Alexa Chung: 'The schoolgirls nudged each other and giggled at me from across the room'

Oh dear. So now I'm addicted to Twitter. For those of you who don't know what that means, a) where have you been? And b) worry not, it's not exactly like crack, it's just similar. According to Wikipedia, "Twitter is a social networking and micro-blogging service that enables its users to send and read other users' updates, known as tweets. Tweets are text-based posts of up to 140 bytes in length..." BLAH, BLAH, BLAH – you get the gist.

All you need to know is that the big three are on it: Obama, Britney and Stephen Fry, basically everyone who matters. Twitter gives you a fascinating insight into the inner workings of their minds, their deepest fears, hopes for the future, evaluation of past mistakes. (I'm kidding, they post unreasonably banal sentences about potentially interesting things. Apart from Fry, who always finds time to say something awesome, such as: "Watching proboscis monkeys feed. My dear, the noise...".

I have a Twitter account but I'm rubbish at it, if it's possible to be rubbish at something so permissive. I find it hard to write the truth in fear of the 1,276 "followers" (or random strangers) I gathered in the space of a week abandoning me.

I've just arrived in Williamsburg, Brooklyn, where the streets are awash with ATM machines and pretty girls in ugly T-shirts. I wandered in to the nearest café I could find, only to discover MGMT sitting cosily in the corner. This is the equivalent of venturing towards Central Park and finding the entire cast of Friends on a sofa in a coffee house. I wolfed down my arugula salad and promptly left.

To get to Williamsburg, I first had to endure the tedium of the flight from London to JFK. I was sidetracked by Chanel (strictly window shopping only) and then got busted by a group of 30 schoolkids in the departure lounge. I don't remember ever being that unsubtle when I was a teenager, they nudged one another and giggled at me from the other side of the room. I felt as though I was being weirdly bullied. It was the second time that week I had been jeered at by schoolkids (OK, the first time was by polite primary schoolchildren).

Once onboard, I noticed the man in the seat next to me had a dictaphone in his left hand and a mobile phone is his right. For the entirety of the flight he spoke into his contraption in hushed tones, weighted to his seat by a toppling pile of paperwork. Why did I choose the business flight?

To mask the sounds of yet another report being filed, I searched the movie listings for something to watch. I settled upon Twilight first, closely followed by The Reader, all washed down with a depressing documentary on Britney Spears. Twilight made me wish I was 13 again. If I loved it now, I would have been positively obsessed with it then. When Baz Luhrman's Romeo + Juliet was released, when I was a young teen, I learned every single line in the movie. I was convinced that I'd grow up to marry Leonardo DiCaprio. But when I popped the question in an interview I was doing with him, he politely declined and so I had to move on with my life and let it go.

The Britney documentary was rather moving. Not being able to leave your own house without a barrage of security and a thousand eyes staring must be bleak. I actually started to tear up when she said she had dreams of being free and doing normal things like walking in a park with her friends and then she'd wake up and realise it wasn't possible. Imagine your dreams being of a humdrum life and your reality being a nightmare. None of this is covered on her Twitter page.

Two facts I learned this week: a mouse can fit through a hole the diameter of a pencil; and the longest word you can make without repeating a single letter is "uncopyrightable".

Having stumbled across these facts through conversations with friends, I then endeavoured to collect more, so here you go: Thomas Edison, light bulb inventor, was afraid of the dark; Florence Nightingale invented the pie chart; and 100 people can fit in the mouth of a blue whale.