtful. He’s cute too, pretty cute – like, indie-movie cute. Mum loves him. M thinks he’s extraordinarily lame, but I get to have a nice time every weekend when he’s in town, whereas she’s always having to deal with guys whose idea of a conversation is describing their workout routine in detail, or who think Tarantino is god. Meanwhile she looks like Zendaya, so a lot of people like her. The list of her blocked people on Instagram is as long as a Dickens novel.)

Me: Yes, M, I’m not offended that you don’t want a boyfriend. I am comfortable with my pedestrian life choices. Whatever, then, a boy you’re seeing.

M: A lover.

Me: All right Madam Bovary. I thought you needed a husband to have a lover.

M: No – it’s when you want a bit of romance with the sex, but not a full-on thing, you know. That’s what I’m aiming for.

Me: But you haven’t had the sex at all yet, so we are several steps removed from this.

M: [glaring at me] Anyway, after this invigorating bit of generational advice, which softened me up perfectly, Mum suddenly came up with a perfect example of an activity that would be happy, interesting and fulfilling: helping her run the party she's organising at the youth centre.

Me: Ah, clever. She really is a genius.

M: She did teach me everything I know.

Me: And that’s saying something.

(No really – try not doing something M wants you to do and… well, you’ll be doing the thing M wants you to do.)

After Maths we walked to lunch, only to see a big commotion around Alice. I will say that there has been a major improvement in my school life this year: now that our timetables are based on our interests and intellectual capacities, I am free from taking even a single class in common with Alice and Rayna. This has reduced our contact to mere brushes in the corridor here and there, which is perfectly survivable. Mum forced me to take Biology to AS Level last year in a deluded dream that I would one day follow in her footsteps at the hospital, thereby condemning me to one more year of sharing a class with them, but this year I am free. The bad thing about it is that I now only have Maths in common with M – otherwise, she takes Economics and Philosophy. It’s been pretty hard to deal with, I’ll be honest. But I guess the good thing about that is that I have noticed a marked reduction in how often teachers ask me to stop talking in class.

Seeing as I couldn’t join the cluster of people around Alice clamouring for info – on the grounds of us hating each other – I had to listen in from a distance. All I could make out was something to do with Ty and his older brother.

‘Do you think they’re talking about why Ty hasn’t been in school?’ M whispered to me.

I shrugged, as if the thought hadn’t crossed my mind, but the truth was, I really wanted to be part of that discussion. Because, you see, the biggest improvement in my life this year, even more than the aforementioned lack of Alice and Rayna, is the fact that Ty sits right in front of me in Maths. And that is good, because Ty is extremely hot. Like, HOT. He’s also very nice and funny and all that. But when you’re talking to him, to be honest, you're not thinking about that part. He’s got a brooding resting face and a cute smile. He’s got those muscles that do that ripple thing in the forearms. He’s tall but not in the weird, unconscious-stoop-whenever-I-go-through-a-doorway way, more in the let-me-just-grab-that-for-you way. He has thick dark hair that he gets cut too short and then grows back too long and it looks like the softest thing in the world. And he has a really, really nice ass. The kind of ass that jeans were invented for. The kind that suddenly makes you very creative about thinking up ways to engineer situations where you’re walking up the stairs behind him. Dreaaaamy.

Unfortunately for me and for the state of the world, Ty is Alice’s boyfriend. They've been together for a while – before Ty joined our school in sixth form. It seems impossible, on account of the fact that he is lovely and kind and she is the opposite of that, but there it is. Of course, there is also another fact, which is that Alice is stupidly beautiful. She looks like a Boden model (I mean, she is a Boden model – I can’t escape that fact because Mum gets all the catalogues and insists on going through them and circling stuff for me to look at even though I have never ever not once wanted anything from there) – healthy and sunny and perfect. I, on the other hand, am around chin-height for the average Boden model, and I have an unphotogenic nose. (M refuses to admit this but I have a bump if you look on my right side – that’s why I’ve become an expert at making sure no photos of me from that angle ever make it onto social media.)

For the last couple of days, Ty hadn’t been in class, and I had no idea why. He seemed totally fine last week. M tried to convince me to message him and ask what was going on, but I felt too embarrassed – I’d never texted him before. I did have his number in my phone, but that was just from one time last year where we ended up in a WhatsApp group together. Sure, we talk a bit in class, but to be honest, the stuff that comes out of my mouth in his presence is usually so bad that M has to kick me under the desk to shut me up. I can’t help it! I get struck by the way his T-shirt fits a little bit snug on his shoulders and it just happens. M is fully supportive of my crush though, because she hopes it will mean an end to Sam. She herself doesn’t share my Ty infatuation, seeing as she likes guys who look like they’ve stepped out of a French film about a vitamin D-deficient poet who’s in love with his sister. If someone looks like they eat a balanced diet she is not interested.

I looked back over at the commotion. Rayna stood by Alice’s side, lapping up the attention with her arm around Alice’s shoulders, telling people off for talking over her.

Ugh, Rayna. We’ve been in the same school since we were six years old, like some cosmic joke played by our parents. I think they should study her to find out if there's a gene for bullying. What started off as giggling over my – I’ll admit, late-ish – thumb-sucking phase in primary school grew into a lot worse at secondary. Once, she stole my pants from the swimming pool changing room after gym class. Then, she told everyone that I wasn’t wearing any – and of course, I was in a skirt that day. It was the stuff recurring nightmares are made of. But eventually I had M on my side, and suddenly it was much easier not to care. And when I stopped caring, well, I guess that made it less fun for Rayna, so she stopped bothering me so much. The last few years she’s been content with mostly ignoring me, which has been restful.

Alice and Rayna were friends from outside school, from when they were little – they met at Pony Club, because of course they did. When Alice joined our school, she slotted straight in with Rayna’s crew, and now Rayna got to know more about Ty than I did.

So that’s what had happened before I walked out of school at the end of the day and saw him there, Ty, waiting for someone. Waiting for… me.

‘Clara, I need your help,’ he said, and my heart skipped approximately thirty beats.

I stared at him in silence. In truth, I just forgot to answer because my heart had jumped all the way into my throat and my brain was occupied with thoughts such as, Oh my god, oh my god, and, Is he possibly even more hot up close?

He eventually gave up waiting for me to speak and went on: ‘I’m looking for my brother. He’s