Luna Lovegood walked through the barrier between Platforms Nine and Ten to Platform Nine and Three-Quarters. Luna wondered what happened to Platform Nine and One-Half. Numbers like "three quarters" only appear when you divide an integer in half twice in a row.
Luna looked around for someone who might know the answer and spied a unicorn. She wore clothes, walked on two feet and had curly brown hair. None of that fooled Luna. The unicorn radiated peace and her fingernails were made out of alicorn.
"What happened to Platform Nine and One-Half?" Luna asked the unicorn.
"There is no Platform Nine and One-Half," the unicorn replied.
"How do you know?" Luna asked.
"It would have been in Hogwarts: A History," the unicorn replied, "nor is there mention of a Platform Nine and One-Half in Modern Magical History, Important Modern Magical Discoveries, or any other book in the Hogwarts library. There is only a Platform Nine and Three Quarters."
"What about Platform Nine and Seven Eighths?" Luna asked.
"There is no Platform Nine and Seven Eights either." The unicorn turned around and walked away before Luna could ask "How do you know?"
If Platform Nine and Three Quarters does not appear in Muggle libraries then Platform Nine and One-Half is unlikely to appear in wizard libraries, except for double-witches' libraries. The Hogwarts library is not a double-witch library.
"How are you?" a Weasley-headed first-year girl asked Luna.
"I'm trying to find Platform Nine and One-Half. The unicorn told me it doesn't exist. If it does exist then it must be hidden by powerful magics. How are you?" said Luna.
"What unicorn?" the first-year girl asked.
"That one, right there," Luna said, pointing.
The girl invented an excuse to end the conversation.
Luna didn't know how to make friends. She had a vague idea that as a first-year, the Hogwarts Express was a one-time opportunity to do so. She wore a necklace she had painted herself which nobody else seemed to notice. She had brought kettle of home-brewed Comed-Tea, but it had got her jeered out of a compartment.
Nobody was interested in the troll she had smelled at Platform Nine and Three Quarters or her discovery of a lich in the second year or that the Chamber of Secrets had been opened or any of Dark Lord Harry Potter's various plots. The other first-years seemed unfocused and confused.
Wrackspurts are invisible creatures that float into your ears and make your brain go fuzzy. The train could be full of them. They could be floating into her ears right now. Luna stuck her index fingers in her ears to block the possible Wrackspurts. The first-years in the nearby compartment looked at Luna as if she were already unpopular.
Wrackspurts are cognitohazardous which means they mess with your thoughts. Luna learned all about Wrackspurts and other cognitohazards in her work on The Quibbler. The most important thing about cognitohazards is to check yourself regularly and figure out if you've already been affected by one.
Luna observed her own mind. Fuzzy? No. Unfocused? No. Confused? No. Wrackspurts had not yet entered her brain. (Unless it already had and was inhibiting her meta-cognition—but she didn't think that was happening.) Luna observed the other students. Maybe they were infected by Wrackspurts or maybe they were behaving normally. It was hard to tell without a Wrackspurt-free baseline to compare them to.
Before she could unplug her ears, Luna had to figure out if there were Wrackspurts roaming the train. But Wrackspurts are invisible. How can she test whether such a thing exists?
Wrackspurts are attracted to people so the safest place to go would be an empty compartment. Smaller would be better since that would decrease the likelihood of a Wrackspurt having drifted in randomly. Luna walked past cabin after cabin with her fingers in her ears. Eventually she found a suitable compartment, boring and cramped. She shut the door with her knee and then unplugged her ears. She counted to eighty-nine and then observed her mind again. Still no Wrackspurt symptoms.
She had hoped Hogwarts would be an opportunity to make friends. But the other girls and boys her age all seemed wrapped up in amassing power by forming alliances. Even the Muggle-borns were more interested in visible charms like chocolate frogs than invisible creatures like Wrackspurts.
Luna wondered if she was the most invisible first-year in the school. No other compartments had fewer than three students. Presumably, everyone else in first-year was making friends or already had some.
It could be worse. Luna could have a curse that made her unpopular or made people forget who she was. Muggles had a hard time seeing witches and wizards. If double-witches were real then it would be hard for witches to see them just like it's hard for Muggles to see witches. Luna's eyes would drift from one side of the double-witch to the other without noticing the witch in front of her.
Luna looked around her cramped compartment. To her left, in the opposite cabin, four girls were pointing at her and laughing again. Out the window, to her right, the countryside drifted by. Luna was getting distracted.
Luna stuffed her fingers back into her ears. The left index finger went right in. The right index finger didn't.
Luna covered her right ear and then gently squeezed the Wrackspurt into her right hand. From there, she guided the Wrackspurt into an empty Comed-Tea can and wrapped her scarf over the opening.
Luna wondered where the Wrackspurt could have come from. It had to have been there before she shut the door. But the Wrackspurt had not immediately entered Luna's ears when she had first entered the compartment. There may not have been any free Wrackspurts in the compartment when Luna had entered it. Luna's trapped Wrackspurt must have been in someone else's ear.
But who? Luna's eyes slid from one end of her compartment to the other, as if nothing important existed in-between.